Abstract

We model the nonlinear response of a silica toroid microcavity using coupled-mode theory and a finite-element method, and successfully obtain Kerr bistable operation that does not suffer from the thermo-optic effect by optimizing the fiber-cavity coupling. Our rigorous analysis reveals the possibility of demonstrating a Kerr bistable memory with a memory holding time of 500 ns at an extremely low energy consumption.

© 2012 Optical Society of America

1. INTRODUCTION

Optical bistability is a fundamental physical phenomenon where it is possible for certain devices to have two stable transmission states. It occurs when the refractive index or the absorption of the nonlinear medium in an optical cavity is dependent on the light intensity. Optical bistable devices are considered to be important building blocks in all-optical signal processing for such components as optical memories and optical flip-flops [1], and this phenomenon was extensively studied in the 1970s and 1980s [2]. However, at that time, the size of the cavity and the operating energy were too large to be considered for practical applications.

Recent progress in achieving higher-quality factors (Q) in ultrasmall microcavities on-chip [36] has refocused attention on optical bistability [7], due to the possibility of achieving denser integration and lower energy consumption. Since the photon density in a cavity scales with Q/V, where V is the mode volume, a high-Q cavity with a small V enables us to use various nonlinearities at extremely low input powers; hence it allows optical bistability at an ultralow power.

Soljačić et al. [7] demonstrated numerically that optical bistability based on Kerr nonlinearity is possible by using a microcavity at an ultralow driving power of 133 mW. A recent numerical study has reported Kerr bistability at 165 μW [8]. Various experiments have already been reported in silica microspheres [9], silicon photonic crystals [10,11], and silicon microring resonators [12], but by using the thermo-optic (TO) effect. Since the TO effect is accompanied by thermal accumulation, the response is relatively slow. To achieve a faster speed, the carrier-plasma effect has been utilized. This effect is the result of carrier generation [13,14]. The latest research has achieved on 4 bit optical random-access memory operation based on carrier nonlinearity, at a power consumption of only 30 nW, by using InGaAsP photonic-crystal nanocavities [15]. The key to achieving the low power consumption is the smallness of the cavity V.

As introduced above, the power required to achieve optical bistability has been significantly reduced in recent years due to the high Q/V. However, all of the demonstrations use either TO or carrier-plasma effects to drive the bistability whose nonlinearities are accompanied by photon absorption. Recent advances on linear and nonlinear studies of microcavities and chip-based waveguide devices have made it possible to use them both for classical all-optical processing and for loss-sensitive applications such as quantum information processing [1619]. With those applications in mind, we need to reduce significantly the power loss (consumption) of the bistable system. The ultimate goal is to use the optical Kerr effect because it does not absorb photons. In addition, the use of an ultra-high Q allows us to reduce the power scattering loss of the signal light from the system, and this will support all-optical information processing for loss-sensitive applications.

Various optical switches and memories using the Kerr effect have been demonstrated experimentally with various microcavities [2022]. It has been reported that the carrier-plasma effect and the losses related to two- and three-photon absorption are nearly negligible in silica due to its large bandgap [23]. Thus, there have been some preliminary demonstrations on Kerr switching and memory in hybrid silica microspheres [21] and silica bottle microresonators [20]. However, the TO effect can make the Kerr effect difficult to distinguish from other effects in silica. Therefore, we need to carefully analyze whether a Kerr bistable memory is feasible or not in the presence of the TO effect.

In this paper, we demonstrate numerically that an optical bistable memory based on the optical Kerr effect is possible without suffering from the TO effect by controlling the coupling between the cavity and the tapered fiber. We employ a silica toroid microcavity [5] as a platform for the Kerr bistable memory, because it has an ultrahigh Q and is capable of integration on a chip. As discussed above, a high-Q cavity is attractive for achieving optical Kerr bistability and low-loss applications at the same time.

Our model combined coupled-mode theory (CMT) and the finite-element method (FEM). The finite-difference time-domain (FDTD) method can model Kerr bistability in a cavity very accurately. However, it has been shown that CMT can describe the behavior of the light in a cavity as accurately as FDTD [24]; thus, we decided to use CMT and FEM. It should be noted that CMT is a powerful tool for analyzing the couping between two cavity modes [25,26].

The paper is organized as follows. First in Section 2, we provide a simple picture of the physics that we are going to employ. In Section 3, we describe a numerical simulation model that combines CMT and FEM. In Section 4, we show the calculation result, and in Section 5 we discuss the energy consumption. We finish with a conclusion.

2. SIMPLE MODEL

As described in the previous section, it is still difficult to use the optical Kerr effect in ultrahigh-Q silica microcavities, even though the material has a large bandgap. This is because of the small light absorption at the surface, which is caused by a thin water layer [9,27]. Therefore, we need to analyze this carefully by using rigorous modeling and applying realistic physical parameters to reveal the conditions required for obtaining Kerr bistability. However, before undertaking a rigorous analysis, we start with a simple model to gain an intuitive understanding of the strategy for obtaining Kerr bistability. In this section, we pursue an analytical discussion about how we can obtain the Kerr effect without exhibiting any significant TO effect.

First we derive the relationship between the wavelength shift and the input energy required for Kerr nonlinearity. The energy U of an electromagnetic wave in a dielectric medium is given by [28]

U=14εE02V,
where ε, E0, and V are the dielectric constant, the electric field amplitude, and the mode volume, respectively. Using Eq. (1) and I=vε|E0|2/2, where v is the light speed in the medium, we obtain the relation between the power density I and the optical energy U as
I=2cn0UV,
where c is the velocity of light and n0 is the refractive index of the cavity medium. Then, the refractive index change caused by the Kerr effect is given by
ΔnKerr=n2I=2n2cn0UV,
where n2 is the nonlinear refractive index. Equation (3) allows us to calculate the refractive index change as a function of the energy in the cavity.

Next we discuss the TO nonlinearity. The refractive index change caused by the TO effect ΔnTO is given by

ΔnTO=n0ξT.
Here, ξ=(1/n)(n/T) is the TO coefficient. The energy required to increase the temperature by 1 K for volume V is given by CρV, where C is the heat capacity and ρ is the density of the material. Then, using Eq. (4), we obtain
ΔnTO=n0ξCρ1VUabs,
where Uabs is the energy absorbed by the material. Equations (3) and (5) describe the refractive index change at a given energy for the Kerr and TO effects, respectively. For the Kerr effect to be larger than the TO effect, the following condition is required:
ΔnKerrΔnTO=2n2cρCn02ξUUabs>1.
To gain a simple understanding, we assume a steady-state model. The light energy in the cavity is constant and generates heat at a constant rate. Thus, U(t) and Uabs(t) are expressed as
{U(t)=U0dUabs(t)dt=1τdiffUabs+1τabsU(t),
where U0, τdiff, and τabs are the steady energy in the cavity, the thermal relaxation time, and the thermal generation rate caused by photon absorption, respectively. When we neglect the thermal diffusion (τdiff1=0), Eq. (6) is simply expressed as
t<2n2cρCn02ξτabs.
This provides a direct view as to how we should design the cavity system in order to obtain the Kerr effect without the TO effect being too great. When we use the following parameters for SiO2, ξ=5.2×106K1, n2=3.67×1020m2/W n=1.47, C=7.41×101J/(g·K), and ρ=2.65g/cm3, Eq. (8) gives the following condition:
t<3.84τabs.
This equation provides a simple understanding of how we can achieve Kerr nonlinearity in SiO2 microcavities. Although the Kerr effect governs the refractive index change (ΔnKerr>ΔnTO) at an early stage of the operation, the TO effect becomes dominant after a period of time given by Eq. (9). When we employ a τabs of 329 ns (the selection of this value is discussed in detail in Section 3.C), Eq. (9) gives t<1.26μs, which is the time during which ΔnKerr is larger than ΔnTO. Note that even if we consider the thermal relaxation time in our model as τdiff=8μs (obtained from Fig. 3), this time does not change greatly and is about 1.35 μs.

To achieve Kerr nonlinearity, we must complete our operation before this time, namely the time that the light is absorbed by the material, has passed. This simple picture is straightforward to understand. If we are to obtain a faster operation speed, we require a smaller τtot because it determines the rise and fall time of the light energy in the cavity. τtot is given by τtot1=τloss1+τcoup1+τabs1, where τloss and τcoup are the photon lifetimes defined by the loss rate that do not contribute to the generation of heat and coupling to the waveguides. Since τabs and τloss are mainly determined by the material and the structure that we use, the only parameter that we can control is τcoup. This discussion suggests that optical Kerr operation is possible by controlling the coupling between the cavity and the waveguides, because it enables us to release light into the waveguides before it is absorbed by the material.

In the following section, we perform a rigorous analysis showing that Kerr operation is indeed possible by changing τcoup.

3. RIGOROUS MODELING OF THE OPTICAL KERR EFFECT AND THERMO-OPTIC EFFECT IN A TOROID MICROCAVITY

A. CMT in Whispering-Gallery-Mode Resonator

First we describe our master equation based on CMT in a whispering-gallery-mode (WGM) resonator to obtain the linear and nonlinear transmittance. The structure is shown in Fig. 1(a). Because a two-port system (a side-coupled cavity with one waveguide) makes the bistable operation difficult to observe, we focus on a side-coupled four-port system [29] throughout this paper. It consists of a toroid (ring) cavity and two waveguides for input and output light. A detailed discussion comparing side-coupled two- and four-port systems will be provided elsewhere [30]. Briefly, as discussed in Section 2, we need to make the coupling large in order to prevent heat accumulating in the system. However, the transmittance spectrum of a two-port system is shallower in an overcoupled configuration, which makes the switching contrast of the output light very low and difficult to distinguish. Hence, optical-bistable switching with high contrast is difficult to achieve in a two-port system in the presence of the TO effect.

 

Fig. 1. (a) Cavity structure used for numerical analysis. (b) Cross section of the mode-intensity profile of a toroid microcavity [32].

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The mode amplitude a in the cavity is given as [31]

dadt=[jω012(1τabs+1τloss+1τcoup1+1τcoup2)]a+1τcoup1exp(jθ)sin,
where ω0 is the resonant frequency of the cavity. The input wave sin excites the counterclockwise (CCW) mode in the cavity. We assume an ideal cavity where there is no coupling between the clockwise (CW) and CCW modes. τcoup1 and τcoup2 are photon lifetimes determined by the coupling with the lower and upper waveguides, respectively. θ is the relative phase between the mode amplitude in the cavity and the optical wave in the lower waveguide and is given as
θ=4π2n0(R+r)(1λ01λ).
Here R, r, λ, and λ0 are the major and minor radii of the cavity [shown in Fig. 1(b)], the input wavelength, and the resonant wavelength of the cavity, respectively. Equation (11) shows that the phase between a and sin becomes unmatched in an off-resonant state. Output waves sout1 and sout2 are given as
sout1=exp(jβ1d)×[sin1τcoup1exp(jθ1)a],
sout2=exp(jβ2d)1τcoup2a,
where β1 and β2 are the propagation constants of the lower and upper waveguides and d is the waveguide length. Note that the relative phase between the mode amplitude in the cavity a and the upper waveguide sin is always zero because there is no incident wave in the upper waveguide.

When we use a slowly varying envelope approximation, i.e.,

a(t)=A(t)exp(jωt),
sin(t)=Sin(t)exp(jωt),
we can rewrite Eq. (10) as
dA(t)dt=[j2πcn0(1λ01λ)12(1τabs+1τloss+1τcoup1+1τcoup2)]A(t)+1τcoup1exp(jθ)Sin(t).
Here A(t), Sin(t), and ω=2πc/(n0λ) are the envelopes of the cavity mode and the waveguide mode and the frequency of the input wave, respectively. Equation (16) is the master equation of the linear system. By using this equation, we now can calculate the energy in the cavity and the output power at an arbitrary time.

B. Modeling the Nonlinearities

To describe the nonlinear effects in our model, we take account of the nonlinear refractive index modulation caused by the Kerr effect (ΔnKerr) and the TO effect (ΔnTO) in the master equation. (Note that the carrier-plasma effect is negligible in silica due to its large bandgap.) The nonlinearities in an optical cavity result in a shift in the resonant wavelength because the optical path length changes. Thus, the shift of the resonant wavelength of a cavity is given as

δλ(t)=Δn(t)n0λ0,
where Δn(t) is the effective nonlinear refractive index change of the cavity. To add the nonlinear effects into Eqs. (11) and (16), we replace n0 and λ0 by no+Δn(t) and λ0+δλ(t), as
dA(t)dt=[j2πcn0+Δn(t)(1λ0+δλ(t)1λ)12(1τabs+1τloss+1τcoup1+1τcoup2)]A(t)+1τcoup1exp(jθ)Sin(t),
θ=4π2(n0+Δn(t))(R+r)(1λ0+δλ(t)1λ).
These are the master equations that we used in our model, which take the nonlinearities into account.

Next, we describe how we calculated the nonlinear refractive index change ΔnKerr and ΔnTO. We can directly calculate ΔnKerr from Eq. (3). Taking the spatial dependency into account, we obtain,

ΔnKerr(x,y,t)=n2I(x,y,t)=2n2cn0U˜p(x,y,t),
where U˜p(x,y,t) is the energy density distribution of the cavity mode in x, y cross-sectional coordinates. It is given as
U˜p(x,y,t)=Up(t)2πRI˜(x,y),
where Up=|A(t)|2 is the energy of the light stored in the cavity and I˜(x,y) is the normalized cross-sectional power density distribution of the WGM obtained by FEM (see [32]). It is normalized as I˜(x,y)dxdy=1, and the profile is shown in Fig. 1(b).

The refractive index change ΔnTO, which is induced by the TO effect, is described as

ΔnTO(x,y,t)=nξ[T(x,y,t)300[K]].
The cross-sectional temperature distribution is calculated by using two-dimensional FEM (COMSOL Multiphysics). By setting the heat source in the dielectric cavity as
Q(x,y,t)={τabs1U˜p(x,y,t),in cavity,0,in air,
where τabs1 is the thermal generation rate caused by the material absorption, we can obtain the temperature T(x,y,t) at any time and at any position by performing a FEM calculation.

Finally, we obtain the effective nonlinear refractive index change Δn(t) as

Δn(t)=[ΔnTO(x,y,t)+ΔnKerr(x,y,t)]I˜(x,y)dxdyI˜(x,y)dxdy.

Now by solving Eq. (18) sequentially using Eqs. (17)–(24), we can obtain the light energy in the cavity Up(t) and the output powers Pout1=|Sout1|2 and Pout2=|Sout2|2.

C. Determining the Absorption and the Photon Lifetimes

The total photon lifetime τtot is defined as

τtot=(τmat1+τwater1+τcont1+τrad1+τsurf1+τcoup11+τcoup21)1,
where τmat, τwater, τcont, τrad, τsurf, τcoup1, and τcoup2 are photon lifetimes determined by the absorption of the material, water absorption that is usually present on the surface of the cavity, absorption caused by surface contamination, radiation loss, scattering loss, coupling to the lower waveguide, and coupling to the upper waveguide, respectively. Since this expression is very complicated, we define the photon lifetime that is related to the absorption as τabs1=τmat1+τwater1+τcont1, losses to the outside of the cavity τloss1=τrad1+τsurf1, and the couplings τcoup1,2. By using these photon lifetimes, we can simplify our analysis, because τabs contributes on the generation of heat, but the other factors (τloss and τcoup1,2) do not.

Here we describe the photon lifetimes that we used in our analysis. The material absorption of silica at telecom wavelengths is usually very small (α=0.2dB/km [33]), but it is known that silica toroid microcavities have much larger absorption due to the water layer and contamination on their surfaces. And in practice the Q factor is limited by these absorptions [9]. Thus, we decided to consider two cases, which we call an ideal case and a realistic (worst) case. In an ideal case, we assume that the absorption loss is determined by solely the material (this means that the absorption loss is extremely small) and the experimental Q is limited by the losses to the outside of the cavity τloss1. On the other hand, we assume that the experimental Q is limited by the absorption loss τabs1 in a realistic case. This implies the worst case in terms of thermal accumulation, because a large part of the incident light eventually turns into heat. Any result should be better than that obtained with this latter condition.

To consider those two cases, first we fix the intrinsic photon lifetime τint=(τabs1+τloss1)1 at 329 ns (corresponding to Qint=4×108 [34], where Qint is the intrinsic Q), since this is the record largest experimental τint yet obtained. In the ideal case we disregard losses other than the intrinsic material absorption; so we use τabs=164μs (corresponding to QabsQmat=2×1011 [35]) and τloss=330ns; i.e., τint1τloss1τabs1. On the other hand, we use τabs=329ns (corresponding to Qabs=4×108 [27,34]) and τloss= for the realistic case. This Qabs value is the same as the highest experimentally obtained Qint, for the reason discussed above; i.e., τint1τabs1τloss1.

Although τint is determined by the material and structure, we can control τcoup1 and τcoup2 by adjusting the distance between the fiber and the cavity [36]. With this in mind, we conducted numerical simulations for various τcoup2 values. Note that τcoup1 is controlled to satisfy τcoup1=(τint1+τcoup21)1 and thus achieve critical coupling [24,31,37] between the cavity and the lower waveguide. In this condition, the power transmittance through the lower waveguide Tout1=Pout1/Pin decreases to zero on resonance, and high contrast can be obtained between two output states [30].

4. NUMERICAL CALCULATIONS

A. An Ideal Case: Small Material Absorption

In this section, we show that a Kerr bistable memory is easily feasible, without careful adjustment of τcoup, if only the inherent material absorption of silica is present.

First, we input a rectangular pulse to investigate the refractive index changes ΔnKerr and ΔnTO. The result is shown in Fig. 2(a), where τcoup2 is equal to τint. It shows that ΔnKerr is always larger than ΔnTO, which tells us that the influence of the absorption-induced thermal generation is nearly negligible. Hence the Kerr effect is easily obtained without it suffering from the TO effect.

 

Fig. 2. Figures obtained in an ideal case where the absorption loss in the cavity is determined only by the material. (a) ΔnKerr and ΔnTO versus time when a 6 μW rectangular pulse is input. The wavelength detuning δ between the input light and the initial cavity resonance is 27 fm. τcoup2 is set equal to τint. (b) Pout1 versus Pin of a triangular input pulse with different δ values, where Pout1=|sout1|2. (c) Pout2 versus Pin with different δ, where Pout2=|sout2|2. δ=13, 20, and 27 fm correspond to (3/2)ΔλFWHM, (33/4)ΔλFWHM, and 3ΔλFWHM, respectively. ΔλFWHM is the full-width at half-maximum of the cavity resonant spectrum width. (ΔλFWHM15fm). (d) Optical bistable memory operation. The solid, dotted, and dashed curves represent Pin, Pout1, and Pout2, respectively.

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Next, we input a triangular pulse to investigate the relationship between the input and output of the system. To allow us to charge and discharge the cavity gradually, we set the pulse rising/falling rate of the triangular inputs at dPin/dt=62.5nW/μs. Figures 2(b) and 2(c) are plotted from the input–output response of a triangular input with different detuning values δ. The lower coupling photon lifetime τcoup1 is set equal to (τint1+τcoup21)1 to achieve critical coupling. When δ is greater than 20 fm, clear hysteresis is observed, which is direct evidence of optical bistability. Optical bistability is observed in the longer side of the wavelength detuning, because the Kerr effect increases the refractive index (shifts the resonance toward the longer wavelength). Note that we obtained a large contrast between the two bistable states in Fig. 2(b) because the cavity transmittance Pout1 falls to zero on resonance in the critical coupling [24].

Finally, we performed optical memory operations as shown in Fig. 2(d). Again, we set τcoup2 equal to τint and the detuning δ equal to 27 fm. The solid curve is an input with a drive power Pindrive of 3.2 μW. The peak power of the 0.8 μs square set pulse is Pinset=5μW. To reset the system, we reduce the input power to Pinreset=2μW for a duration of 0.8 μs, which we call a reset pulse. The duration of the negative reset pulse must be longer than the discharging time of the cavity, which is equal to τtot; otherwise the cavity does not reset. The set and reset pulses are input at t=8 and 20.8 μs, respectively. Pout2 (shown as the dashed curve) rises to high (ON) state when the set pulse is input. It maintains the ON state until the reset pulse is injected. After the reset pulse has been input, Pout2 drops to the low (OFF) state and maintains it. Pout1 [indicated by the dotted curve in Fig. 2(d)] shows the inverse behavior of Pout2. Figure 2(d) clearly shows optical memory operation, which is based on Kerr nonlinearity. Although the “memory holding time” demonstrated with this calculation [shown in Fig. 2(d)] is about 30 μs, it can be much larger, since Pout1 and Pout2 exhibit an almost plateau response due to the small material absorption.

B. A Realistic Case: Large Material Absorption

As shown in Section 4.A, the realization of a Kerr bistable memory is feasible without it suffering from the TO effect, even when the coupling is not large, if only the inherent absorption of silica is present in the cavity. In reality, however, other sources of absorption occur in a microcavity, such as surface absorptions caused by water and contamination. Thus, in this section, we use τabs=329ns to simulate a case with faster thermal generation. As discussed above, here we assume that the Qint of the cavity is limited by absorption and not by losses to the outside of the cavity, since it appears to be the worst (but realistic case) for toroid microcavities. We employ τabs, which is derived from the highest experimental Qint (τabs=329ns corresponds to Qint=4×108). If we can clarify the requirements for demonstrating a Kerr bistable memory under this condition, it is a significant step toward the experimental realization of a Kerr bistable memory in silica toroid microcavities.

First, in a similar way to that shown in Fig. 2(a), we employ a rectangular pulse to obtain the refractive index change ΔnKerr and ΔnTO. The calculation results are shown in Fig. 3 for three different τcoup2 values (τcoup1 is adjusted to satisfy τcoup11=τcoup21+τint1). Figure 3 shows that ΔnTO is larger than ΔnKerr in all three cases when t is larger than 2.3μs. This number gives us the upper limit of the Kerr memory holding time without the memory suffering from the TO effect. It also tells us that this number is insensitive to τcoup2. This result is consistent with Eq. (8) obtained from a simple model, where the equation is dependent on τabs but independent of τcoup. Figure 3 also shows the effect of the different charging speeds caused by different τcoup2 values. The cavity charging time is much faster for τcoup2=τint/100, which allows the cavity to reach a plateau ΔnKerr domain much faster. This enables us to have a longer “Kerr memory usable” regime, which allows us to use the cavity for longer as an optical Kerr memory. Figure 3 shows that we can maximize the Kerr dominant “Kerr memory usable” regime by setting τcoup2 as small as possible. Again, this result is consistent with that obtained from the simple analysis described in Section 2.

 

Fig. 3. ΔnKerr (solid curve) and ΔnTO (dashed curve) versus time for different τcoup2 values in a realistic case. The input pulse power is set at 500×(Qtotτcoup2=τint/100/Qtot)2 in microwatts. The detuning δ is set at 3ΔλFWHM, where ΔλFWHM is 15 fm, 85 fm, and 782 pm when τcoup2 is τint, τint/10, and τint/100, respectively.

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Next, we show how we can obtain Kerr optical bistability when the absorption is large. Figures 4(a) and 4(b) show the input and output power relationships (Pout1 and Pout2) for different τcoup2 values when a triangular pulse is input. As shown in Figs. 4(a) and 4(b), a hysteresis loop is observed when τcoup2=τint/100, but the loops are deformed when τcoup2τint/10. This is because the light cannot charge and discharge the cavity quickly enough before the heat accumulates in the system when τcoup2 is large. Again, we obtained a clear hysteresis loop only when we made the coupling strong (i.e., τcoup2 is small).

 

Fig. 4. Input–output response of a triangular pulse input in a realistic case. (a) Pout1 versus Pin for different τcoup2. (b) Pout2 versus Pin for different τcoup2. The x-axis and y-axis are normalized as Pout1max=Pout2max=Pinmax=1. The detuning δ is set at 3ΔλFWHM. The input pulsewidth is 15 μs, 3 μs, and 0.3 μs and the pulse height is 4.5 μW, 160 μW, and 15 mW when τcoup2 is τint, τint/10, and τint/100, respectively.

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Finally, the memory operation for various τcoup2 values is shown in Fig. 5. Since the response speeds of Pout1 and Pout2 depend on the total photon lifetime τtot, we normalized the temporal axis t by τtot. Figure 5 shows clearly that the reset pulse does not work when τcoup2=τint and τint/10, and the memory operation cannot be obtained under this condition. If the system is operating in the Kerr dominant regime, we should be able to reset the state by injecting a negative reset pulse. The pulsewidth needed for the reset pulse is >τtot, since we can discharge the cavity within this time. However, Fig. 5 shows that significant heat is accumulating in the system, which prevents the system from resetting because ΔnTO cannot be reset by such a short negative pulse due to its much longer relaxation time.

 

Fig. 5. Optical memory operation in a realistic case, when δ is 3ΔFWHM. The input power of the drive light is 2 μW, 80 μW, and 7.3 mW, when τcoup2 is τint, τint/10, and τint/100, respectively. The horizontal axis is normalized with the photon lifetime τtot and the vertical axes are normalized as Pout1max=Pout2max=Pinmax=1.

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On the other hand, when τcoup2τint/100, we can successfully set and reset the system, and use the device as a Kerr bistable memory. However, the TO effect cannot be eliminated completely even in this case, and thus there is a holding time. Pout1 is automatically switched from ON to OFF, or vice versa for Pout2, due to the thermal accumulation. Figure 5 shows that the memory holding time for the realistic case is about 500 ns. This value is inconsistent with the length of the “Kerr memory usable” regime shown in Fig. 3 since the thermal nonlinearity depends on the accumulation of Uabs while the Kerr nonlinearity depends on the instantaneous Up.

In this section we achieved Kerr bistable memory operation and obtained a sufficiently long memory holding time of 500 ns by allowing the system to charge and discharge quickly by adjusting τcoup2.

5. DISCUSSION: POWER CONSUMPTION

We showed in previous sections that Kerr bistable operation is possible by adopting a large coupling constant. The basic idea is to allow the light to charge and discharge before it turns into heat. However, stronger coupling with waveguides (i.e., a smaller τcoup2) results in a lower total Q, which decreases the photon density in a cavity and makes the nonlinearity small. Hence, there is a tradeoff between operating speed and operating power.

Here, we consider two measures for evaluating the loss of our system: Qint and Ucons. Qint is the figure of merit of a cavity, whose value gives the cavity loss, and Ucons is the energy consumed for the operation. We often want to increase Qint and reduce Ucons to build a lossless system. Table 1 compares these values for different systems. A bistable memory based on an ultrahigh-Q silica toroid microcavity with Kerr nonlinearity has a clear advantage over other schemes in terms of both losses. The lossless nature of this memory is the advantage of this system.

Tables Icon

Table 1. Comparison of the Power Consumption of Different Systems

First, a system with a high Qint yields a low loss, because Qint corresponds to the fundamental loss characteristics of a cavity. As shown in Table 1, the Qint of a toroid cavity is much higher than that of other types of cavities. Furthermore, we would like to note that both linear and nonlinear losses are significant in other systems, especially those that use TO and carrier-based nonlinearities to achieve bistability. This is because carrier generation is unavoidable. Free carrier absorption (FCA) significantly decreases both the Qint and the transmittance of the system [38]. On the other hand, a Kerr bistable memory does not generate carriers and hence the system does not suffer from FCA loss.

Secondly, Ucons is extremely low in our system because Kerr nonlinearity does not absorb photons. Ucons is the energy consumed for a bistable operation. We can estimate Ucons from the required refractive index change, which is needed to obtain the cavity resonance shift for the operation. The values are large in memories based on heat and carrier even though they have large nonlinear efficiencies, which is because they incorporate photon absorption. On the other hand, the total photon number for the Kerr effect remains unchanged after the operation. Only the wavelength (energy) of the photons changes, which results in an extremely low energy consumption. Hence Ucons is almost negligible as shown in Table 1.

As shown in Fig. 5, we need Pindrive=7.3mW to drive the system, which is significantly smaller than the value shown in [7], which uses the same Kerr nonlinearity. This is due to the high Qint of our system. However, this value is still larger than the experimentally demonstrated value in a photonic-crystal nanocavity using carrier-based nonlinearity [15]. Since the coefficients of carrier nonlinearities in semiconductor materials are normally larger than the Kerr nonlinearity in SiO2, it is not an easy task to reduce the driving power of our system to the same level. However, glass has a low propagation loss [39,40], which is usually difficult to obtain with devices made of semiconductors.

Although the driving power Pdrive of our system is not necessarily the smallest, the linear, nonlinear, and consumption losses are significantly smaller than those of other devices. With this in mind, this device is attractive for applications that require high efficiency η=Pout/Pin, such as quantum information processing [18].

6. CONCLUSION

We rigorously modeled the Kerr and the TO effects in a silica toroid microcavity by combining CMT and FEM. We gained a clear understanding of the impact of adjusting the coupling, and showed that Kerr optical bistable memory operation is possible by adjusting the coupling between the cavity and the waveguides. The memory holding time was about 500 ns. Although the driving power was 7.3 mW, the energy consumed by the system was extremely low. This is because unlike other nonlinearities such as carriers of TO effects, Kerr nonlinearity does not absorb photons. In addition due to the ultrahigh-Q of the system, the energy loss outside the system is also low. Our Kerr bistable memory in a silica toroid microcavity exhibits extremely low loss and is thus suitable for applications such as quantum signal processing.

ACKNOWLEDGMENTS

This work is supported in part by the Strategic Information and Communications R&D Promotion Programme (SCOPE) from the Ministry of Internal Affairs and Communications, the Canon Foundation, the Support Center for Advanced Telecommunications Technology Research, Foundation, and the Leading Graduate School program for “Science for Development of Super Mature Society” from the Ministry of Education, Culture, Sports, Science, and Technology in Japan.

REFERENCES

1. H. Tsuda and T. Kurokawa, “Construction of an all-optical flip-flop by combination of 2 optical triodes,” Appl. Phys. Lett. 57, 1724–1726 (1990). [CrossRef]  

2. H. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).

3. Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003). [CrossRef]  

4. T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photon. 1, 49–52 (2007). [CrossRef]  

5. D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003). [CrossRef]  

6. K. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003). [CrossRef]  

7. M. Soljacic, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002). [CrossRef]  

8. M. Shafiei and M. Khanzadeh, “Low-threshold bistability in nonlinear microring tower resonator,” Opt. Express 18, 25509–25518 (2010). [CrossRef]  

9. L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993). [CrossRef]  

10. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005). [CrossRef]  

11. L.-D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21108–21117 (2009). [CrossRef]  

12. V. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29, 2387–2389 (2004). [CrossRef]  

13. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005). [CrossRef]  

14. A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008). [CrossRef]  

15. K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012). [CrossRef]  

16. S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005). [CrossRef]  

17. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004). [CrossRef]  

18. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008). [CrossRef]  

19. H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007). [CrossRef]  

20. M. Pöllinger and A. Rauschenbeutel, “All-optical signal processing at ultra-lowpowers in bottle microresonators using the Kerr effect,” Opt. Express 18, 17764–17775 (2010). [CrossRef]  

21. I. Razdolskiy, S. Berneschi, G. N. Conti, S. Pelli, T. V. Murzina, G. C. Righini, and S. Soria, “Hybrid microspheres for nonlinear Kerr switching devices,” Opt. Express 19, 9523–9528 (2011). [CrossRef]  

22. G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011). [CrossRef]  

23. K. Ikeda and Y. Fainman, “Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities,” Solid-State Electron. 51, 1376–1380 (2007). [CrossRef]  

24. M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003). [CrossRef]  

25. G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, “Whispering-gallery-mode phase matching for surface second-order nonlinear optical processes in spherical microresonators,” Phys. Rev. A 77, 043817 (2008). [CrossRef]  

26. J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011). [CrossRef]  

27. H. Rokhsari, S. Spillane, and K. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85, 3029–3031 (2004). [CrossRef]  

28. A. Yariv, Optical Electronics in Modern Communications (Oxford University, 1997).

29. H. Rokhsari and K. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004). [CrossRef]  

30. W. Yoshiki and T. Tanabe, “Analysis of four-port system for bistable memory in silica toroid microcavity,” in The 2nd International Symposium on Photonics and Electronics Convergence (ISPEC2012) (ISPEC, 2012), paper C-4.

31. C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999). [CrossRef]  

32. M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theor. Tech. 55, 1209–1218 (2007). [CrossRef]  

33. T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55 μm,” Electron. Lett. 15, 106–108 (1979). [CrossRef]  

34. T. Kippenberg, S. Spillane, and K. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (2004). [CrossRef]  

35. A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804 (2004). [CrossRef]  

36. S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003). [CrossRef]  

37. M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000). [CrossRef]  

38. P. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005). [CrossRef]  

39. J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Planar waveguides with less than 0.1dB/mpropagation loss fabricated with wafer bonding,” Opt. Express 19, 24090–24101 (2011). [CrossRef]  

40. H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012). [CrossRef]  

References

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  • |

  1. H. Tsuda and T. Kurokawa, “Construction of an all-optical flip-flop by combination of 2 optical triodes,” Appl. Phys. Lett. 57, 1724–1726 (1990).
    [Crossref]
  2. H. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).
  3. Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
    [Crossref]
  4. T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photon. 1, 49–52 (2007).
    [Crossref]
  5. D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
    [Crossref]
  6. K. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
    [Crossref]
  7. M. Soljacic, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
    [Crossref]
  8. M. Shafiei and M. Khanzadeh, “Low-threshold bistability in nonlinear microring tower resonator,” Opt. Express 18, 25509–25518 (2010).
    [Crossref]
  9. L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
    [Crossref]
  10. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
    [Crossref]
  11. L.-D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21108–21117 (2009).
    [Crossref]
  12. V. Almeida, and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29, 2387–2389 (2004).
    [Crossref]
  13. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
    [Crossref]
  14. A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
    [Crossref]
  15. K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
    [Crossref]
  16. S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
    [Crossref]
  17. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
    [Crossref]
  18. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
    [Crossref]
  19. H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
    [Crossref]
  20. M. Pöllinger and A. Rauschenbeutel, “All-optical signal processing at ultra-lowpowers in bottle microresonators using the Kerr effect,” Opt. Express 18, 17764–17775 (2010).
    [Crossref]
  21. I. Razdolskiy, S. Berneschi, G. N. Conti, S. Pelli, T. V. Murzina, G. C. Righini, and S. Soria, “Hybrid microspheres for nonlinear Kerr switching devices,” Opt. Express 19, 9523–9528 (2011).
    [Crossref]
  22. G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
    [Crossref]
  23. K. Ikeda and Y. Fainman, “Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities,” Solid-State Electron. 51, 1376–1380 (2007).
    [Crossref]
  24. M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
    [Crossref]
  25. G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, “Whispering-gallery-mode phase matching for surface second-order nonlinear optical processes in spherical microresonators,” Phys. Rev. A 77, 043817 (2008).
    [Crossref]
  26. J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
    [Crossref]
  27. H. Rokhsari, S. Spillane, and K. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85, 3029–3031 (2004).
    [Crossref]
  28. A. Yariv, Optical Electronics in Modern Communications (Oxford University, 1997).
  29. H. Rokhsari and K. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004).
    [Crossref]
  30. W. Yoshiki and T. Tanabe, “Analysis of four-port system for bistable memory in silica toroid microcavity,” in The 2nd International Symposium on Photonics and Electronics Convergence (ISPEC2012) (ISPEC, 2012), paper C-4.
  31. C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
    [Crossref]
  32. M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theor. Tech. 55, 1209–1218 (2007).
    [Crossref]
  33. T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55 μm,” Electron. Lett. 15, 106–108 (1979).
    [Crossref]
  34. T. Kippenberg, S. Spillane, and K. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (2004).
    [Crossref]
  35. A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804 (2004).
    [Crossref]
  36. S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
    [Crossref]
  37. M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
    [Crossref]
  38. P. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005).
    [Crossref]
  39. J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Planar waveguides with less than 0.1  dB/mpropagation loss fabricated with wafer bonding,” Opt. Express 19, 24090–24101 (2011).
    [Crossref]
  40. H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
    [Crossref]

2012 (2)

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[Crossref]

H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[Crossref]

2011 (4)

J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Planar waveguides with less than 0.1  dB/mpropagation loss fabricated with wafer bonding,” Opt. Express 19, 24090–24101 (2011).
[Crossref]

I. Razdolskiy, S. Berneschi, G. N. Conti, S. Pelli, T. V. Murzina, G. C. Righini, and S. Soria, “Hybrid microspheres for nonlinear Kerr switching devices,” Opt. Express 19, 9523–9528 (2011).
[Crossref]

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[Crossref]

J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
[Crossref]

2010 (2)

2009 (1)

2008 (3)

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref]

A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
[Crossref]

G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, “Whispering-gallery-mode phase matching for surface second-order nonlinear optical processes in spherical microresonators,” Phys. Rev. A 77, 043817 (2008).
[Crossref]

2007 (4)

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theor. Tech. 55, 1209–1218 (2007).
[Crossref]

K. Ikeda and Y. Fainman, “Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities,” Solid-State Electron. 51, 1376–1380 (2007).
[Crossref]

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[Crossref]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photon. 1, 49–52 (2007).
[Crossref]

2005 (4)

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[Crossref]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[Crossref]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[Crossref]

P. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005).
[Crossref]

2004 (6)

V. Almeida, and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29, 2387–2389 (2004).
[Crossref]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

H. Rokhsari, S. Spillane, and K. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85, 3029–3031 (2004).
[Crossref]

H. Rokhsari and K. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004).
[Crossref]

T. Kippenberg, S. Spillane, and K. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (2004).
[Crossref]

A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804 (2004).
[Crossref]

2003 (5)

S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref]

M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[Crossref]

D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref]

K. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref]

2002 (1)

M. Soljacic, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[Crossref]

2000 (1)

M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref]

1999 (1)

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

1993 (1)

L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

1990 (1)

H. Tsuda and T. Kurokawa, “Construction of an all-optical flip-flop by combination of 2 optical triodes,” Appl. Phys. Lett. 57, 1724–1726 (1990).
[Crossref]

1979 (1)

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55 μm,” Electron. Lett. 15, 106–108 (1979).
[Crossref]

Akahane, Y.

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref]

Almeida, V.

Armani, D.

D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref]

Asano, T.

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref]

Barclay, P.

Barton, J. S.

Bauters, J. F.

Bazin, M.

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[Crossref]

Berneschi, S.

Blumenthal, D. J.

Bowers, J. E.

Bruinink, C. M.

Brune, M.

L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

Cai, M.

M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref]

Chen, T.

H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[Crossref]

Claudon, J.

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[Crossref]

Collot, L.

L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

Conti, G. N.

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref]

Ctistis, G.

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[Crossref]

Deppe, D.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

Dominguez-Juarez, J. L.

J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
[Crossref]

G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, “Whispering-gallery-mode phase matching for surface second-order nonlinear optical processes in spherical microresonators,” Phys. Rev. A 77, 043817 (2008).
[Crossref]

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

Fainman, Y.

K. Ikeda and Y. Fainman, “Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities,” Solid-State Electron. 51, 1376–1380 (2007).
[Crossref]

Fan, S.

M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[Crossref]

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

Fink, Y.

M. Soljacic, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[Crossref]

Fukuda, H.

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[Crossref]

Gerard, J.-M.

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[Crossref]

Gibbs, H.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

H. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).

Goh, K.

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[Crossref]

Haret, L.-D.

Haroche, S.

L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

Hartsuiker, A.

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[Crossref]

Haus, H.

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

Heck, M. J. R.

Heideman, R. G.

Hendrickson, J.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

Hosaka, T.

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55 μm,” Electron. Lett. 15, 106–108 (1979).
[Crossref]

Ibanescu, M.

M. Soljacic, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[Crossref]

Ikeda, K.

K. Ikeda and Y. Fainman, “Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities,” Solid-State Electron. 51, 1376–1380 (2007).
[Crossref]

Ilchenko, V.

A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804 (2004).
[Crossref]

Itabashi, S.-i.

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[Crossref]

Joannopoulos, J.

M. Soljacic, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[Crossref]

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

John, D. D.

Johnson, S.

M. Soljacic, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[Crossref]

Kakitsuka, T.

Kawaguchi, Y.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[Crossref]

Khan, M.

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

Khanzadeh, M.

Khitrova, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

Kimble, H.

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[Crossref]

Kippenberg, T.

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[Crossref]

T. Kippenberg, S. Spillane, and K. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (2004).
[Crossref]

S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref]

D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref]

Kira, G.

Kozyreff, G.

J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
[Crossref]

G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, “Whispering-gallery-mode phase matching for surface second-order nonlinear optical processes in spherical microresonators,” Phys. Rev. A 77, 043817 (2008).
[Crossref]

Kuramochi, E.

Kurokawa, T.

H. Tsuda and T. Kurokawa, “Construction of an all-optical flip-flop by combination of 2 optical triodes,” Appl. Phys. Lett. 57, 1724–1726 (1990).
[Crossref]

Lee, H.

H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[Crossref]

Lefevreseguin, V.

L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

Leinse, A.

Li, J.

H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[Crossref]

Lipson, M.

Maleki, L.

A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804 (2004).
[Crossref]

Manolatou, C.

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

Martorell, J.

J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
[Crossref]

G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, “Whispering-gallery-mode phase matching for surface second-order nonlinear optical processes in spherical microresonators,” Phys. Rev. A 77, 043817 (2008).
[Crossref]

Matsko, A.

A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804 (2004).
[Crossref]

Matsuo, S.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[Crossref]

A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
[Crossref]

Mitsugi, S.

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[Crossref]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[Crossref]

Miya, T.

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55 μm,” Electron. Lett. 15, 106–108 (1979).
[Crossref]

Miyashita, T.

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55 μm,” Electron. Lett. 15, 106–108 (1979).
[Crossref]

Murzina, T. V.

Noda, S.

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref]

Notomi, M.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[Crossref]

L.-D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21108–21117 (2009).
[Crossref]

A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
[Crossref]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photon. 1, 49–52 (2007).
[Crossref]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[Crossref]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[Crossref]

Nozaki, K.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[Crossref]

O’Brien, J. L.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref]

Oxborrow, M.

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theor. Tech. 55, 1209–1218 (2007).
[Crossref]

Painter, O.

H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[Crossref]

P. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005).
[Crossref]

S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref]

M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref]

Pelli, S.

Politi, A.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref]

Pöllinger, M.

Raimond, J.

L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

Rarity, J. G.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref]

Rauschenbeutel, A.

Razdolskiy, I.

Righini, G. C.

Rokhsari, H.

H. Rokhsari and K. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004).
[Crossref]

H. Rokhsari, S. Spillane, and K. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85, 3029–3031 (2004).
[Crossref]

Rupper, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

Sato, T.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[Crossref]

A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
[Crossref]

Savchenkov, A.

A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804 (2004).
[Crossref]

Scherer, A.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

Segawa, T.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[Crossref]

Shafiei, M.

Shchekin, O.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

Shinya, A.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[Crossref]

A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
[Crossref]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photon. 1, 49–52 (2007).
[Crossref]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[Crossref]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[Crossref]

Soljacic, M.

M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[Crossref]

M. Soljacic, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[Crossref]

Song, B.

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref]

Soria, S.

Spillane, S.

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[Crossref]

H. Rokhsari, S. Spillane, and K. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85, 3029–3031 (2004).
[Crossref]

T. Kippenberg, S. Spillane, and K. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (2004).
[Crossref]

S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref]

D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref]

Srinivasan, K.

Suzaki, Y.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[Crossref]

Takahashi, R.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[Crossref]

Takesue, H.

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[Crossref]

Tanabe, T.

L.-D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21108–21117 (2009).
[Crossref]

A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
[Crossref]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photon. 1, 49–52 (2007).
[Crossref]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[Crossref]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[Crossref]

W. Yoshiki and T. Tanabe, “Analysis of four-port system for bistable memory in silica toroid microcavity,” in The 2nd International Symposium on Photonics and Electronics Convergence (ISPEC2012) (ISPEC, 2012), paper C-4.

Taniyama, H.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photon. 1, 49–52 (2007).
[Crossref]

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[Crossref]

Tokura, Y.

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[Crossref]

Tsuchizawa, T.

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[Crossref]

Tsuda, H.

H. Tsuda and T. Kurokawa, “Construction of an all-optical flip-flop by combination of 2 optical triodes,” Appl. Phys. Lett. 57, 1724–1726 (1990).
[Crossref]

Vahala, K.

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[Crossref]

T. Kippenberg, S. Spillane, and K. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (2004).
[Crossref]

H. Rokhsari and K. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004).
[Crossref]

H. Rokhsari, S. Spillane, and K. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85, 3029–3031 (2004).
[Crossref]

S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref]

D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
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K. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
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M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
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Vahala, K. J.

H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
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C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
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G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[Crossref]

Watanabe, T.

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[Crossref]

Wilcut, E.

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[Crossref]

Yamada, K.

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[Crossref]

Yanik, M.

M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[Crossref]

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications (Oxford University, 1997).

Yoshie, T.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

Yoshiki, W.

W. Yoshiki and T. Tanabe, “Analysis of four-port system for bistable memory in silica toroid microcavity,” in The 2nd International Symposium on Photonics and Electronics Convergence (ISPEC2012) (ISPEC, 2012), paper C-4.

Yosia,

Yu, S.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref]

Yuce, E.

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[Crossref]

Appl. Phys. Lett. (7)

H. Tsuda and T. Kurokawa, “Construction of an all-optical flip-flop by combination of 2 optical triodes,” Appl. Phys. Lett. 57, 1724–1726 (1990).
[Crossref]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[Crossref]

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[Crossref]

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[Crossref]

M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[Crossref]

H. Rokhsari, S. Spillane, and K. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85, 3029–3031 (2004).
[Crossref]

T. Kippenberg, S. Spillane, and K. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (2004).
[Crossref]

Electron. Lett. (1)

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55 μm,” Electron. Lett. 15, 106–108 (1979).
[Crossref]

Europhys. Lett. (1)

L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[Crossref]

IEEE J. Quantum Electron. (1)

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

IEEE Trans. Microwave Theor. Tech. (1)

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theor. Tech. 55, 1209–1218 (2007).
[Crossref]

Nat. Commun. (2)

J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
[Crossref]

H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[Crossref]

Nat. Photon. (1)

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photon. 1, 49–52 (2007).
[Crossref]

Nat. Photonics (1)

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[Crossref]

Nature (4)

D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref]

K. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

Opt. Express (8)

M. Pöllinger and A. Rauschenbeutel, “All-optical signal processing at ultra-lowpowers in bottle microresonators using the Kerr effect,” Opt. Express 18, 17764–17775 (2010).
[Crossref]

I. Razdolskiy, S. Berneschi, G. N. Conti, S. Pelli, T. V. Murzina, G. C. Righini, and S. Soria, “Hybrid microspheres for nonlinear Kerr switching devices,” Opt. Express 19, 9523–9528 (2011).
[Crossref]

M. Shafiei and M. Khanzadeh, “Low-threshold bistability in nonlinear microring tower resonator,” Opt. Express 18, 25509–25518 (2010).
[Crossref]

A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
[Crossref]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[Crossref]

L.-D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21108–21117 (2009).
[Crossref]

P. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005).
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J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Planar waveguides with less than 0.1  dB/mpropagation loss fabricated with wafer bonding,” Opt. Express 19, 24090–24101 (2011).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (3)

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[Crossref]

G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, “Whispering-gallery-mode phase matching for surface second-order nonlinear optical processes in spherical microresonators,” Phys. Rev. A 77, 043817 (2008).
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A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804 (2004).
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Phys. Rev. E (1)

M. Soljacic, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[Crossref]

Phys. Rev. Lett. (3)

H. Rokhsari and K. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004).
[Crossref]

S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref]

M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref]

Science (1)

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref]

Solid-State Electron. (1)

K. Ikeda and Y. Fainman, “Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities,” Solid-State Electron. 51, 1376–1380 (2007).
[Crossref]

Other (3)

W. Yoshiki and T. Tanabe, “Analysis of four-port system for bistable memory in silica toroid microcavity,” in The 2nd International Symposium on Photonics and Electronics Convergence (ISPEC2012) (ISPEC, 2012), paper C-4.

A. Yariv, Optical Electronics in Modern Communications (Oxford University, 1997).

H. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).

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Figures (5)

Fig. 1.
Fig. 1. (a) Cavity structure used for numerical analysis. (b) Cross section of the mode-intensity profile of a toroid microcavity [32].
Fig. 2.
Fig. 2. Figures obtained in an ideal case where the absorption loss in the cavity is determined only by the material. (a) ΔnKerr and ΔnTO versus time when a 6 μW rectangular pulse is input. The wavelength detuning δ between the input light and the initial cavity resonance is 27 fm. τcoup2 is set equal to τint. (b) Pout1 versus Pin of a triangular input pulse with different δ values, where Pout1=|sout1|2. (c) Pout2 versus Pin with different δ, where Pout2=|sout2|2. δ=13, 20, and 27 fm correspond to (3/2)ΔλFWHM, (33/4)ΔλFWHM, and 3ΔλFWHM, respectively. ΔλFWHM is the full-width at half-maximum of the cavity resonant spectrum width. (ΔλFWHM15fm). (d) Optical bistable memory operation. The solid, dotted, and dashed curves represent Pin, Pout1, and Pout2, respectively.
Fig. 3.
Fig. 3. ΔnKerr (solid curve) and ΔnTO (dashed curve) versus time for different τcoup2 values in a realistic case. The input pulse power is set at 500×(Qtotτcoup2=τint/100/Qtot)2 in microwatts. The detuning δ is set at 3ΔλFWHM, where ΔλFWHM is 15 fm, 85 fm, and 782 pm when τcoup2 is τint, τint/10, and τint/100, respectively.
Fig. 4.
Fig. 4. Input–output response of a triangular pulse input in a realistic case. (a) Pout1 versus Pin for different τcoup2. (b) Pout2 versus Pin for different τcoup2. The x-axis and y-axis are normalized as Pout1max=Pout2max=Pinmax=1. The detuning δ is set at 3ΔλFWHM. The input pulsewidth is 15 μs, 3 μs, and 0.3 μs and the pulse height is 4.5 μW, 160 μW, and 15 mW when τcoup2 is τint, τint/10, and τint/100, respectively.
Fig. 5.
Fig. 5. Optical memory operation in a realistic case, when δ is 3ΔFWHM. The input power of the drive light is 2 μW, 80 μW, and 7.3 mW, when τcoup2 is τint, τint/10, and τint/100, respectively. The horizontal axis is normalized with the photon lifetime τtot and the vertical axes are normalized as Pout1max=Pout2max=Pinmax=1.

Tables (1)

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Table 1. Comparison of the Power Consumption of Different Systems

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

U=14εE02V,
I=2cn0UV,
ΔnKerr=n2I=2n2cn0UV,
ΔnTO=n0ξT.
ΔnTO=n0ξCρ1VUabs,
ΔnKerrΔnTO=2n2cρCn02ξUUabs>1.
{U(t)=U0dUabs(t)dt=1τdiffUabs+1τabsU(t),
t<2n2cρCn02ξτabs.
t<3.84τabs.
dadt=[jω012(1τabs+1τloss+1τcoup1+1τcoup2)]a+1τcoup1exp(jθ)sin,
θ=4π2n0(R+r)(1λ01λ).
sout1=exp(jβ1d)×[sin1τcoup1exp(jθ1)a],
sout2=exp(jβ2d)1τcoup2a,
a(t)=A(t)exp(jωt),
sin(t)=Sin(t)exp(jωt),
dA(t)dt=[j2πcn0(1λ01λ)12(1τabs+1τloss+1τcoup1+1τcoup2)]A(t)+1τcoup1exp(jθ)Sin(t).
δλ(t)=Δn(t)n0λ0,
dA(t)dt=[j2πcn0+Δn(t)(1λ0+δλ(t)1λ)12(1τabs+1τloss+1τcoup1+1τcoup2)]A(t)+1τcoup1exp(jθ)Sin(t),
θ=4π2(n0+Δn(t))(R+r)(1λ0+δλ(t)1λ).
ΔnKerr(x,y,t)=n2I(x,y,t)=2n2cn0U˜p(x,y,t),
U˜p(x,y,t)=Up(t)2πRI˜(x,y),
ΔnTO(x,y,t)=nξ[T(x,y,t)300[K]].
Q(x,y,t)={τabs1U˜p(x,y,t),in cavity,0,in air,
Δn(t)=[ΔnTO(x,y,t)+ΔnKerr(x,y,t)]I˜(x,y)dxdyI˜(x,y)dxdy.
τtot=(τmat1+τwater1+τcont1+τrad1+τsurf1+τcoup11+τcoup21)1,

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