We demonstrate experimentally an all-optical switching operation using the Kerr effect in a silica toroid microcavity. Thanks to the small mode volume and high quality factor of the silica toroid microcavity, we achieved on-chip optical Kerr switching with an input power of 2 mW. This value is the smallest among all previously reported on-chip optical Kerr switches. We also show that this value can be reduced to a few tens of μW by employing a mode with a Q factor of > 2 × 107.
© 2014 Optical Society of America
All-optical switches have been intensively studied with the expectation that they will dispense with opto-electro and electro-optic converters in telecom networks. All-optical switches based on optical microcavities are particularly attractive because they can be driven with an extremely low input power thanks to their high quality (Q) factor and small mode volume V. A high Q/V is needed because these switches employ optical nonlinearity for their operation. Among various microcavity-based switches, the most prominent are those fabricated on a semiconductor substrate, such as photonic crystal (PhC) nanocavity switches [1–3] and microring switches [4, 5], because of their high nonlinearity and their potential for large-scale integration on a chip . Microcavity-based switches often employ a carrier-induced effect [1,2] to modulate the refractive index. However, the response time of carrier-induced switching is limited by the carrier relaxation time. Moreover, these switches suffer from absorption loss originating from free carrier absorption. So, there is a need for a carrier-free microcavity-based switch.
Recently, all-optical on-chip switches using the Kerr effect have been demonstrated by a number of groups [7, 8]. The Kerr effect is instantaneous and has a small loss. However, the threshold of the Kerr effect is usually higher than that of the carrier-induced effect ; thus the demonstrated switches usually require a switching peak power of > 100 mW. To overcome this problem, optical Kerr switches were developed by using whispering gallery mode (WGM) microcavities. WGM microcavities typically have an ultra-high Q, thus they require an input power of less than 50 μW . Switching has been demonstrated by using a hybrid silica microsphere , a hydrogenated amorphous silicon (a-Si:H) microcylindrical cavity  and a silica bottle cavity . Although, they are not fabricated on a chip, they can be efficiently coupled to a tapered fiber [13,14], and thus have a small coupling loss. This is a clear advantage for both optical telecommunication and loss-sensitive applications such as quantum information processing [15, 16].
Of the various WGM microcavities, those that can be fabricated on a silicon chip (i.e. a silica microdisk [17, 18], a silicon microdisk  and a silica microtoroid ) are attractive for future on-chip integration. In particular, we are interested in the silica toroid microcavity, because it exhibits an ultra high Q of > 108 and a small mode volume of < 200 μm3 and can be integrated with a waveguide ; other WGM cavities cannot achieve these characteristics simultaneously. In addition, carrier generation is greatly suppressed in silica thanks to the large bandgap (corresponding to λ = 140 nm) of the material, which enables us to use the Kerr effect. The modulation of a signal pulse by the Kerr effect has been demonstrated by taking advantage of these properties . Numerical analysis has shown that even a memory operation is possible .
In this paper, we demonstrate experimentally an all-optical switch using the Kerr effect in a silica toroid microcavity. The purpose of this study is to show how small an operating power a Kerr based switch can achieve. Indeed we will report successful operation at an input power of 2 mW, which is the smallest value for any previously reported on-chip optical Kerr switch [7,8]. Moreover we will show that a minimum modulation power of 36 μW is possible by employing a mode where Q > 2 × 107.
This paper is organized as follows. In §2, we describe the fabrication of the microcavity and show the experimental setup we used for our all-optical switching demonstration. After that we show the results of the all-optical switching experiment and confirm that our optical switch is indeed based on the Kerr effect by comparison with the result of a numerical calculation. In §3, we discuss the switching contrast and the required input power of our switch and compare the values with those of previously reported Kerr switches. Finally, in §4, we summarize this study and conclude the paper.
2. Experimental results
2.1. Device fabrication & experimental setup
We fabricated our silica toroid microcavity using (1) photolithography, (2) SiO2 etching, (3) XeF2 dry etching and (4) laser reflow . The major and minor diameters were 70 μm and 4.5 μm, respectively. A tapered fiber was used to couple the light into the microcavity . It was fabricated by heating and stretching a commercial single mode fiber so that it had a diameter of ∼ 1 μm. Our tapered fiber had a transmittance of about 90%.
Figure 1 shows a block diagram of our experimental setup. We used two laser lights, one as control signal a control and the other as a signal. The wavelengths of the two laser lights , were tuned to the resonance of each mode , . An electro-optical modulator (10 GHz) was used to modulate the control, which had rectangular pulses. At the output, we used band-pass filters to filter out the control light. A photo diode was used to monitor the coupling efficiency of the control light into the microcavity. We performed all of the experiments under critical-coupling conditions so that we maximized the light energy in the microcavity. Critical coupling condition is obtained when a perfect destructive interference between the light transmitted through a tapered fiber and from a microcavity is achieved. As a result, the transmittance is zero at the resonance.
2.2. Demonstration of Kerr based all-optical switching
First, we describe our demonstration of all-optical switching. When strong control light is coupled to a microcavity, it changes the refractive index via a Kerr effect (i.e. cross-phase modulation). The refractive index change then causes the shift of the resonance of the signal mode. As a result, the transmittance of the signal light changes and the modulation is achieved.
In a silica toroid microcavity, both Kerr and thermo-optic (TO) effects can change refractive index. Although the material absorption is small in silica, the actual absorption of the silica-based microcavity is much larger [24, 25]. This is because a thin water layer, that works as an absorber, exists on a surface of a silica toroid microcavity when the cavity is placed in the air. As a result, the TO effect is often larger than the Kerr effect when the system is in equilibrium, and it is necessary to distinguish the TO and Kerr effects. As shown in the references [22, 23], the response time of the Kerr effect is around a few tens of ns (limited by the cavity photon lifetime), but that of the TO effect is much longer than μs. So we can obtain Kerr switching when we input control pulses whose duration is much shorter than the response time of the TO effect.
Figure 2 shows the results of all-optical switching with different control pulse durations. The loaded Q factors of the control and signal modes ( , ) are 3.3 ×106 and 5.1 × 106, respectively. When the modulation speed is slow, the signal recovery takes much longer than the cavity photon lifetime. Figure 2(a) shows the modulated signal light when the input control peak power is 1.9 mW and the control pulse duration Tcont is set at 1 ms. The signal recovery time is 80 μs (the time where the signal output is 1/e of its maximum), and it is clear from the speed that this switching is due to the TO effect.
On the other hand, when we switch the cavity with Tcont = 64 ns and , we observe Fig. 2(b). Now the signal recovery time is 6 ns, which is much shorter than the thermal response time of > μs . Since the Kerr effect is instantaneous, the recovery time of the signal should be of about the same order as the sum of the photon lifetimes of the control and signal modes. To confirm this, we performed a numerical simulation based on coupled mode theory (CMT) [23, 26] and calculated the behavior of the signal output after the control light was turned off. The result is shown as a red dotted line in Fig. 2(b) and it agrees well with the experimental result. Therefore, we can conclude that we obtained all-optical switching thanks to the Kerr effect.
As shown in Fig. 2(b), the signal output exhibits ringing and instantaneously exceeds “1” (corresponding to the off-resonance signal output). This behavior is due to the interference between the signal light transmitted through the tapered fiber and from the microcavity. The wavelength of the signal light stored in the cavity is slightly changed in response to the resonance shift due to the control light (i.e. adiabatic wavelength shift ). As a result, the beat (i.e. overshooting) occurs at the output due to the interference between two lights that have slightly different wavelengths. Note that the average signal output never exceeds “1”.
3. Analysis and discussion
3.1. Influence of control pulse duration
Next, we examine the influence of Tcont in more detail. Since the response times for the TO and Kerr effects are different, there are two switching slopes in the signal output; the faster one is caused by Kerr effect and the slower one is caused by the TO effect. Figure 3(a)–(d) show the switching operation for control pulses with different control pulse durations Tcont. There is only a fast switching slope when the control pulse duration is shorter than 128 ns (Figs. 3(a) and (b)). Hence, the Kerr effect dominates the TO effect in this regime. However, we observe a slow decay when the pulse duration is longer than 512 ns (Figs. 3(c) and (d)). In this regime, we can observe both fast and slow switching slopes; thus both the Kerr and TO effects are responsible for the switching. This result tells us that we need to operate the system at a speed faster than Tcont at < 128 ns if we are to use Kerr effect.
3.2. Switching contrast versus switching power
Next we study the switching contrast. Figure 4(a) shows the switching contrast for different input control powers. The experiments in this study were performed under the condition where the heat is in a steady state. This means that the resonance changes when different average control power is applied. So we adjusted the wavelengths of the both signal and control light in order to have accurate detuning from the resonance at the steady state. We calculate the switching contrast by dividing the modulated signal output by the off-resonance signal output (See the inset of Fig. 4(a)). The blue dots are the experimental data, and the black curve shows the theory. The theoretical curve considers only the Kerr effect (it disregards TO effect) and is drawn by using Eqs. (4), (5) and (9), which are shown in Appendix. In addition, we assume that both the control and the signal modes are fundamental WGMs (i.e. (q,l) = (0,0)). The spatial distributions of the WGMs are calculated by using the finite element method (COMSOL multiphysics) . Although we use parameters drawn from the literature and experiments (i.e. no fitting parameters), the experimental results agree well with the theory. This is further evidence that this switch operates with the Kerr effect.
Figure. 4(a) shows that an input control power of 3.3 mW is necessary to obtain a large switching contrast of about 80%. A contrast of about 3 dB is obtained at a power of 2.1 mW, and the modulation is still observed when we reduce the input control power to 830 μW. The waveforms for different control powers are shown in Fig. 4(b). Since the low switching power is due to the high-Q factor (Qload > 106), we performed switching experiments using a silica toroidal microcavity with and , as shown in Fig. 5. Although the use of an ultra-high Q factor makes the switching operation sensitive to various fluctuations, because of the narrower resonance of an ultra high-Q cavity, we now observe modulation even at an input control power of 36 μW.
Finally, we compare the required control power of our switch with those of other optical Kerr switches. Table 1 summarizes the performance of various optical Kerr switches [7, 8, 10–12]. The peak control power in the table is the raw power at the fiber and is shown with the obtained switching contrast. As shown in the table, the control power of 3.3 mW and 2.1 mW for the contrast of 0.8 and 0.5 in our switch are two orders of magnitude lower than those in the other on-chip optical Kerr switches such as a-Si:H microring  and GaInP PhC Fabry-Perot . In addition, the threshold power of 36 μW is on the same order to that demonstrated with silica microbottle  and is much lower than that demonstrated with the other WGM microcavities such as hybrid silica microsphere  and a-Si:H microcylinder .
An optical switch fabricated on a semiconductor chip generally suffers from a large insertion loss, which is attributed to propagation loss and the coupling loss between a chip and an optical fiber. But our device has an extremely small loss, which is a key feature when using the switch for such applications as quantum information processing [15, 16]. In addition, the silica toroid microcavity that we use for the platform of the optical Kerr switch can be fabricated on a chip  and it exhibits highly efficient coupling with a tapered fiber . Therefore, our switch is advantageous in terms of on-chip fabrication and the negligible insertion loss in addition to the low required control power.
In conclusion, we demonstrated an all-optical switching operation in a silica toroid microcavity using the Kerr effect. Thanks to the small mode volume and high Q factor of the silica toroid microcavity, we developed an on-chip optical Kerr switch driven with an input control power of 2 mW, which is the smallest among all previously reported on-chip optical Kerr switches. This value can be reduced to 36 μW by using a higher-Q factor. In addition, our switch is advantageous in terms of on-chip fabrication and the negligible insertion loss. We believe that our low-power driven optical Kerr switch can be applied for both optical telecommunication and loss-sensitive applications such as quantum information processing.
Appendix A: Theory describing switching contrast
Here, we develop the equation that models the switching contrast of our optical switch. The Kerr effect is caused by the light energy stored in a microcavity. Thus, we first derive the relationship between the light energy in the cavity Ucavity and the input control power by using CMT [23, 26], as,Eq. (1) correspond to the under- and over-coupling conditions, respectively. We assumed that the wavelength of the control light is tuned to the resonant wavelength of the control mode and we neglected the light energy stored due to the signal light.
Next, we obtain an equation that will gives the relationship between the resonant wavelength shift of the control mode δλcont and the input control power . According to Ref. , the refractive index change caused by the Kerr effect ΔnKerr(r, z) is written as,Eq. (2), we obtain the wavelength shift of the control mode induced by the Kerr effect δλcont as, 30]. Then, we derive the complete equation for δλcont by combining Eqs. (1), (2) and (3), as,
Here, we obtain the change in the transmittance of the signal light induced by the control light. The wavelength shift of the control mode reflects that of the signal mode, thus the wavelength shift of the signal mode δλcont is written, as,31]. By using CMT [23, 26], the transmittance of the signal light Trsig is written as, Equation (6) shows that if the wavelength of the signal mode is shifted (δλsig > 0), the transmittance Trsig is also changed. When we initially set the signal wavelength at the resonance , the switching contrast η is defined as follows: Eqs. (4)–(9), we obtain the switching contrast.
This work is supported in part by the Strategic Information and Communications R&D Promotion Programme (SCOPE) of the Ministry of Internal Affairs and Communications in Japan 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.
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