Journal of Nonlinear Optical Physics & Materials Vol. 9, No. 3 (2000) 365–411 c World Scientific Publishing Company NONLINEAR OPTICAL RESPONSE OF CYANOBIPHENYL LIQUID CRYSTALS TO HIGH-POWER, NANOSECOND LASER RADIATION SVETLANA G. LUKISHOVA Liquid Crystal Institute, Kent State University, Kent, OH, 44242, USA Also Institute of Radioengineering and Electronics of the Russian Academy of Sciences, 11 Mokhovaya, 103907, Moscow, Russia Present address: IRE-SL, 172 Works Rd., Honeoye Falls, NY 14472, USA Received 7 June 2000 Results from investigations are summarized into: (1) transient refractive and absorptive (two-photon) nonlinearities at 0.532 μm by the Z-scan method, and (2) reflective non- linearity in the near-IR, of linearly nonabsorbing cyanobiphenyl liquid crystals under nanosecond laser irradiation. (1) For isotropic liquid crystals at the several-nanosecond time scale and several tens-micrometers beam-waist-diameter, transient molecular-reorientation and ther- mal/density refractive nonlinearities compete in changing the sign of the total transient refractive nonlinearity. For the different, given pulse durations, the influence of cou- pled thermal and density effects on nonlinear refraction depends, through buildup time, on the beam-waist diameter. Nonlinear absorption coefficients depend on the incident intensity. For planar nematic layers, cumulative effects in heating (and in refractive nonlinearity) were observed even at low, 2–10 Hz pulse repetition rate. These results are useful for optical power limiting applications, and for intensity and beam-quality sensors of pulsed, high-power lasers. (2) Reflective nonlinearity of chiral-nematic (cholesteric) mirrors near selective reflec- tion conditions for circular polarized light at λ =1.064 μm was studied both under free space irradiation and inside a laser resonator. Specially chosen experimental irradiation conditions make it possible to attribute the observed changing of reflectivity to athermal helix unwinding by the optical field. The results can find applications in laser-resonator mirrors, Q-switches and soft apertures for beam-profile formation, and also in showing the limits of use cholesteric optical elements in high-power laser beams. 1. Introduction Liquid crystals (LC) 1,2 have become essential in display technology. 3 Much less well known is the use of LCs in, and the potential for improvement of, coherent optical devices, such as lasers. For example, linear optical and electrooptical laser elements 4–8 made of LCs (mirrors, filters, retardation plates, modulators (light valves)) are successfully used for more than 20 years. Discovery in 1980 of a giant refractive optical nonlinearity 9,10 in LCs and its athermal, ten- to hundredfold 365
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Liquid Crystal Institute, Kent State University, Kent, OH, 44242, USAAlso Institute of Radioengineering and Electronics of the Russian Academy of Sciences,
11 Mokhovaya, 103907, Moscow, RussiaPresent address: IRE-SL, 172 Works Rd., Honeoye Falls, NY 14472, USA
Received 7 June 2000
Results from investigations are summarized into: (1) transient refractive and absorptive(two-photon) nonlinearities at 0.532 µm by the Z-scan method, and (2) reflective non-linearity in the near-IR, of linearly nonabsorbing cyanobiphenyl liquid crystals undernanosecond laser irradiation.(1) For isotropic liquid crystals at the several-nanosecond time scale and severaltens-micrometers beam-waist-diameter, transient molecular-reorientation and ther-mal/density refractive nonlinearities compete in changing the sign of the total transientrefractive nonlinearity. For the different, given pulse durations, the influence of cou-pled thermal and density effects on nonlinear refraction depends, through buildup time,on the beam-waist diameter. Nonlinear absorption coefficients depend on the incidentintensity. For planar nematic layers, cumulative effects in heating (and in refractivenonlinearity) were observed even at low, 2–10 Hz pulse repetition rate. These results areuseful for optical power limiting applications, and for intensity and beam-quality sensorsof pulsed, high-power lasers.(2) Reflective nonlinearity of chiral-nematic (cholesteric) mirrors near selective reflec-tion conditions for circular polarized light at λ = 1.064 µm was studied both under freespace irradiation and inside a laser resonator. Specially chosen experimental irradiation
conditions make it possible to attribute the observed changing of reflectivity to athermalhelix unwinding by the optical field. The results can find applications in laser-resonatormirrors, Q-switches and soft apertures for beam-profile formation, and also in showingthe limits of use cholesteric optical elements in high-power laser beams.
1. Introduction
Liquid crystals (LC)1,2 have become essential in display technology.3 Much less
well known is the use of LCs in, and the potential for improvement of, coherent
optical devices, such as lasers. For example, linear optical and electrooptical laser
elements4–8 made of LCs (mirrors, filters, retardation plates, modulators (light
valves)) are successfully used for more than 20 years. Discovery in 1980 of a giant
refractive optical nonlinearity 9,10 in LCs and its athermal, ten- to hundredfold
365
366 S. G. Lukishova
enhancement by dissolving a small amount (∼ 0.1%) of dye (chromophore) in the
LC-fluid,11 prompted further studies of the nonlinear optical response in these
materials, see, e.g. Refs. 4, 10 and 12–20. It is safe to say that, to date, no nonlinear
optical LC devices, in particular of χ(3) type, have progressed past the prototype
stage. In no small measure, this is caused by the uncertainties in values, i.e. lack of
reliable values, of nonlinear hyperpolarizabilities found in the literature.
The key characteristics of liquid crystals as a fluid material are the long-range
correlation between anisotropic molecules and the cooperative nature of their inter-
action with different, external fields.1–3 Figure 1 shows schematically the molecular
order of the so-called nematic (a) and isotropic (b) phases of LCs made of “rod-
like” molecules. The nematic phase with largely unidirectionally aligned molecules,
director (see arrows in Fig. 1), exists only within a restricted temperature interval
below the nematic/isotropic-liquid phase transition. While in this phase, the long
axis of the LC molecules can be uniformly aligned both perpendicular (homeotropic)
and/or parallel (planar, see Fig. 1(c)) to the fluid container’s walls, by special sur-
face treatment. Alignment is readily achieved in thin (less than∼ 200 µm thickness)
The attractiveness of LCs as a material includes their relatively low cost, ease
of use, including the possibility of filling various volumes (e.g. optical fibers21 and
porous glasses22), their very low absorption over a wide spectral interval including
the visible and IR,13 high damage threshold to laser radiation,4,5 and large electro-
optical and thermooptical coefficients.12,13 Molecular design provides wide latitude
in modifying structure/propertie relations. At least 80 000 LCs are now synthe-
sized. The present paper considers only simple model systems, cyanobiphenyl LCs3
(widely used in display technology), with a stable room-temperature nematic phase.
In addition to nematic phases, there exists the possibility to create spatially peri-
odic structures (chiral nematic, smectic phases).1–3 Furthermore LCs may serve as
solvent for different chromophores11 and/or dispersed as micrometer-size particles
in a polymeric matrix,23 adding to the variability of properties of possible liquid
crystalline devices.
The purpose of this paper is to update the reader on reliable values for LCs
nonlinear-optical materials parameters for several-nanosecond pulse duration. This
is a timely issue as comparing reported values is fraught by a multitude of potential
pitfalls that were not considered yet in the literature (to my knowledge). For in-
stance, the irradiation geometry and various time constants play a momentous role
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 367
in what value, and even sign, the transient nonlinear parameters may take. The
consideration of these problems will be useful for constructing liquid-crystalline
nonlinear optical devices, e.g. optical power limiters8 (using both pure and chro-
mophore-doped LCs12,13) and/or intensity and laser beam quality meters,24 for very
often used commercial green-irradiation Nd:YAG lasers, with several nanosecond
pulse duration and 2–10-Hz pulse repetition rate. As to the switching application,
an athermal reflective nonlinearity in chiral nematic mirrors will be considered in
connection with spatial and temporal profile formation of laser radiation.
The structure of this paper is as follows. In the present section, Sec. 1 (Intro-
duction), a short review of two principal mechanisms of refractive nonlinearities
in nematic LCs (orientational (Sec. 1.1) and/or thermal and density (Sec. 1.2))
is presented next for both the oriented-nematic and isotropic case. In Sec. 1.1,
the electronic refractive nonlinearity will be introduced, characterized much smaller
value for these materials. Mechanisms of nonlinear absorption will be reviewed in
Sec. 1.3. Reflective nonlinearity of chiral nematic mixtures based on helix unwind-
ing will be reported in Sec. 1.4. Section 1.5 contains short preview of problems
considered in present paper. Section 2 describes characterization of materials and
LC-cell fabrication (Sec. 2.1 — nematic and isotropic cells, Sec. 2.2 — chiral ne-
matic (cholesteric) mirrors). Section 3 presents two frequently used experimental
set ups (Z-scan (Sec. 3.1) and for measurements of reflective nonlinearity (Sec. 3.2)).
Section 3.1.1 describes determining the absorptive and refractive nonlinearities from
Z-scan data. The experimental results of author’s Z-scan measurements of transient
nonlinear refraction and nonlinear absorption of cyanobiphenyl LCs under several
nanosecond, 0.532-µm laser irradiation will be considered in Sec. 4 for isotropic LC
layers and in Sec. 5 for planar nematic layers. In Sec. 6, various transverse effects
in laser beam will be presented including cumulative spatial self-phase modulation
elliptical ring formation (Sec. 6.1), “dark” spot formation, asymmetric scattering
and cross-structure formation (Sec. 6.2). Numerical modeling of heat diffusion will
be discussed in Sec. 7. Section 8 contains experimental results on athermal reflective
nonlinearity of cholesteric liquid crystal mirrors under selective-reflection conditions
for free space irradiation (Sec. 8.1) and inside laser resonator (Sec. 8.2). Section 9
concludes the paper and provides an outlook for further possible experiments.
1.1. Orientational Refractive Nonlinearity
This section deals with the difference between molecular orientation in an optical
field (and its contribution to the nonlinear refraction) of LCs,25,26 and of ordinary
organic liquids with dipole molecules which also possess strong orientational non-
linearity, e.g. CS2.
As in ordinary organic liquids, individual (or pseudoindividual) molecular re-
sponse (nuclear reorientation) in LCs has been detected in the picosecond range.27,28
The peculiarity of a liquid crystalline material is the collective and correlated molec-
ular reorientation in the optical field (the so-called optically induced Freedericksz
368 S. G. Lukishova
transition). It is much slower than individual molecular response but contributes
enormously stronger to the nonlinear susceptibility χ(3)(−ω, ω, ω,−ω) and nonlinear
refractive index n2 (see Sec. 3.1.1) than optically driven reorientation by individual
molecules. The giant optical nonlinearity9,10 observed in nematic layers for CW-
laser-operation has nine orders of magnitude higher χ(3)(−ω, ω, ω,−ω) and n2 than
CS2 (n2(CS2) = 1.2.10−11 esu29), but its response time is slow (submilliseconds to
seconds).17
1.1.1. Nematic Layers
Once experimental progress permitted, it was realized that for intense fields,
fast collective and correlated orientational response of nematic molecules is
possible16,17,30,31 even for nanosecond irradiation. The buildup time and the mag-
nitude of the refractive nonlinearity are determined by the incident intensity.30 For
instance, for 6-ns excitation, the orientational-relaxation time of aligned nematic
5CB was observed to be of the order ≤ 1–100-µs.30 In a separate work,31 20-ns
pulses were shown to trigger formation of elliptical diffraction rings (similar to the
CW-optical-Freedericksz-transition9,10,32,33) as the result of orientational spatial
self-phase modulation.
For picosecond irradiation of oriented nematics the collective orientational effects
are weaker. Z-scan measurements for 0.532-µm, 33-ps pulse duration, yield values
for 5CB LC34 of n2par = 0.87n2(CS2) and n2perp = 0.58n2(CS2).
At high laser intensities the nonlinear response to picosecond and nanosecond
laser irradiation can be accompanied by intense hydrodynamic flow which cou-
ples to the reorientational process, the so-called flow-reorientational (alignment)
effects.35,36 This effect is not driven by density or temperature modulations but by
photoelastic stresses.
1.1.2. Isotropic LCs
Isotropic LCs are very attractive because of their excellent transparency even for
beam paths as long as tens of cm, opening an opportunity for use as nonlinear
materials in fibers.21 (Nematic LCs do not scatter light and are transparent only
in oriented layers). First experiments on short-pulse laser irradiation of isotropic
LCs have been reported in the early 1970–80s in connection with the optical Kerr-
effect and steady-state and transient self-focusing studies in organic liquids.37–42
The peculiarity of isotropic LCs (in difference with ordinary organic liquids) is
that its response time can be varied by temperature over a wide range, because its
temperature dependence scales as (T − Tc)−1, where Tc is the nematic/isotropic
phase transition temperature.18,37–44
For isotropic LCs, the value of steady-state n2 was measured to be more than
∼ 100 times in excess of CS2 with a dependence on the temperature buildup time
tbup of the order of several tens to hundreds of nanoseconds.18,37–44 For 6–9-ns pulse
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 369
duration, the orientational nonlinear refraction of isotropic LCs is transient41 and
transient n2 is expected to have a smaller value than the steady-state n2.18,37–44 It is
very important to note that the value of steady-state n2 depends on the temperature
as (T − Tc)−1 as does the response time, but the transient value of n2 is nearly
independent of the temperature.41 As an example, the transient values for MBBA
were reported to be of one order of magnitude larger than that of CS2.38,39
For picosecond irradiation of isotropic LCs, values of n2 range from 0.05 to
0.13 n2(CS2) for 1.064-µm, 30-ps pulse duration, for both Schiff base and ester
compounds.45
1.1.3. Electronic Nonlinearity
By comparison with the above mentioned orientational effects, electronic contribu-
tions to n2 that are fast (10−15s) for well-known LCs can be considered negligible.
Experimental value of electronic χ(3) (CARS) were found to be only ∼ 5 times
higher than that for glass (χ(3)(glass) ∼ 10−2 χ(3)(CS2)), for MBBA LC (both in
the nematic and isotropic state).46,47 Measurements of electronic contribution of
naphthyl core compounds6,48 both in the ordered and isotropic state (nearly degen-
erate four-wave mixing) at 1.053 µm showed values of χ(3) ∼ (0.1− 0.8) χ(3) (CS2).
These small electronic contributions are not straightforward to explain, especially as
similar conjugated structures of some polymers49 have thousand times higher value
of electronic n2. There is an opinion,50 that molecules with high hyperpolarizabil-
ities do not possess LC phases or have LC-phase in very narrow and unpractical
temperature region.
1.2. Thermal and Density Refractive Nonlinearity
As in any absorbing medium, thermal mechanism causes refractive nonlinearity
in nematic and isotropic LCs. Thermal nonlinearity coupled with density
changes12,13,21,36 competes with the orientational nonlinearity in changing the sign
of the total refractive nonlinearity. Another mechanism of density changes,
electrostriction,51 with buildup time in the nanosecond range, is comparable with
thermal/density contributions if the medium’s absorption coefficients are low. As
will be seen later (Sec. 1.3), at 0.532 µm a strong heating mechanism exists for the
LC model compounds considered here. That is why electrostriction is neglected
from now on.
Refractive index changes by heating are the sum of two contributions:
∆n = (∂n/∂ρ)T∆ρ+ (∂n/∂T )ρ∆T , (1)
where ρ is the density, T is the temperature. It is very important in the current
context that each term in (1) has its own characteristic turn-on time, and will
contribute differently under transient and steady-state regimes.52,53
370 S. G. Lukishova
1.2.1. Thermal-Density Nonlinearity
For several nanosecond pulse duration and several tens of micrometers beam waist,
the buildup time tac of the thermal-density-nonlinearity (∆n = (∂n/∂ρ)T∆ρ) can
be close to the laser pulse duration to.
tac = ro/Vs , (2)
where ro is the beam radius and Vs is the velocity of sound (Vs (LCs) ∼ 1500 m/s).
For tac > to the thermal-density-nonlinearity will not develop during the pulse.
Experimental values of n2 for this transient regime were reported in Ref. 52 for
absorbing organic liquid. It was found experimentally, that the transient absolute
value of n2 for to = 5 ns diminishes with ro increasing from 9 to 32-µm.
Acoustic-grating generation in LCs have been intensively studied both under
subpico-, pico- and nanosecond excitations.12,13,17,27,54
1.2.2. Thermooptical Effects
The thermooptic coefficient dn/dT in nematics is extraordinarily large, ranking
among the largest of all known materials.16 Not unexpected for these highly aniso-
tropic molecules, it depends on the orientation of the molecules. E.g., dnpar/dT ∼−2.5 · 10−3grad−1 for 5CB in the temperature interval 26–31◦C for incident polar-
ization parallel to the molecular orientation direction.55 For “perpendicular” po-
larization, dnperp/dT is of opposite sign and equals ∼ −1/2dnpar/dT .16 In the
proximity of the phase transition to the isotropic state, the slope of both dnpar/dT
and dnperp/dT steepens.55
For nematic LCs it was well-known that the thermooptical effect experiences
a lengthening of its buildup time (tens–hundreds of nanoseconds), rendering it in-
significant on a several-nanosecond time scale.12,13,36,56 Similar buildup times are
reported in Ref. 52 for absorbing organic fluid. Thermooptical effects for ro = 32 µm
were found to be more significant for pulses longer than ∼ 100 ns.52
Because of the slow buildup time, thermooptical (thermal-lens) spatial self-
phase-modulation rings in beam cross-section were observed only for CW laser
radiation.57–59 LC heating was in this case due to absorbing coatings on cell glass-
substrates, dissolving absorbing dyes in LCs and/or irradiation by high-average
power (∼ 1 W for 100-µm spot-size57) beams.
For pulsed lasers there exist, to my knowledge, no reports on thermal spatial self-
phase modulation rings, even at repetition rate regimes, although in Ref. 60 cumu-
lative effects (thermal memory) at repetition rate higher than 5 Hz for nanosecond
irradiation of planar-aligned nematic LC layers are mentioned.
Also important for the current paper is the thermal diffusion-relaxation time14
τdif ∼ D−1(1/r2o + π2/L2
o)−1 , (3)
where D is the thermal diffusion coefficient, Lo is the thickness of the cell. Coeffi-
cient D of nematic LCs is anisotropic. Typical τdif ∼ 10−2 − 10−6s14 for nematics
layers.
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 371
1.3. Nonlinear Absorption Mechanisms and
Laser-induced Damage
Heating of cyanobiphenyl LCs by short-pulse laser radiation in the visible range
that drives photoacoustical and thermooptical effects, is caused by two-photon
absorption,27,61 concurrent or subsequent excited-state absorption,17,27,54 and
the efficient decay of the excited states through radiationless-recombination
channels.17,27 Strong nonlinear absorption was observed in optical power limiting
studies of LCs12,13,20,45,62–65 and Z-scan measurements.34,66–70
Linear absorption coefficients α of cyanobiphenyl LCs are incapable, however,
to produce heating effects at low incident average powers. Table 1 lists data13,71
for linear absorption coefficients α for 5CB and E7 (see Sec. 2).
Table 1. Linear absorption coefficients (α) of 5CB and E7.
ternational (Continuum) model YG-682S-10), using a feedback-stabilized, injection-
seeded, single-longitudinal-mode, unstable resonator with Gaussian cavity end
mirror124 and two, single-pass amplifiers, provided, at 2, 5 and 10-Hz repetition
rate, an output beam-spot diameter of ∼ 8 mm at 0.532 µm.
To optimize beam quality, a 1.5-mm-diameter Teflon aperture was placed in the
central part of the beam,125 such that an Airy spot at a reasonable distance from the
Teflon aperture (using mirrors M and beamspliter BS) was formed. A converging,
Sample
Detector
Z
ApertureLens
Fig. 7. Schematic of Z-scan measurements.
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 381
Fig. 8. Experimental set up for measurements of nonlinear refraction and absorption by the Z-scanmethod.
9.5 or 10.5-cm focal-length lens L was placed at 4 m from the Teflon aperture.
To remove far-field side lobes caused by the Teflon aperture, a 2.75-mm-diameter,
metal aperture MA was placed in front of the lens. The same aperture MA was
placed at the reference channel. For maintaining a linear incident polarization and
changing the input-pulse energy to the sample, a Glan-prism-polarizer and a quartz
λ/2 waveplate combination was placed in the beam.
Signal D1 and reference D2 pyroelectric joulemeters (Gentec ED-100A with
amplifier EDX-1, vendor recalibrated) or fast photodetectors (Hamamatsu S1722-
01 and Motorola MRD510, respectively) were connected to a digitizing oscilloscope
(Textronix TDS 640). An AT-GPIB/TNT board from National Instruments was
used for data acquisition and processing. Laser pulse shape was monitored by a
sub-ns-risetime Motorola MRD510 photodiode, connected to a Hewlett Packard
HP 54111D digitizing oscilloscope. For closed-aperture Z-scan measurements, a
“small” aperture was placed in front of D1. Sometimes the entire photodetector
was used as the “aperture”. For open-aperture measurements, an additional lens in
front of D1 was used to collect all laser radiation leaving the sample. The samples
were placed on an Aerotech mechanical translation stage controlled by an Unidex
1 motion controller. To measure the average126 beam diameter near the waist
produced by the focusing lens of the Z-scan set up, an 8-bit, WinCam CCD-beam
analyzer by Merchantek (pixel size 8.3 µm × 8.6 µm) was used in a separate, low-
intensity, equivalent channel formed with beamspliter BS and additional lens with
the same focal length as the lens in the Z-scan channel. Beam-waist diameter was
also measured with knife-edge technique and using Z-scan of CS2 with well-known
nonlinear refractive index n2.
The same CCD-camera was also employed for acquisition and analysis of beam
profile on the lens and far-field patterns during the Z-scan. For adjusting the size
of the pattern to the size of the sensor, an additional lens was used between the
sample and the camera. Some far-field patterns were recorded from a screen by
382 S. G. Lukishova
Fig. 9. Beam profile at the lens along X-axis (a) and Y -axis (b); beam diameter in the waistregion (c): • — for X-axis, � — for Y -axis; and pulse shape (d).
a standard video camera/digitizer combination, permitting the recording of each
pulse.
Figure 9 shows near Gaussian spatial distribution of the laser-beam intensity at
the lens in the Z-scan set up (a), (b), typical beam caustic near the waist (c) and
near Gaussian temporal pulse shape (d). Figure 9(d) is a result of storage of ∼ 100
shots.
It must be noted next that both sensitivity and accuracy of the absolute Z-scan
measurements critically depend on the incident beam profile and laser beam quality.
In Ref. 127, numerical modeling showed that, even with a slight deviation from a
perfect Gaussian beam distribution, the Z-scan curve calculation using the standard
formula for the Gaussian beams can yield erroneous, nonlinear optical parameters.
Influence of laser beam quality was studied numerically,122,128 where even for beam
quality factor M2 > 1.2, errors were found in the absolute Z-scan measurements
(M2 (see Ref. 129) expresses in terms of beam divergence as M2 = θ/θ00, where θ
and θ00 are the real beam divergence and TEM00 mode divergence). In difference
to absolute measurements, in relative measurements by Z-scan method even low-
quality beams are found to be useful.130
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 383
In order to remove errors connected with deviation of the spatial profile from
the Gaussian shape,127 relative Z-scan measurements are presented here through
the use of CS2 as a calibration material before and after each measurements of an
LC-sample.
For every translation-stage step (1 mm) 30 irradiation pulses were accumulated,
and, after 5% “windowing”,122 these data were averaged. The accuracy of measure-
ments of n2 and β is estimated to be ∼ ±20% dominated by the incident-intensity
fluctuations.
3.1.1. Evaluation of n2 and β from the Z-scan Data
In light of different definitions of n2 in the literature,51,117,118,131 the value of the
nonlinear refractive index n2 and the nonlinear refractive coefficient γ are defined
in this paper by n = no + 1/2n2|E|2 and n = no + γI. Here n is the total refractive
index of the material, and no is the linear refractive index, E is the (complex) optical
electric field amplitude inside the material, I is the optical intensity. Conversion
between n2 and γ is made via n2[esu] = (cno/40π)[m2/W ], where c is the light
speed (m/s) in vacuum.
For isotropic materials and a linearly polarized laser beam, n2 and the nonlinear
susceptibility χ(3)(−ω, ω, ω,−ω)49–51,117,118,131–134 are related simply by51
n2 = (12π/no)χ(3)1111(−ω, ω, ω,−ω) , (4)
where χ(3)1111 is one of three nonzero elements of χ(3).
For the Gaussian profiles the values of γ and n2 can be calculated from the
Z-scan curves using the following formula29
∆T tr = 0.406|∆Φ|(1− S0.25) , (5)
where ∆T tr is the difference between the maximum value of the normalized trans-
mittance T tr and its minimum value, ∆Φ is the nonlinear phase shift on axis during
Z-scan, S is the linear transmittance of the “small” aperture for a Gaussian input
beam (S = 1 − exp(−2r2a/R
2o)), where ra is the “small” aperture radius, Ro is the
beam radius at the place of “small” aperture in the linear regime).
The nonlinear phase shift ∆Φ = 2πλ−1γIL, where I is the peak axial intensity
at the waist, assuming a temporally and spatially Gaussian-shaped pulse, L is the
sample length.
In this paper intensity is defined as
I(r, t) = 2E(τπ3/2r2o)−1 exp(−2r2/r2
o − t2/τ2) . (6)
Here E is the total energy, the pulse-length full width at half maximum (FWHM)
to = 2τ(ln 2)1/2, ro is the beam waist-radius at 1/e2 level. Using these pulse and
beam parameters,
Ipeak = 4E(ln 2)1/2(toπ3/2r2
o)−1 ≈ 2E/(toπr2o) . (6′)
384 S. G. Lukishova
As to nonlinear absorption, here an assumption is made that two-photon absorp-
tion135 is the principal loss mechanism. The fundamental equation describing this
intensity loss with depth z is
dI/dz = −βI2 . (7)
The solution to (7) at z = L is
I(L) = I(0)/(1 + βI(0)L) = I(0)/(1 +Q) . (7′)
Sample transmittance, T tr(L) = (1 + Q)−1 = 1 −∆T trabs, where ∆T tr
abs is obtained
from the open-aperture Z-scan curve. For a Gaussian spatial and temporal profile
T tr(L) = 2Q−1π−1/2
∫ ∞0
ln(1 +Qe−x2)dx . (8)
Expansion of the logarithmic function yields a linear relationship (valid for small
Q) between T tr(L) and I(0) where the slope is proportional to the nonlinear co-
efficient β:
T tr(L) ≈ 1 + 2−3/2βI(0)L , and ∆T trabs ≈ −23/2βI(0)L . (8′)
3.2. Measurements of Nonlinear Transmittance of
Cholesteric Mirrors
Nonlinear irradiation of cholesteric LC mirrors was carried out by two approaches:
cholesteric LC samples were either irradiated in the focus of a freely propagating
laser beam (for the experimental layout see Fig. 10) or inside a laser resonator
(Fig. 11) in which the cholesteric LC structure served as output coupler.
Nd:YAG laser
Quartz polarizer
Photodiode
λ/4
Glass filters
Lens
CLC mirror
Power meter
Fig. 10. Experimental set up for free-space experiments with cholesteric LC mirrors.
Fig. 11. Schematic of the cholesteric-LC-mirror-equipped laser oscillator.
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 385
A Nd:YAG laser operated in two-regimes: (1) in CW mode and (2) in an acousto-
Fig. 19. Tight focusing: far-field asymmetric scattering CCD-image (a); 3D-rendering of spatialbeam profile (b); X-axis spatial intensity distribution (c); Y -axis spatial intensity distribution (d).
Fig. 20. Tight focusing: elliptical rings in the far-field with increasing incident intensity from leftto right.
details of asymmetric scattering and the “donut ”-shape “dark ” spot at the beam
initial spot. The central bright spot and the “donut” black ring are circles. At the
1/e2 level, the asymmetric scattering spot diameter at the X-direction (parallel to
the incident polarization) is ∼ 1.5 times larger than that in the Y -direction.
At higher intensity (I ∼ 0.5 GW/cm2), asymmetric scattering becomes stronger,
and the first ring appears (Fig. 20, left for 25-µm pathlength of 5CB). At still
higher intensities (∼ 0.7 GW/cm2), asymmetric scattering evolves into the multiple-
elliptical ring pattern whose major axis is oriented perpendicular to the incident po-
larization (Fig. 20, right for 105-µm pathlength of 5CB). Under certain conditions,
the divergence angle of the elliptical fringes abruptly increases, exceeding the spa-
tial capture range of the CCD-camera’s detector. This necessitates capturing the
fringe pattern on a white paper screen, and imaging the screen on to the detector
by a conventional objective. Figure 20, right is the result of such imaging. For scale
comparison, the absolute size of the initial beam spot observed in Fig. 20 left and
right does not change throughout the evolution of the pattern.
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 393
Fig. 21. Tight focusing: far-field elliptical ring pattern (left) and result of 45◦ rotation (right).
Fig. 22. Different types of the cross-structure in the far-field.
When the LC cell was rotated around the light-propagation direction, the ellip-
tical rings’ major and minor axes rotated in the same handedness, but the number
of rings diminished as the angle between LC director and incident, linear polar-
ization increased (Fig. 21, 50-µm cell thickness: left I = 0.77 GW/cm2, right
I = 0.88 GW/cm2). By the time the LC director is oriented fully perpendicular to
the light polarization, the effect vanishes entirely.
At the highest employed intensity (I ∼ 0.8–1 GW/cm2 for tight focusing), the
elliptical ring pattern may develop into a cross structure139 for both tight focusing
and slow focus. Figure 22 shows different versions of such cross structures (left —
for tight focusing (5CB, 25-µm layer thickness), right — for slow focus (5CB and
7CB mixture with chromophore, 125-µm layer thickness)), depending on specific
laser-pulse or irradiation-geometry parameters. Each specific form is reproducible
for a defined laser operational mode. Equally important, the polarization state
of the far-field laser light depicted in Fig. 22 remains the same as in the incident
beam, in difference with cross patterns resulting from the sample being held between
crossed-polarizers, reported, e.g. in Ref. 141. Under CW-excitation of equivalent
power, we did not observe any of the above described effects.
7. Numerical Modeling of Cumulative Effects and Explanation
of Spatial Self-phase Modulation Effects
For an explanation of the slow buildup time spatial self-phase modulation as well
as of its absence under CW irradiation of comparable power density, the
394 S. G. Lukishova
heating of LC was further scrutinized. In a pure LC-material, the major contrib-
utor to heating is radiationless decay from excited states addressed by two-photon
absorption and excited-state absorption17,27 (see Sec. 1.3). Assuming that the glass
substrates do not absorb at all, numerical solutions have been sought for the heat
balance equation. The finite-element solutions were obtained using the commercial
ANSYS/Thermal code),b including thermal conduction in the LC-material and the
two glass-walls of the LC-cells, convection from the glass walls to air, and enthalpy
effects at the phase-transition temperature. Two-dimensional transient thermal
analysis was carried out for the initial condition of a Gaussian spatial temperature
distribution written by the laser pulse into the material. Temperature-dependent
material parameters for 5CB (thermal conductivity, specific heat) were provided in
file form by the authors of Ref. 142.
For lack of literature data on radiationless energy coupling efficiencies from two-
photon and excited-state absorption, here the assumption is made of a Gaussian
temperature profile equivalent to the in-focus laser-beam profile (1/e2 diameter =
160 µm) with maximum temperature Tmax. Other device parameters used in
the simulation were: LC layer thickness L = 125 µm, glass substrate thickness
Lglass = 375 µm, room temperature Troom = 26◦C. In order to comply with the
experimental 10-Hz repetition rate, the decay evolution of the initial temperature
profile was followed out to 0.1 seconds, with the smallest time step set at 10−6
seconds. Values for Tmax = ∆Tmax + Troom were chosen such that throughout a
sequence of equal pulses, Tmax at any node did not exceed the temperature limit
set by the available material-parameter142 lookup table (44.9◦C maximum). This
Fig. 23. Numerical modeling of the heat diffusion: center-node temperature relaxation in timeafter first pulse.
bNumerical modeling was made by Dr. A. Schmid (University of Rochester, Laboratory for LaserEnergetics) using code of ANSYS, Inc., PA.
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 395
∆∆∆∆Tmax = 10oC ∆∆∆∆Tmax = 5oC
Short number
Cen
ter-
node
tem
pera
ture
, oC
Fig. 24. Numerical modeling of the heat diffusion: center-node temperature versus the numberof pulses.
constraint is strictly methodological and is not to imply that in an actual experiment
the temperature did not exceed, or could not have exceeded, the values chosen here.
Figure 23 shows the temperature relaxation with time after the first pulse at the
central node of the 5CB-cell (∆Tmax = 5◦C). During the first 10 milliseconds the
temperature relaxes fast, followed by slower relaxation thereafter. Even after 100
milliseconds the temperature remains ∆T ∼ 0.15◦C above room temperature.
Numerical calculations of heating as cumulative action of many, 10-Hz repetition-
rate pulses yield results presented in Fig. 24, ∆Tmax = 10◦C (solid curve) and
∆Tmax = 5◦C (dotted curve). After 60 pulses (∼ 6 s of irradiation) the tempera-
ture in the center of the LC-cell increased by ∆T = 5◦C for ∆Tmax = 10◦C, and
∆T ∼ 4.5◦C for ∆Tmax = 5◦C. The slopes of the curves increase faster for the first
15–20 pulses, and for ∆Tmax = 5◦C, ∆T is close to the temperature saturation
value at the end of the sequence.
Evaluation of the phase shift caused in a laser beam by this temperature increase
is equal to ∆Ψ = 2π∆nL/λ, where ∆n = ∆Tdn/dT . The number of rings as a
result of self-phase modulation in space on the transverse profile of a beam134 is
equal to N = ∆Ψ/2π = ∆TL(dn/dT )/λ. For 5CB in the region from 26◦C to
31◦C dn/dT ∼ 2.5 · 10−3 grad−1. For λ = 0.532 µm, L = 125 µm, and ∆T =
5◦C, N = 3. A temperature increase after single pulse irradiation (∆T ∼ 0.15◦C)
results in no diffraction rings in the beam. Only the cumulative action of many
pulses approaching a steady-state value yields a stable spatial self-phase modulation
elliptical ring picture as displayed in Figs. 16 and 17. Given the approximations
in the model, this apparent agreement between simulation and experiment cannot
serve as a rigorous proof of the cumulative heating mechanism. Instead, it provides
substantial plausibility for such a mechanism to be active in this situation.
396 S. G. Lukishova
The observation of the effect only for incident polarization parallel to the LC-
director is explained by two-photon absorption dichroism,61 and more effective LC
heating by “parallel” — polarization light, and approximately twice larger absolute
value of dn/dT for “parallel” polarization in comparison with “perpendicular”.
The scattering asymmetry and ellipticity of the ring pattern can be explained by
the anisotropy of the thermal diffusion constant, which has for 5CB a ∼ 1.6 times
larger value along the long molecular axis than perpendicular to it.142,143
The nature of the cross-structure is not yet clear. Stresses similar to those con-
sidered in Ref. 144 can create movement of LC fluid in two perpendicular directions
and destruction of the planar structure in these directions.
8. Changes of Reflectivity of Cholesteric Mirror by Light Field
Near Selective Reflection Conditions
8.1. Free-space Results
An increase in cholesteric LC-mirror transmittance was observed in free space,
i.e. outside the cavity, when laser radiation with 500-ns pulse duration and a repe-
tition rate of 4.5 kHz was focused into the cholesteric LC layer. The mirror trans-
mittance increased from 5% up to 30–80% for mirrors 1–3 and from 15% up to
25–50% for mirror 4. The intensity drop appeared 30 s–10 min after irradiation
onset (Fig. 25 for two mirrors (a) and (b)), depending on the peak power density
of the incident radiation, which was different for each mirror.
It is interesting, that the effect did not depend on the average power density. Just
as in Refs. 103–104, in the CW lasing mode no reflectance drop was observed, even
for a power density twice as high as the high-repetition rate average pulsed mode.
Moreover, even in the high-repetition-rate mode the bleaching effect was recorded
only when the reflection occurred from the side of the cholesteric LC mirror with
the strong anchoring. No bleaching was observed in the case of reflection from the
weak-anchoring side (flipping of the cell by 180◦).
It should first be noted that a high-quality beam reflection was obtained only
from the strong-surface-anchoring side of the cholesteric LC mirror, while a beam
reflected from the other, weak-anchoring side, had poor quality (e.g. amplitude
inhomogeneities were observed in beam cross-section).107
According to measurements, the temperature shift of the selective-reflection
curve of the experimental cholesteric LC mixture is approximately +1 nm/◦C, i.e. to
obtain a transmittance of ∼ 70% for CLC mirrors at λ = 1.064 µm the prepared
cholesteric LC mirrors must be heated to a temperature above 50◦C. Monitoring the
cell temperature by an attached thermocouple, no increase in the cell temperature
was recorded.
In the case of weak bleaching, it was observed that the transmittance of the
cholesteric LC mirror returned to its previous state after the laser was either
switched off or switched to the CW mode (Fig. 25(b)).
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 397
(a)
(b)
Time interval , minTr
ansm
ittan
ce, %
Time interval, min
Tran
smitt
ance
, %
Fig. 25. Dependence of two cholesteric LC mirrors ((a) and (b)) transmittance on irradiation timeunder high repetition rate, pulsed irradiation. For mirror (b) lasing action intentionally terminated(*) and restarted again (**).
8.2. Cholesteric LC Mirror in an Nd:YAG Laser Cavity
No significant difference was observed between the slope efficiency of the laser with
dielectric or cholesteric LC output mirrors when the reflection coefficients were the
same. The advantage of the cholesteric LC mirror was a lower sensitivity of the
laser operation to cavity misalignment. At low pumping rate and in the pulsed
high-repetition-rate regime, the slope efficiency and the lasing stability were the
same for cholesteric LC and dielectric mirrors. At high pumping rates, the average
output power obtained in the high-repetition-rate decayed rapidly and disappeared
after 0.5–5 min from switching, but only when the side of the cholesteric LC mirror
with strong surface anchoring was facing the gain medium. The pump threshold
(i.e. the current to the flashlamp) at which lasing was suppressed was a function of
the mirror characteristics (method of their fabrication): it was 28.5–29.5 A for the
output mirrors 1–3 with R = 95% and ∼ 24.5 A for the mirror 4 with R = 85%.
398 S. G. Lukishova
Time interval, min
Out
put P
ower
, W
t1 t2t1 t2 t2t1
Fig. 26. Time dependence of the average output power of a laser with cholesteric mirror withchanging the regime from CW to high-repetition rate (t1) and back to CW (t2). Solid and dashedcurves present results for different mirrors.
Figure 26 depicts the time dependence of the laser output power obtained for
two cholesteric LC mirrors differing in the method of their fabrication (different
degrees of surface anchoring) when a change from the CW to the pulsed regime
occurred above the pump threshold. Turning on the acousto-optical switch (at t1)
quenched the lasing action because of a drop in the reflection coefficient of the
cholesteric LC mirror. Turning off the switch (at t2) gradually restored the lasing
action. A second change to the pulsed regime suppressed lasing again and it was
restored when the laser was made to operate in the CW regime again. Adjustment
of the polarization of the radiation by rotating the λ/4 wave plate in the pulsed
regime sometimes increased the output power only slightly.
The observed reflectivity drop of the cholesteric LC mirror can be explained on
the basis of a model in which the pitch of the cholesteric helix increases in the electric
field of light pulses with high power density (intensity) ∼ (1 − 10) × 106 W/cm2.
Indeed, according to the calculations in Ref. 96, for a “thick” cholesteric LC layer
of thickness L > 2λ/(π∆n) the critical field for unwinding the cholesteric helix by
the light field is determined by the expression
|E|2cr = 4π(ω/c)2(εa/ε)K22 , (9)
where ∆n = npar − nperp, ε ∼ n2av, and the dielectric anisotropy at optical fre-
quencies is
εa = εpar − εperp = n2par − n2
perp ≈ 2∆nnav . (10)
Using the relation (10), we obtain from Eq. (9)
|E|2cr ≈ (32π3K22/λ2)(∆n/nav) . (11)
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 399
For λ = 1.064 µm, ∆n = 0.174, nav = 1.6, and K22 = 5 × 10−7 dyn we obtain
Ecr = 2.1× 104 V/cm and 2λ/(π∆n) = 3.9 µm, i.e. less than L for all four mirrors.
In the described experiments the electric field strength at the center of the beam is
∼ (2.2–7) ×104 V/cm, i.e. higher than Ecr.
The unwinding of the cholesteric helix by the field of a powerful light wave in
the region of selective reflection is substantially different from the unwinding of the
helix in a low-frequency field, since in the latter case E2cr ∼ ε−1
a (Refs. 145 and
146). In contrast to the field with a constant direction in the low-frequency case,
the direction of the electric field vector of a circularly polarized light wave changes
over the thickness of the cholesteric LC layer. The field of the light wave decays
exponentially over a distance Lc ∼ ε−1a and does not “see” the remaining thickness
of the cholesteric LC.96 Comparing results described here with the experimental
investigations of the pitch increase in a low-frequency electric field lying in the
plane of the cholesteric LC layer,145–147 it is possible to say that the electric field
reached in our experiments was much higher than the unwinding field in Refs. 145–
147 (∼ 104 V/cm).
It should be noted that in Ref. 148, the pitch of the cholesteric helix in a
cholesteric LC layer on whose surfaces the director was anchored increased in a
nonmonotonic, step-like manner. Apparently, this explains the nonmonotonic (step)
dependence of the cholesteric LC-mirror transmittance on the irradiation time in
the experiments described here (Fig. 25). The smearing of the steps is due to the ra-
dial intensity distribution in the beam and the corresponding change in electric-field
magnitude cross the beam. Deformation energy is accumulated in the cholesteric
LC layer over the interaction time of a single laser pulse (500 ns), and this energy
is partially dissipated during the “quiet” period between the pulses (200 µs), since
the relaxation time of the deformed helix is of the order of 1000 µs. Therefore,
the unwinding of a cholesteric helix in an optical field occur only over quite a long
time (accumulation of nonlinear changes149) during pulsed high-repetition rate laser
irradiation.
For a complete picture it should be noted that step-like changing the trans-
mittance was observed in Ref. 150, owing to pitch changes by heating. In difference
to our experiments, the authors of Ref. 150 used LCs with large temperature
sensitivity.
9. Conclusion and Future Developments
9.1. χ(3)(− ω,ω,ω,−ω) Measurements of Liquid Crystals
The main result of this paper is a warning of caution that, to date, results of
nanosecond and picosecond χ(3) measurements of cyanobiphenyl LCs remain in a
state of unsettlement that all but precludes the effective use of these materials in
the device engineering of power-limiting and other χ(3)-based applications. In par-
ticular, several nanosecond laser irradiation experiments involving such LCs under
400 S. G. Lukishova
two-photon absorption conditions need to be rethought. The unresolved challenges
are these:
• “Thin” (≤ 100 µm thickness) layer measurements, including the ones reported
here, tend to overestimate values of nonlinear optical parameters, in particular
when purification of “as received” materials by degassing and other means is
omitted. In the benign case, transient, micrometer-sized bubble formation will
cause wide-angle scattering that the detector will “interpret” as enhanced nonlin-
ear absorption. In the more aggravated case, microscopic carbonization will float
and remain in the medium with the potential for massive damage and device loss
later on. Both effects do “limit”, but quantification of such artifacts is tedious,
and reproducibility between devices based on such artifacts is impossible.
• Planar-nematic layers irradiated by pulses at moderate repetition-rate (2–10 Hz)
with linear polarization parallel to the director seem to experience cumulative,
laser-driven heating effects. Among the consequences of this local heating is
the important difference in LC response between first irradiation and much later
ones. LC devices, such as power limiters, that are expected to show specified
performance on the first shot without preconditioning, cannot be based on mea-
surements that do not distinguish this difference.
• Critical emphasis needs to be placed on irradiation geometry (beam-waist diam-
eter) and its precise knowledge as the nanosecond nonlinear response of “thick”
LC layers changes not only magnitude but even sign, depending on the geometry.
With much of this information absent or guessed in past measurements, reliable
χ(3) values are sparse indeed.
• It remains a vexing puzzle why the value for nonlinear absorption coefficient β in
the nanosecond case is ten- to hundred times larger than in the picosecond case.
Moreover, β depends on the incident intensity in both cases. Whether this is a
manifestation of a “clean” effect such as added triplet-state absorption or another
“dirt” effect (either bubbles or carbonization) needs to be clarified.
I would like to mark the importance of studies of materials with high two-photon
absorption, especially in optical power limiting application. It is also important to
mention that in difference with linear absorption, the two-photon absorption process
has a quadratically increase the absorption rate. This property allows activation of
photo-chemical or physical processes with high spatial resolution in 3D,151 e.g. for
data recording and storage application. Recently LCs doped with two-photon ab-
sorbing chromophores began to be used under short-pulse laser irradiation. A large
enhancement of the nonlinear absorption properties of dye molecules was observed,
dissolved in cyanobiphenyl nematic LCs.151
9.2. Cholesteric Mirrors
This paper shows the possibility to control the chiral-nematic (cholesteric) pitch
length (up to its unwinding) by a light-field alone under irradiation conditions
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 401
without either two-photon or linear absorption. Macroscopically this effect mani-
fests itself as a reflectivity drop of planar-aligned cholesteric mirrors. Previous at-
tempts to observe this drop failed because the threshold intensity (∼ MW/cm2)
must be maintained for the entire unwinding time ∼millisecond. Experiments
should also be able to distinguish between light-field-induced and thermal effects
that are present even at very low absorption coefficients of the LC medium.
Experiment described in this paper succeeded owing to specially chosen irradia-
tion conditions (∼ 4.5 kHz high-repetition rate) that enabled the cumulative action
of many pulses, each with above-threshold peak intensity. Low average power den-
sity did not permit heating of the sample.
Further development in this field should distinguish between “slow” (1) and
“fast” (2) unwinding experiments. (1) “Slow” unwinding, at near-threshold inten-
sities (I ∼ 2.2–10 MW/cm2) is presented in this paper. At such “low” intensities,
several minutes duration unwinding time offers the possibility to observe the un-
winding process in the microscope, i.e. imaging of how the chiral order changes
during the unwinding process. (2) Fast unwinding observed in Refs. 112 and 113 at
I ∼ 0.1–1 GW/cm2 opens the opportunity to use a cholesteric mirror for temporal
pulse shaping in a laser resonator with Q-switching or as the Q-switcher. It should
be added that nonlinear pitch dilation in cholesteric LC mirrors in laser resonator
gives the possibility to improve mode composition and output power stability of
CW and repetitively pulsed laser sources.
Acknowledgments
The author is very grateful to Prof. P. Palffy-Muhoray (Liquid Crystal Institute,
Kent State University) for his hospitality and help, Dr. A. Schmid (Laboratory for
Laser Energetics, the University of Rochester) for numerical simulations, providing
purified chiral mixture, and numerous discussions and help, Prof. S. Belyaev and N.
Malimonenko (Moscow Organic Intermediate and Dyes Institute (NIOPIK), Russia)
for fabrication cholesteric LC mirrors and discussions, K. Lebedev and E. Magu-
lariya (former students of Moscow Institute of Physics and Technology, Russia) for
assistance in chiral nematic experiments, Dr. T. Kosa (Liquid Crystal Institute) for
providing software and help, Dr. M. Groom (Liquid Crystal Institute) for the help
in maintaining electronics, Dr. B. Taheri (Liquid Crystal Institute) for the help in
maintaining laser system, Prof. J. Perry (University of Arizona) for providing chro-
mophore for some experiments, Prof. F. Scudiery and Dr. M. Marinelli (University
of Roma II) for providing their data in electronic form, Prof. V. Zolin, Dr. C.
Briskina, Dr. A. Lichmanov, Dr. V. Markushev, Dr. N. Ter-Gabrielyan from the
Institute of Radioengineering and Electronics of the Russian Academy of Sciences
(Moscow, Russia) for valuable advice and/or technical assistance, Dr. A. Zolot’ko
and Prof. V. Kitaeva from the P. N. Lebedev Institute of the Russian Academy of
Sciences (Moscow, Russia) for valuable references and advice.
This work was supported by NSF under ALCOM grant DMR-890147 and Cal-
ifornia Institute of Technology/AFOSR NoPC218970. In Russia this work was
402 S. G. Lukishova
partially supported by the International Science (Soros) Foundation (Grants Nos
MF2000 and MF2300), the Government of the Russian Federation (Grant No
MF2300), and the Russian Foundation for Basic Research (Grant No 96-02-18762).
References
1. G. Vertogen and W. H. de Jeu, Thermotropic Liquid Crystals, Fundamentals(Springer-Verlag, Berlin, 1988).
2. P. J. Collings and J. S. Patel, eds., Handbook of Liquid Crystal Research (Oxford Univ.Press, New York - Oxford, 1997). See also P. J. Collings and M. Hird, Introductionto Liquid Crystals. Chemistry and Physics (Taylor & Francis, London, 1997).
3. G. W. Gray, ed., Thermotropic Liquid Crystals. Critical Reports on Appl. Chem. 22(John Wiley & Sons, New York, 1987).
4. S. D. Jacobs, K. L. Marshall and A. Schmid, “Liquid crystals for laser applications”,in Handbook of Laser Science and Technology, Supplement 2: Optical Materials, ed.M. J. Weber (CRC Press, Boca Raton, FL, 1995), pp. 509–577.
5. S. D. Jacobs, K. A. Cerqua, K. L. Marchal, A. W. Schmid, M. J. Guardalben andK. J. Skerrett, “Liquid-crystal laser optics: design, fabrication and performance”,J. Opt. Soc. Am. B5(9), 1962 (1988).
6. A. Schmid, S. Papernov, Z.-W. Li, K. Marshal, T. Gunderman, J.-C. Lee, M. Guardal-ben and S. D. Jacobs, “Liquid-crystal materials for high peak-power laser applica-tion”, Mol. Cryst. Liq. Cryst. 207, 33 (1991).
7. W. Rupp and P. Greve, “Various possibilities of applying liquid crystals in (laser-)optics”, Laser und Optoelektronik 21(1), 46 (1989), in German.
8. J. A. Hermann and J. Staromlynska, “Trends in optical switches, limiters and dis-criminators”, Int. J. Nonlin. Opt. Phys. 2, 271 (1993).
9. B. Zel’dovich, N. Pilipetskii, A. Sukhov and N. Tabiryan, “Giant optical nonlinearityof nematic liquid crystals in mesophase”, JETP Lett. 31, 263 (1980). See also N. F.Pilipetski, A. V. Sukhov, N. V. Tabiryan and B. Ya. Zel’dovich, “The orientationalmechanism of nonlinearity and the self-focusing of He-Ne laser radiation in nematicliquid crystal mesophase (theory and experiment)”, Opt. Comm. 37(4), 280 (1981).
10. N. V. Tabiryan, A. V. Sukhov and B. Ya. Zel’dovich, “The orientational opticalnonlinearity of liquid crystals”, Mol. Cryst. Liq. Cryst. 136, 1 (1986). See also B. Ya.Zel’dovich and N. V. Tabiryan, “Orientational optical nonlinearity of liquid crystals”,Sov. Phys. Uspekhi 28(12), 1059 (1985).
11. I. Janossy and T. Kosa, “Influence of anthraquinone dyes on optical reorientation ofnematic liquid crystals”, Opt Lett. 17, 1183 (1992). See also I. Janossy, L. Csillag andA. D. Lloyd, “Temperature dependence of the optical Fredericksz transition in dyednematic liquid crystals”, Phys. Rev. A44, 8410 (1991), and also I. Janossy, “Opticalreorientation in dye-doped liquid crystals”, J. Nonlin. Opt. Phys. Mat. 8(3), 361(1999).
12. I.-C. Khoo, Liquid Crystals, Physical Properties and Nonlinear Optical Phenomena(John Wiley & Sons, New York, 1995).
13. I.-C. Khoo and S.-T. Wu, Optics and Nonlinear Optics of Liquid Crystals (WorldScientific, Singapore, 1993).
14. F. Simoni, Nonlinear Optical Properties of Liquid Crystals and Polymer DispersedLiquid Crystals (World Scientific, Singapore, 1997).
15. S. M. Arakelyan, G. A. Lyakhov and Yu. S. Chilingaryan, “Nonlinear optics of liquidcrystals”, Sov. Phys. Uspekhi 23(5), 245 (1980). See also S. M. Arakelyan and Yu. S.Chilingaryan, Nonlinear Optics of Liquid Crystals (Nauka Publ., Moscow, 1984), inRussian.
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 403
16. P. Palffy-Muhoray, “The nonlinear optical response of liquid crystals”, in LiquidCrystals: Applications and Uses, ed. B. Bahadur (World Scientific, Singapore, 1990),Vol. 1, 493–545.
17. R. Macdonald and H. E. Eichler, “Transient grating optical nonlinearities in ne-matic, cholesteric and smectic liquid crystals”, Appl. Phys. B60, 543 (1995). Seealso R. Macdonald and H. E. Eichler, “Fast liquid crystal optics in light-induced dy-namic gratings”, in The Optics of Thermotropic Liquid Crystals, eds. S. Elston andR. Sambles (Taylor & Francis, London, 1998), 137–153.
18. I. C. Khoo and Y. R. Shen, “Liquid crystals: nonlinear optical properties andprocesses”, Opt. Eng. 24, 579 (1985).
19. L. Marucci and Y. R. Shen, “Nonlinear optics of liquid crystals”, in The Opticsof Thermotropic Liquid Crystals, eds. S. Elston and R. Sambles (Taylor & Francis,London, 1998), pp. 115–135. See also E. Santamato and Y. R. Shen, “Liquid crystalsfor nonlinear optical studies”, in Handbook of Liquid Crystal Research, eds. P. J.Collings and J. S. Patel (Oxford Univ. Press, New York - Oxford, 1997), pp. 539–566.
20. I. C. Khoo, “A review of nonlinear optical properties of nematic liquid crystals”,J. Nonlin. Opt. Mat. 8(3), 305 (1999).
21. I. C. Khoo, S. Lee, P. LoPresti, R. G. Lindquist and H. Li, “Isotropic liquid crystallinefilm and fiber structures for optical limiting application”, Int. J. Nonlin. Opt. Phys.2(4), 559 (1993). See also I. C. Khoo, “Liquid crystal fiber array for optical limitingof laser pulses and for eye/sensor protection”, US Patent, No. 5,589,101 (Dec. 1996).
22. F. M. Aliev, “Dielectric and optical properties of heterogeneous microcomposite ma-terials based on porous matrices and liquid crystals”, Proc. SPIE 2949, 22 (1997).See also W. I. Goldburg, F. Aliev and X. I. Wu, “Behavior of liquid crystals andfluids in porous media”, Physica A213(1–2), 61 (1995), and also F. M. Aliev, G. Yu.Vershovskaya and L. A. Zubkov, “Optical properties of the isotropic phase of a liquidcrystal in pores”, Sov. Phys. JETP 72, 846 (1991).
23. G. P. Crawford, J. W. Doane and S. Zumer, “Polymer dispersed liquid crystals:nematic droplets and related systems”, in Handbook of Liquid Crystal Research, eds.P. J. Collings and J. S. Patel (Oxford Univ. Press, NewYork - Oxford, 1997), pp. 347–414.
24. N. V. Tabiryan, P. LiKamWa, B. Ya. Zel’dovich, T. Tschudi and T. Vogeler,“Characterization of high power laser beams with the aid of nonlinear opticalprocesses”, Proc. SPIE 2870, 12 (1996). See also N. V. Tabiryan, V. Vogeler, T.Tshudi and B. Ya. Zel’dovich, “All-optical, in-line, unperturbing and parallel mea-surement of laser beam intensity with transparent thin layers of liquid crystals”,J. Nonlin. Opt. Phys. Mat. 4(4), 843 (1995), and also T. Vogeler, T. Tschudi, N.Tabirian and B. Zel’dovich, “Apparatus and method for measuring the power den-sity of a laser beam with a liquid crystal”, US Patent, No. 5,621,525 (1997), andalso M. A. Bolshtyansky, N. V. Tabiryan and B. Ya. Zel’dovich, “BRIEFING: beamreconstruction by iteration of an electromagnetic field with an induced nonlinearitygauge”, Opt. Lett. 22, 22 (1997), and also N. V. Tabiryan, “Liquid crystals measurelight intensity”, Laser Focus World 4, 165 (1998).
25. R. M. Herman and R. J. Serinko, “Nonlinear optical processes in nematic liquidcrystals near a Freedericksz transition”, Phys. Rev. A19, 1757 (1979).
26. I. C. Khoo and S. L. Zhuang, “Nonlinear light amplification in a nematic liquidcrystal above the Freedericksz transition”, Appl. Phys. Lett. 37, 3 (1980).
27. F. W. Deeg and M. D. Fayer, “Analysis of complex molecular dynamics in an or-ganic liquid by polarization selective subpicosecond transient grating experiments”,
404 S. G. Lukishova
J. Chem. Phys. 91, 2269 (1989).28. J. R. Lalanne, J. Buchert and S. Kielich, “Fast molecular reorientation in liquid
crystals probed by nonlinear optics”, in Modern Nonlinear Optics, Part 1, eds.M. Evans and S. Kielich, Advances in Chemical Physics Series (John Wiley & Sons,New York, 1993), LXXXV, pp. 159–216.
29. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan and E. W. Van Stryland, “Sen-sitive measurements of optical nonlinearities using a single beam”, IEEE J. QuantumElectron. 26, 760 (1990).
30. H. Hsiung, L. P. Shi and Y. R. Shen, “Transient laser-induced molecular reorientationand laser heating in a nematic liquid crystal”, Phys. Rev. A30, 1453 (1984).
31. I. C. Khoo, R. R. Michel and P. Y. Yan, “Optically-induced molecular reorientationin nematic liquid crystals and nonlinear optical processes in the nanosecond regime”,IEEE J. Quantum Electron. QE-23, 267 (1987).
32. A. S. Zolot’ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev and L. Csillag, “The effect ofan optical field on the nematic phase on the liquid crystal OCBP”, JETP Lett. 32(2),158 (1980). See also V. F. Kitaeva and A. S. Zolot’ko, “Optically induced Fredericszeffect”, J. Sov. Laser Res. 10(4), 275 (1989).
33. S. Durbin, S. Arakelyan and Y. Shen, “Optical-field-induced birefringence and Freed-ericksz transition in a nematic liquid crystal”, Phys. Rev. Lett. 47, 1411 (1981). Seealso S. Durbin, S. Arakelyan and Y. Shen, “Strong optical diffraction in a nematicliquid crystals with high nonlinearity”, Opt. Lett. 7, 1145 (1982).
34. L. Li, H. J. Yuan, G. Hu and P. Palffy-Muhoray, “Third order optical non-linearitiesof nematic liquid crystals”, Liq. Cryst. 16, 703 (1994).
35. H. J. Eichler and E. Macdonald, “Flow-alignment and inertial effects in picosecondlaser-induced reorientation phenomena of nematic liquid crystals”, Phys. Rev. Lett.67, 2666 (1991). See also H. J. Eichler and E. Macdonald, “Inertial effects in thedynamics of picosecond laser-induced molecular reorientation in nematic liquid crys-tals”, Mol. Cryst. Liq. Cryst. 207, 117 (1991).
36. I. C. Khoo, R. G. Lindquist, R. R. Michael, R. J. Mansfield and P. LoPresti, “Dynam-ics of picosecond laser-induced density, temperature and flow-reorientation effects inthe mesophases of liquid crystals”, J. Appl. Phys. 69, 3853 (1991).
37. J. Prost and J. R. Lalanne, “Laser-induced optical Kerr effect and the dynamicsof orientational order in the isotropic phase of a nematogen”, Phys. Rev. A8, 2090(1973).
38. G. K. L. Wong and Y. R. Shen, “Optical-field-induced ordering in the isotropic phaseof a nematic liquid crystal”, Phys. Rev. Lett. 30, 895 (1973).
39. D. V. G. L. Narasimha Rao and S. Jayaraman, “Self-focusing of laser light in theisotropic phase of a nematic liquid crystals”, Appl. Phys. Lett. 23, 539 (1973).
40. G. K. L. Wong and Y. R. Shen, “Study of pretransitional behavior of laser-inducedmolecular alignment in isotropic nematic substances”, Phys. Rev. A10, 1277 (1974).
41. G. K. L. Wong and Y. R. Shen, “Transient self-focusing in a nematic liquid crys-tal in the isotropic phase”, Phys. Rev. Lett. 32, 527 (1974). See also E. G. Hanson,Y. R. Shen and G. K. L. Wong, “Experimental study of self-focusing in liquid crys-talline medium”, Appl. Phys. 14, 65 (1977).
42. H. J. Coles and B. R. Jennings, “The optical and electrical Kerr effect in 4-n-pentyl-4′-cyanobiphenyl”, Mol. Phys. 36, 1661 (1978).
43. P. A. Madden, F. C. Saunders and A. M. Scott, “Degenerate four-wave mixing inthe isotropic phase of liquid crystals: the influence of molecular structure”, IEEE J.Quantum Electron. QE-22, 1287 (1986).
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 405
44. K. J. McEwan, K. J. Harrison and P. A. Madden, “Polarisation and material depen-dence of degenerate four-wave mixing transients in molecular fluids”, Mol. Phys. 69,1025 (1990).
45. M. J. Soileau, E. W. Van Stryland, S. Guha, E. J. Sharp, G. L. Wood and J. L. W.Pohlmann, “Nonlinear optical properties of liquid crystals in the isotropic phase”,Mol. Cryst. Liq. Cryst. 143, 139 (1987).
46. A. F. Bunkin, S. G. Ivanov, N. I. Koroteev, A. V. Rezov and M. L. Sybeva, “Measure-ment of nonlinear optical susceptibilities of the liquid crystal MBBA in isotropic andnematic phases, using coherent active spectroscopy”, Vest. Mosk. Univ. Fiz. 32(5),35 (1977).
47. V. M. Avetisyan, N. N. Badalyan, M. S. Petrosyan, M. A. Khursudyan and Yu. S.Chilingaryan, “Investigation of nonlinear optical susceptibility of liquid crystals bymeans of the coherent active spectroscopy”, Rep. Acad. Sci. Armenian SSR, Phys.14, 127 (1979), in Russian. See also L. S. Aslanyan, N. N. Badalyan, A. A. Petrosyan,M. A. Khurshudyan and Yu. S. Chilingaryan, “Determination of cubic optical sus-ceptibilities of liquid crystals by coherent four-photon spectroscopy”, Opt. Spectrosc.(USSR) 53, 54 (1983).
48. Y.-H. Chuang, Z.-W. Li, D. D. Meyerhofer and A. W. Schmid, “Nonresonant χ(3)1111
obtained by nearly degenerate four-wave mixing using chirped-pulse technology”,Opt. Lett. 16, 7 (1991).
49. P. N. Prasad and D. J. Williams, Introduction to Nonlinear Optical Effects inMolecules and Polymers (John Wiley & Sons, New York, 1991).
50. L. G. Koreneva, V. F. Zolin and B. L. Davydov, Nonlinear Optics of MolecularCrystals (Nauka Publ., Moscow, 1985), in Russian.
51. W. Lee Smith, “Nonlinear refractive index”, in Handbook of Laser Science and Tech-nology, III: Optical Materials, ed. M. J. Weber (CRC Press, Boca Raton, FL, 1986),pp. 259–281.
52. P. Brochard, V. Grolier-Mazza and R. Cabanel, “Thermal nonlinear refraction in dyesolutions: a study of the transient regime”, J. Opt. Soc. Am. B14, 405 (1997).
53. D. I. Kovsh, S. Yang, D. J. Hagan and E. W. Van Stryland, “Nonlinear optical beampropagation for optical limiting”, Appl. Opt. 38, 5168 (1999). See also D. I. Kovsh,D. J. Hagan and E. W. Van Stryland, Opt. Express 4(8), 315 (1999).
54. H. J. Eichler, R. Macdonald and B. Trosken, “Multi-photon excitation and relaxationof thermal gratings in the nematic liquid crystal 5CB”, Mol. Cryst. Liq. Cryst. 231,1 (1993).
55. R. G. Horn, “Refractive indices and order parameters of two liquid crystals”,J. Physique 39, 105 (1978).
56. D. Armitage and S. M. Delwart, “Nonlinear optical effects in the nematic phase”,Mol. Cryst. Liq. Cryst. 122, 59 (1985).
57. V. Volterra and E. Wiener-Avnear, “CW thermal lens effect in thin layer of nematicliquid crystal”, Opt. Comm. 12, 194 (1974).
58. P. Wang, H. Zhang and J. Dai, “Laser-heating-induced self-phase modulation, phasetransition, and bistability in nematic liquid crystals”, Opt. Lett. 13, 479 (1988).
59. F. Bloisi, L. Vicari, F. Simoni, G. Cipparone and C. Umeton, “Self-phase modulationin nematic liquid-crystal films: detailed measurements and theoretical calculations”,J. Opt. Soc. Am. B5, 2462 (1988).
60. C. Umeton, G. Cipparrone and F. Simoni, “Power limiting and optical switchingwith nematic liquid-crystal films”, Opt. Quantum Electron. 18(5), 312 (1986).
61. S. D. Durbin and Y. R. Shen, “Two-photon dichroism studies of molecular-orientational distribution in a nematic liquid crystal”, Phys. Rev. A30, 1419 (1984).
406 S. G. Lukishova
62. M. J. Soileau, S. Guha, W. E. Williams, E. W. Van Stryland, H. Vanherzeele, J. L. W.Pohlmann, E. J. Sharp and G. Wood, “Studies of the nonlinear switching propertiesof liquid crystals with picosecond pulses”, Mol. Cryst. Liq. Cryst. 127, 321 (1985).
63. A. Hochbaum, J. L. Fergason and J. D. Buck, “Optical limiting with liquid crystalmaterials”, Proc. SPIE 1692, 96 (1992). See also A. Hochbaum, Y. Y. Hsu and J.L. Fergason, “Molecular structure and its relation to optical limiting”, Proc. SPIE2229, 48 (1994).
64. K. McEwan and R. C. Hollins, “Two-photon-induced excited-state absorption inliquid crystal media”, Proc. SPIE 2229, 122 (1994).
65. K. J. McEwan and R. C. Hollins, “Picosecond-induced nonlinear absorption in liquidcrystal media”, J. Nonlin. Opt. Phys. Mat. 4, 245 (1995).
66. H. J. Yuan, L. Li and P. Palffy-Muhoray, “Nonlinear birefringence of liquid crystals”,Mol. Cryst. Liq. Cryst. 199, 223 (1991).
67. P. Palffy-Muhoray, H. J. Yuan, L. Li, M. A. Lee, J. R. DeSalvo, T. H. Wei, M. Sheik-Bahae, D. J. Hagan and E. W. Van Stryland, “Measurements of third order opticalnonlinearities of nematic liquid crystals”, Mol. Cryst. Liq. Cryst. 207, 291 (1991).
68. T. Kosa, A. Dogariu, P. Palffy-Muhoray and E. W. Van Stryland, “Nonlinear ab-sorption in the liquid crystal 5CB”, Opt. Soc. Am. Tech. Dig. Ser. 21, 57 (1995).
69. W. Zhao and P. Palffy-Muhoray, “Z-scan measurements of χ(3) using top-hat beams”,Appl. Phys. Lett. 65, 673 (1994).
70. P. Palffy-Muhoray, T. Wei and W. Zhao, “Z-scan measurements on liquid crystals:some considerations and results”, Mol. Cryst. Liq. Cryst. 251, 19 (1994).
71. S.-T. Wu and K. C. Lim, “Absorption and scattering measurements of nematic liquidcrystals”, Appl. Opt. 26, 1722 (1987). See also S.-T. Wu, “Absorption measurementsof liquid crystals in the ultraviolet, visible and infrared”, J. Appl. Phys. 84, 4462(1998).
72. I. C. Khoo, M. V. Wood, B. D. Guenter, M.-Y. Shih and P. H. Chen, “Nonlinearabsorption and optical limiting of laser pulses in a liquid-cored fiber array”, J. Opt.Soc. Am. B15, 1533 (1998).
73. I. C. Khoo, P. H. Chen, M. V. Wood and M.-Y. Shih, “Molecular photonics of ahighly nonlinear organic fiber core liquid for picosecond-nanosecond optical limitingapplication”, Chem. Phys. 245, 517 (1999).
74. G. E. O’Keefe, J. C. De Mello, G. J. Denton, K. J. McEwan and S. J. Till,“Transient excited state absorption of the liquid crystal CB15 [4-(2-methylbutyl)-4-cyanobiphenyl] in its isotropic phase”, Liq. Cryst. 21, 225 (1996).
75. H. J. Eichler, R. Macdonald, R. Manzel and R. Sander, “Excited state absorption of5CB (4′-n-pentyl-4-cyanobiphenyl) in cyclohexane”, Chem. Phys. 195, 381 (1995).
76. R. Sander, V. Herrmann and R. Menzel, “Transient absorption spectra and bleachingof 4′-n-pentyl-4-cyanoterphenyl in cyclohexane — determination of cross sections andrecovery times”, J. Chem. Phys. 104, 4390 (1996).
77. G. A. Askar’yan, A. M. Prokhorov, G. F. Chanturiya and G. P. Shipulo,“The effectof a laser beam in a liquid”, Sov. Phys. JETP 17, 1463 (1963).
78. S. G. Eyring and M. D. Fayer, “Holographic generation of bubble grating at liquid-glass interfaces and the dynamics of bubbles on surfaces”, Chem. Phys. Lett. 98, 428(1983).
79. A. V. Butenin and B. Ya. Kogan, “Mechanism of optical breakdown in transparentdielectrics”, Sov. J. Quantum Electron. 1(5), 561 (1972). See also A. V. Butenin andB. Ya. Kogan, “Nature of cumulative laser damage to optical materials”, Sov. J.Quantum Electron. 20(2), 187 (1990).
80. A. W. Schmid (see Refs. 4–6, 48), private communication.
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 407
81. A. Vogel, S. Busch and U. Parlitz, “Shock wave emission and cavitation bub-ble generation by picosecond and nanosecond optical breakdown in water”,J. Acoust. Soc. Am. 100, 148 (1996). See also A. Vogel, J. Noack, K. Nahen,D. Theisen, S. Busch, U. Parlitz, D. X. Hammer, G. D. Noojin, B. A. Rockwelland R. Birngruber, “Energy balance of optical breakdown in water at nanosecondto femtosecond time scales”, Appl. Phys. B68, 271 (1999) and also J. Noack, D. X.Hammer, G. D. Noojin, B. A. Rockwell and A. Vogel “Influence of pulse duration onmechanical effects after laser-induced breakdown in water”, J. Appl. Phys. 83(12),7488 (1998) and also D. X. Hammer, E. D. Jansen, M. Frenz, G. D. Noojin, R. J.Thomas, J. Noack, A. Vogel, B. A. Rockwell and A. J. Welch, “Shielding propertiesof laser-induced breakdown in water for pulse durations from 5 ns to 125 fs”, Appl.Opt. 36(22), 5630 (1997).
82. P. K. Kennedy, D. X. Hammer and B. A. Rockwell, “Laser-induced breakdown inaqueous media”, Prog. Quantum Electron. 21(3), 155 (1997).
83. N. F. Bunkin and F. V. Bunkin, “The new concepts in the optical breakdown oftransparent liquids”, Laser Phys. 3(1), 63 (1993).
84. A. V. Butenin and B. Ya. Kogan, “Pyrolysis of organic liquids subjected to laserbreakdown”, Pis’Ma V Zhurnal Tekhnicheskoi Fiziki (Sov. Tech. Phys. Lett.) 3(10),433 (1977), in Russian.
85. J. Pola, M. Urbanova, Z. Bastl, Z. Plzak, J. Subrt, V. Vorlıcek, I. Gregora, C. Crowleyand R. Taylor, “Laser photolysis of liquid benzene and toluene: graphitic and poly-meric carbon formation at ambient temperature”, Carbon 35(5), 605 (1997). See alsoM. Urbanova, Z. Bastl, Z. Plzak, J. Subrt, I. Gregora, V. Vorlıcek and J. Pola, “Laserphotolysis of liquid benzene and hexafluorobenzene: graphitic and polymeric carbonformation at ambient temperature”, Carbon 36(5–6), 517 (1998) and also J. Pola, M.Urbanova, Z. Bastl, Z. Plzak, J. Subrt, I. Gregora and V. Vorlıcek, “Laser photolysisof liquid hexafluorobenzene: graphitic and fluorine-containing carbon formation atambient temperature”, J. Mat. Chem. 8(1), 187 (1998).
86. D. A. Dunmur, “Physical origin of liquid crystal optical properties”, in The Opticsof Thermotropic Liquid Crystals, eds. S. Elston and R. Sambles (Taylor & Francis,1998), pp. 2–40.
87. V. A. Belyakov and A. S. Sonin, Optics of Cholesteric Liquid Crystals (Nauka Publ.,Moscow, 1982) in Russian.
88. S. Chandrasekhar, Liquid Crystals (Cambridge Univ. Press, Cambridge, 1977).89. I. P. Ilchishin, E. A. Tikhonov, V. G. Tischenko and M. T. Shpak, “Frequency tuning
in a dye laser with a Bragg mirror utilizing a cholesteric liquid crystals”, Sov. J.Quantum Electron. 8, 1487 (1978).
90. Yu. V. Denisov, V. A. Kizel’, V. A. Orlov and N. F. Perevozchikov, “Properties ofradiation emitted by a laser with liquid crystal reflectors”, Sov. J. Quantum Electron.10, 1447 (1980).
91. J.-C. Lee and S. D. Jacobs, “Design and construction of 1064-nm liquid crystal cavityend mirrors”, J. Appl. Phys. 68, 6523 (1990).
92. J.-C. Lee, J. H. Kelly, D. L. Smith and S. D. Jacobs, “Gain squaring in Cr:Nd:GSGGactive-mirror amplifier using a cholesteric liquid crystal mirror”, IEEE J. QuantumElectron. 24, 2238 (1988).
93. D. II Chang, H. Y. Kim, M. Y. Jeon, H. K. Lee, D. S. Lim, K. H. Kim, I. Kim andS. T. Kim, “Short pulse generation in the mode-locked fibre laser using cholestericliquid crystal”, Opt. Comm. 162, 251 (1999).
94. S. V. Belyaev, M. I. Barnik and N. V. Malimonenko, “Spectral and polarization filtersbased on cholesteric liquid crystals”, Sov. J. Opt. Technol. 56(9), 579 (1989).
408 S. G. Lukishova
95. V. V. Danilov, O. B. Danilov, A. L. Sidorov and E. N. Sosnov, “Transversely ex-cited atmospheric CO2 laser with an intracavity liquid crystal diaphragm”, Sov. J.Quantum Electron. 21, 1099 (1991).
96. H. G. Winful, “ Nonlinear reflection in cholesteric liquid crystals: mirrorless opticalbistability”, Phys. Rev. Lett. 49, 1179 (1982).
97. B. Ya. Zel’dovich and N. V. Tabiryan, “Orientational effect of a light-wave on acholesteric mesophase”, Sov. Phys. JETP 55, 99 (1982).
98. L. I. Zagainova, G. V. Klimusheva, I. P. Kryzhanovskii and N. V. Kukhtarev, “Opticalhysteresis in liquid crystals with helicoidal distributed feedback”, JETP Lett. 42(9),435 (1985).
99. R. B. Alaverdyan, S. M. Arakelyan and Yu. S. Chilingaryan, “Optical bistability inthe nonlinear system with distributed feedback (experiment)”, JETP Lett. 42(9),451 (1985).
100. R. B. Meyer, F. Lonberg and C.-C. Chang, “Cholesteric liquid crystal smartreflectors”, Mol. Cryst. Liq. Cryst. 288, 47 (1996).
101. R. S. Becker, S. Chakravorti and S. Das, “Unique optical changes in cholesteric liquidcrystals using guest mediated single laser beam excitation”, J. Chem. Phys. 90, 2802(1989).
102. H. Espinet, M. Lesieski, M. Ramsburg and D. Jenkins, “Attempt to observe Nd:YAGlaser-induced nonlinear reflection in cholesteric and cholesteric/nematic mixtures ofliquid crystals”, J. Appl. Phys. 59, 1386 (1986).
103. J.-C. Lee, S. D. Jacobs, T. Gunderman, A. Schmid, T. J. Kessler and M. D. Skeldon,“TEM00-mode and single-longitudinal-mode laser operation with a cholesteric liquid-crystal laser end mirror”, Opt. Lett. 15, 959 (1990).
104. J.-C. Lee, S. D. Jacobs and R. J. Gingold, “Nd:YAG laser with cholesteric liquidcrystal cavity mirrors”, Proc. SPIE 824, 7 (1987).
105. J.-C. Lee, S. D. Jacobs and A. W. Schmid, “Retro self-focusing and pinholing effectin a cholesteric liquid crystal”, Mol. Cryst. Liq. Cryst. 150b, 617 (1987).
106. J.-C. Lee, A. W. Schmid and S. D. Jacobs, “Effect of anchoring under intense opticalfields in a cholesteric liquid crystal”, Mol. Cryst. Liq. Cryst. 166, 253 (1989).
107. S. G. Lukishova, E. A. Magulariya and K. S. Lebedev, “Nd:YAG laser induced nonlin-ear selective reflection by a cholesteric liquid-crystal mirror”, Bulletin Russian Acad.Sci., Phys. 59(12), 2086 (1995). See also S. G. Lukishova, E. A. Magulariya andK. S. Lebedev, “Experimental observation of Nd:YAG laser field-induced nonlinearfrustration of selective Bragg reflection in the cholesteric liquid crystal”, Proc. SPIE(ICONO’95 (St.-Petersburg, Russia, June 1995)), 2800, 196 (1996) and also S. G.Lukishova, K. S. Lebedev and E. A. Magulariya, “Influence of nonlinear effects inthe CLC end mirror on the output characteristics of the Nd:YAG laser”, Proc. SPIE2795, 14 (1996) and also S. G. Lukishova, K. S. Lebedev and E. A. Magulariya,“Light-induced nonlinear bleaching of the CLC film under the conditions of selectivereflection”, Proc. SPIE 2795, 24 (1996).
108. S. G. Lukishova, K. S. Lebedev, E. A. Magulariya, S. V. Belyaev, N. V. Malimonenkoand A. W. Schmid, “Nonlinear “brightening” of a film of nonabsorbing chiral nematicunder selective reflection conditions”, JETP Lett. 63(6), 423 (1996). See also S. G.Lukishova, K. S. Lebedev and E. A. Magulariya, “Nonlinear optics of nonabsorb-ing chiral media: experiments on frustration of selective reflection by powerful laserradiation”, Opt. Soc. Am. Tech. Dig. Ser. QELS’96 10, 5 (1996).
109. S. G. Lukishova, S. V. Belyaev, K. S. Lebedev, E. A. Magulariya, A. W. Schmidand N. V. Malimonenko, “Behaviour of nonlinear liquid-crystal mirrors, made of annonabsorbing cholesteric, in the cavity of an Nd:YAG laser operating in the cw regime
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 409
and at a high pulse repetition frequency”, Quantum Electron. (Moscow/UK ), 26(9),796 (1996). See also S. G. Lukishova, K. S. Lebedev and E. A. Magulariya, “cw andhigh-repetition rate Nd:YAG laser with nonlinear cholesteric liquid crystal mirror”,Opt. Soc. Am. Tech. Dig. Ser. CLEO’96 9, 382 (1996).
110. S. G. Lukishova, S. V. Belyaev, K. S. Lebedev, E. A. Magulariya, A. W. Schmid andN. V. Malimonenko, “Nonlinear bleaching in the selective reflection of nonabsorbingchiral-nematic liquid-crystal thin films”, Mol. Cryst. Liq. Cryst. 303, 79 (1997).
111. S. G. Lukishova, S. V. Belyaev, K. S. Lebedev, E. A. Magulariya, A. W. Schmidand N. V. Malimonenko, “Reflective nonlinearity of nonabsorbing cholesteric liquidcrystal mirrors driven by pulsed high-repetition rate laser radiation”, Proc. SPIE3800, 164 (1999).
112. D. Grebe, K. Contag, R. Macdonald and H. J. Eichler, “Nonlinear optical effects incholesteric liquid crystals for lasers and photonic switching applications”, Abstr. 6thInt. Topical Meeting on Optics of Liquid Crystals’95 (Le Touquet, France, September1995).
113. D. Grebe, R. Macdonald and H. J. Eichler, “Cholesteric liquid crystal mirrors forpulsed solid-state lasers”, Mol. Cryst. Liq. Cryst. 282, 309 (1996).
114. BDH/EM Chemicals (E. Merck), Data Sheets.115. H. Ono and N. Kawatsuki, “High- and low-molar-mass liquid crystal mixtures for
photorefractive applications”, J. Nonlin. Opt. Phys. Mat. 8(3), 329 (1999).116. J. E. Ehrlich, X.-L. Wu, I.-Y. S. Lee, Z.-Y. Hu, S. R. Marder and J. W. Perry, “Two-
photon absorption and broadband optical limiting with bis-donor stilbenes”, Opt.Lett. 22, 1843 (1997).
117. L. L. Chase and E. W. Van Stryland, “Nonlinear refractive index”, in Handbook ofLaser Science and Technology, III: Optical Materials, ed. M. J. Weber (CRC Press,Boca Raton, FL, 1995), pp. 299–328.
118. R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, New York, 1996).119. A. N. Azarenkov, G. B. Al’tshuler, N. R. Belashenkov and S. A. Kozlov, “Review: Fast
nonlinearity of the refractive index of solid-state dielectric active media”, QuantumElectron. (Moscow/UK ) 23(8), 633 (1993).
120. R. Adair, L. L. Chase and S. A. Payne, “Nonlinear refractive index of opticalcrystals”, Phys. Rev. B39, 3337 (1989).
121. M. Sheik-Bahae, A. A. Said and E. W. Van Stryland, “High-sensitivity single beamn2 measurements”, Opt. Lett. 14, 955 (1989).
122. P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. McKay and R. G. McDuff,“Single-beam Z-scan: measurement technique and analysis”, J. Nonlin. Opt. Phys.Mat. 6, 251 (1997).
123. P. B. Chapple, J. Staromlynska and R. G. McDuff, “Z-scan studies in the thin- andthick-sample limits”, J. Opt. Soc. Am. B11, 975 (1994).
124. A. Caprara, S. Butcher and R. Aubert, “Injection seeding of a Nd:YAG laser utilizinga radially variable reflectivity output coupler”, Proc. SPIE 912, 21 (1988).
125. B. K. Rhee, J. S. Byun and E. W. Van Stryland, “Z-scan using circularly symmetricbeams”, J. Opt. Soc. Am. B13, 2720 (1996).
126. A. Caprara and G. C. Reali, “Time varying M2 in Q-switched lasers”, Opt. QuantumElectron. 24, S1001 (1992). See also A. Caprara and G. C. Reali, “Time-resolved M2
of nanosecond pulses from Q-switched variable-reflectivity-mirror Nd:YAG laser”,Opt. Lett. 17, 414 (1992).
127. S. Hughes and J. M. Burzler, “Theory of Z-scan measurements using Gaussian-Besselbeams”, Phys. Rev. A56, R1103 (1997).
128. P. B. Chapple and P. J. Wilson, “Z-scan with near-Gaussian laser beams”, J. Nonlin.
410 S. G. Lukishova
Opt. Phys. Mat. 5(2), 419 (1996).129. A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality
from a multimode stable-cavity laser”, IEEE J. Quantum Electron. 29, 1212 (1993).130. R. E. Bridges, G. L. Fischer and R. W. Boyd, “Z-scan measurement technique
for non-Gaussian beams and arbitrary sample thicknesses”, Opt. Lett. 20(17), 1821(1995).
131. R. W. Boyd, Nonlinear Optics (Academic Press, Boston, 1992).132. N. Bloembergen, Nonlinear Optics (W. A. Benjamin, New York, 1965).133. S. A. Akhmanov and R. V. Khokhlov, Problems of Nonlinear Optics (Electromagnetic
Waves in Nonlinear Dispersive Media) (Gordon & Breach, New York, 1972).134. Y. R. Shen, The Principles of Nonlinear Optics (John Wiley & Sons, New York,
1984).135. E. W. Van Stryland and L. L. Chase, “Two-photon absorption”, in Handbook of Laser
Science and Technology, III: Optical Materials, ed. M. J. Weber (CRC Press, BocaRaton, FL, 1995), pp. 299–328.
136. S. G. Lukishova, “Nonlinear absorption and refraction of linearly polarized nanosec-ond laser radiation by liquid crystals in the transient regime”, Proc. SPIE 3796, 100(1999). See also S. G. Lukishova, “Nonlinear absorption and refraction of linearly po-larized nanosecond laser radiation by liquid crystals in the transient regime: 532-nm,2–10-Hz mode”, Opt. Soc. Am. Tech. Dig. CLEO’99, 266 (1999).
137. S. G. Lukishova, “Nanosecond Z-scan measurements of optical nonlinearities in 5CBand CB15 at 532 nm”, Mol. Cryst. Liq. Cryst. 331, 609 (1999).
138. S. G. Lukishova, “Cumulative self-phase modulation in planar nematics driven by532-nm nanosecond laser pulses”, Proc. SPIE 3798, 128 (1999). See also S. G. Luk-ishova, “Cumulative negative nonlinearity in planar nematics driven by nanosecond,532-nm laser pulses with linear polarization parallel to the liquid crystal director”,Opt. Soc. Am. Tech. Dig. QELS’99, 126 (1999).
139. S. G. Lukishova, “Nonlinear optical response of liquid crystals to nanosecond laserradiation”, Proc. SPIE 3900, 102 (1999). See also S. G. Lukishova, “High-intensity,far-field transverse effects in a 532-nm, nanosecond laser beams as a result of nonlinearinteraction with nematics”, Opt. Soc. Am. Tech. Dig. QELS’99, 129 (1999).
140. R. G. Harrison, L. Dambly, D. Yu and W. Lu, “A new self-diffraction pattern forma-tion in defocusing liquid media”, Opt. Comm. 139, 69 (1997). See also D. Yu, W. Lu,R. G. Harrison and N. N. Rosanov, “Analysis of dark spot formation in absorbingliquid media”, J. Mod. Opt. 45, 2597 (1998).
141. A. S. Zolot’ko, V. F. Kitaeva and D. B. Terskov, “Light scattering by structurescreated by a laser beam in an OCBP liquid crystal near the smectic-nematic phasetransition; memory effect”, Sov. Phys. JETP 74(6), 974 (1992). See also M. I. Barnik,A. S. Zolot’ko and V. F. Kitaeva, “Interaction of light with a dye-doped nematic liquidcrystal”, JETP 84(6), 1122 (1997).
142. M. Marinelli, F. Mercuri, U. Zammit and F. Scudieri, “Thermal conductivity andthermal diffusivity of the cyanobiphenyl (nCB) homologous series”, Phys. Rev. E58,5860 (1998).
143. S. G. Ahlers, D. S. Cannell, L. I. Berge and S. Sakurai, “Thermal conductivity of thenematic liquid crystal 4-n-pentyl-4′-cyanobiphenyl”, Phys. Rev. E49, 545 (1994).
144. R. Elschner, R. Macdonald, H. J. Eichler, S. Hess, and A. M. Sonnet, ”Molecularreorientation of a nematic glass by laser-induced heat flow”, Phys. Rev. E60, 1792(1999).
145. P. G. de Gennes, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1974).146. L. M. Blinov, Electro-Optical and Magneto-Optical Properties of Liquid Crystals
Nonlinear Optical Response of Cyanobiphenyl Liquid Crystals 411
(John Wiley & Sons, New York, 1983). See also L. M. Blinov and V. G. Chigri-nov, Electrooptic Effects in Liquid Crystal Materials (Springer Verlag, New York,1992).
147. L. M. Blinov, S. V. Belyaev and V. A. Kisel, “High-order reflections from a cholesterichelix induced by an electric field”, Phys. Lett. A65, 33 (1978).
148. S. V. Belyaev and L. M. Blinov, “Step unwinding of a spiral in a cholesteric liquidcrystal”, JETP Lett. 30(2), 99 (1979).
149. S. M. Arakelyan, O. V. Garibyan, A. S. Karayan and Yu. S. Chilingaryan, “Orienta-tional effects in the mesophase under short laser pulses; nonlinearity buildup”, Sov.Tech. Phys. Lett. 8(9), 452 (1982).
150. H. Zink and V. A. Belyakov, “Temperature variations in the director orientation andanchoring energy at the surface of cholesteric layers”, JETP Lett. 63(1), 43 (1996).
151. J. W. Perry, Web-page (http://www.chem.arizona.edu/faculty/perr/perrx.html).