We experimentally and theoretically clarified that a Fano resonant system based on a coupled optical cavity has better performance when used as an all-optical switch than a single cavity in terms of switching energy, contrast, and operation bandwidth. We successfully fabricated a Fano system consisting of doubly coupled photonic-crystal (PhC) nanocavities, and demonstrated all-optical switching for the first time. A steep asymmetric transmission spectrum was clearly observed, thereby enabling a low-energy and high-contrast switching operation. We achieved the switching with a pump energy of a few fJ, a contrast of more than 10 dB, and an 18 ps switching time window. These levels of performance are actually better than those for Lorentzian resonance in a single cavity. We also theoretically investigated the achievable performance in a well-designed Fano system, which suggested a high contrast for the switching of more than 20 dB in a fJ energy regime.
©2013 Optical Society of America
Photonic nanostructures are expected to be used as ultrasmall active devices such as all-optical switches, memories and other logical elements when constructing photonic processing circuits . Among them, the all-optical switch will provide the most fundamental functions, and it is expected to play a key role in high-data-rate optical processing that does not require electrical-to-optical conversion. The realization of an ultrasmall all-optical switch that operates at an ultrafast speed with ultralow energy should pave the way for the development of a novel photonic network on chip (PhNoC). While many types of optical nonlinear phenomena can be employed for all-optical switches, carrier-induced nonlinearity in a semiconductor cavity makes it possible to achieve low-power optical switching at a fast switching speed [2–4]. However, in these kinds of switches it is generally difficult to reduce energy consumption and increase switching speed simultaneously because of their trade-off relationship. A photonic crystal (PhC) nanocavity with a high Q factor and a small volume V comparable to (λ/n)3 (λ is the wavelength of light, n is the refractive index) allows us to improve both characteristics since it concentrates photons in a tiny region thus enhancing the nonlinearity. It also enables us to achieve a high-speed recovery owing to the fast carrier diffusion . Indeed, a low-energy switching demonstration has been reported using PhC nanocavities fabricated on Si, GaAs, and InGaAsP slabs [2–4]. Specifically, a record low switching energy of 440 aJ and a switching time of 20 ps were achieved by employing an ultrasmall InGaAsP PhC nanocavity .
These PhC-cavity-based optical switches were all demonstrated by using single nanocavities with a Lorentzian line shape. Since optical switching is realized by a shift in the resonant spectrum, the spectral shape substantially determines the switching contrast. From this point of view, a Lorentzian spectrum should be effective for switching with a contrast of around 3 dB. However, it is difficult for a single cavity to obtain a high switching contrast of more than 10 dB because of its gradual change in the tail of a Lorentzian spectrum. Therefore, the reduction in switching energy and the increase in switching contrast will also be in a trade-off relationship, although both are very significant for an all-optical switch. Optical switches based on optical interference with optical nonlinearity can have a significantly large switching contrast of over 20 dB [6, 7]. However, the large size of these kinds of switches generally makes it difficult to integrate many of them on a chip.
Fano resonance, which has been discussed in relation to a variety of physical platforms such as electromagnetic induced transparency and metamaterials [8, 9], originates from the interference of a discrete energy state with a continuum background. It can also be realized on classical optical systems such as coupled optical cavities or the combination of a cavity and a Mach-Zehnder interferometer, and has been investigated both theoretically [10–12] and experimentally [13, 14]. Fano resonance exhibits an abrupt change in its transmission spectrum compared with Lorentzian resonance. Therefore, it will require a smaller resonance shift to obtain a high contrast when it is applied to an all-optical switch. If a Fano system can be realized with PhC nanocavities, the entire system size could be reduced to a footprint of less than 10 × 10 μm2, and thereby enable us to achieve ultrasmall all-optical switches that can operate with a fJ switching energy, ultrafast speed and a high switching contrast. Yang et al. have reported Fano resonance based on a Si PhC cavity, and demonstrated optical bistable behavior . However, their system consists of a PhC cavity and a large Fabry-Perot cavity formed by two waveguide facets. So, it is not compact, and the on-off contrast is less than 10 dB due to the weak interference between the cavities. The weak nonlinearity in a Si-based cavity means that the bistable switching power is also still as large as 100 μW, which is much larger than those of InP-based PhC nanocavities, which consume less than 100 nW for their operation.
Even though a Fano system might offer the potential to realize low switching energy, high contrast all-optical switches, there has been no clear experimental demonstration of the dynamic operation that would reveal their potential performance. Specifically, ultrasmall optical switches that can be integrated on a chip have never been investigated. In this paper, we demonstrate an ultracompact Fano system consisting of doubly-coupled PhC nanocavities for the first time. The system clearly exhibits a steep asymmetric transmission spectrum with a contrast of nearly 20 dB. We used it to achieve all-optical switching with an ultralow pump energy of a few fJ and a fast response time of less than 20 ps, which are superior to the values obtained for a Lorentzian resonance. In addition, we investigated the potential performance of the Fano system in relation to well-fabricated devices, and found that that a contrast of more than 20 dB can be expected for switching in a fJ energy regime. As a consequence, we theoretically and experimentally revealed clear evidence that indicates the good applicability of the Fano system to high-performance all-optical switches.
2. Device design and transmission spectrum
Figure 1(a) shows a scanning electron microscope image of our coupled PhC nanocavities for a Fano system. We used a lattice-shifted cavity (we call it an H0 cavity) [2, 15], because it has an ultrasmall modal volume (0.025 μm3 ~0.26(λ/n)3) and thus directly contributes to both switching energy reduction and fast carrier diffusion. We employed InGaAsP with a photoluminescence peak at 1.47 μm as a slab material. InGaAsP exhibits a strong carrier-induced nonlinearity as a result of the band-filling dispersion at an operation wavelength of 1.55 μm . During fabrication, air holes are patterned into the slab by a combination of electron beam lithography and Cl2-based inductively coupled plasma etching. The air-hole diameter 2r, the lattice period a and the slab thickness t are 230, 460 and 200 nm, respectively. The H0 cavity is formed by shifting four adjacent air holes (sa = 85 nm, sb = 20 nm) as shown in Fig. 1(a). H0 cavity 1 is coupled with line-defect waveguides in the Γ-M direction for the input and output of light, while H0 cavity 2 is only coupled with H0 cavity 1. The air-hole shift of H0 cavity 2 is slightly different from that of H0 cavity 1 to detune these resonant wavelengths and form a Fano spectrum.
Figure 1(b) is a simple schematic of the optical interference between two incident light paths. Light passes through both H0 cavity 1 and 2 for path A, while it only passes through H0 cavity 1 for path B. With path A, the light takes a large phase change between below and above the resonant wavelength of cavity 2. This induces an abrupt change in the transmission spectrum due to optical interference with path B. Since strong interference can occur when the optical loss in cavity 2 is small, a sufficiently large intrinsic Q is important for high-contrast switching as discussed in a later section.
Figure 1(c) shows a transmission spectrum scanned by a wavelength-tunable continuous-wave (CW) laser. When there is only cavity 1, the spectrum exhibits a single peak with a Q factor of around 1000. On the other hand, the coupled-cavity system has an asymmetric transmission spectrum. In this system, the spectrum tail of the low-Q mode (cavity 1) works as a continuum while the high-Q mode (cavity 2) works as a discrete mode, which clearly results in an asymmetric Fano spectrum [10, 11]. When the resonant wavelength of cavity 2 was detuned from cavity 1 by changing the lattice shift sa, anti-crossing behavior was observed, suggesting strong optical coupling between the cavities. The peak-to-bottom contrast of the Fano spectrum is nearly 20 dB when the cavity detuning is small, which is significantly larger than that for the previously reported nanocavity-based Fano system . On the other hand, the peak-to-bottom contrast becomes small for large detuning, because the photon coupling rate between two cavities becomes small compared with the intrinsic cavity loss, causing weak interference between the two paths. Simulated results obtained with the finite-difference time-domain (FDTD) method, which are shown in Fig. 1(d), exhibit similar behavior to the experimental spectrum.
3. Operation overview for all-optical switching
Figure 2 shows the spectrum and overview for an all-optical switching operation, where we compared results obtained with a single cavity that had a Lorentzian line shape with the same loaded and unloaded Q factors. Figure 2(a) shows the transmission spectrum. We chose the device (iv) in Fig. 1(b) for the Fano system, because it has a high contrast with asymmetry. By fitting the spectrum with a numerical calculation based on coupled-mode theory (CMT), the loaded and unloaded Q factors were estimated to be Qload = 2900 and Qunload = 8000, respectively. (Qunload is defined from the optical loss only in the cavity, which excludes the optical coupling with the waveguide. On the other hand, Qload includes the loss induced by the optical coupling with the waveguide.) It is difficult to estimate Qload from the full width at half maximum (FWHM) of the transmission spectrum because of its asymmetric line shape. However, it can be estimated from the energy-in-cavity spectrum as shown in Fig. 2(b), because it has a rather Lorentzian line shape. The Qload value of 2900 for our system is low to allow a signal throughput of nearly 50 Gbps. The cavity photon lifetime is τph = 2.4 ps, which is shorter than the simulated carrier lifetime of 3.5 ps , and is thus not likely to restrict the switching recovery time. The coupling Q between H0 cavity 1 and the waveguide Qcpl is 3000 and the inter-coupling Q between two H0 cavities Qcc is 1800 . The absorption coefficient at a resonant wavelength was estimated to be 5 cm−1, which can be converted to the absorption Q factor as Qabs = 34700. This suggests that Qunload is not restricted by the absorption loss but by other intrinsic losses (scattering and radiation loss, which are caused by fabrication error and/or the cavity design), indicating that a Qint of 10500 strongly determines the Qunload of 8000.
For all-optical switching, the probe light wavelength was set at the resonant dip of 1556.0 nm, because we intended to perform a switching-on operation (normally-off operation). On the other hand, the pump light wavelength was set at 1556.5 nm, because it is the peak wavelength of the energy spectrum for cavity 2, as shown in Fig. 2(b), suggesting that the pump light can be absorbed most efficiently. Since the Fano system has two cavities, there may be an increase in the switching energy compared with single cavity. However, the partition ratio of the pump energy launched into two cavities is not a half; the ratio into H0 cavity 2 is 0.71. This high value results from wavelength detuning between the two H0 cavities. We confirmed that the partition ratio into H0 cavity 2 becomes higher as the wavelength detuning becomes larger. Therefore, almost all the pump light would be absorbed in cavity 2 if the Fano system were designed well enough to have large detuning. Figure 2(c) shows the expected resonant shift calculated by CMT, in which the appropriate carrier-based nonlinearities including band-filling dispersion, carrier-plasma dispersion, and free-carrier absorption were taken into account . It suggests that switching with a contrast of nearly 20 dB for the probe light can be expected by a carrier generation of 2 × 1016 cm−3 in cavity 2. In comparison with a single cavity with a Lorentzian spectrum and the same cavity Q, the energy in stored the cavity is larger than that in the Fano system even for the same input power, as shown in Fig. 2(b). However, the switching contrast is still about 5 dB for the same carrier generation because of the gradual change in transmission, as shown in Fig. 2(c). This suggests that a Fano system has better potential for being an all-optical switch with a lower switching energy and a higher contrast than a single cavity, even when the cavity Q is the same.
4. All-optical switching characteristics
To evaluate the all-optical switching dynamics experimentally, we employed a quasi-degenerate pump-probe technique with a ~14 ps pulse width and a 10 MHz repetition rate. The method has been described in detail elsewhere . Figure 3 shows the switching dynamics of the probe light when we varied the input pump energy Up, which is defined as the energy of the pump pulse launched into the cavity. Up is estimated by measuring the energy in the fiber and an insertion loss (before a cavity) of −14 dB. As is evident in the plot, the transmitted intensity of the probe light is clearly switched on when the pump pulse temporally overlaps the probe pulse. These dynamics are understood to be the result of a nonlinear blue shift caused by photo-generated carriers in the cavity. The switching energies for contrasts of 3 and 10 dB are 0.4 and 1 fJ, respectively. These energies are more than two orders of magnitude lower than those of switches based on Si- and GaAs-based single PhC nanocavities, and also lower than that for an InGaAsP-based single H0 nanocavity, as described later.
The switching time window observed for Up = 1.91 fJ is only 18 ps, which is much faster than that considered from the carrier recombination lifetime (~several hundred ps). One reason is the localized carrier generation and the fast carrier diffusion from the cavity, which reduces the carrier relaxation lifetime. This situation is uniquely achievable by using an ultrasmall cavity [2, 5]. Our simulation indicated a carrier relaxation time of only 3.5 ps. When we take the pulse width of 14 ps into consideration, a switching time window of 18 ps is quite reasonable. Another reason for the low switching energy and fast switching recovery is the steep slope of the Fano spectrum. There is still a slow decay component after the fast component of the carrier diffusion on the switching dynamics. This may be caused by a slow carrier recombination. This can be improved by employing certain techniques such as ion implantation to enhance the nonradiative recombination or the formation of a p-i-n junction for carrier sweeping [5, 18].
Next, we compare the switching characteristics with a single H0 cavity to clarify the effectiveness of the Fano system. Figure 4(a) shows the switching contrast and switching time window as a function of Up, in which we compare the switch-on dynamics with Lorentzian resonance (λcav = 1568 nm, loaded Q = 6500). We adjust the probe wavelength detuning from the resonant peak Δλprobe/δ, where δ is the full width at half maximum (FWHM) of the resonance, to obtain the maximum switching contrast for the switch-on dynamics in the Lorentzian case. As is clearly shown by the experimental result, the Fano system exhibits not only a higher switching contrast but also a narrower and steadier switching time window even with a smaller Δλprobe/δ. This difference results from the relationship between the spectrum slope and the nonlinear wavelength shift. The switching energies for a 3 dB contrast are almost the same in both schemes, because the spectral slope within a 3 dB bandwidth is very similar for both systems. However, for a larger switching contrast of 10 dB or more, the high contrast in the Fano resonance makes it possible to realize a smaller wavelength shift and a lower pump energy than with Lorentzian resonance. The switching time window with the Fano resonance is shorter than that with the Lorentzian resonance, because the recovery in the transmission becomes fast as a result of the steep spectral slope.
For the experiment, we have only a single cavity with a loaded Q of 6500, which is larger than the value of 2900 for our Fano system. Therefore, we carried out a CMT-based switching simulation to achieve a fair comparison. In the simulation, CMT formulae for photon density and a rate equation for carrier density in a cavity were employed and the pulse response of the cavity was obtained by taking a finite-difference scheme in the time domain . The equations and material parameters used here are described in Appendix. We assumed that the pump and probe pulses were injected into the cavity so that the transmission change of the probe light was simulated exactly like the situation in the pump-probe experiment. The simulated results are shown in Fig. 4(b), where a single cavity with a loaded Q of 2900 was also included. We confirmed that the simulated and experimental results were in good agreement. More importantly, if we consider the same loaded Q for both systems, the Fano system has more advantages than the Lorentzian case in terms of pump energy and switching time window. In particular, the pump energy needed for the Fano system is nearly an order of magnitude lower than in the Lorentzian case for obtaining a switching contrast of more than 3 dB. These are clear advantages of the Fano system as regards employing it as an all-optical switch.
5. Expected switching performance for Fano system
Finally, we theoretically investigated the potential switching performance for a Fano system with achievable cavity parameters. Figure 5(a) shows the available signal bandwidth as a function of resonance detuning between two cavities Δλdet while the Q factors are set as parameters, both of which determine the shape of the transmission spectrum as shown in the inset. The increase in Qunload enhances the interference between two optical paths A and B in Fig. 1(b), and enhances the peak-to-bottom contrast of the Fano spectrum. On the other hand, the increase in Δλdet enhances the asymmetric shape of the spectrum and reduces the photon coupling rate between two cavities, therefore reducing the signal bandwidth. The signal bandwidth is estimated from the FWHM of the transmission peak, and the switching energy is defined as the energy required for a wavelength shift from the bottom to the peak of a Fano spectrum. Figure 5(b) shows the switching contrast and switching energy for a signal bandwidth of 40 Gb/s. The blue plot denotes the current experimental parameters of Qunload = 8000, Qcpl = 3000, Qcc = 1800, and Δλdet = 0.8 nm. This agrees with the theoretical result (shown by the black curve), indicating a signal bandwidth of 50 Gb/s, a contrast of 14 dB and a switching energy of 6 fJ for a bottom-to-peak wavelength shift. Several ways of improving the switching performance can be considered. One is to increase Qunload from 8000 to 26000 (shown in the red curve), which means an increase in Qint from 10500 to 105 with a constant Qabs of 34700. This can greatly enhance the peak-to-bottom contrast of the transmission spectrum, as seen in the comparison of spectra (I) and (II) in Fig. 5(a). It results in an improvement in the switching contrast and energy, as shown in Fig. 5(b). Although the effect is not so great for a signal bandwidth of 40 Gb/s, it becomes more apparent for 10 Gb/s, as shown in Fig. 5(c). For Δλdet = 5 nm, the switching contrast remains at 20 dB and the switching energy falls to around 1 fJ. As another way of improving the switching contrast for a signal bandwidth of 40 Gb/s, we reduced Qcpl and Qcc to make the signal bandwidth larger, as shown by the green curve and spectrum (IV). This can strongly enhance the switching contrast to above 20 dB, while the switching energy becomes around 10 fJ for Δλdet = 3 nm.
We compared the switching energy using a single cavity with the same Q, for which we optimized Qcpl at 12000 and 52000 for signal bandwidths of 40 and 10 Gb/s, respectively. The dashed lines in Fig. 5(b) and 5(c) denote the switching energy of a single cavity needed to obtain the switching contrast indicated in the figure. We compared the results with those for the Fano system, where the red curve is for a 15-dB contrast and green curve for a 20-dB contrast at 40 Gb/s in Fig. 5(b). Consequently, the energy of the Fano system (40 fJ and 11 fJ for 15 dB and 20 dB contrast, respectively) is more than an order of magnitude lower than that of the single cavity (50 fJ and 370 fJ for 15 dB and 20 dB contrast, respectively). On the other hand, at 10 Gb/s in Fig. 5(c), the energy of the Fano system (1.6 fJ) is about two orders of magnitude lower than that of the single cavity (180 fJ) when compared with the red curve. As mentioned above, the Lorentzian spectrum should be effective for switching with a contrast of around 3 dB. When considering a switching contrast of 20 dB, a wavelength shift of 3-4 times larger than that with the Fano system is needed in the Lorentzian case, as suggested in Fig. 2(c). However, we found that the required switching energy is much larger than expected, as compared above. This can be explained as follows. When a strong pump pulse is injected at the resonant wavelength, the wavelength is shifted during the pulse duration. Therefore, the absorption efficiency of the pump pulse would be strongly restricted as the required wavelength shift becomes larger, because the resonant wavelength is shifted away from the wavelength of the pump pulse. As a result, the switching energy required for a contrast of more than 10 dB in a single cavity becomes more than an order larger than that with a Fano system. This definitely indicates that Fano resonance is much more effective than Lorentzian resonance for high-contrast switching.
In addition, the carrier relaxation time τc was assumed to be 5 ps in this simulation, which might limit carrier accumulation in the cavity. If we set τc = 20 ps, which does not restrict the operation speed for 10 Gb/s, the simulated switching energy was 0.4 fJ for the Fano system. Consequently, a well-designed and appropriately fabricated Fano system enables us to make a switch with a sub-femtojoule switching energy, a switching contrast of more than 20 dB, and a signal throughput of more than 10 Gbps. In addition, since our Fano system is fabricated with a footprint of less than 10 × 10 μm2, we could integrate more than ten thousand devices in 1 mm2. Such a high performance, ultrasmall all-optical switch is unique by comparison with previously reported optical switches.
In this work, we demonstrated a Fano system consisting of coupled InGaAsP-H0 nanocavities, and observed an asymmetric transmission spectrum with a contrast of nearly 20 dB. Thanks to the strong carrier-induced nonlinearity and the steep spectral slope, we successfully obtained all-optical switching with a pump energy of 1 fJ, a contrast of more than 10 dB, and an 18 ps switching time window. The advantages in switching performance over a single cavity were clarified experimentally and theoretically. We showed that switching with sub-femtojoule energy and a 20-dB contrast is achievable for a 10 Gb/s bandwidth and 10 fJ and a 20-dB contrast is achievable for a 40 Gb/s bandwidth by optimizing both design and fabrication. These levels of performance are difficult for a single cavity switch to achieve. Consequently, a nanocavity-based Fano system should offer the potential to realize integrable all-optical processing elements for use in constructing an on-chip photonic network.
Appendix: Coupled-mode theory for Fano system based on coupled cavities
We consider the amplitude denoted by ai for cavity i (i = 1, 2). The squared magnitude of this amplitude is equal to the energy Ui in the mode. The amplitudes of the incoming (outgoing) waves in the input waveguide and output waveguide are denoted by s1+ (s1-) and s2+ (s2-), respectively. The squared magnitude of these amplitudes is equal to the power in the waveguide mode. The equation for the evolution of the cavity mode in time is given by [17, 18]
When only the incoming wave s1+ is assumed, the reflected wave s1- and outgoing wave s2- are given by
The carrier density Ni in the cavity i is given asEquations (1)-(6) are solved for an input pump pulse by a finite-difference formula, and the dynamic behavior of a cavity transmission for a probe light is obtained.
In the simulation, we employed parameters of n = 3.44, Γ = 0.8, V1 = V2 = 0.025 μm3,αLA = 5.0 cm−1, βTPA = 84 cm/GW, σ = 8.6×10−20 cm3, and τc = 5 ps, which are referred from a combination of H0 cavity and InGaAsP with a photoluminescence peak at 1.47 μm. The Q factors used in the simulation are described in the main text.
The authors thank T. Tamamura, H. Onji, Y. Shouji for support in fabricating the device.
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