Electromagnetically induced transparency-like effect in a two-bus waveguides coupled microdisk resonator Qingzhong Huang,1,* Zhan Shu,1 Ge Song,1 Juguang Chen,1 Jinsong Xia, 1 and Jinzhong Yu1,2 1
Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China 2 Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083, China * [email protected]
Abstract: We observe theoretically and experimentally electromagnetically induced transparency (EIT)-like effect in a single microdisk resonator (MDR) evanescently coupled with two bus waveguides. This structure is modeled using transfer matrix method, and it is revealed that the EIT-like spectrum originates from the coherent interference between two nearby low-order whispering-gallery modes (WGMs) with comparable quality factors. The EIT-like properties have been investigated analytically with respect to coupling efficiency, round-trip power attenuation, as well as phase spacing between two resonances. The resonance spacing and mode coupling are adjustable by varying the effective indices of WGMs and waveguide mode. Consequently, fully integrated MDRs were fabricated in silicon. Resonant modes and coupling efficiency are studied in one-bus waveguide coupled MDRs. Finally, EIT-like resonance is observed in a two-bus waveguides coupled MDR of 3 μm in radius with a quality factor of 4,200 and central transmission larger than 0.65. The experimental results agree with our modeling well and show good internal consistency, confirming that two WGMs coupled in a point-to-point manner are required for EIT-like effect. ©2014 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (230.3990) Micro-optical devices; (230.5750) Resonators; (030.4070) Modes.
References and links 1.
I. Novikova, R. L. Walsworth, and Y. Xiao, “Electromagnetically induced transparency-based slow and stored light in warm atoms,” Laser Photon. Rev. 6(3), 333–353 (2012). 2. X. D. Yang, S. J. Li, C. H. Zhang, and H. Wang, “Enhanced cross-Kerr nonlinearity via electromagnetically induced transparency in a four-level tripod atomic system,” J. Opt. Soc. Am. B 26(7), 1423–1434 (2009). 3. R. G. Beausoleil, W. J. Munro, D. A. Rodrigues, and T. P. Spiller, “Applications of electromagnetically induced transparency to quantum information processing,” J. Mod. Opt. 51(16–18), 2441–2448 (2004). 4. R. W. Boyd and D. J. Gauthier, “Photonics: transparency on an optical chip,” Nature 441(7094), 701–702 (2006). 5. K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98(21), 213904 (2007). 6. M. Tomita, K. Totsuka, R. Hanamura, and T. Matsumoto, “Tunable Fano interference effect in coupledmicrosphere resonator-induced transparency,” J. Opt. Soc. Am. B 26(4), 813–818 (2009). 7. C. Zheng, X. Jiang, S. Hua, L. Chang, G. Li, H. Fan, and M. Xiao, “Controllable optical analog to electromagnetically induced transparency in coupled high-Q microtoroid cavities,” Opt. Express 20(16), 18319– 18325 (2012). 8. Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental Realization of an On-Chip All-Optical Analogue to Electromagnetically Induced Transparency,” Phys. Rev. Lett. 96(12), 123901 (2006). 9. Q. Xu, J. Shakya, and M. Lipson, “Direct measurement of tunable optical delays on chip analogue to electromagnetically induced transparency,” Opt. Express 14(14), 6463–6468 (2006). 10. Q. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3(6), 406–410 (2007).
#200486 - $15.00 USD Received 30 Oct 2013; revised 19 Jan 2014; accepted 28 Jan 2014; published 4 Feb 2014 (C) 2014 OSA 10 February 2014 | Vol. 22, No. 3 | DOI:10.1364/OE.22.003219 | OPTICS EXPRESS 3219
11. S. Darmawan, L. Y. M. Tobing, and D. H. Zhang, “Experimental demonstration of coupled-resonator-inducedtransparency in silicon-on-insulator based ring-bus-ring geometry,” Opt. Express 19(18), 17813–17819 (2011). 12. Y. Zhang, S. Darmawan, L. Y. M. Tobing, T. Mei, and D. H. Zhang, “Coupled resonator-induced transparency in ring-bus-ring Mach-Zehnder interferometer,” J. Opt. Soc. Am. B 28(1), 28–36 (2011). 13. L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonic applications,” Opt. Lett. 33(17), 1978–1980 (2008). 14. X. Zhou, L. Zhang, A. M. Armani, R. G. Beausoleil, A. E. Willner, and W. Pang, “Power enhancement and phase regimes in embedded microring resonators in analogy with electromagnetically induced transparency,” Opt. Express 21(17), 20179–20186 (2013). 15. X. Zhou, L. Zhang, W. Pang, H. Zhang, Q. Yang, and D. Zhang, “Phase characteristics of an electromagnetically induced transparency analogue in coupled resonant systems,” New J. Phys. 15(10), 103033 (2013). 16. Z. Zou, L. Zhou, X. Sun, J. Xie, H. Zhu, L. Lu, X. Li, and J. Chen, “Tunable two-stage self-coupled optical waveguide resonators,” Opt. Lett. 38(8), 1215–1217 (2013). 17. L. Zhou, T. Ye, and J. Chen, “Coherent interference induced transparency in self-coupled optical waveguidebased resonators,” Opt. Lett. 36(1), 13–15 (2011). 18. X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “All-Optical Analog to Electromagnetically Induced Transparency in Multiple Coupled Photonic Crystal Cavities,” Phys. Rev. Lett. 102(17), 173902 (2009). 19. X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “Coupled resonances in multiple silicon photonic crystal cavities in all-optical solid-state analogy to electromagnetically induced transparency,” IEEE J. Sel. Top. Quantum Electron. 16(1), 288–294 (2010). 20. C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B 42(21), 215401 (2009). 21. Y.-F. Xiao, L. He, J. Zhu, and L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane coated silica microtoroid,” Appl. Phys. Lett. 94(23), 231115 (2009). 22. B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98(2), 021116 (2011). 23. Q. Huang, X. Zhang, J. Xia, and J. Yu, “Dual-band optical filter based on a single microdisk resonator,” Opt. Lett. 36(23), 4494–4496 (2011). 24. Q. Huang, X. Zhang, J. Xia, and J. Yu, “Systematic investigation of silicon digital 1×2 electro-optic switch based on a microdisk resonator through carrier injection,” Appl. Phys. B 105(2), 353–361 (2011). 25. E. S. Hosseini, S. Yegnanarayanan, A. H. Atabaki, M. Soltani, and A. Adibi, “High quality planar silicon nitride microdisk resonators for integrated photonics in the visible wavelength range,” Opt. Express 17(17), 14543– 14551 (2009). 26. D. Dai, Y. Shi, S. He, L. Wosinski, and L. Thylen, “Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides,” Opt. Express 19(24), 23671–23682 (2011). 27. G. Rasigade, M. Ziebell, D. Marris-Morini, J.-M. Fédéli, F. Milesi, P. Grosse, D. Bouville, E. Cassan, and L. Vivien, “High extinction ratio 10 Gbit/s silicon optical modulator,” Opt. Express 19(7), 5827–5832 (2011). 28. M. Popovic, C. Manolatou, and M. Watts, “Coupling-induced resonance frequency shifts in coupled dielectric multi-cavity filters,” Opt. Express 14(3), 1208–1222 (2006).
1. Introduction Electromagnetically induced transparency (EIT) has attracted considerable attentions in the past decades, due to its wide applications in slowing/stopping light, nonlinear optics, and quantum information processing [1–3]. Similar to EIT effect caused by quantum interference in multi-level atomic systems, EIT-like spectrum, having a narrow transparency peak residing in a broader absorption valley, also can be generated by coherent interference between coupled resonant modes [4]. All-optical analogies to EIT have been demonstrated in various configurations comprising coupled two resonators, including microsphere [5,6], microtoroid [7], microring [8–15], self-coupled optical waveguide resonator [16,17], and photonic crystal microcavity [18,19]. Recently, without employment of additional optical resonator, EIT-like phenomenon has been demonstrated in a single microsphere/microtoroid coupled with a single fiber taper waveguide [20–22]. The EIT-like effect is induced by the indirect interaction between two whispering-gallery modes (WGMs), which are simultaneously triggered by a coupled fiber waveguide. In this case, it is necessary that the two WGM resonances are fully overlapped and differ by no less than two orders of magnitude in quality factor to obtain EIT-like spectral response. However, these structures are either non-planar or hardly integrated with bus waveguide, since they are fabricated by reflowing the resonator material. In this paper, we have demonstrated EIT-like effect in a microdisk resonator (MDR) coupled with two bus waveguides. A theoretical model is given using transfer matrix method [23], and then applied to study the mechanism and analyze the influencing factors of this
#200486 - $15.00 USD Received 30 Oct 2013; revised 19 Jan 2014; accepted 28 Jan 2014; published 4 Feb 2014 (C) 2014 OSA 10 February 2014 | Vol. 22, No. 3 | DOI:10.1364/OE.22.003219 | OPTICS EXPRESS 3220
device. It is found that the EIT-like resonance in a planar MDR stems from the coherent interference between two low-order WGMs with comparable quality factors [23–25]. Unlike microsphere/microtoroid, it is not easy for an on-chip MDR to achieve two WGM resonances of tremendously different quality factor. Using nanofabrication processing, we realized silicon based 3-μm radius MDRs with one bus and two buses coupled. One-bus waveguide coupled MDRs are characterized to study the properties of resonant modes and coupling efficiency. Finally, EIT-like resonance is observed in a two-bus waveguides coupled MDR with a quality factor of 4,200 and central transmission larger than 0.65. The experimental results fit our modeling well and show good internal consistency. 2. Model and mechanism Figure 1(a) shows the schematic structure of a two-bus waveguides coupled MDR, or a onebus waveguide coupled MDR as one bus is removed. It is supposed that the first-order radial WGM (WGM1) and second-order radial WGM (WGM2) are excited simultaneously and indirectly coupled through the 3 × 3 couplers.
Fig. 1. (a) Schematic of a two-mode MDR coupled with two bus waveguides. (b) A SEM image of the fabricated device.
Using transfer matrix method, the input-output relations for a 3 × 3 coupler can be expressed by b0 t0 b1 = − jk1 b2 − jk2
− jk1 t1 − kc
− jk2 a0 − kc a1 t2 a2
(1)
where a0,1,2 and b0,1,2 are the optical fields (the subscripts 0, 1, and 2 represent the waveguide mode, WGM1, and WGM2, respectively) at the input and output ports; -jk1,2 and -kc are the field coupling coefficients between these modes; t0,1,2 is the field transmission coefficient. We use θ = 2π2R (neff1 + neff2)/λ to describe the phase shift of two-bus waveguides coupled MDR, where R, neff1,2 and λ denote the MDR radius, effective mode index of WGM1,2, and vacuum wavelength, respectively. The optical fields of WGMs are phase shifted and crosscoupled in the resonator, and the relations are described as for (2m-0.5) π0.13 for coupling efficiency of 0.08. Exactly, in the case of Δψ/π>0.13 and k12 = k22 = 0.08, the EIT-like resonance no longer exists and it evolves into two separated WGM resonances. 4. Resonance spacing and mode coupling As analyzed previously, EIT-like phenomenon is sensitive to the resonance spacing between two WGMs and the coupling efficiency between WGM and waveguide mode. Here, we use resonance spacing in wavelength instead of phase spacing, while they are intrinsically the same. The resonance position and spacing are mostly determined by the effective index of WGM, and slightly influenced by the coupling induced phase shift. The simulation of WGM effective index is performed for silicon-on-insulator (SOI) based MDRs with a 340-nm-thick top silicon layer, 3-μm MDR radius, and refractive indices of Si and SiO2 referred from [26]. The effective indices of transverse magnetic (TM) polarized WGM1 and WGM2 for slab thicknesses of 40 nm and 80 nm are calculated respectively using finite mode matching method, as shown in Fig. 6. It is seen that the mode effective index decreases with the wavelength, while it increases with the slab height. According to the relation 2πRneff = mλ0, where m is the azimuthal order of WGM, the resonant wavelengths (λ0) are obtained for WGM1 and WGM2, as denoted by the black dots in Fig. 6. Obviously, the resonance spacing between WGM1 and WGM2 varies with the slab height and wavelength. It is expected that the resonance spacing is also affected by the thickness of top silicon layer and MDR radius, and even can be tuned by local heating [21] or carrier injection [27] in the MDR. With respect to the coupling, mode matching is very essential for enhancing the coupling between two modes. Hence, with the aim of higher k12 and k22, the effective index of waveguide mode should fall in between the effective indices of WGM1 and WGM2. The inset of Fig. 6 shows that the effective index of TM0 mode in the waveguide increases monotonously with the waveguide width, indicating that optimal waveguide width is achievable to approach mode matching between WGM and waveguide mode. The gap between MDR and waveguide, as another important factor, also has an impact on the coupling efficiency between WGM and waveguide mode, and the coupling efficiency becomes lower as the gap enlarged.
Fig. 6. Effective indices of WGM1 (red lines) and WGM2 (blue lines) as a function of wavelength, insets: effective index of TM0 mode (black lines) in the waveguide as a function of width at the wavelength of 1550 nm, and the Ey field profiles of WGM1, WGM2, and TM0 mode. The solid and dashed lines are for slab thicknesses of 40 nm and 80 nm, respectively.
#200486 - $15.00 USD Received 30 Oct 2013; revised 19 Jan 2014; accepted 28 Jan 2014; published 4 Feb 2014 (C) 2014 OSA 10 February 2014 | Vol. 22, No. 3 | DOI:10.1364/OE.22.003219 | OPTICS EXPRESS 3225
5. Experiment and discussion MDRs with one bus and two buses coupled were fabricated on a SOI wafer with a 340-nmthick top silicon layer and a 2-μm-thick buried oxide layer. The fine pattern was defined by electron beam lithography, followed by inductively coupled plasma etching with a depth of 300 nm. The radius of MDR is 3 μm, and the waveguide width is 290 nm. On the basis of measured structure dimensions, the effective indices of TM-polarized WGM1, WGM2 and TM0 mode in waveguide are evaluated to be about 2.35, 2.00, and 2.18 at 1550-nm wavelength, respectively, indicating comparable k12 and k22 due to mode matching. For speculating the power attenuation and coupling efficiency, transmissions of one-bus waveguide coupled MDRs are measured and analyzed for different gaps. Figure 7(a) and 7(b) show the measured power transmissions for gaps of 180 nm and 270 nm, respectively. It is seen that two low-order WGMs are excited by the bus waveguide and exhibit comparable resonance linewidths. The influence of roughness-induced backscattering is neglectable here, since the resonance splitting is hardly observed in the spectra, except the resonance of WGM1 near 1488 nm for the gap of 180 nm. Using the proposed model, the fitting curves are given and agree well with the experimental results, as seen in the insets of Fig. 7(a) and 7(b). The fitting parameters are obtained as follows: for a gap of 180 nm, we have k12 = 0.031, k22 = 0.048, α12 = 0.990 and α22 = 0.981; and for a gap of 270 nm, we have k12 = 0.004, k22 = 0.011, α12 = 0.989 and α22 = 0.981. As the quality factors of two WGMs are on the same order of magnitude, the one-bus waveguide coupled MDRs do not behavior as reported in literatures [20,21].
Fig. 7. (a) The measured power transmission for a gap of 180 nm, inset: experimental results (blue circles) and theoretical fitting (red line), and a SEM image. (b) The measured power transmission for a gap of 270 nm, inset: experimental results (blue circles) and theoretical fitting (red line).
As shown in Fig. 1(b), a two-bus waveguides coupled MDR with a gap of 180 nm was fabricated and characterized. It is observed that a narrow EIT-like transparency window appears between two broader dips around the wavelength of 1546 nm, with central transmission larger than 0.65, and a central bandwidth of 0.37 nm, corresponding to a quality factor of 4,200. The theoretical fitting in Fig. 8 exhibits good agreement with the experiment, when we set k12 = 0.031, k22 = 0.048, α12 = 0.990, α22 = 0.981, neff1 = 2.37917 and neff2 = 2.04998. It shows a good internal consistency with the result of one-bus waveguide coupled MDR with the same dimensions. Note that a blueshift of the resonant spectrum occurs as compared with the spectrum in the inset of Fig. 7 (a), due to the additional phase shift in the 3
#200486 - $15.00 USD Received 30 Oct 2013; revised 19 Jan 2014; accepted 28 Jan 2014; published 4 Feb 2014 (C) 2014 OSA 10 February 2014 | Vol. 22, No. 3 | DOI:10.1364/OE.22.003219 | OPTICS EXPRESS 3226
× 3 coupler at the drop channel [28]. The experimental results confirm that two-bus waveguides coupled MDR with two WGMs coupled in a point-to-point manner is required for EIT-like effect. Making use of the two modes in a MDR, this structure offers us another way to achieve EIT-like effect on a chip, and it is more compact than conventional coupled double resonators, as the resonator number is decreased by a half.
Fig. 8. The measured power transmission (blue circles) and theoretical fitting (red line) of the fabricated two-bus waveguides coupled MDR.
6. Conclusion In summary, EIT-like effect has been demonstrated theoretically and experimentally in a fully integrated MDR coupled with two buses. The structure is modeled and EIT-like spectral response is found to originate from the destructive interference between two nearby resonances of low-order WGMs with comparable quality factors. The influencing factors of EIT-like effect have been studied, including coupling efficiency, round-trip power attenuation, and phase spacing. EIT-like resonance is experimentally observed in an ultracompact and fully integrated MDR of 3 μm in radius on a SOI platform with a quality factor of 4,200 and central transmission larger than 0.65. The experimental result agrees with our modeling well. It is approved that two buses coupled are required for a two-mode MDR to obtain EIT-like effect. Due to the compactness and integratability, the proposed device is promising for applications in on-chip time delay lines and nonlinear signal processing. Acknowledgments This work was supported by the National Natural Science Foundation of China under Grants 61006045 and 61177049, by the Major State Research Program of China under Grant 2013CB933303, and by the Major State Basic Research Development Program of China under Grants 2013CB632104 and 2010CB923204.
#200486 - $15.00 USD Received 30 Oct 2013; revised 19 Jan 2014; accepted 28 Jan 2014; published 4 Feb 2014 (C) 2014 OSA 10 February 2014 | Vol. 22, No. 3 | DOI:10.1364/OE.22.003219 | OPTICS EXPRESS 3227
Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China 2 Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083, China * [email protected]
Abstract: We observe theoretically and experimentally electromagnetically induced transparency (EIT)-like effect in a single microdisk resonator (MDR) evanescently coupled with two bus waveguides. This structure is modeled using transfer matrix method, and it is revealed that the EIT-like spectrum originates from the coherent interference between two nearby low-order whispering-gallery modes (WGMs) with comparable quality factors. The EIT-like properties have been investigated analytically with respect to coupling efficiency, round-trip power attenuation, as well as phase spacing between two resonances. The resonance spacing and mode coupling are adjustable by varying the effective indices of WGMs and waveguide mode. Consequently, fully integrated MDRs were fabricated in silicon. Resonant modes and coupling efficiency are studied in one-bus waveguide coupled MDRs. Finally, EIT-like resonance is observed in a two-bus waveguides coupled MDR of 3 μm in radius with a quality factor of 4,200 and central transmission larger than 0.65. The experimental results agree with our modeling well and show good internal consistency, confirming that two WGMs coupled in a point-to-point manner are required for EIT-like effect. ©2014 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (230.3990) Micro-optical devices; (230.5750) Resonators; (030.4070) Modes.
References and links 1.
I. Novikova, R. L. Walsworth, and Y. Xiao, “Electromagnetically induced transparency-based slow and stored light in warm atoms,” Laser Photon. Rev. 6(3), 333–353 (2012). 2. X. D. Yang, S. J. Li, C. H. Zhang, and H. Wang, “Enhanced cross-Kerr nonlinearity via electromagnetically induced transparency in a four-level tripod atomic system,” J. Opt. Soc. Am. B 26(7), 1423–1434 (2009). 3. R. G. Beausoleil, W. J. Munro, D. A. Rodrigues, and T. P. Spiller, “Applications of electromagnetically induced transparency to quantum information processing,” J. Mod. Opt. 51(16–18), 2441–2448 (2004). 4. R. W. Boyd and D. J. Gauthier, “Photonics: transparency on an optical chip,” Nature 441(7094), 701–702 (2006). 5. K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98(21), 213904 (2007). 6. M. Tomita, K. Totsuka, R. Hanamura, and T. Matsumoto, “Tunable Fano interference effect in coupledmicrosphere resonator-induced transparency,” J. Opt. Soc. Am. B 26(4), 813–818 (2009). 7. C. Zheng, X. Jiang, S. Hua, L. Chang, G. Li, H. Fan, and M. Xiao, “Controllable optical analog to electromagnetically induced transparency in coupled high-Q microtoroid cavities,” Opt. Express 20(16), 18319– 18325 (2012). 8. Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental Realization of an On-Chip All-Optical Analogue to Electromagnetically Induced Transparency,” Phys. Rev. Lett. 96(12), 123901 (2006). 9. Q. Xu, J. Shakya, and M. Lipson, “Direct measurement of tunable optical delays on chip analogue to electromagnetically induced transparency,” Opt. Express 14(14), 6463–6468 (2006). 10. Q. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3(6), 406–410 (2007).
#200486 - $15.00 USD Received 30 Oct 2013; revised 19 Jan 2014; accepted 28 Jan 2014; published 4 Feb 2014 (C) 2014 OSA 10 February 2014 | Vol. 22, No. 3 | DOI:10.1364/OE.22.003219 | OPTICS EXPRESS 3219
11. S. Darmawan, L. Y. M. Tobing, and D. H. Zhang, “Experimental demonstration of coupled-resonator-inducedtransparency in silicon-on-insulator based ring-bus-ring geometry,” Opt. Express 19(18), 17813–17819 (2011). 12. Y. Zhang, S. Darmawan, L. Y. M. Tobing, T. Mei, and D. H. Zhang, “Coupled resonator-induced transparency in ring-bus-ring Mach-Zehnder interferometer,” J. Opt. Soc. Am. B 28(1), 28–36 (2011). 13. L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonic applications,” Opt. Lett. 33(17), 1978–1980 (2008). 14. X. Zhou, L. Zhang, A. M. Armani, R. G. Beausoleil, A. E. Willner, and W. Pang, “Power enhancement and phase regimes in embedded microring resonators in analogy with electromagnetically induced transparency,” Opt. Express 21(17), 20179–20186 (2013). 15. X. Zhou, L. Zhang, W. Pang, H. Zhang, Q. Yang, and D. Zhang, “Phase characteristics of an electromagnetically induced transparency analogue in coupled resonant systems,” New J. Phys. 15(10), 103033 (2013). 16. Z. Zou, L. Zhou, X. Sun, J. Xie, H. Zhu, L. Lu, X. Li, and J. Chen, “Tunable two-stage self-coupled optical waveguide resonators,” Opt. Lett. 38(8), 1215–1217 (2013). 17. L. Zhou, T. Ye, and J. Chen, “Coherent interference induced transparency in self-coupled optical waveguidebased resonators,” Opt. Lett. 36(1), 13–15 (2011). 18. X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “All-Optical Analog to Electromagnetically Induced Transparency in Multiple Coupled Photonic Crystal Cavities,” Phys. Rev. Lett. 102(17), 173902 (2009). 19. X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “Coupled resonances in multiple silicon photonic crystal cavities in all-optical solid-state analogy to electromagnetically induced transparency,” IEEE J. Sel. Top. Quantum Electron. 16(1), 288–294 (2010). 20. C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B 42(21), 215401 (2009). 21. Y.-F. Xiao, L. He, J. Zhu, and L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane coated silica microtoroid,” Appl. Phys. Lett. 94(23), 231115 (2009). 22. B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98(2), 021116 (2011). 23. Q. Huang, X. Zhang, J. Xia, and J. Yu, “Dual-band optical filter based on a single microdisk resonator,” Opt. Lett. 36(23), 4494–4496 (2011). 24. Q. Huang, X. Zhang, J. Xia, and J. Yu, “Systematic investigation of silicon digital 1×2 electro-optic switch based on a microdisk resonator through carrier injection,” Appl. Phys. B 105(2), 353–361 (2011). 25. E. S. Hosseini, S. Yegnanarayanan, A. H. Atabaki, M. Soltani, and A. Adibi, “High quality planar silicon nitride microdisk resonators for integrated photonics in the visible wavelength range,” Opt. Express 17(17), 14543– 14551 (2009). 26. D. Dai, Y. Shi, S. He, L. Wosinski, and L. Thylen, “Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides,” Opt. Express 19(24), 23671–23682 (2011). 27. G. Rasigade, M. Ziebell, D. Marris-Morini, J.-M. Fédéli, F. Milesi, P. Grosse, D. Bouville, E. Cassan, and L. Vivien, “High extinction ratio 10 Gbit/s silicon optical modulator,” Opt. Express 19(7), 5827–5832 (2011). 28. M. Popovic, C. Manolatou, and M. Watts, “Coupling-induced resonance frequency shifts in coupled dielectric multi-cavity filters,” Opt. Express 14(3), 1208–1222 (2006).
1. Introduction Electromagnetically induced transparency (EIT) has attracted considerable attentions in the past decades, due to its wide applications in slowing/stopping light, nonlinear optics, and quantum information processing [1–3]. Similar to EIT effect caused by quantum interference in multi-level atomic systems, EIT-like spectrum, having a narrow transparency peak residing in a broader absorption valley, also can be generated by coherent interference between coupled resonant modes [4]. All-optical analogies to EIT have been demonstrated in various configurations comprising coupled two resonators, including microsphere [5,6], microtoroid [7], microring [8–15], self-coupled optical waveguide resonator [16,17], and photonic crystal microcavity [18,19]. Recently, without employment of additional optical resonator, EIT-like phenomenon has been demonstrated in a single microsphere/microtoroid coupled with a single fiber taper waveguide [20–22]. The EIT-like effect is induced by the indirect interaction between two whispering-gallery modes (WGMs), which are simultaneously triggered by a coupled fiber waveguide. In this case, it is necessary that the two WGM resonances are fully overlapped and differ by no less than two orders of magnitude in quality factor to obtain EIT-like spectral response. However, these structures are either non-planar or hardly integrated with bus waveguide, since they are fabricated by reflowing the resonator material. In this paper, we have demonstrated EIT-like effect in a microdisk resonator (MDR) coupled with two bus waveguides. A theoretical model is given using transfer matrix method [23], and then applied to study the mechanism and analyze the influencing factors of this
#200486 - $15.00 USD Received 30 Oct 2013; revised 19 Jan 2014; accepted 28 Jan 2014; published 4 Feb 2014 (C) 2014 OSA 10 February 2014 | Vol. 22, No. 3 | DOI:10.1364/OE.22.003219 | OPTICS EXPRESS 3220
device. It is found that the EIT-like resonance in a planar MDR stems from the coherent interference between two low-order WGMs with comparable quality factors [23–25]. Unlike microsphere/microtoroid, it is not easy for an on-chip MDR to achieve two WGM resonances of tremendously different quality factor. Using nanofabrication processing, we realized silicon based 3-μm radius MDRs with one bus and two buses coupled. One-bus waveguide coupled MDRs are characterized to study the properties of resonant modes and coupling efficiency. Finally, EIT-like resonance is observed in a two-bus waveguides coupled MDR with a quality factor of 4,200 and central transmission larger than 0.65. The experimental results fit our modeling well and show good internal consistency. 2. Model and mechanism Figure 1(a) shows the schematic structure of a two-bus waveguides coupled MDR, or a onebus waveguide coupled MDR as one bus is removed. It is supposed that the first-order radial WGM (WGM1) and second-order radial WGM (WGM2) are excited simultaneously and indirectly coupled through the 3 × 3 couplers.
Fig. 1. (a) Schematic of a two-mode MDR coupled with two bus waveguides. (b) A SEM image of the fabricated device.
Using transfer matrix method, the input-output relations for a 3 × 3 coupler can be expressed by b0 t0 b1 = − jk1 b2 − jk2
− jk1 t1 − kc
− jk2 a0 − kc a1 t2 a2
(1)
where a0,1,2 and b0,1,2 are the optical fields (the subscripts 0, 1, and 2 represent the waveguide mode, WGM1, and WGM2, respectively) at the input and output ports; -jk1,2 and -kc are the field coupling coefficients between these modes; t0,1,2 is the field transmission coefficient. We use θ = 2π2R (neff1 + neff2)/λ to describe the phase shift of two-bus waveguides coupled MDR, where R, neff1,2 and λ denote the MDR radius, effective mode index of WGM1,2, and vacuum wavelength, respectively. The optical fields of WGMs are phase shifted and crosscoupled in the resonator, and the relations are described as for (2m-0.5) π0.13 for coupling efficiency of 0.08. Exactly, in the case of Δψ/π>0.13 and k12 = k22 = 0.08, the EIT-like resonance no longer exists and it evolves into two separated WGM resonances. 4. Resonance spacing and mode coupling As analyzed previously, EIT-like phenomenon is sensitive to the resonance spacing between two WGMs and the coupling efficiency between WGM and waveguide mode. Here, we use resonance spacing in wavelength instead of phase spacing, while they are intrinsically the same. The resonance position and spacing are mostly determined by the effective index of WGM, and slightly influenced by the coupling induced phase shift. The simulation of WGM effective index is performed for silicon-on-insulator (SOI) based MDRs with a 340-nm-thick top silicon layer, 3-μm MDR radius, and refractive indices of Si and SiO2 referred from [26]. The effective indices of transverse magnetic (TM) polarized WGM1 and WGM2 for slab thicknesses of 40 nm and 80 nm are calculated respectively using finite mode matching method, as shown in Fig. 6. It is seen that the mode effective index decreases with the wavelength, while it increases with the slab height. According to the relation 2πRneff = mλ0, where m is the azimuthal order of WGM, the resonant wavelengths (λ0) are obtained for WGM1 and WGM2, as denoted by the black dots in Fig. 6. Obviously, the resonance spacing between WGM1 and WGM2 varies with the slab height and wavelength. It is expected that the resonance spacing is also affected by the thickness of top silicon layer and MDR radius, and even can be tuned by local heating [21] or carrier injection [27] in the MDR. With respect to the coupling, mode matching is very essential for enhancing the coupling between two modes. Hence, with the aim of higher k12 and k22, the effective index of waveguide mode should fall in between the effective indices of WGM1 and WGM2. The inset of Fig. 6 shows that the effective index of TM0 mode in the waveguide increases monotonously with the waveguide width, indicating that optimal waveguide width is achievable to approach mode matching between WGM and waveguide mode. The gap between MDR and waveguide, as another important factor, also has an impact on the coupling efficiency between WGM and waveguide mode, and the coupling efficiency becomes lower as the gap enlarged.
Fig. 6. Effective indices of WGM1 (red lines) and WGM2 (blue lines) as a function of wavelength, insets: effective index of TM0 mode (black lines) in the waveguide as a function of width at the wavelength of 1550 nm, and the Ey field profiles of WGM1, WGM2, and TM0 mode. The solid and dashed lines are for slab thicknesses of 40 nm and 80 nm, respectively.
#200486 - $15.00 USD Received 30 Oct 2013; revised 19 Jan 2014; accepted 28 Jan 2014; published 4 Feb 2014 (C) 2014 OSA 10 February 2014 | Vol. 22, No. 3 | DOI:10.1364/OE.22.003219 | OPTICS EXPRESS 3225
5. Experiment and discussion MDRs with one bus and two buses coupled were fabricated on a SOI wafer with a 340-nmthick top silicon layer and a 2-μm-thick buried oxide layer. The fine pattern was defined by electron beam lithography, followed by inductively coupled plasma etching with a depth of 300 nm. The radius of MDR is 3 μm, and the waveguide width is 290 nm. On the basis of measured structure dimensions, the effective indices of TM-polarized WGM1, WGM2 and TM0 mode in waveguide are evaluated to be about 2.35, 2.00, and 2.18 at 1550-nm wavelength, respectively, indicating comparable k12 and k22 due to mode matching. For speculating the power attenuation and coupling efficiency, transmissions of one-bus waveguide coupled MDRs are measured and analyzed for different gaps. Figure 7(a) and 7(b) show the measured power transmissions for gaps of 180 nm and 270 nm, respectively. It is seen that two low-order WGMs are excited by the bus waveguide and exhibit comparable resonance linewidths. The influence of roughness-induced backscattering is neglectable here, since the resonance splitting is hardly observed in the spectra, except the resonance of WGM1 near 1488 nm for the gap of 180 nm. Using the proposed model, the fitting curves are given and agree well with the experimental results, as seen in the insets of Fig. 7(a) and 7(b). The fitting parameters are obtained as follows: for a gap of 180 nm, we have k12 = 0.031, k22 = 0.048, α12 = 0.990 and α22 = 0.981; and for a gap of 270 nm, we have k12 = 0.004, k22 = 0.011, α12 = 0.989 and α22 = 0.981. As the quality factors of two WGMs are on the same order of magnitude, the one-bus waveguide coupled MDRs do not behavior as reported in literatures [20,21].
Fig. 7. (a) The measured power transmission for a gap of 180 nm, inset: experimental results (blue circles) and theoretical fitting (red line), and a SEM image. (b) The measured power transmission for a gap of 270 nm, inset: experimental results (blue circles) and theoretical fitting (red line).
As shown in Fig. 1(b), a two-bus waveguides coupled MDR with a gap of 180 nm was fabricated and characterized. It is observed that a narrow EIT-like transparency window appears between two broader dips around the wavelength of 1546 nm, with central transmission larger than 0.65, and a central bandwidth of 0.37 nm, corresponding to a quality factor of 4,200. The theoretical fitting in Fig. 8 exhibits good agreement with the experiment, when we set k12 = 0.031, k22 = 0.048, α12 = 0.990, α22 = 0.981, neff1 = 2.37917 and neff2 = 2.04998. It shows a good internal consistency with the result of one-bus waveguide coupled MDR with the same dimensions. Note that a blueshift of the resonant spectrum occurs as compared with the spectrum in the inset of Fig. 7 (a), due to the additional phase shift in the 3
#200486 - $15.00 USD Received 30 Oct 2013; revised 19 Jan 2014; accepted 28 Jan 2014; published 4 Feb 2014 (C) 2014 OSA 10 February 2014 | Vol. 22, No. 3 | DOI:10.1364/OE.22.003219 | OPTICS EXPRESS 3226
× 3 coupler at the drop channel [28]. The experimental results confirm that two-bus waveguides coupled MDR with two WGMs coupled in a point-to-point manner is required for EIT-like effect. Making use of the two modes in a MDR, this structure offers us another way to achieve EIT-like effect on a chip, and it is more compact than conventional coupled double resonators, as the resonator number is decreased by a half.
Fig. 8. The measured power transmission (blue circles) and theoretical fitting (red line) of the fabricated two-bus waveguides coupled MDR.
6. Conclusion In summary, EIT-like effect has been demonstrated theoretically and experimentally in a fully integrated MDR coupled with two buses. The structure is modeled and EIT-like spectral response is found to originate from the destructive interference between two nearby resonances of low-order WGMs with comparable quality factors. The influencing factors of EIT-like effect have been studied, including coupling efficiency, round-trip power attenuation, and phase spacing. EIT-like resonance is experimentally observed in an ultracompact and fully integrated MDR of 3 μm in radius on a SOI platform with a quality factor of 4,200 and central transmission larger than 0.65. The experimental result agrees with our modeling well. It is approved that two buses coupled are required for a two-mode MDR to obtain EIT-like effect. Due to the compactness and integratability, the proposed device is promising for applications in on-chip time delay lines and nonlinear signal processing. Acknowledgments This work was supported by the National Natural Science Foundation of China under Grants 61006045 and 61177049, by the Major State Research Program of China under Grant 2013CB933303, and by the Major State Basic Research Development Program of China under Grants 2013CB632104 and 2010CB923204.
#200486 - $15.00 USD Received 30 Oct 2013; revised 19 Jan 2014; accepted 28 Jan 2014; published 4 Feb 2014 (C) 2014 OSA 10 February 2014 | Vol. 22, No. 3 | DOI:10.1364/OE.22.003219 | OPTICS EXPRESS 3227
