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Φsat ≈ 70 µJ/cm2 Ans ≈ 0.3 A0 1 mm x 1 mm, 4 mm x 4 mm (other on request) 400 µm (other on request) unmounted 12.7 mm ∅ (1/2" ∅) 25.0 mm ∅ 25.4 mm ∅ (1" ∅) fiber coupled (SMF, PM)
Cu-Mount ∅ 12.7 mm: Cu-Mount ∅ 25.4 mm:
SAM 1064-70-X Spectral reflection: Pump-probe relaxation measurement*:
● 1. Aim of SAM ● 2. Parameters ● 3. Saturable absorption ● 4. Non-saturable loss ● 5. Relaxation time ● 6. Saturation fluence ● 7. Reflection and absorption bandwidth
> 1. Aim of SAM
Passive mode-locking techniques for the generation of ultra-short pulse trains are preferred over active techniques due to the ease of incorporation of passive devices into various laser cavities.
A passive mode-locking device, the saturable absorber mirror (SAM), can be used to mode-lock a wide range of laser cavities. Pulses result from the phase-locking (via the loss mechanism of the saturable absorber) of the multiple lasing modes supported in continuous-wave laser operation. The absorber becomes saturated at high intensities, thus allowing the majority of the cavity energy to pass through the absorber to the mirror, where it is reflected back into the laser cavity. At low intensities, the absorber is not saturated, and absorbs all
incident energy, effectively removing it from the laser cavity resulting of suppression of possible Q-switched mode-locking. Moreover, due to the absorption of the pulse front side the pulse width is slightly decreased during reflection.
A SAM consists of a Bragg-mirror on a semiconductor wafer like GaAs, covered by an absorber layer and a more or less sophisticated top film system, determining the saturable loss. Although semiconductor saturable absorber mirrors have been employed for mode-locking in a wide variety of laser cavities, the SAM has to be designed for each specific application. The differing loss, gain spectrum, internal cavity power, etc, of each laser necessitates slightly different absorber characteristics.
The most important parameters of a SAM are:
● saturable absorption ● non-saturable loss ● relaxation time ● saturation fluence ● reflection and absorption bandwidth.
> 3. Saturable absorption
A SAM is a nonlinear optical device. Therefore the absorption A depends on the light intensity I in the laser cavity by
eq.(1)
with Α absorption A0 small signal absorption (saturable absorption) I light intensity (measured in W/m2) Isat saturation intensity
The absorption A is proportional to the square of the electric field strength of the standing wave at the position of the absorber layer. Therefore the saturable absorption of the SAM can be adjusted by the design.
Typical values of the small signal (saturable) absorption A0 and the saturation intensity Isat
Non-saturable losses are caused by the transmission and the absorption of the Bragg mirror. The absorption of the thin film stack can be very low (< 0.1 %). The transmission loss of the Bragg mirror decreases with increasing number of the high and low index film pairs. The transmission loss of an AlAs/GaAs multilayer stack of 25 film pairs at the design wavelength is < 0.1 %. Beside this the high reflection band width and the group delay dispersion of the mirror has to be taken into account, especially in the case of ultra short pulses. The sum of the non-saturable losses can be described by a value Ans, which is typical < 0.3
% at the design wavelength.
> 5. Relaxation time
The saturable absorber layer consists of a semiconductor material with a direct band gap slightly lower than the photon energy. During the absorption electron-hole pairs are created in the film. The relaxation time τ of the carriers has to be a little bit longer than the pulse duration. In this case the back side of the pulse is still free of absorption, but during the hole period between two consecutive pulses the absorber is non saturated and prevents Q-switched mode-locking of the laser. Because the relaxation time due to the spontaneous photon emission in a direct semiconductor is about 1 ns, some precautions has to be done to shorten it drastically.
Two technologies are used to introduce lattice defects in the absorber layer for fast non-radiative relaxation of the carriers:
● low-temperature molecular beam epitaxy (LT-MBE) ● ion implantation.
The parameters to adjust the relaxation time in both technologies are the growth temperature in case of LT-MBE and the ion dose in case of implantation. Typical values of the relaxation time τ of SAMs are between 0.3 and 2 ps.
> 6. Saturation fluence
The saturation process can be better quantified by the pulse fluence Φ than by the intensity I because of the limited relaxation time τ. To minimise the losses, the absorber should be saturable with the expected pulse fluence Φ, e.g. the pulse energy in the laser should be several times more than the saturation energy, but not too high because then the laser tends to exhibit multiple pulsing. An other limitation is the damage threshold of the SAM. A typical saturation fluence Φsat is about 70 µJ/cm2.
In the laser cavity the incident pulse fluence Φ can be adjusted by varying the illuminated area a on the SAM. If the intracavity pulse power is low, e.g. because of low pump power, then tighter focussing helps to achieve the necessary saturation fluence Φsat of typically
some ten µJ/cm2. In analogy to eq. (1) the (saturable) absorption A of the SAM can be calculated by
The figure right shows the saturable absorption A in dependency of the fluence in case of A0 = 1 % and Φ sat = 0.1 mJ/cm2.
The pulse fluence Φ can be derived from the mean output power P of the laser as follows:
eq.(3)
with Φ pulse fluence (measured in J/cm2) P mean output power of the laser R reflectance of the output mirror f repetition rate of the laser a illuminated area on the SAM
> 7. Reflection and absorption bandwidth 7.1 Time-bandwidth product (TBWP)
From Heisenberg's uncertainty principle for the conjugated variables pulse width ∆t and photon energy E = h. νthe TBWP of a laser pulse is limited to about ∆ t.∆ν >1/(2π).
● h = 6.626 . 10-34 Js is Planck's constant ● ν the pulse mean frequency and ● ∆ν the pulse bandwidth
An accurate calculation shows, that the minimum TBWP for a Gaussian pulse is ∆t. ∆ν = 0.44 (pulse duration in seconds x pulse bandwidth in Hertz > 0.44). The minimum TBWP for a Sech2pulse is ∆t.∆ν = 0.32 . Most people do not work with frequency ν but prefer wavelength λ. Using the relation c=λ.
ν the frequency interval ∆ν is related to the wavelength interval ∆λ by ∆ν = - c. ∆λ/λ2. c = 2.988 . 108 m/s is the speed of light in the vacuum.
Numerical values for the minimum bandwidth ∆ν as a function of pulse duration ∆t
The reflection bandwidth of the SAM has to be larger than the pulse bandwidth. In case of a SAM with an underlying Bragg-mirror the reflection bandwidth is determined by the ratio of the refractive indices nH/nL of the layers in the thin film stack. More about Bragg-
mirrors ... The relative spectral width w = ∆λ/λ of the high reflectance zone of a conventional semiconductor AlAs/GaAs thin film stack is about 0.1. Therefore the width of the high reflection zone of an AlAs/GaAs Bragg-mirror with a center wavelength of 1000 nm is about 100 nm. From the tables above this results in a minimum pulse duration of about 20 fs. For shorter pulses other mirror types, for instance dielectric or metallic mirrors has to be used.
7.3 Absorption bandwidth
An ideal SAM has a constant saturable absorption for all wavelength of the pulse spectrum. In case of a 5 fs pulse the width of this wavelength interval is some hundreds of nanometers.
● Aim of SOC ● SOC parameters ● Transmittance ● Saturable absorption ● Relaxation time ● Reflectance bandwidth ● Absorbance
> Aim of SOC
Using a saturable output coupler (SOC), a self-starting, passively mode-locked diode pumped solid-state laser with a very simple layout can be arranged. A SOC is a combination of the well known saturable absorber mirror (SAM) with an output coupler. In case of using a SOC instead of a SAM for passive mode-locking the optical pump power can be provided through the end mirror of the laser cavity. Mode locking produces stable and coherent pulsed lasers by forcing the faces of the modes to maintain constant values relative to one another. These modes then combine coherently. Fundamental mode-locking results in a train of optical pulses with a period of 2L/c, where L is the cavity length and c the
speed of the light in free space. Mode locking occurs when laser losses are modulated at a frequency equal to the reverse of the pulse period c/2L. The SOC is a passive mode locking device without the use of an external drive signal, which spontaneously locks the modes with fast material response time.
> SOC parameters
A SOC consists of a Bragg-mirror on a semiconductor wafer like GaAs, covered by an absorber layer and a more or less sophisticated top film system, determining the saturable loss. The back side of the SOC wafer is antireflection coated.
The transmittance of the saturable output coupler is mainly governed by the reflectance of the partial reflector and the absorbance of the absorber layer. The number of film pairs in the quarter-wave stack of the AlAs/GaAs partial reflector (Bragg-mirror) determines the reflectance. It follows from the energy conservation law T + R + A = 1 (T - transmittance, R -reflectance, A - absorbance), that the transmittance is given by T = 1 - R - A. The reflectance of the Bragg mirror increases with increasing number of the high and low index film pairs. An AlAs/GaAs multilayer stack of 10 film pairs has at the design wavelength a reflectance of ~ 96 % and consequently a transmitttance of ~ 4%.
> Saturable absorption
The absorbance A of the SOC consists of two parts:
Both parts are proportional to the square of the electric field strength of the standing wave at the position of the absorber layer in front of the Bragg-mirror. Therefore the absorbance of the SOC can be adjusted by changing the field distribution due to the design of the thin film stack.
The dependency of the saturable absorption on the optical pulse fluence can described by
with Α absorption A0 small signal absorption (saturable absorption)
Φ pulse fluence (J/cm2) Φsat saturation fluence
A typical value of the saturation fluence is 70 µJ/cm2.
The figure above shows the saturable absorption A in dependency of the fluence in case of A0 = 1 % and Φsat = 0.1 mJ/cm2.
The non-saturable absorption is the biggest part of the non-saturable losses. Due to the two-photon absorption it depends on the power density. A typical ratio of the saturable and non-saturable absorption is around 1. The modulation depth ∆T of the SOC transmittance is ~ A0 (saturable absorption).
The pulse fluence Φ can be derived from the mean output power P of the laser as follows: Φ = P / (T . f . a) with P mean output power of the laser T transmittance of the output coupler f repetition rate of the laser a illuminated area on the SOC.
The saturable absorber layer consists of a semiconductor material with a direct band gap slightly lower than the photon energy. During the absorption electron-hole pairs are created in the film. The relaxation time τ of the carriers has to be a little bit longer than the pulse duration. In this case the back side of the pulse is still free of absorption, but during the whole period between two consecutive pulses the absorber is non saturated and prevents Q-switching.
Because the typical relaxation time due to the spontaneous photon emission in a direct semiconductor is about 1 ns, some precautions has to be done to shorten it drastically.
Two technologies are used to introduce lattice defects in the absorber layer for fast non-radiative relaxation of the carriers:
● low-temperature molecular beam epitaxy (LT-MBE) ● ion implantation.
The parameters to adjust the relaxation time in both technologies are the growth temperature in case of LT-MBE and the ion dose and annealing parameters in case of ion implantation. Typical values of the relaxation time of SOCs are between τ = 1 .. 10 ps.
> Reflectance bandwidth
The reflectance bandwidth of the SOC has to be larger than the pulse bandwidth. The reflectance bandwidth is determined by the ratio of the refractive indices nH/nL of the layers in the Bragg mirror thin film stack. More
about Bragg-mirrors ...
The relative spectral width w = ∆λ/λ of the high reflectance zone of a common semiconductor AlAs/GaAs thin film stack is about 0.1. Therefore the width of the high reflectance zone of an AlAs/GaAs Bragg-mirror with a centre wavelength of 1000 nm is about 100 nm. This results in a minimum pulse duration of about 20 fs.
> Absorbance
An ideal SOC has a constant saturable absorption for all wavelengths of the pulse spectrum. The absorption of a direct semiconductor increases heavily with increasing photon energy, starting at the gap energy of the semiconductor material. In case of a quantum well structure the absorption increases as a step-like dependency on the photon energy due to the one-dimensional quantisation of free carriers. In any case the result is an increasing saturable absorption of a SOC with decreasing wavelength (increasing photon energy). Consequently, the reflectance versus wavelength curve of a SOC reveals under non-saturated conditions a decreasing reflectance with decreasing wavelength.
● How does a RSAM work? ● RSAM applications ● Resonance wavelength ● Bandwidth ● Saturation intensity ● Intensity dependent reflectance ● Relaxation time
> How does a RSAM work?
The resonant saturable absorber mirror (RSAM) is a similar device as a saturable absorber mirror (SAM), but has a larger saturable absorption, a smaller bandwidth and a lower saturation fluence. The RSAM is designed as a resonant Gires–Tournois interferometer with absorber layers positioned at the antinodes of the optical field inside the resonator cavity. The RSAM is a nonlinear optical device, having a low reflectance for week optical signals like noise and a high reflectance for high power signals like optical pulses. Optical pulses saturate the absorber material inside the resonant cavity of the RSAM. Due to the short recovery time of the absorber material the RSAM blocks immediately after the reflected pulse the optical noise floor.
Important parameters of the RSAM are the
● Resonance wavelength ● Bandwidth ● Saturation power density or the saturation fluence.
> RSAM applications
The main applications for RSAMs are:
● optical noise suppression, for example after an EDFA or a pulse picker (unsaturated RSAM reflectance = 0) --> SANOS (SAturable NOise Suppressor)
Influence of the angle of incidence The resonance wavelength λ of the Gires–Tournois interferometer depends on the angle of incidence ϕ and is given by
Resonance wavelength for perpendicular polarized light at different angles of incidence
Influence of the temperature
There is also a temperature influence on the resonance wavelength λ. The temperature dependency of the optical thickness nd of the absorbing spacer layer, which governs the resonance wavelength λ, is mainly determined by the refractive index. The influence of the thermal expansion of the layer thickness is negligible.
The change of the resonance wavelength λ with the temperature can be calculated by
eq.(2)
with λ (T) resonance wavelength at temperature T λ (T0) resonance wavelength at reference temperature T0 1/n*dn/dT ~ 7.5x10-5K-1, temperature coefficient of the refractive index T0 reference temperature T working temperature
Resonance wavelength λ of a RSAM with λ(0) = 1064 nm after eq. (2)
> Bandwidth
The bandwidth ∆λ of the interferometer resonance dip is gouverned by the round trip loss l of the wave inside the cavity and can be estimated in case of small losses l << 1 by
with ∆λ bandwidth FWHM (full width at half maximum) λ resonance wavelength of the interferometer (rf)2 = Rf reflectance of the front mirror (back mirror reflectance Rb = 1) A single pass absorptance of the spacer layer m order of the resonance; m = 1, 2, 3, ....
l round trip loss: 1 - rf + A
∆λ for RSAM at λ = 1064 nm
RSAM, impedance matched at λ = 1064 nm with front mirror reflection rf = 0.97,
unsaturated absorption of A = 1.5% and resonance order m = 4
The RSAM is a strong nonlinear optical device. The absorptance A of the absorber layer and the reflectance R of the RSAM depend on the incoming light intensity I. Due to the resonance condition of the Gires–Tournois interferometer at the working wavelength the effective saturation intensity Isat,eff of the device shifts by a factor of about (π/F)2 (F -
finesse of the Gires–Tournois interferometer) to lower values in relation to the intrinsic material value Isat, which is
valid for non-resonant saturable absorber mirrors (SAM). The absorptance A of a RSAM with a not too small finesse F > 10 can be estimated by
eq.(3)
with Α absorptance A0 small signal absorptance (saturable absorption) I light intensity (measured in W/m2) Isat intrinsic material saturation intensity F finesse of the RSAM
The effective saturation fluence Φsat,eff of a RSAM can be estimated using the relaxation time τ and the effective
saturation intensity Isat,eff
eq.(4)
with Φsat,eff effective saturation fluence of the RSAM
Isat,eff effective saturation intensity of the RSAM τ relaxation time of the absorber material
With typical values for a non-resonant SAM
● Isat = 10 MW/cm2
● τ = 10 ps ● Φsat = 100 µJ/cm2
the relevant parameters for a RSAM with a finesse F = 20 can be estimated to
● Isat,eff = 250 kW/cm2
● Φsat,eff = 2.5 µJ/cm2
In this way the effective saturation values can be decreased to very low values at the expense of a small usuable spectral bandwidth.
RSAM at λ = 1064 nm with front mirror reflection rf = 0.97,
unsaturated absorption of A = 1.5% and resonance order m = 4
> Relaxation time
The saturable absorber layer consists of a semiconductor material with a direct band gap, which is slightly smaller than the photon energy. During the absorption electron-hole pairs are created in the film. The relaxation time τ of the carriers is very short due to fast non-radiative relaxation channels introduced by low-temperature growth of the absorber layer. Typical values of the relaxation time τ are between 5 and 20 ps. The relaxation of the carriers and the recovery of the absorption A(t) after the saturation can be described as
Recovery of the absorption A0
with a relaxation time τ = 10 ps
A(t) = A0[1 - exp(-t/τ )] with A(t) time dependent absorption A0 small signal saturable absorption t time τ relaxation time
● How works a SANOS? ● SANOS applications ● Free space SANOS ● Fibre coupled SANOS ● Effective saturation fluence Φsat,eff
● Relaxation time constant τ ● Effective saturation intensity Isat,eff
● Bandwidth
> How works a SANOS?
The active element of a SANOS is a resonant saturable absorber mirror (RSAM) with zero reflectance for a low power signal at the resonance wavelength. The RSAM is a nonlinear optical device, having a low reflectance for week optical signals like noise and a high reflectance for high power signals like optical pulses. A typical non-linear transfer function of a SANOS is shown in the figure left. The transmittance of the SANOS is shown as a function of the peak puls intensity I. The typical effective saturation intensity Isat,eff is
~2 MW/cm2.
A SANOS is mainly characterized by the following parameters:
● the effective saturation fluence Φsat,eff
● the relaxation time constant τ ● the effective saturation intensity Isat,eff
● the usuable spectral bandwidth ∆λ ● the insertion loss L
● noise suppression in free space optics, for example after a pulse picker ● reshaping of fibre guided optical signals ● opto-optical wavelength conversion.
For these two applications the following devices has been developed:
● Free space SANOS (FS-SANOS) ● Fibre coupled SANOS (FC-SANOS)
> Free space SANOS (FS-SANOS)
The free space SANOS is devoted to clean a pulsed optical beam from noise. One possible application is after a pulse picker to suppress the residual pulses, which has been passed the picker with a low intensity. An other application is to suppress the amplified spontaneous emission (ASE) of an optical amplifier. The optical beam is twofold reflected inside the FS-SANOS. The first mirror is a nonlinear RSAM. The second mirror is either a common linear high reflectance mirror or a RSAM.
The transmittance T of the FS-SANOS depends on the peak power density I of the input beam according to the nonlinear reflectance of the RSAM. The output beam intensity Iout is related to the input beam
intensity I by
Iout = T(I) I with T(I) intensity dependent transmittance. A typical transmittance curve of a FS-SANOS with one RSAM inside shows the figure above.
> Fibre coupled SANOS (FC-SANOS)
The fibre coupled SANOS can be used for noise suppression in optical fibre channels. To reshape an optical signal the passive FC-SANOS can be simply insert into a fibre channel after an EDFA. Due to the working principle of the SANOS this device reshapes only the amplitude of one wavelength. The active device inside the FC-SANOS is a RSAM, mounted on a circulator.
The effective saturation fluence Φsat,eff of a SANOS can be defined in such a way, that the transmittance T
at Φsat,eff is 50% of the saturated value at a very large fluence Φ >> Φsat.
Corresponding to the finesse of the RSAM Φsat,eff of a SANOS is smaller than the saturation fluence Φsat of
the absorber material inside the RSAM. The finesse also limits the bandwidth FWHM of the resonance dip at the operation wavelength. The figure below shows the relation between the effective saturation fluence Φsat,eff as a function of the bandwidth full width of half maximum (FWHM). For decreasing the FWHM the
effective saturation fluence Φsat,eff is also decreasing if the cavity thickness remains constant. On the other
hand for a fixed FWHM the effective saturation fluence Φsat,eff is increasing if the optical thickness of the
RSAM cavity is increased.
The effective saturation fluence Φsat,eff as a function
of the full width at half maximum (FWHM) of the RSAM resonance dip plotted for different RSAM cavity thicknesses.
> Relaxation time constant τ
The low temperature grown saturable absorber layer inside the SANOS has a relaxation time constant τ, which can be varied over a large region from about 100 fs up to 100 ps. A typical value of the relaxation time τ is 1 ps. The relaxation of the carriers and the change of the transmittance T(t) after the saturation can be described as
Decrease of the transmittance after saturation with τ = 10 ps
T(t) = Tmaxexp(-t/τ )] with T(t) time dependent transmittace Tmax saturated transmittance t time τ relaxation time constant
> Effective saturation intensity Isat,eff
The effective saturation intensity Isat,eff is related to the effective saturation fluence Φsat,eff by
Φsat,eff = Isat,eff τ.
With Φsat,eff = 7 µJ/cm2 and τ = 10 ps the effective saturation intensity is Isat,eff = 700 kW/cm2.
> Bandwidth
The spectral bandwidth of the SANOS is gouverned by the used RSAM bandwidth. A compromise is needed between a large bandwidth and a low saturation fluence Φsat, because the saturation fluence
decreases together with the bandwidth. A typical bandwidth (FWHM) of ~ 20 nm is possible for a SANOS with Φsat = 5 µJ/cm2. The usuable spectral bandwidth ∆λ around the low-intensity minimum transmittance
is by a factor of 5 ... 10 smaller than the FWHM and is therefore only some nanometers.
> Refractive index > GaAs | AlAs | AlxGa1-xAs | InxGa1-xAs
> Devices > Bragg mirror | SAM | SA | RSAM | SOC | SANOS | PCA
SA - Saturable Absorber in transmission
> Contents
● Aim of SA ● SA parameters ● Transmittance ● Saturable absorption ● Relaxation time
> Aim of SA
The saturable absorber in transmission can be used to realize a mode-locked fiber ring laser. On other application is the use as mode-locking device in a diode pumped solid-state laser for longer lasing wavelength > 1600 nm, where the preparation of a saturable absorber mirror (SAM) with an AlAs/GaAs Bragg-mirror is too expensive.
> SA parameters
A SA consists of a group of absorbing InGaAs quantum wells on a semiconductor wafer like GaAs, covered on both sides with an antireflection coating.
The transmittance of the saturable absorber is mainly governed by the absorbance of the quantum well stack. Ideally the reflectance of the device is zero because of the antireflection coating on both sides of the semiconductor chip. It follows from the energy conservation law T + R + A = 1 (T - transmittance, R -reflectance, A - absorbance), that the transmittance is T ~ 1 - A.
The ratio between the saturable and the non-saturable part of the absorption depends mainly on the relaxation time of the excited carriers in the absorbing quantum wells. For a fast absorber with a relaxation time ~ 300 fs, this ratio is about one. It means, that in this case 50% of the absorbance is saturable and the other 50% non-saturable. For absorbers with a relaxation time of about 10 ps the saturable part of the absorption is about 70%. This part incrises further with increasing saturation time. The saturable part of the absorption is also known as modulation depth ∆ R.
> Relaxation time
The saturable absorber layer consists of a semiconductor material with a direct band gap slightly lower than the photon energy. During the absorption electron-hole pairs are created in the film. The relaxation time τ of the carriers has to be a little bit longer than the pulse duration. In this case the back side of the pulse is still free of absorption, but during the whole period between two consecutive pulses the absorber is non saturated and prevents Q-switching.
Because the typical relaxation time due to the spontaneous photon emission in a direct semiconductor is about 1 ns, some precautions has to be done to shorten it drastically.
Two technologies are used to introduce lattice defects in the absorber layer for fast non-radiative relaxation of the carriers:
● low-temperature molecular beam epitaxy (LT-MBE) ● ion implantation.
The parameters to adjust the relaxation time in both technologies are the growth temperature in case of LT-MBE and the ion dose and annealing parameters in case of ion implantation. Typical values of the relaxation time of SAs are between τ = 1 .. 10 ps.