JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 30, NO. 22, NOVEMBER 15, 2012 3525 All-Optical Switches Based on Multiple Cascaded Resonators With Reduced Switching Intensity-Response Time Products Quang Minh Ngo, Sangin Kim, Jaejin Lee, and Hanjo Lim, Member, IEEE Abstract—The general nonlinear behavior of multiple cascaded resonators is analyzed by using the coupled-mode theory in time and then compared to a single resonator from the viewpoint of optical bistable operation. Our analysis reveals that from the per- spective of switching intensity, the multiple resonator structure is more advantageous than the single resonator with an equivalently increasing quality factor. It is also shown that a switching inten- sity-response time product, suggested as a performance metric for optical bistable devices, decreases linearly as the number of cas- caded resonators increases. The effect of coupling resonators is equivalent to a single resonator device with -time increased quality factor in terms of the performance metric. The coupled- mode theory analysis is confirmed by a numerical study of the bistable operation of one-dimensional photonic crystal resonator structures using the finite-difference time-domain method. Index Terms—All-optical devices, bistability, integrated optics devices, nonlinear optics, photonic crystals, resonators. I. INTRODUCTION A LL-OPTICAL switching is a key function for all-optical signal processing applications [1], and the implementa- tion of a power efficient all-optical switch has been a long-cher- ished desire of researchers in optics. With the introduction of photonic crystal (PC) nonlinear cavities, miniaturized optical bistable devices of low switching power suitable for practical applications have been demonstrated theoretically and experi- mentally [2]–[6]. In order to realize monolithically integrated all-optical signal processing circuits, linear waveguides should be integrated with optical bistable devices; in order to mini- mize the unwanted nonlinear phase change in the waveguides of the same material, it is desirable to realize further reduction in switching power. For achieving a reduction in the optical switching power, a high quality-factor resonator is required; a sharp resonance of the high- resonator, which implies a narrow linewidth in the spectral response, demands a less reso- nance frequency (wavelength) shift during the optical switching Manuscript received March 13, 2012; revised August 10, 2012; accepted September 14, 2012. Date of publication September 27, 2012; date of current version November 16, 2012. This work was supported in part by National Research Foundation of Korea under Grants NRF-2011-0014265, NRF-2008-0662256, and NRF-2009-0094046. S. Kim, J. Lee, and H. Lim are with Department of Electrical and Computer Engineering, Ajou University, Suwon 443-749, Korea (e-mail: sangin@ajou.ac. kr). Q. M. Ngo is with the Vietnam Academy of Science and Technology, Hanoi, Vietnam. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JLT.2012.2221076 operation. An ultrahigh- PC resonator can be realized through sophisticated design and fabrication techniques [7]. It is well known that sharp resonances can be achieved not only by increasing for a single resonator, but also by cou- pling multiple resonators. Coupled resonator structures have been thoroughly studied to realize linear filters whose character- istics are close to an ideal box-like passband spectrum [9]–[11]. The stiff roll-off near the edge of the passband of the multiple cascaded resonator filter is useful for reducing the switching power by decreasing the needed spectrum shift [12]. Optical bistable and multistable switching operations in coupled mi- croring resonators as well as one/two-dimensional PC multiple cascaded resonators have been theoretically studied [13]–[17]. Another interesting way to obtain a sharp resonance is to employ an all-optical analogue to electromagnetically induced trans- parency [18], [19]; the application of this device for optical bistable switching with reduced switching power has been the- oretically demonstrated [16], [20]. From these studies, it is ob- vious that the sharpened resonances in the coupled resonator systems reduce the switching power in the optical bistable op- eration compared to a single resonator. However, the switching power reduction dependency on a number of coupled resonators has not been investigated in a quantitative way. Besides, the switching power reduction in the optical bistable devices inevitably results in a slow response time as shown for a single resonator bistable device [8]. Therefore, for a more complete comparison between the single and the multiple res- onator systems, their temporal responses in switching opera- tions should also be considered, which has not been investigated in the previous studies. In this work, the performance of the multiple cascaded resonator based optical bistable device is investigated and compared to that of a single resonator device in terms of the switching power and the response time. The general nonlinear behavior of multiple cascaded resonators is analyzed using the coupled-mode theory in time [21], and it is shown that the switching intensity decreases faster than in a single resonator device with an equivalently increased quality-factor. That is, the multiple resonator structure is more desirable than the single resonator structure with respect to the switching intensity. It is also revealed that a switching intensity-response time product, suggested as a performance metric for the optical bistable device, decreases linearly as the number of cascaded resonators increases. The effect of coupling resonators is equivalent to increasing the quality factor times in a single resonator device in terms of the performance metric. We believe that our 0733-8724/$31.00 © 2012 IEEE