osa _ nonlinear and adiabatic control of high-q photonic crystal nanocavities

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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)

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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.



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



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 (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g001&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g001&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g001&imagetype=pdf)

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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



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 resolution of our set up).Download Full Size (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g002&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g002&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g002&imagetype=pdf)

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.

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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 reference.Download Full Size (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g003&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g003&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g003&imagetype=pdf)

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



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 (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g004&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g004&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g004&imagetype=pdf)

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 nm).Download Full Size (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g005&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g005&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g005&imagetype=pdf)

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 bistable switching.Download Full Size (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g006&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g006&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g006&imagetype=pdf)

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 different detuning conditions.Download Full Size (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g007&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g007&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g007&imagetype=pdf)

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



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 (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g008&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g008&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g008&imagetype=pdf)

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.



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 (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g009&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g009&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g009&imagetype=pdf)

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

+ 14 -2



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



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 (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g010&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g010&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g010&imagetype=pdf)

S R



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

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eff

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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

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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 (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g011&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g011&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g011&imagetype=pdf)

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)

(3)



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 easily realized.Download Full Size (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g012&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g012&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g012&imagetype=pdf)

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



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.



Download Full Size (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g013&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g013&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g013&imagetype=pdf)

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

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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

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3

3 4

G G1 G2

G G2 G1

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M



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 (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g014&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g014&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g014&imagetype=pdf)

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



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



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 (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g015&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g015&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g015&imagetype=pdf)

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

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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 (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g016&imagetype=full) |PPT Slide (/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g016&imagetype=pwr) | PDF(/viewmedia.cfm?uri=oe-15-26-17458&figure=oe-15-26-17458-g016&imagetype=pdf)

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



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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