# On-Chip All-Optical Switching and Memory by  Silicon Photonic Crystal Nanocavities

Authors: Masaya Notomi; Takasumi Tanabe; Akihiko Shinya; Eiichi Kuramochi; Hideaki Taniyama
Journal: Advances in Optical Technologies
 (2008)

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## Abstract

We review our recent studies on all-optical switching and memory operations based on thermo-optic and carrier-plasma nonlinearities both induced by two-photon absorption in silicon photonic crystal nanocavities. Owing to high-Q and small volume of these photonic crystal cavities, we have demonstrated that the switching power can be largely reduced. In addition, we demonstrate that the switching time is also reduced in nanocavity devices because of their short diffusion time. These features are important for all-optical nonlinear processing in silicon photonics technologies, since silicon is not an efficient optical nonlinear material. We discuss the effect of the carrier diffusion process in our devices, and demonstrate improvement in terms of the response speed by employing ion-implantation process. Finally, we show that coupled bistable devices lead to all-optical logic, such as flip-flop operation. These results indicate that a nanocavity-based photonic crystal platform on a silicon chip may be a promising candidate for future on-chip all-optical information processing in a largely integrated fashion.


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## Body

## 1. Introduction

It
used to be a  great challenge to tightly confine light in a wavelength-scale volume,
which had limited the capability of photonics technologies in various aspects.
Recently, however, an optical resonator with ultrahigh-Q (~1 million) and small volume (~(λ/n)3)
becomes possible by employing the state-of-the-art photonic crystal
technologies [1–6]. Figure 1 shows an example of high-Q nanocavities, which we have recently demonstrated in silicon photonic crystals.
This particular cavity shows a theoretical Q of over 108 and an experimental Q of 1.3 million with a mode volume of 1.5(λ/n)3 [4, 7].
These values are hardly available in optical systems other than photonic
crystals. Various forms of light-matter interactions are expected to be
enhanced in such high-Q nanocavities
having large Q/V ratio [8]. Among them, in this article, we
focus on application to all-optical switching and memory operations based on
optical nonlinear interaction. Especially for this, we investigate all-optical operations
based on carrier-induced nonlinearity and examine the features of photonic
crystal nanocavities for such applications.Width-modulated, line-defect photonic crystal cavities. (a) Cavity design.
The cavity has the theoreticalQ. The hole shifts are typically 9 nm
(red holes), 6 nm (green holes), and 3 nm (blue holes). (b) Spectral
measurement of a nanocavity fabricated in a silicon hexagonal air-hole photonic
slab with a=420 nm and 2r=216 nm. The transmission spectrum of a
cavity with a second-stage hole-shift. The inner and outer hole-shifts are 8
and 4 nm, respectively. (c) Time-domain ring-down measurement. The time decay
of the output light intensity from the same cavity as (b). Details can be found
in the reference.
(a)(b)(c)As 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
a resonator-based switch, there is a two-fold enhancement in terms of the
switching power if a small cavity with a high-Q is employed. First, the light intensity inside the cavity should
be proportional to Q/V. Second, the required wavelength shift is
proportional to 1/Q. In total, the switching power should be reduced by
(Q2/V), which can be significantly large for photonic
crystal nanocavities [9].
Although the switching mechanism itself is basically similar to that of
previous resonator-based switches, such as nonlinear etalons  [10], this large enhancement has had an
important impact on optical integration since most optical switching components
require too much power for realistic integration. Furthermore, in the case of
carrier-induced nonlinearity or thermo-optic nonlinearity, the smallness of the
device naturally leads to fast operation speed, since the relaxation time of
such processes normally depends on the size. As we will show below, this
advantage is significant for wavelength-sized cavities.In addition, resonator-based optical switches
are well known to exhibit optical bistability [10] and thus they can be used for optical memory and
all-optical logic [11]. Such functionality is one  of the
most important functions missing from existing photonic devices. Thus, we
believe that all-optical bistable switches based on photonic crystal cavities
are important candidates for future optical integration.In this paper, we investigate all-optical switching
and memory action in silicon photonic crystal nanocavity devices. First, we
study the switching action using thermo-optic nonlinearity. Next, we
investigate similar switching action using much faster carrier-plasma nonlinearity.
Thirdly, we analyze the effect of carrier relaxation process in the switching
action and made an attempt to further decrease the relaxation time by ion implantation.
Furthermore, we demonstrate bistable memory action employing basically the same
nanocavity devices and present an example of design for on-chip all-optical
logic circuits consisting of two bistable nanocavities.


## 2. All-Optical Bistable Switching by Thermo-Optic Nonlinearity

As
described above, photonic crystal nanocavities have a promising potential for
all-optical switching applications. To experimentally confirm this, we have investigated
all-optical bistable switching operations employing the thermo-optic
nonlinearity induced by two-photon absorption (TPA) in silicon [12]. For this study, we
employed an end-hole shifted four-point Si photonic crystal cavity integrated
with input/output photonic crystal waveguides (shown in Figure 2(a)) [13, 14].  Figure 2(b) shows transmission spectra with various input power at 1.5 μm wavelength region. As clearly seen in the
graph, the transmission spectrum is shifted to longer wavelength (red-shifted).
This shift is due to thermo-optic nonlinearity induced by two-photon absorption
in the cavity. At input power higher than 10 μW, there is an abrupt kink in the spectrum. This
kink corresponds to bistable switching. To see this more directly, we measured
the output power as a function of the input power at various detuning
conditions, as shown in Figure 2(c). Now, it is clear that this device exhibits
bistable switching. The most noteworthy point regarding this switching is its
switching power, which is as small as 40 μW. This value is remarkably smaller that of
bulk-type thermo-optic nonlinear etalons (a few to several tens mW) [15]
and also smaller than that of recent miniature-sized thermo-optic silicon
microring resonator devices (~0.8 mW) [16]. In addition, it is important to note that TPA occurs only in the cavity (the
linear absorption of silicon at this wavelength is negligible), and, therefore,
we can easily integrate this device with transparent waveguides in the same
chip.All-optical bistable switching in a silicon hexagonal air-hole photonic
crystal nanocavity (end-hole shifted four-point defect cavity) realized by the
thermo-optic nonlinearity induced by two-photon absorption in silicon. (a)
Schematic of the sample and a scanning electron micrograph of the sample.a=420 nm, 2r=0.55a. The radius of
end-holes of the cavity is 0.125a. V = 0.102 μm3. The radius of end-holes of the
waveguide is 0.15a. (b) Intensity-dependent
transmission spectra taken by a tunable laser in the upsweep condition. Q in the linear regime is 33400. (c)
Output power versus input power for various detuning values. The nonlinear
regime starts from 10 μW, and the bistable regime starts from 40 μW.
(a)(b)(c)Our cavity  shown in Figure2(a)
was intentionally designed to have two resonant modes, and, therefore, we can
perform all-optical switching using independent two inputs with different
wavelengths (signal and control), which is normally required for signal
processing. Since bistable switching for one resonant mode should influence the
transmission intensity of the other resonant mode in the same cavity, we can
easily realize such operation. As we reported in [12], we observe basically similar bistable switching behavior
in the relation between the input power for the control mode and the output
power for the signal mode. This operation is basically what we expect for the so-called
all-optical transistors, and will be basis for various logic functions. The
detail of this operation is described in [12]. For example, we demonstrated that we can amplify an
AC signal using this device.Although the bistable operation itself is
similar to that of nonlinear etalon switches, these photonic crystal switches
can be clearly distinguished in terms of the operating power and capability for
integration. The mode volume of this cavity is only approximately 0.1μm3. This small footprint itself is of
course advantageous for integration, but it is also beneficial for reducing the
switching speed because our device is limited by the thermal diffusion process.
To demonstrate these characteristics, we measured temporal response of the operation
for switch-off and switch-on processes, as shown in Figures 3(a) and 3(b). The
relaxation time of our switch is approximately 100 nanoseconds, which is much
shorter than that of conventional thermo-optic switches (~milliseconds). This
amazingly fast thermo-optic switching is primarily due to the smallness of our
cavity. In addition, we can estimate the required switching energy from the
switch-on measurement. The deduced smallest value is as small as 11 pJ as shown
in Figure 3(c).Temporal response of thermo-optic switching. (a) Switch-off. Temporal
response of the probe output. Att=800 nanoseconds, the pump signal was
switched off. The input instantaneous power for the pump is 64 μW. The pulse width and period are 400 nanoseconds
and 40 microseconds. The exponential fit gives a decay time of approximately
100 nanoseconds. (b) Switch-on operation for various input power. (c) Incident
energy required for the switch-on operation estimated from the product of the
incident energy and the time required for switch-on in (b).
(a)(b)(c)


## 3. All-Optical Switching by Carrier-Plasma Nonlinearity

These
thermo-optic nonlinear bistable switches clearly demonstrate that largeQ/V photonic crystal cavities are very effective in improving the operation power
and speed. However, the speed itself is still not very fast, which is limited
by the intrinsically slow thermo-optic effect. To realize much faster
all-optical switches, here we employ another nonlinear effect, namely, the
carrier-plasma effect [17]. This process is also based on the
same TPA process in silicon. Thus most of the arguments concerning their
advantages are similar to that for thermo-optic nonlinearity. For this
experiment, we used similar photonic crystal cavity devices with a control
pulse input. If the duration of the control pulse is sufficiently short, we can
avoid thermal heating and may be able to observe only carrier-plasma
nonlinearity. In fact, we observed a clear blue shift in the resonance when we
injected a 6-picosecond pulse into this device, which is consistent with the
expected shift induced by the carrier-plasma nonlinearity. Figure 4 shows the
time-resolved output intensity for the signal mode when a 6-picosecond control
pulse is input [17]. We observed clear all-optical AND-type switching
from OFF to ON for the detuning of 0.45 nm (Figure 4(a)) and NOT-type switching
from ON to OFF for the detuning of 0.01 nm (Figure 4(b)). The required
switching energy is only a few hundred fJ, which is much smaller than that of
ring-cavity-based silicon all-optical switches  [18]. If we take the coupling efficiency
between the cavity and waveguide into account, the actual pulse energy used for
the switching is less than 10 fJ. This extremely small switching energy is
attributed to large Q/V ratio in our
cavity.All-optical switching in a silicon photonic crystal nanocavity (end-hole
shifted four point cavity) realized by carrier-plasma nonlinearity induced by
two-photon absorption in silicon.Q for the control mode is 11500, and Q for the signal mode is 23000. (a) AND-type switching at various control pulse
energies with the detuning of −0.3 nm. (b) NOT-type switching at various
control pulse energies with no detuning. Each line is shifted by 500 picoseconds.
(a)(b)The switching time of our device is approximately
from 50 picoseconds to 300 picoseconds depending on the detuning and control
pulse energy. Considering the fact that the carrier lifetime in silicon is
normally very long (~microseconds), this switching time is also surprisingly
fast. This apparently indicates that the switching time is not limited by the
carrier recombination time of bulk silicon. We analyzed the switching behavior
employing simplified rate equations for the photon and carrier density in a
photonic-crystal nanocavity incorporating the effective carrier relaxation
time. We found that this simple model can reproduce the experimental result
fairly well. Figure5 shows simulated and experimental results for the same parameter
condition. In this calculation, we assumed the carrier relaxation time of 80 picoseconds.
This suggests that the effective carrier relaxation time for this all-optical
switch is in the range between 50 to 100 picoseconds. This fast carrier relaxation
may be attributed to the short diffusion time for generated carriers. Note that
the photon lifetime of our cavity is approximately 10 picoseconds, and thus the
operation speed of our device is limited by the carrier relaxation time. This carrier
relaxation time is much shorter than that in other silicon photonic
microdevices [18]. That is, the small footprint of the device is again
effective in improving the operating speed.Comparison between the rate-equation analysis and measurement result. We
modeled the cavity resonance as a Lorentzian function whose center wavelength
is shifting in proportion to the carrier density. (a) Calculation. (b) Experiment.
(a)(b)


## 4. Effect of Carrier Relaxation Process on Switching Operation

In Section3, we demonstrate that silicon all-optical switches based on
carrier-plasma nonlinearity can operate at a significantly fast speed, which is
attributed to the fast carrier relaxation process. We regard that this fast
carrier relaxation is possibly due to the fact that the diffusion process is an
efficient relaxation channel for nanocavities. To verify this explanation, we
performed numerical simulations for the carrier diffusion process in silicon
photonic crystal cavities [19]. In this simulation, we assumed an initial carrier distribution determined
from the optical intensity distribution of the cavity mode, and numerically
solved two-dimensional diffusion equations with assuming a realistic photonic
crystal cavity structure which is the same as that used in the experiment. The
side-wall nonradiative recombination process at the air-hole surface is
incorporated in the equation as effective surface recombination rate (S), and the effect of the top-surface
nonradiative recombination process is incorporated as an effective carrier
lifetime parameter which is determined from another calculation for a simple
slab. We calculated the time-dependent resonance wavelength shift using
instantaneous carrier concentration in the cavity. The calculated snapshots of
the carrier distribution at t = 0, 8,
and 24 picoseconds are shown in Figures 6(a), 6(b), and 6(c). These snapshots
clearly show that the initial distribution is rapidly spread as a result of
diffusion. This rapid diffusion results rapid switching recovery. Figure 6(d)
shows the calculated shift of the resonance wavelength for the cavity. The
initial wavelength shift caused by the carrier plasma shift is recovered
quickly. As shown in the figure, the nonradiative recombination does not
seriously affect the initial recovery. Therefore, we believe that the fast
operation of our optical switches is explained by the rapid carrier diffusion
process.Numerical simulation of carrier diffusion process for a silicon
end-hole-shifted photonic crystal cavity. (a), (b), (c) snapshots of the carrier
distribution att=0,8,24 picoseconds.
(c) Shift of the resonance wavelength for the cavity as a function of time with
the sidewall nonradiative recombination rate  S=0 and S=8×103 cm/s.
(a)(b)(c)(d)If we wish to increase the operation speed
further, we have to somehow decrease the carrier relaxation time. Although
there are several ways to do so, we have recently employed an Ar-ion
implantation process in order to introduce extremely fast nonradiative
recombination centers into silicon. If the carrier recombination time becomes
faster than the diffusion time, we can expect an improvement in the operation
speed. When we implanted silicon photonic crystal nanocavity switches with
Ar+ dose of 2.0×1014 cm−2 and an acceleration voltage of 100 keV, we observed a significant improvement in switching speed as shown in Figures
7(a), 7(b). The implantation condition was carefully determined so as to keep
almost the same cavity Q but to
significantly decrease the carrier lifetime in the cavity. In the case of
detuning for an NOT gate (Figure 7(a),  it was reduced from 110 picoseconds to
50 picoseconds. In the case of detuning for an AND gate, the switching time was
reduced from 220 picoseconds to 70 picoseconds (Figure 7(b)) [20].
As shown in Figure 7(c), the ON/OFF ratio is mostly the same between two
conditions. In addition, the required switching energy was almost the same as
that without the implantation. Although the reduction of the carrier lifetime
may lead to increase in the switching energy, this change is not significant as
far as the carrier lifetime is longer than the photon lifetime and the control
pulse length (which was the case in our experiment). These results clearly
demonstrate the effect of ion-implantation on the improvement in the switching
speed.All-optical switching for samples with and without ion-implantation. (a)
NOT-type switching. (b) AND-type switching. (c) Signal transmission at the time
when the control pulses enters the cavity. The ON/OFF contrast of the signal is
shown in relation to the input control pulse energy. The circles are the
minimal transmission for the nonimplanted sample, and the squares are for the
implanted sample.
(a)(b)(c)


## 5. All-Optical Memory Operation and Logic Circuit

In
the same way as thermo-optic switching, carrier-plasma switching also provides
bistable operation. Figure8 shows bistable operations realized by employing a
pair of set and reset pulses [21].
When a set pulse is fed into the input waveguide, the output signal is switched
from OFF to ON and remains ON even after the set pulse exits (green curve).
When a pair of set and reset pulses is applied (as shown in Figure 8(a)), the
output is switched from OFF to ON by the set pulse and then ON to OFF by the
reset pulse (blue curve). This is simply a memory operation using optical
bistability. The energy of the set pulse 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 photonic
crystal cavity. It is worth noting that the largest Q/V should
always result in the smallest switching power, but the operation speed can be
limited by Q. In the present situation, the switching speed is still
limited by the carrier relaxation time, and thus a large Q/V is
preferable. In the case when the photon lifetime limits the operation speed, we
have to choose appropriate loaded Q for the required speed. Even in such a case, it is better to have high unloaded Q because loaded Q can be controlled by changing the cavity-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 the designated loaded Q (depending on the operation speed). The lowest loss with the  designated loadedQ can be obtained  only when we employs an
ultrahigh unloadedQ cavity. Compared with other types of
all-optical memories, this device has several advantages, such as small
footprint, low-energy consumption, and the capability for integration. The fact
that all the light signals used for the operation are transparent in waveguides
is important for the application, which is fundamentally different from bistable-laser-based
optical memories.All-optical bistable memory operation in a silicon photonic crystal
nanocavity (end-hole shifted four-point defect cavity) realized by the
carrier-plasma nonlinearity induced by two-photon absorption in silicon.Q for the control mode is 7640, and Q for the signal mode is 12400. (a)
Injected control light consisting of a pair of set and reset pulses. (b)
Output signal intensity as a function of time for three different cases: with
no set/reset pulses (red curve), with set pulse only (green curve), and with
set and reset pulses (blue curve).
(a)(b)In the above, we showed that a single photonic
crystal cavity coupled to waveguides functions as a bistable switch or a
memory. If we couple two or more bistable cavities, we can create much more
complex logic functions [11], in the same way as with transistor-based logic in
electronics. As an example, here we show our numerical design for an
all-optical flip-flop consisting of two bistable cavities integrated in a photonic
crystal. It has been proposed that all-optical flip-flops be realized by using
two nonlinear etalons with appropriate cross-feedback [22],
but this proposal is unsuitable for on-chip integration. Here, we propose a
different design using two photonic crystal nanocavities [23].A typical example of flip-flop operation in the
high-speed information processing is a retiming circuit, which corrects the
timing jitter of an information bitstream and synchronizes it with the clock
pulses. This function is normally accomplished by high-speed electronic
circuits, but if it can be done all optically, it will be advantageous for
future ultrahigh-speed data transmission.
Here, we propose a simple flip-flop design for realizing the retiming
function. Figure9(a)  shows a design for the retiming circuit. The coupled
cavities (C1 and C2) have one common resonant mode (λ2=1548.48 nm, Q2=4500) extended to
both cavities and two modes (λ1=1493.73 nm, Q1=6100, and λ3=1463.46 nm, Q3=4100) localized in
each cavity. Here, we use two bistable switching operations for C1 and C2. The
cross-feedback is realized as follows. C1 is switched ON only when λ1 and λ2 are both applied (PIN1 and PIN2
are ON). C2 is ON only when λ3 are applied (PIN3 is ON) and
simultaneously λ2 is supplied from C1 (which means C1 is ON).
Thus the output signal of λ3 (POUT3) becomes ON only if PIN3
is turned ON when C1 is already ON in advance. These results achieve retiming
process. We set PIN1 and PIN3 as two different clock
signals as shown in Figure 9(b), and assume PIN2 to be bit-stream
NRZ (nonreturn-to-zero) data with finite timing jitter. The resultant POUT3
is precisely synchronized to the clock signals and is actually an RZ
(return-to-zero) data stream converted from PIN2 with jitter
corrected.All-optical retiming circuit based on two
bistable cavities. (a) Design based on a hexagonal air-hole 2D photonic crystal
witha=400 nm and  2r=0.55a. Two waveguides in the upper area (PA and PC)
are W1 and the other two in the lower area (PB and PD) are
W0.8. (b) Simulated operation.
(a)(b)We designed this function in a photonic crystal
slab system, and numerically simulated its operation using the FDTD method. The
structural parameters are shown in the figure caption. We assumed realistic
material parameters (with a Kerr coefficientχ(3)/ε0=4.1×10−19 (m2/V2), a typical value for AlGaAs) and the
instantaneous driving power is assumed to be 60 mW for all three inputs.  Figure 9(b) shows three input signals (a data
stream with jitter, and two clock pulses), and the output from PD(POUT3).
As seen in this plot, POUT3 is the RZ signal of the input with the
jitter corrected. We confirmed that the operation speed corresponds to 50 GHz
operation. Note that this work was intended to demonstrate the operation
principle and the structure has not yet been optimized. We expect ~mW operation
may be possible after the optimization since our rough estimation shows that a
single cavity switch can operate at sub-mW input power for the similar
condition. In addition, if we manage to employ the carrier-plasma effect for
this operation (as was done in Figure 8), we can expect further decrease in
terms of the input power.In addition to this work, we have reported
another design of all-optical logic circuit which is mostly equivalent to an SR
flip-flop employing two bistable cavities [8].


## 6. Summary

Recent
rapid progress in photonic crystal nanocavities is enabling low-power,
all-optical switching and memory actions on a silicon chip. We have shown that
our experimental demonstration of all-optical switching operation using
thermo-optic nonlinearity and carrier-plasma nonlinearity, both based on
two-photon absorption in silicon. For both cases, we observed significant
decrease in the switching power (energy) and also significant increase in the switching
speed. In this article, we numerically investigated the diffusion process concerning
photonic-crystal nanocavities, which is fundamentally different from that in conventional
optical devices with much larger size. Moreover, we have demonstrated their
potential for optical logic by a combination of bistable elements. For the
application in all-optical processing, a photonic crystal has several important
advantages, such as small footprint, small energy consumption, high speed, and
significant integratability. Thus we believe that it may be a promising
candidate for all-optical information processing on a silicon chip.



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