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OSA Publishing (https://www.osapublishing.org) > Optics
Express (/oe/) > Volume 15
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Nonlinear and adiabatic control of high-Q photonic crystal
nanocavities
M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S.
Mitsugi, and M. Morita
Optics Express Vol. 15, Issue 26
(/oe/issue.cfm?volume=15&issue=26), pp. 17458-17481 (2007) doi:
10.1364/OE.15.017458 (http://dx.doi.org/10.1364/OE.15.017458)
(viewmedia.cfm?uri=oe-15-26-17458&seq=0)
(/user/favorites_add_article.cfm?articles=148439)
AccessibleOpen Access
Abstract
This article overviews our recent studies of ultrahigh-Q and
ultrasmall photonic-crystal cavities, andtheir applications to
nonlinear optical processing and novel adiabatic control of light.
First, we showour latest achievements of ultrahigh-Q
photonic-crystal nanocavities, and present extreme slow-light
demonstration. Next, we show all-optical bistable switching and
memory operations based onenhanced optical nonlinearity in these
nanocavities with extremely low power, and discuss
theirapplicability for realizing chip-scale all-optical logic, such
as flip-flop. Finally, we introduce adiabatictuning of high-Q
nanocavities, which leads to novel wavelength conversion and
another type ofoptical memories.
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2007 Optical Society of America
1. IntroductionRecently, there has been rapid progress in terms
of the cavity quality factor (Q) of miniature-sizedoptical
micro-resonators,[1] such as whispering-gallery-mode cavities [2]
and photonic-crystal (PhC)cavities [3,4, 5, 6, 7]. Of these, PhC
cavities have been considered the most advantageous in terms ofQ
per unit mode volume (V), that is, Q/V, because confinement by the
photonic bandgap (PBG) is themost efficient way to confine light in
a wavelength-scale volume. Q/V appears in various situationsin
optics relating to light-matter interactions, and is directly
related to the photonic density of statesand also to the field
intensity (photon density) in a cavity per unit input power.
Therefore, if largeQ/V cavities were to be realized, various
light-matter interactions (which are generally very weakcompared
with interactions governing electrons) would be greatly enhanced.
For example,spontaneous emission rate is enhanced by Q/V (Purcell
effect) as a result of the modification of thedensity of states.
Most of optical nonlinear interactions are also enhanced by the
field intensityenhancement and long photon lifetime. Extensive
studies are being conducted for this purpose,including spontaneous
emission control [4,8, 9, 10, 11], and solid-state cavity
quantumelectrodynamics [12]. This feature is especially important
for nonlinear-optic applications, sincemost optical nonlinear
interaction is too weak for practical applications. In addition,
large Q/Vcavities enable us to employ a novel light-matter
interaction of light based on the adiabatic tuning ofoptical
systems, as described later. In addition to their large Q/V, PhC
cavities have anotherdistinctive feature compared with other types
of cavities. That is, they are highly suited tointegration. It is
not difficult to integrate many cavities in a tiny chip, and they
can be coupled witheach other or connected via single-mode PBG
waveguides. The flexibility of various coupling formsand the
precise controllability of the coupling strength distinguish them
from other cavities. Webelieve that all of these features of PhC
cavities make them particularly important for all-opticalprocessing
applications in an integrated form. All-optical integration for
optical processing has along research history, but certain
fundamental difficulties still remain. We can summarize
thesedifficulties as follows: 1) the circuits require too much
power, 2) they are difficult to integrate, and 3)have poor
functionality. We believe that PhC-nanocavity-based systems have
the potential toovercome these problems.
In this review article, we aim in particular to describe recent
progress on PhC cavities and theirapplications to optical nonlinear
control and novel adiabatic control, with a view to
convincingreaders of their potential as a breakthrough for optical
integration. First, we show the latest statusof the performance of
our ultrahigh-Q PhC nanocavities by using the spectral-and
time-domainanalysis. We also report the achievement of slow-light
propagation in these ultrahigh-Qnanocavities, and discuss the issue
of the nanocavity size disorder, which is of great
practicalimportance as regards this system. Second, we employ these
cavities for all-optical switching andmemory operations based on
optical nonlinearity, in which the driving power (energy)
issubstantially reduced thanks to large Q/V. In the third part, we
discuss the possibility of constructing
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on-chip optical logic based on these bistable nonlinear
PhC-nanocavity elements. In the final part,we introduce a novel
adiabatic tuning of micro-optical systems with a long photon dwell
time, anddiscuss another form of optical memory based on a pair of
PhC nanocavities, where we dynamicallychange Q by employing
adiabatic control of nanocavities.
2. Ultrahigh-Q PhC nanocavities
2.1 Realizing high-Q in 2D PBG systemsAs described in the
introduction, a large Q/V is one of the most important and
promising features ofPhC cavities. Conventional optical cavities
are always limited by the fundamental trade-off betweenQ and V ,
but, in principle, PBG cavities do not involve trade-off between Q
and V . Contrary tothis naive expectation, the realization of
high-Q and simultaneously small-V cavities in PhCs did notprove
easy for two reasons. First, it remains extremely difficult to
realize sufficiently-good 3D PBGcavities. Second, if we employ a 2D
PBG to realize a high-Q cavity, light easily leaks in the
verticaldirection where there is no PBG. Owing to this leakage, 2D
PBG cavities actually suffer from a Q-V trade-off. At first, it was
believed that 3D PBG cavities were essential to overcome the Q-V
trade-off. However, this tuned out to be untrue. The vertical
leakage can be substantially suppressed byappropriately designing
the momentum (k-) space distribution of cavity modes in the 2D
plane [13,14]. The strategy is very simple. If the cavity mode is
concentrated outside the light cone of air in the2D k space, the
cavity mode cannot be coupled to the radiation modes. In fact,
there are many waysto achieve this situation so, as evidenced by
studies of many researches in this area. Here weintroduce two of
our design examples of ours. The first is a cavity based on a
single-missing-holeline defect with local width modulation. The
second is a cavity based on a single-missing-hole pointdefect
having a hexapole mode.
2.2 Ultrahigh-Q width-modulated line-defect nanocavities and
ultrahigh-QmeasurementsIf we terminate a PhC line-defect waveguide
(shown in the left panel of Fig. 1(a)), it forms a cavity.This is
something similar to the formation of conventional Fabry-Perot
cavities because we fold backpropagating waves to form standing
waves. If we start from a theoretically lossless waveguide,
thedesign requirement is simply to reduce the effect of this
termination to keep the original losslessmode profile in the k
space. Our latest design for this strategy is shown in Fig. 1(a),
in which alossless line-defect waveguide is not abruptly terminated
but the positions of several holes alongthe line defect are locally
shifted toward the outside to create in-line light confinement.[5]
Therequired hole shift is generally very small, typically several
nanometers. In other words, here welocally modify the position of
the mode gap of the line-defect waveguides to create
theconfinement. We proposed this idea before [15], but the design
at that time was not optimized forhigh Q. The latest design enables
us to realize spatially gradual confinement which is effective
inpreserving the original localized mode distribution in the k
space of the starting waveguide. The
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basic mechanism is similar to that used in hetero-structure
cavities where the lattice constant of thebackground PhC is altered
[3]. In our case, we introduced only local modification of the
backgroundPhC, which is suited for integration. The use of the mode
gap for creating cavities was also reportedin different
designs.[16] We numerically examined this type of cavities using
the finite-differencetime-domain (FDTD) method, and found that
after optimizing the hole shift values, the theoretical Qis higher
than 10 and the mode volume is 1.1~1.7(/n) where n is the
refractive index.
Fig. 1. Width-modulated line-defect PhC cavities. (a) Cavity
design: (from left to right) a startingstraight line defect
waveguide without theoretical loss and cavities with gradual
lightconfinement. The rightmost cavity has the highest theoretical
Q. The hole shifts are typically 9nm (red holes), 6 nm (green
holes), and 3 nm (blue holes). (b) Spectral measurement of
ananocavity fabricated in a silicon hexagonal air-hole photonic
slab with a=420 nm and 2r=216nm. The transmission spectrum of a
cavity with a second-stage hole-shift. The inner and outerhole
shifts are 8 and 4 nm, respectively. (c) Time-domain ring-down
measurement. The timedecay of the output light intensity from the
same cavity as (b). Details can be found in [17].Download Full Size
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We fabricated this type of cavities coupled to input/output
waveguides in silicon PhC slabs byelectron-beam lithography and dry
etching. Figure 1(b) shows the transmission spectrum of thesample,
which exhibits extremely sharp resonance as a result of resonant
transmission via thecavity. The measured transmission width is as
narrow as 1.2 pm, which corresponds to a Q value of1.3
million.[6,17] As is clear from its definition, Q can be also
deduced from independent time-domain measurements, which become
more accurate as Q becomes higher. We performed time-domain
ring-down measurements to deduce the cavity Q for the same
cavity.[6,17] This method, inwhich we abruptly switch off the CW
input and monitor the temporal output from the outputwaveguide, is
the most accurate way to determine the photon lifetime of a cavity
[2]. If we have alinear Lorentzian cavity, we expect single
exponential decay whose time constant is =Q/. Figure1(c) shows
ring-down measurement results. The deduced photon lifetime is 1.1
ns.
With such small and high-Q cavities, both of spectral and
time-domain measurements are easilyperturbed by small fluctuations
in the environment or samples and this may limit the accuracy
andreproducibility. Thus, we made a substantial effort to confirm
the accuracy and reproducibility ofour Q estimation. We performed a
series of measurements for the same cavity to clarify
thereproducibility and statistical error of our measurements.[17]
As a result, we found that the photonlifetime =1.070.05 ns for 12
independent spectral-domain measurements and =1.12 0.07ns for 16
independent time-domain measurements, which directly proves that
both measurementsprovide good accuracy and reproducibility. In
addition, we systematically checked the correlationbetween the
spectral and time-domain measurements, and confirmed that both
methods give usapproximately identical results (Q and ) as long as
Q>10 . When Q
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modification makes hexapole modes to be located in the middle of
the PBG. Interestingly, thisparticular cavity has a strange
characteristic as regards the waveguide coupling. It shows
nullwaveguide coupling if it is side-coupled or in-line end-coupled
to the waveguide. Thus, it took ussome time to find appropriate
structures (the answer is off-aligned end-coupling, as shown in
thefigure) for the experimental verification of their high-Q [23].
Very recently, we succeeded inmeasuring the Q value of the sample
shown in Fig. 2(a) [24]. Figure 2(b) shows the transmissionspectrum
of the hexapole-mode cavity through the input waveguide to the
output waveguide. Weobserve a sharp resonance peak at 1547.52 nm
with a width of 4.8 pm, which corresponds to a Q of3.210 . Figure
2(c) shows a ring-down measurement result. The deduced lifetime is
300 ps, whichleads to a Q of 3.6510 . This is sufficiently close to
the value we deduced from the spectral domainmeasurement. This Q is
the largest value reported for point-defect type cavities, as far
as we know.
Fig. 2. Hexapole-mode single-point-defect silicon PhC cavities.
(a) FDTD simulation of the fieldintensity profile for a hexapole
cavity coupled to input and output waveguides. The insetshows the
geometrical design of the hexapole cavity. (b) Spectral measurement
of a hexapolecavity fabricated in a silicon hexagonal air-hole
photonic slab with a=420 nm and 2r=176 nm
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The transmission spectrum across the input and output waveguides
is shown. The hole shiftis 0.23a. (c) Time-domain ring-down
measurement. The time decay of the output lightintensity from the
same cavity as (b). The solid line is an exponential fit for the
data. Ref is thereference data without the cavity (showing the time
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2.4 Slow-light application of nanocavitiesRecently, slow-light
media, in which the group velocity of light is greatly reduced,
have attractedmuch attention [25]. They are considered to be
possible candidates for optical buffermemories/quantum memories,
and they are also expected to be efficient tools for the
hugeenhancement of light-matter interaction. We have reported a
reduction in the group velocity toapproximately c/100 in W1 PhC
waveguides (W1: a single-missing-hole line defect without
adjustingthe width in a hexagonal PhC) owing to their huge
dispersion in the vicinity of the mode edge.[26,15]However, it is
difficult to slow down the pulse propagation in W1 waveguides since
thesewaveguides have too much group-velocity dispersion (GVD).
Recently, we performed pulsepropagation experiments using
dispersion-managed slow-light PhC waveguides, and observed agroup
delay of 180 ps.[27] There are several ways to reduce the GVD for
slow-light PhC waveguides.One of the simplest ways is to employ a
cavity to delay the pulse. Generally a cavity has a
Lorentzianspectral response, which leads to a cosine-like phase
response. It is easily shown that the groupdelay of a single cavity
is 2 (=2Q/) and simultaneously GVD=0 at the resonance
frequency.Thus, a cavity produces a substantially large group delay
with zero GVD if Q is high. Coupled-resonator optical waveguides
(CROWs) have the same feature only except that the delay
ismultiplied by the number of the cavities.[28] Another important
issues is that the resultant groupvelocity should be scaled to the
cavity size. Thus, an ultrahigh-Q and simultaneously
ultrasmallcavity is a good candidate for slow-light media.
With such features in mind, we performed pulse transmission
experiments using our ultrahigh-Qnanocavities based on
width-modulated line-defects [6, 17]. Figure 3 shows the
experimental setupand results. We observed a group delay of 1.45 ns
by comparison with the output from thereference straight PhC
waveguide. From this value we estimated the group velocity of this
pulse tobe 5.8 km/s, which is approximately c/50,000. To the best
of our knowledge, this is the smallestgroup velocity ever reported
for all-dielectric slow-light media. Note that this group velocity
wasobtained via direct pulse transmission experiments. In the past,
the group velocity has beenobtained in indirect ways (such as an
interference method) for many of the all-dielectric
slow-lightwaveguides. Both of the small footprint and high-Q
contribute to this small group velocity, and thusthis result
clearly demonstrates one of the advantages of ultrahigh-Q
nanocavities.
ph
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Although the above result shows promising potential of
ultrahigh-Q nanocavities in slowing light,there are still many
things to be overcome considering the real applications. This
single cavity is notvery practical, because it can delay the pulse
by approximately the same length as the input pulselength. However,
if we cascade a number of cavities to form a CROW, we can increase
the groupdelay or extend the bandwidth. In terms of the delay (not
the group velocity) bandwidth product,apparently cascaded long
devices are more advantageous than a single cavity. In terms of the
groupvelocity itself, the above result gives us a very rough
estimate of the lower limit for the achievablegroup velocity in
CROWs based on the same cavity. Concerning the transmission
intensity, there is atrade-off with the group delay because higher
loaded Q means low transmittance and longer groupdelay. In
practice, the transmission loss may limit the degree of
cascadability. Currently, we areinvestigating coupled resonator
structures based on the similar cavities for slow-light
investigation.
Fig. 3. Slow-light propagation measurement of a width-modulated
line-defect cavity coupledto input and output waveguides. Sample
and measurement setup (left). Measured outputintensity as a
function of time (right). The cavity is a width-modulated
line-defect cavity with athree-stage hole shift. The shifts are 9,
6, and 3 nm in Fig. 1(a). The vertical scale for twocurves is
normalized. The transmittance via a cavity is less than 10% of the
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2.5 Disorder issues with waveguides and cavitiesAs described
above, experimental Q is always smaller than the theoretical Q with
our high-Q PhCcavities. We believe this difference to be due to the
disorder-induced scattering in fabricatedsamples. Before discussing
disorder issues with cavities, we briefly summarize the disorder
issue for
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PhC waveguides. Recently, the propagation loss of PhC waveguides
has been greatly reduced. Wecarefully studied this problem both
experimentally and theoretically, and found that a disorder-induced
scattering process dominates the propagation loss of fabricated PhC
waveguides [29].Figure 4 shows our latest record as regards
propagation loss measured for W1 PhC waveguides[30]. It shows a
pronounced wavelength dependence that has been well explained by
theory [29],and the lowest loss is 2dB/cm which is the lowest value
for a single-mode PhC waveguides. A roughestimate of the disorder
in terms of the RMS of the width fluctuation is less than 2 nm,
which isconsistent with the scanning electron microscope
observation.
Fig. 4. Propagation loss measurement of W1 waveguides fabricated
in silicon hexagonalairhole PhCs with a=430 nm. The loss was
determined from the transmitted light intensity asa function of the
waveguide length (left). The loss spectrum (right). The minimum
loss is2dB/cm around the center of the transmission window. The
horizontal axis in the right plot isnormalized angular frequency ,
which is deduced as a/ (a is the lattice constant). The
lossmeasurement scheme is the same as that reported in
[29].Download Full Size
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Considering the fact that ultrahigh-Q line-defect cavities are
based on the same W1 waveguides andare fabricated by the same
lithography-and-etching process, it is naturally expected that Q
isprimarily limited by the lowest propagation loss of W1
waveguides. However, this is not true. If weassume a loss of 2dB/cm
and a group refractive index of n =6, the estimated photon lifetime
isshorter than 300 ps. Thus, Q should be limited to below 410 .
This will be something of an
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underestimation because the loss should be much larger if the
group index is larger than n =6 [29],which must be the case for the
line-defect cavity mode. Note that this cavity mode is
locatedsignificantly close to the mode gap of the W1 waveguide
where the group index should besubstantially large. (In other
words, the line-defect cavity mode is based on slow-light modes in
theW1 waveguide.) Contrary to this estimation of the photon
lifetime from the waveguide loss, weobserved much longer photon
lifetime (1.1 ns) for fabricated cavities, as described in the
previoussection. This means that cavities are much less sensitive
to disorder than waveguides, at least in thepresent situation. We
have not yet investigated this issue in detail, but we believe that
thepropagation loss of PhC waveguides is dominated by disorder with
a sufficiently long correlationlength, and therefore the same
disorder does not affect the cavity Q. Another issue worth
pointingout is the effect of backscattering. The backscattering can
be significant in a PhC waveguide [29] butmay not be so in a
cavity, which could contribute to the difference in loss.
We have numerically investigated the effect of disorder on the
cavity Q using the 3D FDTD method.We assumed a set of random
distributions (Gaussian) in terms of the hole radius for all the
air holesin the PhC cavities, and calculated Q with the standard
statistical method. We performed thiscalculation for three
different cavities, namely a width-modulated line-defect cavity
(cavity A) withQ=4.210 , a hexapole-mode point-defect cavity
(cavity B) with Q=1.810 , and a five-point end-hole-shifted cavity
(cavity C) with Q=210 [31]. Figure 5 summarizes the results. If the
size variationis large, all the cavities have practically the same
Q. However, if the size variation is less than 5 nm,there is a
large difference between different cavities. For PhC waveguides, we
roughly estimatedthat the width variation is less than 2 nm. If we
use the same value for the radius variation, the Qvalues for the
disordered cavies are Q=1.510 , Q=510 and Q=110 for cavities A, B,
and C,respectively. In fact, these values are not so different from
the experimentally observed Q values forthese cavities (1.310 , 310
and 0.910 ). Although the estimation of the radius variation is
verycrude, we can guess that the experimentally observed Q for our
PhC cavities is limited by the holeradius variation. It is worth
noting that as long as the variation is sufficiently small, a
highertheoretical Q leads to a higher experimental Q.
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Fig. 5. Effect of size disorder on Q for various PhC cavities.
Cavity A is a width-modulated line-defect cavity. (a=432 nm, 2r=230
nm, shift=9, 6, 3 nm). Cavity B is a hexapole cavity. (a=420nm,
2r=168 nm, shift=0.23a). Cavity C is an end-hole shifted cavity.
(a=420 nm, 2r=230 nm,shift=55 nm, 2r for the shifted holes=126
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3. All-optical switching and memory
3.1 Nonlinear switch based on high-Q nanocavitiesAs has been
studied in various forms, all-optical switches can be realized
using optical resonators,where a control optical pulse induces a
resonance shift via optical nonlinear effects. For such
aresonator-based switch, there is a two-fold enhancement in terms
of the switching power if a smallcavity with a high Q is employed.
First, the light intensity inside the cavity should be proportional
toQ/V. Second, the required wavelength shift is proportional to
1/Q. In total, the switching powershould be reduced by (Q /V),
which can be significantly large for PhC nanocavities.[32] Although
theswitching mechanism itself is basically similar to that of
previous resonator-based switches, such asnonlinear etalons, [33]
this large enhancement has had an important impact on optical
integrationsince most optical switching components require too much
power for realistic integration. Inaddition, resonator-based
optical switches are well known to exhibit optical bistability,[33]
and thusthey can be used for optical memory and all-optical
logic.[43] Such functionality is one of the mostimportant functions
missing from existing photonic devices. Thus, we believe that
all-optical bistable
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switches based on PhC cavities are important candidates for
future optical integration. Besides highQ/V cavities, we can expect
enhancement of nonlinearity using slow-light media as well.
Applicationof slow light for all-optical switching and logic has
been reported by Asakawas group. [34]
3.2 Bistable operation by thermo-optic nonlinearityFirst, we
investigate an all-optical bistable switching operation employing
the thermo-opticnonlinearity induced by two-photon absorption (TPA)
in silicon.[35] It is worthwhile to note thatsilicon is not an
efficient nonlinear material in comparison with III/V
semiconductors. For this study,we designed an end-hole shifted
four-point PhC cavity (shown in Fig. 6) [31] having two
resonantmodes, one of which we used for a control (mode A) and the
other for a signal (mode B). Theinjection of the control light
(mode A) with appropriate detuning ( ) pulls in the mode A as a
resultof the nonlinear shift of the index in the cavity, and the
mode A is switched to ON state. This type ofswitching using a
resonator is known to exhibit bistability [33]. Simultaneously, we
inject the signallight (mode B) with another detuning ( ). The mode
B shifts as a result of the index change inducedby the bistable
switching in the mode A. In total, the output signal light shows
bistable switching byvarying the input control light. The condition
for both detuning is shown in the lower-left panel inFig. 6. Note
that we can select switching parity (OFF to ON or ON to OFF) by
selecting . The rightpanel in Fig. 6 shows the output power for
mode B as a function of the input power for mode A,which exhibits
an apparent bistable switching behavior for two different detuning
conditions. Thisoperation is basically what we expect for so-called
all-optical transistors, and will be basis forvarious logic
functions. The detail of this operation is described in [35]. For
example, wedemonstrated that we can amplify an AC signal using this
device. The most noteworthy pointregarding this switching is its
switching power, which is as small as 40 W. This value is
remarkablysmaller that of bulk-type thermo-optic nonlinear etalons
(a few to several tens mW) [36] and alsosmaller than that of recent
miniature-sized thermo-optic silicon micro-ring resonator devices
(~0.8mW).[37] In addition, TPA occurs only in the cavity, and
therefore we can easily integrate this devicewith transparent
waveguides in the same chip. Although the bistable operation itself
is similar tothat of nonlinear etalon switches, these PhC switches
can be clearly distinguished in terms of theoperating power and
capability for integration. The mode volume of this cavity is
onlyapproximately 0.1 m . This small footprint is of course
advantageous for integration, but it is alsobeneficial for reducing
the switching speed because our device is limited by the thermal
diffusionprocess. The relaxation time of our switch is
approximately 100 ns, which is much shorter than thatof
conventional thermo-optic switches (~msec).
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Fig. 6. All-optical bistable switching in a silicon hexagonal
air-hole PhC nanocavity realized bythe thermo-optic nonlinearity
induced by two-photon absorption in silicon. a=420 nm,2r=0.55a. The
radius of end-holes of the cavity is 0.125a. The radius of
end-holes of thewaveguide is 0.15a. The output is switched from ON
to OFF with =20 pm, and OFF to ONwith =260 pm. Both show similar
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3.3 Bistable operation by carrier-plasma nonlinearity and memory
actionThese thermo-optic nonlinear bistable switches clearly
demonstrate that large Q/V PhC cavities arevery effective in
improving the operation power and speed. However, the speed itself
is still not veryfast, which is limited by the intrinsically slow
thermo-optic effect. To realize much faster all-opticalswitches,
here we employ another nonlinear effect, namely the carrier-plasma
effect [38]. Thisprocess is also based on the same TPA process in
silicon. Thus, most of the arguments concerningtheir advantages are
similar to 3.2. For this experiment, we used basically similar PhC
cavity deviceswith a control pulse input. If the duration of the
control pulse is sufficiently short, we can avoidthermal heating
and may be able to observe only carrier-plasma nonlinearity. In
fact, we observed aclear blue shift in the resonance when we
injected a 6-ps pulse into this device, which is consistentwith the
expected shift induced by carrier-plasma nonlinearity. Figure 7
shows the time-resolvedoutput intensity for the signal mode when a
6-ps control pulse is input [39]. We observed clear all-optical
switching from OFF to ON (ON to OFF) for the detuning of 0.45 nm
(0.01 nm). The requiredswitching energy is only a few hundred fJ,
which is much smaller than that of ring-cavity-basedsilicon
all-optical switches.[40] In addition, numerical estimations showed
that the carrier relaxationtime (which limits the switching speed
of this device) is approximately 80 ps. This relaxation time
isgreatly shorter than the conventional carrier lifetime in silicon
(~s). The model simulation tells us
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that the diffusion process in our tiny devices is significantly
fast, and thus the relaxation time isdetermined by the fast carrier
diffusion time not by the carrier recombination time. Note that
thisshort carrier relaxation time is much shorter than that in
other silicon photonic micro-devices. [40]That is, the small
footprint of the device is again effective in improving the
operating speed.
Fig. 7. All-optical switching in a silicon PhC nanocavity
realized by carrier-plasma nonlinearityinduced by two-photon
absorption in silicon. The right panel shows the output intensity
of thesignal light when applying a 6-ps control pulse with two
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In the same way as thermo-optic switching, carrier-plasma
switching also provides bistableoperation. Figure 8 shows bistable
operations realized by employing a pair of set and reset
pulses.[41] When a set pulse is fed into the input waveguide, the
output signal is switched from OFF to ONand remains ON even after
the set pulse exits (green curve). When a pair of set and reset
pulses isapplied, the output is switched from OFF to ON by the set
pulse and then ON to OFF by the resetpulse (blue curve). This is
simply a memory operation using optical bistability. The energy of
the setpulse is less than 100 fJ, and the DC bias input for
sustaining the ON/OFF states is only 0.4 mW.These small values are
primarily the results of the large Q/V ratio of the PhC cavity. It
is worth notingthat the largest Q/V should always result in the
smallest switching power, but the operation speedcan be limited by
Q. In the present situation, the switching speed is still limited
by the carrierrelaxation time, and thus a large Q/V is preferable.
In the case when the photon lifetime limits theoperation speed, we
have to choose appropriate loaded Q for the required speed. Even in
such acase, it is better to have high unloaded Q because loaded Q
can be controlled by changing thecavity-waveguide coupling, and
high unloaded Q means low loss of the device. The best design
of
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out device would be a device with the smallest volume, the
lowest transmission loss, and thedesignated loaded Q (depending on
the operation speed). The lowest loss with the designatedloaded Q
can be obtained only when we employs an ultrahigh unloaded Q
cavity.
Compared with other types of all-optical memories, this device
has several advantages, such assmall footprint, low energy
consumption, and the capability for integration. The fact that all
the lightsignals used for the operation are transparent in
waveguides is important for the application, whichis fundamentally
different from bistable-laser-based optical memories.
Fig. 8. All-optical bistable memory operation in a silicon PhC
nanocavity realized by thecarrier-plasma nonlinearity induced by
two-photon absorption in silicon. (left) Injected controllight
consisting of a pair of set and reset pulses. (right) Output signal
intensity as a function oftime for three different cases: with no
set/reset pulses (red curve), with set pulse only (greencurve), and
with set and reset pulses (blue curve).Download Full Size
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3.4 High speed operationAs described above, although
carrier-induced nonlinearity is generally considered to be a
slowprocess, the present all-optical switches based on
carrier-induced nonlinearity can operate atsignificantly high
speed. In fact, we have recently demonstrated the 5GHz operation of
all-opticalswitching as shown in Fig. 9. In this demonstration, a
5GHz clock signal (A) is modulated by arandom bit stream (B) using
a PhC nanocavity switch (similar to that used in 3.3). In the case
for thedetuning of 0.06 nm, the device operates as a NOT gate, and
the resultant output is NOT of A andB. In the case for the detuning
of -0.2 nm, it operates as an AND gate, and the resultant output
isAND of A and B.
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If we wish to increase the operation speed further, we have to
decrease the carrier relaxation time.To do this, we have recently
employed an Ar-ion implantation process in order to
introduceextremely fast non-radiative recombination centers into
silicon. If the carrier recombination timebecomes faster than the
diffusion time, we can expect an improvement in the operation
speed.When we implanted silicon PhC nanocavity switches with Ar
dose of 2.010 cm and anacceleration voltage of 100 keV, we observed
a significant improvement in switching speed. In thecase of
detuning for an AND gate, the switching time was reduced from 220
ps to 70 ps. In the caseof detuning for an NOT gate, it was reduced
from 110 ps to 50 ps. The detail has been reportedelsewhere.
[42]
Fig. 9. All-optical 5Gb/s demultiplexing operation by a random
bit stream using a silicon PhCnanocavity switch.Download Full Size
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4. Towards all-optical logic
4.1 Flip-flop operation by double nanocavitiesIn the previous
section, we showed that a single PhC cavity coupled to waveguides
functions as abistable switch or a memory. If we couple two or more
bistable cavities, we can create much morecomplex logic
functions,[43] in the same way as with transistor-based logic in
electronics. As an
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example, here we show our numerical design for an all-optical SR
(set and reset) flip-flop consistingof two bistable cavities
integrated in a PhC. Asakawas group proposed different type of
flip-flopoperation using symmetric Mach-Zehnder switches
implemented in PhCs.[34]
It has been proposed that all-optical flip-flops be realized by
using two nonlinear etalons withappropriate cross-feedback,[44] but
this proposal is unsuitable for on-chip integration. Here wepropose
a different design using two PhC nanocavities.[45] Figure 10(a)
shows an actual designimplemented in a 2D PhC and Fig. 10 (b) shows
a schematic of the design concept. Each of twobistable cavities (Cv
and Cv ) has two resonant modes (lower and upper modes) and one of
them(lower mode) is common for two cavities (Fig. 10 (d)). Each
cavity exhibits bistable switching, and weset the bias input for
the lower mode at the OFF state in the bistable regime with
appropriatedetuning as shown in the left panels of Fig. 10(d). At
such condition, we can switch each cavity to theON state by
injecting a light pulse closely resonant to the upper mode (CS or
CR). The dotted verticallines in the right panels of Fig. 10(d)
schematically shows appropriate detuning required for thethree
inputs (B, CS, and CR). Each operation is equivalent to bistable
switching using twowavelengths described in Fig. 6. The crucial
point is that here we introduce cross-feedback betweenthese two
bistable cavities. The cross-feedback is introduced by making two
cavities coupled to thesame input waveguide. Therefore, two
cavities share the same single CW bias input (B) at forachieving
their own bistable operation, which leads to the cross-feedback.
That is, if one cavity isswitched to ON, then the bias input for
the other cavity is reduced. This leads to flip-flop operation,as
we will describe below.
To realize required operation, there are some essential points
to this design. First, two nanocavitiesare located very close to
each other, but they are decoupled because the parity of the two
cavities isdifferent. This is advantageous for reducing the size.
Second, the input and output waveguides havespecific transmission
windows by which we can selectively couple each cavity mode to a
differentwaveguide channel. This simplifies the system very much
because we do not need additionalwavelength filters.
R S
B
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Fig. 10. All-optical SR flip-flop consisting of two bistable
cavities coupled to waveguides. (a)Structural design based on a
hexagonal air-hole 2D PhC. The air-hole diameter for the latticeis
0.55a. Two cavities are both seven-point end-hole shifted cavities.
The end hole is shifted by-0.30a with 2r=0.24a. (b) Schematic of
the design. (c) Equivalent electronic SR flip-flop. (d)Schematic
operation of two bistable cavities. (e) Detailed design of Cv and
Cv . (f) Detaileddesign of WG2. The hole diameter in the waveguide
is 0.60a. (g) Time sequence of threeinputs (bias, and set clock
pulse, and reset clock pulse) and two outputs. (h)
Simulatedoperation using 2D FDTD. A blue and red curves correspond
to the output intensity of the twoports. The bottom plots are
snapshots of intensity profiles in the device.Download Full Size
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S R
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Next, we explain the operation sequence. As described, both
cavities have two resonant modes. Thecommon lower mode is used for
the CW bias input (B). The other upper modes are used for
thecontrol set pulse inputs (CS and CR) for each of cavities. CS
and CR are close to resonant to Cv andCv , respectively. Fig. 10(g)
explains the operation sequence in terms of three inputs (B, CS,
and CR)and two outputs (Q and Q). Suppose that both cavities are
initially in the OFF state. First, we send aset pulse CS, the
cavity Cv is switched to ON and it remains ON. Then, we send a set
pulse CR, thenthe cavity Cv is switched ON and simultaneously
cavity Cv is switched down to OFF because the DCinput (B) is now
shared by two cavities and this is insufficient to hold the ON
state of cavity Cv .Next, we send a pulseCS, then cavity Cv is ON
and cavity Cv is OFF. This is nothing but a typical SRflip-flop
operation. Note that this operation is equivalent to conventional
SR flip-flop in electroniccircuits as shown in Fig. 10(c).
We implemented this design in a 2D hexagonal air-hole (2r=0.6a)
PhC slab (n =2.8) with a=400 nm.We employ relatively long
(seven-point-defect) end-hole shifted cavities [31] as shown in
Fig. 10(e),and set the first-order mode in Cv and the second-order
mode in Cv to have almost the sameresonant wavelengths at 1620.80
nm and 1620.88 nm (lower modes). Therefore, these two cavitiesshare
the same resonant wavelength, but the mutual coupling is
sufficiently reduced. For S and R,we use the third-order modes
(1563.61 nm and 1578.52 nm) in Cv and Cv , respectively
(uppermodes). For adjusting the position of the modes [15], we
varied the width (w) of both cavities by-0.02a and +0.018a for Cv
and Cv , respectively. Next, we design the waveguides. B should
exit onlyfrom Q and Q. S and R should exit from B. For this
requirement, we employ three differentwaveguides that have a
different transmission window. WG1 is a W1 waveguide that transmits
allthe resonant modes in cavities. WG2 is a W3 waveguides filled
with five holes in the core as shownin Fig. 10(f), which transmits
only lower modes (~1621 nm) and rejects other upper modes. WG3 is
amodified W1 whose width is narrowed by 0.06a. WG3 transmits two
upper modes, but reject lowermodes. Thus they meet our requirement.
Finally, we adjust the coupling between waveguides andcavities by
adjusting the distance and the size of end holes. The resultant Qs
are 10003000 for allmodes.
We numerically simulated this operation using the 2D FDTD method
assuming Kerr nonlinearity.[46] The detuning is set at +2.5 nm,
respectively. Figure 10(h) shows the simulated output for Q andQ,
which shows expected SR ip-op operation at a repetition rate of
approximately 44GHz. Theintensity proles show snapshots obtained at
dierent times. Although this design is not yetoptimized (for
example, the output intensity is not constant for the Q=1 state)
and thus theoperation quality is still poorer than that of the
electronic counterpart, the present resultdemonstrates that ip-op
operation is possible by using double bistable cavities
appropriatelycoupled to waveguides in a PhC platform. Note that if
we have an SR ip-op, we can realize variousmuch complex logic
processing based on it.
4.2 Retiming circuit based on Flip-flop operation
S
R
S
R S
S
S R
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A typical example of the flip-flop operation in the high-speed
information processing is a retimingcircuit, which corrects the
timing jitter of an information bit stream and synchronizes it with
theclock pulses. This function is normally accomplished by
high-speed electronic circuits, but if it can bedone all-optically,
it will be advantageous for future ultrahigh-speed data
transmission. Althoughthis operation is basically possible by
cascading several SR flip-flops, here we propose another
muchsimpler design for realizing the retiming function.
Figure 11(a) shows a design for the retiming circuit. Its
operation principle detailed in our previousreport [47]. The
coupled cavities (C1 and C2) have one common resonant mode (
=1548.48 nm,Q =4500) extended to both cavities and two modes (
=1493.73 nm, Q =6100, and =1463.46 nm,Q =4100) localized in each
cavity. Here, we use two bistable switching operations for C1 and
C2. Thecross feedback is realized as follows. C1 is switched ON
only when and are both applied (P 1and P 2 are ON). C2 is ON only
when are applied (P 3 is ON) and simultaneously is suppliedfrom C1
(which means C1 is ON). Thus, the output signal of (P 3) becomes ON
only if P 3 isturned ON when C1 is already ON in advance. This
results achieves retiming process. We set P 1and P 3 as two
different clock signals as shown in Fig. 11(b), and assume P 2 to
be bit stream NRZ(non-return- to-zero) data with finite timing
jitter. The resultant P 3 is precisely synchronized tothe clock
signals and is actually an RZ (return-to-zero) data stream
converted from P 2 with jittercorrected.
We designed this function in a PhC slab system, and numerically
simulated its operation. Thestructural parameters are shown in the
figure caption. We assumed realistic material parameters(with a
Kerr coefficient / =4.110 (m /V ), a typical value for AlGaAs) and
the instantaneousdriving power is assumed to be 60 mW for all three
inputs. Figure 11(b) shows three input signals (adata stream with
jitter, and two clock pulses), and the output from P (P 3). As seen
in this plot,P 3 is the RZ signal of the input with the jitter
corrected. We confirmed that the operation speedcorresponds to
50GHz operation. Note that this work was intended to demonstrate
the operationprinciple and the structure has not yet been
optimized.
2
2 1 1 3
3
1 2 IN
IN 3 IN 2
3 OUT IN
IN
IN IN
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Fig. 11. All-optical retiming circuit based on two bistable
cavities. (a) Design based on ahexagonal air-hole 2D PhC with a=400
nm and 2r=0.55a. Two waveguides in the upper area(P and P ) are W1
and the other two in the lower area (P and P ) is W0.8. (b)
Simulatedoperation.Download Full Size
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5. Photon DRAM by adiabatic control of nanocavities
5.1 Adiabatic tuning of high-Q nanocavitiesThe previous sections
concerned the enhancement of the light-matter interaction
especially withrespect to optical nonlinearity. These are not the
only advantages for high-Q and ultrasmall cavitiesin terms of
optical processing. In principle, various kinds of light-matter
interaction can beenhanced, such as light amplification or light
emitting processes. In addition, high-Q and ultrasmallcavities can
produce novel functionalities. We look at this aspect in this final
section. If the photondwell-time in an optical system is long and
its size is small, then we can change the optical systemwithin the
photon dwell-time. This process is sometimes called dynamic tuning.
[48,49, 50, 51, 52]Since the light velocity in the material is so
fast, such tuning is normally difficult. However, itbecomes
meaningful for high-Q ultrasmall cavities or slow-light media.
Recently, it has been clarifiedthat this dynamic tuning allows
light to be controlled in various surprising ways.
Recently, we have shown that the simple dynamic tuning of a
cavity within the photon lifetime leadsto adiabatic wavelength
conversion, [50, 52] which is completely different from
conventionalwavelength conversion using optical nonlinear ( or )
crystals. We investigated the followingsituation. When a light
pulse is stored in a PhC cavity (we assumed five-point end-hole
shiftedcavities) shown in Fig. 12(a), we change the resonance
frequency of the cavity as a function of timeby tuning the
refractive index as shown in Fig. 12(b). Using FDTD simulations, we
found that theoptical spectrum of the light in a cavity shifts
after the tuning, as shown in Fig. 12(c). The importantthing is
that this wavelength shift does not depend on the tuning rate, and
is completely determinedby the shift of the resonance frequency.
Thus, this process is fundamentally different from theconventional
process. In fact, this process is analogous to the adiabatic tuning
of classicaloscillators, such as a guitar. This is verified by the
fact that U/ is preserved in this process, which isa signature of
adiabatic tuning process. Such tuning is very trivial in sonic
vibrations, but it has notbeen seriously considered in optics
because such tuning is rather difficult to achieve in
conventionaloptical systems. However, it is possible in high-Q
microcavities, such as PhC cavities. This means thatsmall optical
systems with high Q enable us to realize novel ways of controlling
light. Very recentlyour prediction was experimentally confirmed in
a silicon microcavity [53].
A C B D
(2) (3)
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In addition, we have also found that this conversion process can
be employed for enhancing opto-mechanical interaction. [52] We
numerically confirmed that high-Q PhC double-layer cavities
canconvert optical energies to mechanical energies extremely
efficiently, and it may be possible toemploy this phenomenon in
some types of optical micro-machines. This efficient energy
conversionis made possible by adiabatic optomechanical wavelength
conversion in a cavity.
Fig. 12. Adiabatic wavelength conversion. (a) A five-point
end-hole shifted PhC cavity used forthe simulation. (b) Tuning of
the refractive index for the tuned area in (a) as a function
oftime. (c) Wavelength spectra with and without tuning obtained by
3D FDTD calculation. (d) U,, and U/ obtained by FDTD calculations.
(e) Examples of classical oscillators, for whichdynamic tuning is
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5.2 Photon DRAM based on directly-coupled double cavitiesIn the
following two sections, we show another aspect of dynamic tuning,
namely the dynamiccontrol of Q, which may be useful for future
all-optical processing using nanocavities. We havealready shown
that high-Q nanocavities are useful for enhancing light-matter
interaction. But it is
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not always advantageous to have high Q because high-Q means a
slow response and a narrowbandwidth. If Q is a static value within
its photon lifetime, this is a fundamental limitation. Here, wewill
show that high-Q does not necessarily mean a slow response or a
narrow bandwidth. Inaddition, this dynamic control of Q leads to a
novel type of photon memory, in which we can store(or trap) photons
in a cavity. In the previous section, we showed that optical
bistability innanocavities leads to optical memory operation, which
can be employed in various types of opticallogic. The photon
dynamic memory that we introduce here is somewhat different from a
bistablememory because the latter memorizes the state of the
optical system, not the photon itself.
Fig. 13. Photonic memory based on a directly-coupled cavity
pair. (a) Design based on a 2Dhexagonal air-hole PhC with a=400 nm
and 2r=0.55a. Cavity M is a four-point-long cavity andCavity G is a
two-point-long cavity. (b) The resonant wavelength versus the
detuning of thegate cavity calculated by FDTD. (c) Q versus the
detuning calculated by FDTD. (d) A model forcoupled-mode theory
calculation. (e) The resonant wavelength versus the detuning
calculatedby the coupled-mode theory. (f) Q versus the detuning
calculated by the coupled-modetheory.
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To change the Q of the optical system dynamically, we employ a
pair of cavities. Here we show twoways to do this [54,55, 56]. The
first example is shown in Fig. 13(a). The system consists of a
gateand memory cavities. The memory cavity (C ) is coupled to the
waveguide only via coupling to thegate cavity (C ). If C is
resonant to C , C can be coupled to the waveguide. Thus, we can
switch onand off the coupling of C to the waveguide by tuning the
resonance frequency of C . In otherwords, we can change the loaded
Q of the cavity by tuning the cavity-waveguide coupling.
This explanation of the operation mechanism is slightly
over-simplified, and in reality we have tohandle this system
accurately as a doubly-coupled cavity system. We calculated the
resonancewavelength and cavity-Q of the whole system (including the
waveguide) as a function of therefractive index detuning of the
gate cavity n by the 2D FDTD method, as shown in Fig. 13(b, c).Note
that since it does not include the vertical radiation loss, all the
cavity Qs are determined by thecoupling to the waveguide, which is
a good approximation for ultrahigh-Q cavities. The result in
Fig.13(b) shows a typical behavior of a coupled-resonator system.
Figure 13(c) shows that the Q of thetwo modes sensitively depends
on n . Under large detuning conditions, the two cavities are
welldecoupled, and the memory cavitys Q (QM) is over 1.510 . When
the detuning becomes small, QMdrastically decreases. With zero
detuning, QM falls to 310 . This clearly shows that the tuning of
thegate cavity switches on and off the inter-cavity coupling. As
shown in Fig. 13(b), the low-QM stateand high-Q state are on the
same branch of the coupled cavity system, and thus we
canadiabatically change the system from low-Q to high-Q and vice
versa by tuning n .
Since this is a simple coupled-resonator system connected to a
single bus line, it is relatively easy toanalyze with the
coupled-mode theory established by Haus [57] as shown in Fig.
13(d). The coupled-mode equation is given by
M
G M G M
M G
G
G5
3
M
M M G
J B J
EB
.
EU
(
B
(
J 2
J
EB
(
EU
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(
B
(
B
.
(
T
( (((((((((((
:
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where a, , , are the field amplitude in a cavity, the resonance
frequency, the decay rate, and thecoupling rate, respectively. s1+
is the input power. The calculated solution is shown in Fig. 13(e,
f),where we set G/ =0.0002 and / =0.0017. The behavior in Fig. 13
(b, c) is well explained by Fig.13 (d, e), although we do not
discuss more quantitative comparison of this analysis.
Next, we investigate write/read operations using the
time-dependent tuning of this cavity. First, wenumerically simulate
the read-out operation with the 2D FDTD method, as shown in Fig.
14(a).Initially, there is a light pulse stored in a cavity, and
then we change the refractive index as shown bythe gray broken
line. The green line is the field amplitude in the memory cavity
without tuning,which shows a single exponential decay with Q=1.210
, as expected. When the index is tuned, theamplitude decays faster
as shown by the red line. This clearly shows that Q is switched
from 1.210to 4.910 by this tuning. Figure 14(b) shows the write-in
operation where the index is tuned when alight pulse arrives at the
gate cavity. This shows that Q is switched from 3.710 to 4.710 .
Figure14(c) shows the write-read operation (that is, the memory
operation). A signal light pulse is injectedinto the input
waveguide. When the pulse arrives at the gate cavity, n is switched
from n to n .After a certain time period, n is switched back from n
to n . Figure 14(c) clearly shows that theoptical pulse is trapped
in the cavity after the first switching, and then it is released
after the secondswitching. This is exactly the expected operation
for a photon dynamic memory. The upper limit ofthe memory time is
determined by the highest Q and the switching speed is limited by
the lowestQ . Finally, we add a comment on the bandwidth of the
pulse. In our process, the bandwidth of thepulse is equivalently
scaled to 1/Q. In the reading-out process, the bandwidth is
expanded. In thewrite-in process, it is squeezed. As was discussed
in [49], the pulse bandwidth is varied during theadiabatic tuning
process. It also occurs in our situation, and that is why we can
keep a wide-bandwidth pulse within a cavity having the narrow
bandwidth.
0 0
5
5
3
3 4
G G1 G2
G G2 G1
M
M
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Fig. 14. Temporal operation of the photonic memory simulated by
FDTD. (a) Read out. Astored pulse is read out by the index tuning.
The green line is without index tuning otherwisethe condition is
the same as the red line. (b) Write in. An injected pulse is stored
by indextuning. (d) Read and write. The combination of (a) and (b)
results in the memory operation.Download Full Size
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5.3 Photon DRAM based on indirectly-coupled double cavitiesIn
this section, we describe another design of the photon memory based
on a pair of cavities, asshown in Fig. 15(a). Here, a cavity is
side-coupled to the waveguide, and another cavity is end-coupled to
the waveguide. Both two cavities are interacting with each other
via the waveguide, andthey form effectively a doubly-coupled cavity
system, which is similar to that described in 5.2. Incontrast to
the case in 5.2 where the inter-cavity interaction is
evanescent-wave coupling, the inter-cavity interaction in this case
involves propagating-wave coupling via the waveguide. Thus,
thiscoupling can be switched on and off by managing the
interference condition of the propagatingwaves. When propagating
waves from two cavities destructively interfere perfectly, both
cavities aredecoupled from the waveguide, and thus the loaded Q of
the coupled cavity system becomesinfinitely high (when we ignore
the intrinsic loss of cavities). If we dynamically change the
resonancewavelength of one of the two cavities, we can change this
interference condition dynamically, whichshould lead to dynamic
tuning of the total Q. It is worthwhile noting that although the
configuration
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is different, the physical mechanism of this interference effect
itself is similar to the previous work[58], which discusses the
dynamic tuning of coupled-cavity waveguides for stopping light.
They useinterference to change the coupling between cavities and a
waveguide. Very recently, dynamic Qtuning was experimentally
demonstrated using a pair of ring cavities [59] and a single cavity
with areflection mirror in a PhC slab [60]. They also use a similar
interference effect for tuning Q.
We calculated the resonance wavelength and cavity-Q of the whole
system as a function of therefractive index detuning of the
end-coupled cavity (C ) as shown in Fig. 15(b, c). The
resonancewavelength plot shows typical behavior for coupled
resonators similar to Fig. 13(b), and the Q of theentire system
sensitively depends on the detuning whose behavior is different
from that in Fig.13(c). Under large detuning condition, two
cavities are independently coupled to the waveguide, andQ is
substantially low (3,500 at minimum). When the detuning becomes
small, Q for the upper modeincreases greatly. At zero detuning,
this mode is completely decoupled from the waveguide, and Qreaches
up to 9.2x10 . This clearly shows that the tuning of the end cavity
can change Qsignificantly. As shown in Fig. 15(c), the low-Q state
and high-Q state are on the same branch of thecoupled cavity
system, and thus we can adiabatically change the system from low-Q
to high-Q andvice versa by tuning n . (Of course, we can do the
same thing by tuning the side-coupled cavity).
E
7
E
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Fig. 15. Photonic memory based on an indirectly-coupled cavity
pair. (a) Design based on a 2Dhexagonal air-hole PhC with a=400 nm
and 2r=0.55a. (b) The resonant wavelength versus thedetuning of the
gate cavity calculated by FDTD. (c) Q versus the detuning
calculated by FDTD.(d) A model for coupled-mode theory calculation.
(e) The resonant wavelength versus thedetuning calculated by the
coupled-mode theory. (f) Q versus the detuning calculated by
thecoupled-mode theory. There is slight deviation between low-Q
modes in (b, c) and (e, f), whichmight be due to numerical errors
in FDTD, since it becomes difficult to resolve a low-Q modewhen a
high-Q mode coexists.Download Full Size
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We also analyze this system with the simplified model shown in
Fig. 15(d) using the coupled-modetheory. In this case, the
coupled-mode equations are given by
where S and E denote side-coupled and end-coupled cavities. is
the phase difference determinedby the distance between two
cavities. As with the case for directly-coupled memories (5.2), we
alsoconfirmed that the FDTD simulation is well explained by this
simple mode, as shown in Fig. 15(e andf).
Next, we investigate write/read operations using time-dependent
tuning of this cavity in a similarway to that undertaken for a
directly-coupled cavity memory in Fig. 14. Figures 16(a) and (b)
showthat we can switch Q from high to low and from low to high by
index tuning. Unlike Fig. 14, therequired index shift is much
smaller and the Q contrast is much larger than those in Fig. 15.
Figure16(c) shows the write-and-read operation (memory operation).
A signal light pulse is injected intothe input waveguide. When the
pulse arrives at the end cavity, n is switched from n to n . Aftera
certain time period, n is switched back from n to n . The simulated
intensity inside the end-coupled cavity shown in Fig. 16(c) clearly
reveals that the optical pulse is trapped in the cavity afterthe
first switching, and then it is released after the second
switching. This memory operation is
J 2
2 DPT
2
EB
4
EU
4
4
B
4
4
4
( ((((((((
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F
2J
B
&
4
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2J
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J 2
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&
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&
4
( (((((((((
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E E2 E1
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similar to Fig. 14(c) but the operation in Fig.16(c) requires a
smaller index change and a longermemory time. This is because the
achievable Q is much higher and Q is more sensitive to theresonance
wavelength detuning than directly-coupled memories.
Fig. 16. Temporal operation of the photonic memory simulated by
FDTD. (a) Read out. Astored pulse is read out by the index tuning.
The red curve is the light intensity in cavity E, andthe dark
yellow line is the light intensity at the waveguide. The monitoring
positions aremarked by crosses in Fig. 15(a). It is clearly seen
that the light pulse is released from the cavityto the waveguide
after the tuning. (b) Write in. An injected pulse is stored by the
index tuning,and there is very little leak into the waveguide. (c)
Read and write. The combination of (a) and(b) results in the memory
operation.Download Full Size
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6. ConclusionWe have described our latest results for
ultrahigh-Q PhC nanocavities and their applications foroptical
nonlinear processing and the adiabatic control of light. It is now
becoming possible toconfine light in a wavelength-scale volume for
over a nanosecond. In addition, we can introducevarious types of
coupling between nanocavities and with waveguides in a single chip.
This has
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scarcely been possible in any previous optical systems. When we
consider some form of all-opticalprocessing, the weak light-matter
interaction and difficulty in integration generally limit
itsapplicability. PhC nanocavities can potentially overcome this
problem, or at least offer a significantadvantage over other
approaches. As described in the last part, strong light confinement
is alsooffering novel functionalities that are realized by the
dynamic tuning of optical systems. Consideringthese three features,
namely the enhancement of the light-matter interaction, the
potential forintegration and the novel functionality, we believe
that these nanocavities in PhCs are nowproviding new opportunities
for photonics technology. In terms of the integration, our work is
stillvery limited in a small scale. For pursuing large-scale
optical integrated circuits, it will becomeimportant to realize
cascading many elements with low coupling loss which will be a hard
task. It isworth noting that ultrahigh-Q cavities are also
effective in reducing the coupling loss.
AcknowledgmentsWe are grateful for invaluable support and
collaborations by T. Tamamura, I. Yokohama, Y.Hirayama, S.
Kawanishi, M. Kato, S.C. Huang, G-K. Kim, H-Y. Ryu, Y-H. Lee, D.
Takagi, S. Kondo, G.Kira. K. Nishiguchi, H. Inokawa, K. Yamada, T.
Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, andS. Itabashi.
Part of this work was supported by CREST-JST.
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