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Abstract
We propose and demonstrate an on-chip coupling resonant system to generate electromagnetically induced transparency (EIT)-like effect and Fano resonance on silicon platform. It is composed of a microring resonator (MRR) and two cascaded Sagnac-loop mirrors (SLMs) assisted Fabry–Perot (FP) cavity on silicon-on-insulator. According to the coupling conditions of the MRR, two cases are studied theoretically. When the MRR is over coupling, EIT-like transmission can be observed. In contrast, Fano resonances can be generated by the condition of under coupling. In the experiment, the add-drop MRR is under coupling, leading to a sharp asymmetric line shape for Fano resonance. The resonance wavelength of the MRR can be dynamically tuned based on thermal-optic effects by tuning the micro-heater. The experiment results show Fano resonances with maximum extinction ratio (ER) of 23.22 dB and maximum slope rate (SR) of 252 dB/nm. Moreover, the wavelength of Fano resonance can be shifted widely with a tuning efficiency of 0.2335 nm/mW.
© 2017 Optical Society of America
1. Introduction
Both electromagnetically induced transparency (EIT) and Fano resonance originate from atomic systems [1, 2]. They have attracted considerable research interests in the past decades due to their unique characteristics. The on-chip realization of EIT-like effects and Fano resonances on a compact integrated platform makes a step forward for slow and fast light [3], modulation [4, 5], optical signal processing [6], and high-sensitivity sensing [7, 8]. 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, can be also generated by coherent interference between coupled resonant modes. Classic all-optical analogies to EIT have been realized in various configurations of coupled two resonators, including microring [9, 10], self-coupled optical waveguide resonator [11], photonic crystal microcavities [12], plasmonic nanostructures [13], and metamaterials [14].
Unlike a conventional Lorentz resonance with a symmetric line shape, Fano resonance has an asymmetric line shape, which is ascribed to the interference between a discrete localized state and a continuum state. Considerable works have been reported to achieve a sharp asymmetric Fano resonance theoretically and experimentally on silicon-on-insulator [15–17]. For example, a steep-slope Fano resonance with extinction ratio (ER) of 7.3 dB and slope rate (SR) above 5 dB/nm was observed by using a tiny photonic crystal nanobeam cavity coupled to a waveguide Fabry-Perot (FP) resonator [15]. Obviously, the performance imposes limitations in the practical applications where a Fano resonance with a very sharp line shape is required. Recently, EIT-like effect and Fano resonance were both achieved by using the same structure, which is a grating-based Fabry–Perot (FP) cavity-coupled microring resonator (MRR) on a silicon chip [16, 17]. When the microring is over coupling, EIT-like transmission with an extinction ratio (ER) of 12 dB, a full-width-at-half-maximum (FWHM) of 0.077 nm and a quality factor (Q factor) of 20200 was achieved. In contrast, an optically tunable Fano resonance with a high extinction ratio of 22.54 dB and a large slope rate of 250.4 dB/nm was realized by the condition of under coupling. However, the grating-based FP cavity has only one fixed resonance wavelength, leading to a limited operation bandwidth. Additionally, Bragg gratings are sensitive to grating period, chirp, and etch depth, which are all key parameters that need to be precisely controlled, making it quite challenging to obtain the desired transmission line shape. Furthermore, the nonlinear thermal-optic effect induced maximum tuning range of Fano resonance is also very limited. In this scenario, a laudable goal would be to develop compact tunable photonic integrated devices on silicon platform with enhanced flexibility. It has been reported much that tunable silicon Fabry–Perot comb filters are formed by two cascaded Sagnac-loop mirrors (SLM) [18, 19].
In this paper, a SLM-assisted FP cavity-coupled MRR is employed to realize a tunable EIT-like effect and Fano resonance. According to the coupling condition between microring resonator and FP cavity, both EIT-like effect and Fano resonance are discussed and analyzed. Based on silicon platform, a coupling resonant system including FP cavity-coupled add-drop MRR is fabricated to achieve tunable Fano resonance. In the experiment, Fano resonances with high ER and SR are observed.
2. Concept and operation principle
As shown in Fig. 1(a), the side-coupled waveguide resonator system is implemented by using an FP cavity coupled MRR. By controlling the interference between the MRR and the FP cavity, EIT-like effect and Fano resonance can be generated selectively. To operate in a wider bandwidth range, FP cavity is composed of two cascaded SLMs, having fixed transmission and reflection coefficients over a wide bandwidth, as shown in Fig. 1(b). The resonance wavelength of the add-drop MRR can be dynamically changed based on thermal-optic effects by tuning the micro-heater. According to the coupling conditions of the add-drop MRR, two cases are considered and discussed theoretically. When the MRR is over coupling, an abrupt phase shift is introduced to the light in the MRR, and an EIT-like transmission line can be achieved. On the contrary, Fano resonance can be obtained when the MRR is under coupling (0 phase shift at the resonant wavelength). According to the transfer matrix method, the field transmission and reflection functions of the same two SLMs can be written by
where t and k are the transmission and coupling coefficients of the directional couplers of the SLMs, a1 is the loss factor of SLM, l1 is the length of SLM, and β is the propagation constant of silicon waveguide, which is determined by the group index ng. Total reflection can be reached when the couplers are ideal 3 dB couplers (t2 = κ2 = 0.5). The propagation constant and transmission function of the MRR can be given by where t1 and t2 are the transmission coefficients for add-port coupling and drop-port coupling, respectively. . α, βMRR and nMRR are the loss factor of MRR, the propagation constant of MRR, and the group index of MRR, respectively. LMRR is the circumference of the MRR (related to the radius of the MRR). With tslm, rslm and tMRR, the field transmission function of the coupling resonant system can be expressed aswhere a2 is the loss factor along the cavity length l2. The normalized intensity response of the resonant system can be described byIn the simulations, two cases are considered and discussed as mentioned above: over coupling for EIT-like effect and under coupling for Fano resonance. As shown in Eq. (4), it is the product αt2 (α: loss factor of MRR, t2: drop-port coupling coefficient of MRR) and t1 (add-port coupling coefficient of MRR) that influence the transmission function of the MRR. For a given t1, if the product αt2 is constant (coupling induced phase shift is not considered herein), the transmission function does not change. By comparing the coupling coefficient t1 of add port and the product αt2 of the loss factor α and the coupling coefficient t2 of drop port, over coupling (satisfying t1 < αt2) and under coupling (satisfying t1 > αt2) are determined, respectively. The transmission coefficient of the directional coupler t is set to be 0.68 and satisfies t2 + k2 = 1. The loss factor of silicon waveguide is assessed to be 10.16 dB/cm. The radius of the MRR is 10 μm. The group index ng and nMRR are 4.2 and 4.05, respectively. According to the fabricated device, the SLM length l1 and FP cavity length l2 are assessed to be 89.8 μm and 39.62 μm, respectively.
Fig. 1 (a) Schematic structure for the interference between the MRR and FP cavity. (b) Schematic illustration of tunable EIT-like and Fano transmissions based on SLM-assisted FP cavity-coupled MRR. MRR: microring resonator. SLM: Sagnac-loop mirror. (c) Measured microphotograph of the fabricated coupling resonant structure. (d) Details of the main region.
3. Simulation results
First, the over coupling (satisfying t1 < αt2, t1 = 0.90, αt2 = 0.99) for EIT-like transmission is analyzed in Figs. 2(a) and 2(b). Compared to under coupling, the over coupling for the MRR has a larger phase transition at the resonance wavelength, leading to a narrow transparency peak residing in a broader absorption valley. By tuning the micro-heater, the resonance wavelength can be moved as shown in Fig. 2(b). In the simulations, the refractive index of the phase shifter is nMRR + Δn with Δn representing the change of the refractive index. When Δn is set to be different values (1.1 × 10−3, 1.55 × 10−3 and 2 × 10−3), the center wavelength of the MRR can be moved to 1530.025 nm, 1530.180 nm, and 1530.337 nm, respectively. The EIT-like line shape (green curve in Fig. 2(b)) with an ER of 12.69 dB and a FWHM of 0.031 nm can be achieved. By adjusting the product αt2 from 0.96 to 0.99, the line shapes with different ERs at the wavelength of 1530.180 nm in Fig. 2(c) and 1530.337 nm in Fig. 2(d) can be observed, respectively. One can clearly see that a larger product αt2 results in an enhanced ER and a smaller FWHM. When changing the product αt2 from 0.96 to 0.99, ER increases from 1.55 to 12.56 dB in Fig. 2(c). Similar results at the wavelength of 1530.337 nm are presented in Fig. 2(d).
Fig. 2 (a) Simulated transmission spectra for EIT-like effect with changed resonance wavelengths of the MRR. (b) Zoom-in view of EIT-like transmission. (c)(d) Simulated transmission spectra for different EIT-like line shape with tunable ERs when the product αt2 is changed.
Subsequently, the under coupling (satisfying t1 > αt2, t1 = 0.996, αt2 = 0.99) for Fano resonance is depicted in Figs. 3(a) and 3(b). The coupling between the two resonant modes of the MRR and the FP cavity determines the line shape of Fano resonance. When Δn is set to be different values (1.1 × 10−3, 1.55 × 10−3 and 2 × 10−3), the center wavelength of the MRR can be moved to 1530.012 nm, 1530.181 nm, and 1530.350 nm, respectively. Figure 3(b) shows a zoom-in view of the co-locating part, which exhibits an asymmetrical line shape. When the MRR and FP cavity have the same resonance wavelength (the green line shape in Figs. 3(a) and 3(b)), maximum ER of 24.17 dB can be obtained. When the resonant wavelength of MRR moves away from the FP cavity peak, ER begins to decrease. Similar to Figs. 2(c) and 2(d), the line shapes with different ERs at the wavelength of 1530.181 nm in Fig. 3(c) and 1530.350 nm in Fig. 3(d) are presented. As can be seen, both ER and SR become larger with the increase of the product αt2.
Fig. 3 (a) Simulated transmission spectra for Fano resonance with changed resonance wavelengths of MRR. (b) Zoom-in view of Fano resonance. (c)(d) Simulated transmission spectra for different Fano resonance line shape with tunable ERs when the product αt2 is changed.
4. Experiment and discussion
Figure 1(c) shows the microphotograph of the fabricated silicon photonic device including vertical gratings, micro-heaters and an add-drop MRR coupled with a FP cavity. The proposed resonant system is fabricated by the electron beam lithography (EBL) and inductively coupled plasma (ICP) etching. The grating coupler is fan-shaped and the etch depth is 70 nm. After 900-nm-thick buried oxide deposition, 50-nm-thick nickel-chromium alloy (NiCr) heaters and 190-nm-thick gold metal along the MRR are all deposited. The width of silicon strip waveguide both for the MRR and the straight waveguide, the width of heater, and the radius of the MRR are designed to be 500 nm, 2 μm and 10 µm, respectively. The free spectral range (FSR) of the MRR is about 9.5 nm. The directional 2 × 2 coupler has a coupling length of 13.5 μm and the reflection of SLMs is assessed to be ~0.95. The gaps between the MRR and the straight waveguides are both 200 nm, leading to an under coupling (satisfying t1 > αt2). Hence, tunable Fano resonance can be observed in the experiment. The details of the main region are shown in Fig. 1(d). An amplified spontaneous emission (ASE) light source and an optical spectrum analyzer are employed to measure the spectral response of the fabricated silicon photonic device. Fiber-chip/chip-fiber vertical coupling is employed for TE polarization. The vertical coupling loss is measured to be ~12 dB.
The measured spectral responses of the Fano resonance with different heating power are shown in Fig. 4. The measured channel spacing and bandwidth of the FP cavity are 2.04 nm and 0.059 nm, giving a quality factor of ~26000. The quality factor of the MRR is assessed to be ~7600 at a wavelength of 1530.21 nm. A narrow dip is formed on the left of an FP resonance peak, as shown in Fig. 4(a). The resonance wavelength of the MRR is tuned to 1529.829 nm, 1529.891 nm, 1529.952 nm and 1530.016 nm, respectively, when adjusting the heating power from 0 to 0.9 mW with an interval of 0.3 mW. Figure 4(b) shows a zoom-in view, which shows a clear asymmetrical line shape with gradually varied ERs (11.20 dB, 13.05 dB, 14.50 dB, 17.65 dB) and almost unchanged SRs (~252 dB/nm). With the heating power of 1.8 mW on the micro-heater, the resonance wavelength of the MRR locates right at the FP cavity peak, as shown in Figs. 4(c) and 4(d). In such case, maximum ER of 23.22 dB can be obtained and the corresponding SR is 179.4 dB/nm. In particular, in addition to the simulation results in Fig. 3, according to the device design and experimental results, we also get the optimized theoretical transmission spectra (red line) in Figs. 4(c) and 4(d). The theoretical results are in good agreement with the experimental ones. By fitting, we get t = 0.68, a1 = 0.97, a2 = 0.99, t1 = t2 = 0.9934 and α = 0.9923, respectively. For the loss factor a1 and a2, they are fixed values dependent on the device design and the fabricated process. Obviously, larger cavity loss (e.g. the loss factor a1 of SLM and the loss factor a2 along the cavity length l2) may lead to decreased ER and SR of Fano resonance and larger insertion loss of the device [19]. By increasing the heating power from 2.5 mW to 4 mW with an interval of 0.5 mW on the micro-heater along the MRR, the resonance wavelength of the MRR moves to the left of the FP cavity peak, as shown in Figs. 4(e) and 4(f). Moreover, the resonance wavelength of the MRR can be tuned in a wider range of wavelength by further increasing the heating power. As shown in Fig. 5, the center wavelength of the MRR is depicted as a function of the heating power. By increasing the heating power from 0 to 16 mW, the Fano resonance dip shifts uniformly from 1530 nm to 1533.6 nm. Though linear fitting, the tuning efficiency of the center wavelength is assessed to be ~0.2335 nm/mW.
Fig. 4 Measured transmission spectra for Fano resonance with changed resonance wavelengths of MRR. The resonance wavelength of MRR locates (a) on the left, (c) in the middle, and (e) on the right of the FP cavity peak. (b)(d)(f) Zoom-in views corresponding to (a)(c)(e), respectively.
Fig. 5 Measured wavelength shift of MRR versus heating power applied to micro-heater and the linear fit curve.
Based on the interference between the MRR and the FP cavity, tunable EIT-like effect and Fano resonance are both investigated theoretically. Moreover, Fano resonance is achieved experimentally by fabricating a coupling resonant system on silicon platform. The resonance wavelength of the MRR can be dynamically tuned based on thermal-optic effects by tuning the micro-heater. Such a resonant coupling structure provides a feasible approach to realize flexible Fano resonance. Compared to previous works [15–17], SLM-assisted FP cavity could operate in a wider wavelength range. Tuned asymmetric line shapes with different ERs can be obtained by adjusting the micro-heater along the MRR. With further improvement, the micro-heater can be fabricated along the FP cavity to tune the resonance peak. In such case, the resonances of the MRR and the FP cavity can both cover a wider wavelength range. The coupling between the MRR and the FP cavity could be replaced by a tunable Mach-Zehnder interferometer (MZI) coupler [20], leading to a switch between the EIT-like effect and Fano resonance. Moreover, thermo-optic effect and electro-optic effect (reverse biased p-n diodes or forward-biased p-i-n diodes) [21–27] might be combined together to enable superior tuning performance [27]. In addition, further optimizations of the vertical coupling grating and the etching process can be considered to reduce the insert loss [28].
5. Conclusion
In summary, we present an on-chip coupling resonant system to generate EIT-like effect and Fano resonance on silicon platform. In the device, an add-drop MRR is employed, and one of the two bus waveguides is replaced by an FP cavity consisting of SLMs. According to the coupling conditions of the MRR, both tunable EIT-like effect and Fano resonance are theoretically analyzed. In the experiment, tunable Fano resonances with maximum ER of 23.22 dB and maximum SR of 252 dB/nm are achieved, and the wavelength of Fano resonance can be shifted widely with a tuning efficiency of 0.2335 nm/mW. The demonstrated on-chip resonant coupling structure has a great potential for implementing ultracompact and ultralow power consumption optical switching/modulation and high performance sensing applications.
Funding
National Natural Science Foundation of China (NSFC) (61761130082, 11774116, 11690031, 61222502, 11574001 and 11274131); National Program for Support of Top-notch Young Professionals; Royal Society-Newton Advanced Fellowship; National Basic Research Program of China (973 Program) (2014CB340004); Yangtze River Excellent Young Scholars Program; Program for New Century Excellent Talents in University (NCET-11-0182).
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