All-optical tunable buffering with coupled ultra-high Q whispering gallery mode microcavities

All-optical tunable buffering was recently achieved on a chip by using dynamically tuned coupled mode induced transparency, which is an optical analogue of electromagnetically induced transparency. However, the small Q s of about 105 used in those systems were limiting the maximum buffering time to a few hundred ps. Although employing an ultra-high Q whispering gallery mode (WGM) microcavity can significantly improve the maximum buffering time, the dynamic tuning of the WGM has remained challenging because thermo-optic and pressure tunings, which are widely used for WGM microcavities, have a very slow response. Here we demonstrate all-optical tunable buffering utilizing coupled ultra-high Q WGM cavities and the Kerr effect. The Kerr effect can change the refractive index instantaneously, and this allowed us to tune the WGM cavity very quickly. In addition, from among the various WGM cavities we employed a silica toroid microcavity for our experiments because it has an ultra-high Q factor (>2 × 107) and a small mode volume, and can be fabricated on a chip. Use of the Kerr effect and the silica toroid microcavity enabled us to observe an on-chip all-optical tunable buffering operation and achieve a maximum buffering time of 20 ns.

are too slow to be employed for all-optical tunable buffering. If we can tune the resonance of an ultra-high Q WGM microcavity very quickly, it is possible to achieve all-optical tunable buffering with a long buffering time.
In this letter, we describe an experimental demonstration of all-optical tunable buffering with coupled ultra-high Q microcavities. To tune the resonance we employed the Kerr effect, which can change the refractive index almost instantaneously. This enabled us to tune the resonance of the WGM cavity very fast and achieve all-optical tunable buffering. Although the Kerr effect has already been observed in WGM cavities and applied to all-optical switching and frequency conversion [24][25][26][27] , this is first time it has been employed to tune CMIT. From among various WGM cavities we chose a silica toroid microcavity as the platform for our experiments because it has an ultra-high Q factor (>2 × 10 7 ) and a small mode volume, and can be fabricated on a chip 28 . Taking advantage of the silica toroid microcavity and the Kerr effect, we achieved a maximum buffering time of 20 ns.

Results
Concept and numerical analysis. First of all, we describe the basic concept behind all-optical tunable buffering with coupled silica toroid microcavities. A situation is considered in which two silica toroid microcavities couple together as shown in Fig. 1(a). If the resonant frequencies of the two cavities (C 1 and C 2 ) are the same, the light input into a tapered optical fibre (i.e. signal light) first couples to C 2 , and then reaches C 1 (see " (1) input" in the figure). While the light remains in C 1 , an additional high-power light (i.e. control light) is input into another mode in C 2 as illustrated in " (2) buffer" in the figure. The input control light induces the Kerr effect, and then tunes the resonance of C 2 , which creates a mismatch between the resonances of C 1 and C 2 . This mismatch prevents the signal light in C 1 from escaping to C 2 , and so light is captured in C 1 while the control light is being input. After the control light is turned off, the resonances of the two cavities become matched again. In this condition, the signal light in C 1 is allowed to couple into C 2 , and it is then output to a tapered optical fibre ("(3) output"). Therefore, the signal light can be buffered for an arbitrary time period by changing the duration of the control pulse. This is the concept of all-optical tunable buffering with coupled silica toroid microcavities.
We performed a numerical calculation to confirm the validity of this concept. The results are shown in Fig. 1(b). When there is no control light, the signal light first couples to C 2 , and then moves to C 1 (the dashed lines in the graphs). As soon as the light energy in C 1 reaches its maximum value, it starts to return to C 2 . Eventually, the light (1) Input ( 2) Buffer (3) Output Energy in C 1

Energy in C 2
Output Buffering (~20 ns) (a) (b) f f f Figure 1. Basic concept of all-optical tunable buffering with coupled silica toroid microcavities. (a) Schematic illustration of the buffering operation. The system consists of two cavities denoted C 1 and C 2 , and only C 2 couples to the tapered optical fibre. (b) Numerical results of the buffering operation. The top, middle, and bottom graphs represent the signal light energies in C 1 and C 2 , and the output signal power, respectively. The solid and dashed lines are calculated with and without control lights, respectively. The control light is being input in the red region, and the solid grey line in the bottom graph represents the input signal power. The intrinsic Qs of C 1 and C 2 , and the coupling rate between C 1 and C 2 are set at 5 × 10 7 , 2 × 10 6 , and 2π × 96 MHz, respectively. The peak power of the control pulse is 10 W.
in C 2 is output to the fibre and creates a second peak in the output. On the other hand, if the control light is input (shown as the red regions), the light in C 1 does not couple back to C 2 and is stored in C 1 due the mismatch of the resonant frequencies. After the control light is turned off, the light again begins to transfer from C 1 to C 2 , and then creates the second peak in the output. Compared with the case with no control light, the second peak is delayed for 20 ns, which agrees well with the time width of the control input. This means that the position of the second peak can be arbitrary controlled with the control input, and the concept of all-optical tunable buffering is feasible.
Then, we discuss how to maximize the performance of the all-optical tunable buffering. The performance is basically evaluated using two factors, namely the maximum buffering time and the bandwidth. To increase the maximum buffering time, we should make the Q factor of C 1 as high as possible. As seen in the top graph in Fig. 1(b), the light energy in C 1 is decaying while the control light is being input. This decay rate corresponds to the intrinsic cavity loss rate of C 1 , which is inversely proportional to the Q value of C 1 . If the signal light dissipates completely while the control light is being input, no signal light can be extracted from the output even after the control light is turned off. Thus, a Q of C 1 limits the maximum buffering time and should be set as high as possible. For instance, when we target a holding time of 0.1 μs, we need a Q of 1.2 × 10 8 . In addition, the buffer should have a broad bandwidth; in other words, it should be able to respond to a signal light with a short pulse width. It is intuitive to assume that to capture a short signal light we should minimize the time taken by the signal light to reach C 1 . This time can be divided into two parts, namely the time taken to couple from the fibre to C 2 and that taken to move from C 2 to C 1 . Generally, the former and latter times are determined by the Q of C 2 and the coupling rate between C 1 and C 2 , respectively. Therefore, lowering the Q of C 2 and increasing the coupling rate lead to a broader bandwidth. However, it should be noted that a larger frequency shift is needed to make the resonances of C 1 and C 2 mismatched in the case of a lower Q value for C 2 and a higher coupling rate between C 1 and C 2 . It is intuitive to assume that we have to input a higher control power into the cavity to induce a larger frequency shift. Thus, there is a trade-off between the bandwidth and the control power, and in practice the trade-off sets the upper limit of the bandwidth. The parameters of the coupled silica toroid microcavities must be set after considering the above discussion.

Sample preparation and characterization.
To couple two silica toroid microcavities, we fabricated them near the edges of separate Si chips 29 . This enabled us to place two microcavities very close together (<1 μm) as shown in Fig. 2(a) because the toroidal part of the cavity protrudes from the chip. The transmission spectra of the modes that were used for the experiments are shown in the graphs in Fig. 2(a). We selected two modes (M 1 and M 2 ) for the signal light and a mode (M 3 ) for the control light from the optical modes in C 1 and C 2 . M 1 and M 2 couple together, and so the signal light input into M 2 is transferred into M 1 as illustrated in Fig. 1. On the other hand, M 3 does not couple to any modes because it is used only for inducing the Kerr effect in C 2 . As discussed in the previous subsection, the Q factor of M 1 should be higher to obtain a longer maximum buffering time because the signal light is stored in M 1 during the buffering operation. Taking this into consideration, we chose a mode with a Q of over 2 × 10 7 for M 1 . On the other hand, the Q factor of M 2 and M 3 should have a moderate value. This is because a lower Q results not only in a larger bandwidth but also in a higher required control power. In addition, if M 3 is chosen from the same mode family as M 2 , it should have a comparable Q factor to that of M 2 . Hence, we employed modes with a Q of around 10 6 for M 2 and M 3 .
Next, we tuned the resonant frequency of M 1 to that of M 2 by changing the temperature of C 1 , and then achieved coupling between the two modes. Figure 2(b) shows the transmission spectra of the coupled M 1 and M 2 for a different temperature. As seen from each graph in the figure, there is a split in the transmission spectrum, which is direct evidence of coupling between the two modes. In addition, it shows a clear Fano resonance, which usually occurs when optical modes with very different Q factors are coupled 30 . The transmission spectra for the different gaps between the two cavities are shown in Fig. 2(c). The split width (the coupling rate between M 1 and M 2 ) becomes larger as the gap decreases, which means that the coupling rate is arbitrarily adjustable with the gap. In the buffering experiments, we completely matched the resonance frequencies of M 1 and M 2 and adjusted the split width to around 70 MHz. This is because too large a split width (i.e. a higher coupling rate) results in the need for higher control power as discussed in the previous subsection.

Demonstration of all-optical tunable buffering.
Here we describe the experimental results we obtained for all-optical tunable buffering. Figure 3 shows our experimental configuration. We employed two tunable laser sources (TLSs) for the emitting signal and control lights. Both lights were modulated into rectangular pulses with intensity modulators (IMs). After modulation, the control light was amplified with an erbium-doped fibre amplifier (EDFA). Both lights were input into the coupled silica toroid microcavities via a tapered optical fibre 31 , and at the output the signal light alone was detected with an optical sampling oscilloscope (OSO) after amplification with an L-band EDFA (LEDFA). Note that the output control light was filtered out with a band pass filter (BPF) before the amplification.
The experimental results are presented in Fig. 4. We measured the signal output for the control light with different pulse widths as shown in Fig. 4(a,b). As seen from the figures, all-optical tunable buffering appears to work well. The signal light pulse is stored while the control light is being input (indicated by the red region), and then it is coupled out once the control light has been turned off. In addition, the figures also indicate that the buffering times can be controlled by changing the control pulse widths. We can buffer the signal pulse with a time width of 10 ns for up to 20 ns in the experiment. These results are direct evidence proving that all-optical tunable buffering was achieved. Close observation of Fig. 4(b) implies that a small amount of the signal light leaks out while the control light is being turned on. This is owing to the small coupling that remains between M 1 and M 2 , which allows the signal light to escape to the tapered optical fibre through M 2 . However, the signal light leakage is believed to be small enough to have no influence on the buffering performance. This is because there was no change in the leakage when the input control power (i.e. the amount of resonance shift) was changed. In other words, the dominant loss source during the buffering must be the intrinsic loss of M 1 .
The blue rectangles in Fig. 4(c) plot the peak power of the signal output for different control pulse widths. The signal output becomes smaller as the control pulse width increases, and it is around 8 times smaller (output efficiency of 13%) than the peak power of the input signal pulse even when the control pulse width is 0 ns. This is because the spectrum of the input signal pulse never completely matches the transmission spectrum of the coupled microcavities. This issue is common to applications utilizing a resonant structure. The figure shows that the power becomes about 3 times smaller with a control pulse width of 20 ns than with a width of 0 ns. This attenuation corresponds to a propagation loss of 1.14 dB/m. Considering the fact that even the latest on-chip "fixed" buffers exhibit a propagation loss of about 0.1 dB/m 32 , this value appears to be reasonable. It should be emphasized that the red dashed curve in the figure plots the calculated results and agrees well with the experimental results.

Discussion
Here we compare the results we obtained with those of previous studies. A CMIT-based all-optical tunable buffer is advantageous because of its small size and capacity for on-chip fabrication. However, the previously reported buffer 10 is composed of low-Q (~10 5 ) cavities, thus its maximum buffering time is limited to a few hundred ps. Although there are other kinds of on-chip all-optical tunable buffering, which are achieved with the dynamic tuning of a waveguide-coupled photonic crystal nanocavity 33,34 and a photonic crystal slow light waveguide 35 , they also have an issue in terms of buffering time. Conversely, the all-optical tunable buffering used in this study exhibited a buffering time of 20 ns thanks to the ultra-high Q factor of the silica toroid microcavity. Therefore, we can conclude that our buffer is advantageous as regards buffering time.
On the other hand, our buffer has a narrower signal light bandwidth than previous studies. We buffered a 10-ns signal pulse while the buffering of an optical pulse with a width of less than 100 ps has been reported in previous studies 10, [33][34][35] . As discussed previously, although we can increase the bandwidth by decreasing the Q value of C 2 and strengthening the coupling, this approach results in a higher required control power. Thus we need a way to solve the trade-off between bandwidth and control power. There are several ways of accomplishing this. The first is to coat the silica toroid microcavity with a highly nonlinear material such as plasmonic particles, graphene, or carbon nanotubes (CNTs) [36][37][38] . The size of the Kerr effect is in proportion to the nonlinear refractive index n 2 , and so we can increase the frequency shift by enhancing the n 2 value even if the input control power is fixed. Actually, the enhancement of four-wave mixing was observed experimentally in a CNT/polymer composite-coated tapered optical fibre 38 . Another way is to combine microcavities fabricated with different materials. For example, if a silicon microcavity and a silica toroid microcavity are employed for C 2 and C 1 , respectively, we can utilize the carrier-plasma effect to tune the resonance of C 2 quickly and broadly while maintaining the ultra-high Q of C 1 . In fact, the integration of a silicon platform and an ultra-high Q WGM cavity was recently reported 39 . We believe that we can further improve the bandwidth by taking advantage of these methods.
It should be noted that, in addition to the previous studies reviewed so far, all-optical buffering with optomechanically induced transparency (OMIT) was recently reported [40][41][42] . In contrast to CMIT in which two optical modes couple, OMIT is achieved by coupling between optical and mechanical modes in the microcavity. A mechanical mode generally has a much longer lifetime than an optical mode. Hence these devices can buffer light for a long time (>10 μs) thanks to the long lifetime of the mechanical mode. However, the coupling between the optical and mechanical modes is not usually very strong, which leads to a very narrow bandwidth (<1 MHz). In addition, they are achieved with a silica microsphere, which is difficult to fabricate on a chip. Therefore, our buffer is advantageous in terms of bandwidth and its capacity for on-chip fabrication.

Summary
In summary, we have presented an experimental demonstration of all-optical tunable buffering with coupled ultra-high Q microcavities. The use of the Kerr effect, which can shift the resonance of the cavity almost instantaneously, made it possible to achieve all-optical tunable buffering with coupled ultra-high Q WGM microcavities [24][25][26][27] . It should be noted that this is first time that the Kerr effect has been employed for tuning coupled microcavities. We chose a silica toroid microcavity as the platform for our experiments because it has an ultra-high Q factor (>2 × 10 7 ) and a small mode volume, and can be fabricated on a chip 28 . Thanks to the ultra-high Q factor and the Kerr effect, the maximum buffering time reached 20 ns, which was limited to a few hundred ps in previous studies 10, [33][34][35] . Although the observed bandwidth was narrower than those of previous studies, we believe that it can be improved by coating the silica toroid microcavity with material with a high n 2 value or achieving CMIT using microcavities fabricated with different materials.

Methods
Numerical model. The numerical model is based on coupled mode theory 15,43 . According to the theory, the amplitudes of M 1 and M 2 (a 1 , a 2 ) are given as Enlargement of (a). (c) The peak power of the buffered signal pulse as a function of the control pulse width. The blue rectangles and red dashed lines plot the measured and calculated results, respectively. The same parameters used in Fig. 2(b,c) were employed for the calculation. y axis is normalized by the peak power of the input signal pulse.
SCIENTIFIC REPORTs | 7: 10688 | DOI:10.1038/s41598-017-10035-4 where ω i , γ inti , and γ wavi are the resonant angular frequency, the intrinsic loss rate, and the waveguide coupling rate of M i=1,2 , respectively. s in is the amplitude of the signal input and appears only in Eq. (2) because the tapered optical fibre is coupled only to C 2 . κ is the coupling rate between M 1 and M 2 , and κ/2π corresponds to the split in the transmission spectrum. δω(t) is the shift of the resonant angular frequency induced by the control light via the Kerr effect 27 . The amplitude of the output s out is given as s s a out i n w av2 2 γ = − . Note that the light energy in M 1 and M 2 , and the output signal power are equal to |a 1 | 2 , |a 2 | 2 , and |s out | 2 , respectively.
Fabrication. The silica toroid microcavities employed in the experiments (C 1 and C 2 ) were fabricated using five processes: (1) photolithography, (2) HF etching, (3) dicing, (4) XeF 2 dry etching, and (5) laser reflow 28 . With the photolithography process (1), circular resist patterns 100 μm in diameter were developed on a silicon chip with a 2 μm-thick silica layer. Then, (2) HF etching removed only the parts of the silica layer that were not covered with the resist patterns. As a result, circular silica pads were formed on the silicon chip. Next, by using a high-precision dicing machine (DISCO DAD3430) we cut part of the chip to position the silica pads near the edge of the chip ((3) dicing process). After that, (4) XeF 2 dry etching was used to undercut the silica pads, and then silica disks on a silicon pillar were fabricated. Because the pads were placed near the edge, parts of the disks protruded from the chip as required for coupling two microcavities. Finally, the fabrication was completed by irradiating the silica disks with a CO 2 laser and annealing them so that their surface became very smooth ((5) laser reflow process). Note that C 1 and C 2 were fabricated on different chips to control the gap between them during the characterization.
Coupling silica toroid microcavities. We first measured the transmission spectra of C 1 and C 2 individually. We coupled light emitted by a TLS (Santec TSL-710, linewidth of 100 kHz) into the cavity via the tapered optical fibre and detected the output light with a PD (Thorlabs DET08CFC, bandwidth of 5 GHz). By scanning the laser frequency, we obtained the transmission spectra. Note that we employed a Mach-Zehnder interferometer (NTT Electronics, free spectral range of 1 GHz) as a frequency reference. From the obtained transmission spectra of C 1 and C 2 , we selected three optical modes for M 1 , M 2 , and M 3 . The resonant wavelengths of M 1 and M 2 should be close (e.g. 100 pm) to make M 1 easy to tune to M 2 . Then, we placed the two chips on which C 1 and C 2 were fabricated on automatic xyz stages (resolution of 10 nm) separately to precisely control the gap between the two chips (the two cavities). To tune M 1 to M 2 we changed the temperature of C 1 with a TEC whose temperature was stabilized with a TEC driver (Thorlabs TED200C, temperature stability of 2 mK). We covered the setup with a hood to make the temperature environment stable and achieve good repeatability of the measurement. Data availability. The datasets generated during the current study are available on request from the corresponding author.