## Abstract

In this paper, a single microring resonator structure formed by incorporating a reflectivity-tunable loop mirror is demonstrated for the tuning of resonance spacing. Autler-Townes splitting in the resonator is utilized to tune the spacing between two adjacent resonances by controlling the strength of coupling between the two counter-propagating degenerate modes in the microring resonator. A theoretical model based on the transfer matrix method is built to analyze the device. The theoretical analysis indicates that the resonance spacing can be tuned from zero to one free spectral range (FSR). In experiment, by integrating metallic microheater, the tuning of resonance spacing in the range of the whole FSR (1.17 nm) is achieved within 9.82 mW heating power dissipation. The device has potential for applications in reconfigurable optical filtering and microwave photonics.

© 2015 Optical Society of America

## 1. Introduction

Autler-Townes splitting (ATS) [1] in the photonic devices based on traveling-wave resonators (TWRs) is attracting interest in a variety of application areas, including optical signal processing [2], slow/fast light [3], biological/chemical sensing [4] and microwave photonics [5,6 ]. ATS originates from the lifting of degeneracy induced by the coupling between the frequency-degenerate resonant modes of one or more TWRs [7,8 ]. The degeneracy is lifted to split the resonance into a doublet in frequency. The level of splitting (i.e., resonance spacing of the doublet) depends on the strength of coupling between the degenerate modes. This feature can be utilized to realize the tuning of the spacing between two adjacent resonances.

The tuning of resonance spacing is a desirable functionality for many applications in nonlinear optics [9–11 ], reconfigurable optical filtering and microwave photonics. In conventional TWRs, adjacent resonance modes are separated by the fixed free spectral range (FSR), and shifted for the same amount when tuning the refractive index, leading to an unchanged resonance spacing. An approach to tune the resonance spacing based on the ATS in two coupled microrings have been reported by Atabaki et al. [12]. A tuning range covering 20 percent of the FSR is experimentally demonstrated. However, in order to get two frequency-degenerate resonant modes, the resonance frequencies of the two microrings need to be carefully aligned, which usually requires a post-fabrication trimming or a power-consuming tuning. ATS can also occur in a single microring resonator via the mutual coupling between the clockwise and counterclockwise propagating modes. Since these two counter-propagating modes share the same physical cavity, their resonance frequencies are inherently degenerate. By controlling the coupling strength between these two degenerate modes, the tuning of resonance spacing based on the ATS in a single microring can be realized.

In previous reports, the coupling between the two counter-propagating degenerate modes is usually obtained by introducing nanometer-scaled periodic grating to the sidewall of the microring [2,3,13
]. Such fine grating structures require high accuracy of manufacture and cannot be easily tuned once fabricated. Here, to exactly tune the strength of coupling between the two counter-propagating degenerate modes, a reflectivity-tunable loop mirror is employed to replace the periodic grating. In this paper, we demonstrate a resonance spacing-tunable single microring resonator by incorporating a reflectivity-tunable loop mirror. An analytical model based on the transfer matrix method is established to describe this device. The tuning of resonance spacing over the whole FSR is experimentally demonstrated. After the submission we become aware that very recently Wu *et al.* proposed a similar device structure to work as a tunable second-order photonic differential-equation solver [14]. Although the resonator structures are similar, there are different focuses between these two reports. Our report contributes to the demonstration of the tuning of resonance spacing over the whole FSR and in our experiment, a larger tuning range is obtained with a lower power dissipation.

## 2. Device structure and theoretical analysis

For simplicity in the analysis, a reflective element model is used to represent the reflectivity-tunable loop mirror in the device structure. Figure 1(a) shows the structure of a single microring with a reflective element. The transfer matrix method is utilized to analyze this structure [15, 16 ]. The reflective element can be characterized with a scattering matrix $\text{S}=\left(\begin{array}{cc}{S}_{11}& {S}_{12}\\ {S}_{21}& {S}_{22}\end{array}\right)$. Assuming that the reflective element is lossless and reciprocal, the scattering matrix can be written as

which satisfies the lossless condition ${\text{S}}^{\u2020}\text{S}=\text{I}$ and the reciprocity condition*S*

_{12}=

*S*

_{21}. Here,

*r*and

*t*represent the magnitude of the reflection and transmission coefficients of the reflective element, respectively, and

*r*

^{2}+

*t*

^{2}= 1.

*ϕ*is the transmission phase shift of the reflective element and

*ψ*is the relative phase term.

Combining with the coupling matrix $\left(\begin{array}{cc}\tau & i\kappa \\ i\kappa & \tau \end{array}\right)$ of the evanescent coupling region, the steady state solution of the transmitted field in the through channel can be obtained in the case of normalized input (*a*
_{1} = 1),

*τ*

^{2}+

*κ*

^{2}= 1 is assumed.

*α*and

*θ*are the field propagation factor and transmission phase shift in the ring excluding the reflective element, respectively. By solving Eq. (2), the normalized transmission spectra for different values of

_{t}*t*can be calculated. In the calculation,

*α*= 0.94 and

*τ*= 0.91 are taken as an example. The resonances of the microring resonator significantly split for strong reflection of the reflective element. Figure 1(b) shows the amount of resonance frequency splitting normalized to the FSR of the microring resonator versus the transmission factor of the reflective element

*t*. It indicates that as

*t*decreases from 1, the initial frequency-degenerate modes split and reach the maximum splitting of one whole FSR for

*t*= −1.

Figure 1(c), 1(d) and 1(e) plot the transmission spectra of the microring resonator for three key values of *t* = 1, *t* = 0, and *t* = −1, respectively. The horizontal axes is the frequency detuning with respect to one of the resonance modes of the microring resonator normalized to the FSR. Note that the parameters *α* and *τ* have been assumed to be frequency independent in analysis. One can easily extend the analysis to obtain a more accurate model involving spectrally varying parameters. When *t* = 1 for the reflective element, no reflection occurs in the resonator. Hence, the resonator structure acts like a conventional microring resonator and there is no resonance frequency splitting. As *t* decreases, the coupling between the two counter-propagating degenerate modes is induced by the reflection of the reflective element. The resonances split to doublets due to the lifting of the degeneracy. When *t* = 0, the reflective element provides a complete reflection. In each round-trip, electromagnetic field in the microring resonator travels through the resonator structure twice due to the clockwise and counterclockwise propagation. As a result, the FSR of the resonator is reduced to the half. Additionally, a phase shift of π is introduced by the reflective element, which is indicated by the opposite signs of *S*
_{11} and *S*
_{22}. Due to the additional phase of π, the resonances are shifted by half of an FSR. Note that at *t* = 1, both *S*
_{11} and *S*
_{22} equal to 0 and thus no additional phase is introduced. When *t* decreases to −1, the reflective element provides a complete transmission as the case of *t* = 1. However, compared to the case of *t* = 1, an additional phase of π is introduced in the round-trip phase at *t* = −1. Thus, the resonances are shifted by half of the FSR with respect to the case of *t* = 1, as shown in Fig. 1(e). By observing the evolution of resonance modes in Figs. 1(c) to 1(e), it is found that two splitting supermodes are formed and move in opposite directions as *t* decreases. It is noted that the resonance splits for one whole FSR when *t* decreases from 1 to −1. The arrows in Fig. 1(d) show the directions of the shift in the splitting supermodes. As the amount of resonance splitting increases, the splitting supermodes always show an identical full width at half maximum (FWHM) to that of the unsplit resonance at *t* = 1, as predicted by the previously reported theoretical analysis for the TWRS with backscattering [8, 17
]. The resonance linewidth is determined by *α* and *τ* which represent the intrinsic resonator loss and coupling strength between the resonator and bus waveguide respectively.

A reflectivity-tunable loop mirror can work as a tunable reflective element. A typical loop mirror is made of a single self-coupled waveguide [18]. By controlling the coupling coefficient in coupling region, the reflectivity of the loop mirror can be tuned in the full range from zero to one. An effective method to control the coupling coefficient is to use a Mach-Zehnder interferometer (MZI) as the coupler, as indicated by the red dashed box in Fig. 2(a)
. The MZI-coupler can provide precise and independent tuning of the coupling coefficient and transmission phase shift [19]. The differential phase shift between the two arms of the MZI-coupler tunes the coupling coefficient, while the common phase shift determines the transmission phase shift of the MZI-coupler. Here, *θ _{d}* and

*θ*are used to represent the differential and common phase shifts, respectively:

_{c}*θ*

_{Arm}_{1}and

*θ*

_{Arm}_{2}are the propagation phase shifts of the MZI arms denoted by Arm1 and Arm2 in Fig. 2(a), respectively. Provided that the MZI is driven in push-pull configuration, the differential phase shift

*θ*can be tuned arbitrarily while the common phase shift

_{d}*θ*

_{c}remains constant. Consequently, the coupling coefficient of the MZI-coupler can be tuned and the transmission phase shift remains invariant. One great advantage of this property is that the loop mirror based on the MZI-coupler, as shown in the blue dashed box in Fig. 2(a), can provide a tunable reflectivity and introduce a constant transmission phase delay independent of reflectivity tuning. Assuming that the two directional couplers in the MZI-coupler both have a 3-dB coupling efficiency, the scattering matrix of the MZI-loop mirror can be written as

*θ*is the phase delay in the loop mirror excluding the MZI-coupler. Comparing the scattering matrixes

_{l}**S**of the reflective element model and

**S**

*here, it is found that the transmission factor*

_{l}*t*= cos

*θ*, the reflection factor

_{d}*r*= sin

*θ*, the relative phase term

_{d}*ψ*= 0, and the total transmission phase delay

*ϕ*=

*θ*+

_{l}*θ*+ π. Figure 2(b) shows the magnitude of the transmission coefficient of the MZI-loop mirror

_{c}*t*versus the differential phase shift

*θ*. The value of

_{d}*t*is tunable between 1 and −1 through tuning

*θ*. By introducing such reflectivity-tunable loop mirror into a single ring resonator, a resonance spacing-tunable ring resonator can be realized, as shown in Fig. 2(a). According to the previous analysis, the resonance spacing can be tuned in the range from zero to one whole FSR.

_{d}In the above discussion, we assume that the two directional couplers in the MZI-coupler are identical and have a 3-dB power coupling efficiency. It should be noted that the power coupling coefficients (*κ _{D}*

^{2}) of these two directional couplers have a direct impact on the achievable tuning range of the resonance frequency splitting. Figure 3 shows the tuning ranges of the resonance splitting for different

*κ*

_{D}^{2}. It is observed that splitting occurs even when

*θ*= 0 if

_{d}*κ*

_{D}^{2}moves away from 0.5. Note that for the case of

*κ*

_{D}^{2}= 0.5, when

*θ*is close enough to 0, the corresponding resonance splitting is smaller than the linewidths of the resonances and thus cannot be observed. The resonance splitting of one whole FSR is observed when

_{d}*θ*is close enough to π for all the

_{d}*κ*

_{D}^{2}.

## 3. Experimental results

The single microring resonator structure with a MZI-loop mirror is fabricated on a silicon-on-insulator (SOI) platform with a 220-nm-thick top silicon layer and a 3-μm-thick buried oxide layer. The pattern of the device is defined on the ZEP520A resist using electron-beam lithography (Vistec EBPG 5000 Plus) and then transferred to the top Si layer by inductively-coupled-plasma (ICP) dry etching using SF_{6} and C_{4}F_{8} gases. To integrate microheaters for thermo-optical tuning, 1-μm-thick SiO_{2} upper cladding is deposited using plasma-enhanced chemical vapor deposition (PECVD) in order to optically isolate the waveguides from the metal heaters. Ti is chosen as the heater material because its resistivity leads to a relatively low current density [20]. 100-nm-thick Ti heaters and 150-nm-thick gold contact pads are formed by two lift-off processes. Figure 4
shows the scanning electron microscope (SEM) image of the fabricated device. The total length of the resonator structure is 480 μm and the two arms of the MZI-coupler are both 30 μm long. The two directional couplers used in the Mach-Zehnder interferometer are identical in design and have power coupling efficiencies around 0.5. Two separate Ti heaters (H1 and H2) are placed on the two MZI arms (Arm1 and Arm2) to control the differential and common phase shifts independently. However, limited by the number of our probe channels, only the heater H1 is driven in the measurement.

The transmission is measured by an optical characterization test setup [21]. TE-polarized light from a broadband amplified spontaneous emission (ASE) source is injected into the device and the output of the device is measured by an optical spectrum analyzer. Figure 5(a)
shows the optical transmission spectrum of the device without applying power to the heaters. Due to the zero differential phase shift between the two MZI arms and around 50% power coupling efficiencies of the directional couplers, no resonance splitting is observed in the spectrum. The measured transmission spectrum corresponds to the case of *t* = 1 shown in Fig. 1(c). The FSRs are about 1.17 nm and the extinction ratios (ERs) are about 18 dB. The FWHM of the resonance at 1534.62 nm is about 0.12 nm.

When driving the heater H1, the differential phase shift *θ _{d}* between the two MZI arms is no longer zero, and the reflection is induced by the MZI-loop mirror. As a result, the coupling between the two counter-propagating degenerate modes occurs, leading to the resonance splitting. Figure 5(b) shows the measured transmission spectrum with 4.58 mW heating power in heater H1, which is similar to the case presented in Fig. 1(d). The resonance spacing of 0.57 nm, which is about half of the FSR, is observed between the two splitting supermodes, indicating an almost complete reflection by the loop mirror. It is noted that the splitting supermodes exhibit smaller FWHMs and ERs than the resonance modes in Fig. 5(a). The FWHM of the splitting supermode at 1535.17 nm is about 0.1 nm. In the fabricated device, the coupling coefficients of the directional couplers are slightly deviated from 0.5 due to fabrication error. Therefore, a very small resonance splitting exists even if the differential phase shift is zero. The larger linewidths of the resonances in Fig. 5(a) are most likely due to this indistinguishable splitting [22]. The different levels of extinction can be attributed to the change of the critical coupling condition induced by the reflection. In the presence of reflection, the unidirectional transmission is lost, which would significantly alter the coupling properties [8]. When the heating power is increased to 9.82 mW, a resonance spacing of one whole FSR (1.17 nm) is obtained, as shown in Fig. 5(c), corresponding to the case of

*t*= −1 presented in Fig. 1(e). In this case, almost no reflection is provided by the MZI-loop mirror and the ERs increase.

It is noted that the center of the splitting supermodes red-shifts as the heating power in H1 increases. This is attributed to the change of the transmission phase shift of the MZI-coupler. In practice, by applying a direct-current (DC) voltage to both heaters (H1 and H2) simultaneously and then tuning the applied voltages of the two heaters inversely, the center of the splitting supermodes can be fixed while the resonance spacing is tuned. In this way, the transmission phase shift of the MZI-coupler can be kept constant while the differential phase shift *θ _{d}* is changed [19].

In order to get a better look at the tuning of resonance spacing when increasing the heating power, the measured transmission spectra for six different power dissipations are shown in Fig. 6(a) . The horizontal axis represents the wavelength detuning with respect to the centers of the splitting supermodes. The tuning of the resonance spacing between two splitting supermodes is achieved in the range from zero to one whole FSR. Figure 6(b) shows the change of the resonance spacing for different power dissipations in heater H1. It is expected that a resonance spacing between zero and one FSR can be obtained with a heating power no more than 9.82 mW. Note that the FSR, as the spectral period of resonance modes, is the maximum achievable resonance spacing. When the heating power is further increased from 9.82 mW, the resonance spacing will decrease from the FSR.

The experimental results show that the single ring resonator with a MZI-loop mirror can be used to tune the resonance spacing over the whole FSR by tuning the differential phase shift between the two MZI arms. Compared to the previous report based on two coupled microrings [12], our single ring resonator structure shows a larger tuning range with a lower power dissipation and does not require an additional trimming or tuning for the alignment of resonance frequencies between two microring resonators.

## 4. Discussion

In addition to the tuning of resonance spacing, the demonstrated single ring resonator structure also shows potential to achieve tunable resonance wavelength and bandwidth, and can be configured as a second-order filter. Here, based on the established equations, the case with *τ* = 0.8, *α* = 0.94 and *κ _{D}*

^{2}= 0.5 is theoretically investigated as an example.

Figure 7
shows the calculated transmission spectra of the resonator with different *θ _{d}*. It is observed that before the

*θ*is large enough to induce two distinguishable splitting supermodes, the bandwidth of the resonance mode can be tuned by changing the

_{d}*θ*and a second-order filter with a box-like spectral response can be obtained with a specified

_{d}*θ*. The change of the bandwidth can be attributed to the mode broadening induced by the indistinguishable splitting supermodes [22], as discussed above. The second-order filter response results from the coupling between the two counter-propagating modes and shows a flatter stopband and a faster roll off compared to the resonance mode of a conventional single ring resonator [23].

_{d}In the calculation, the transmission phase shift of the MZI-coupler is set to be constant while the differential phase shift *θ _{d}* is changed. Thus, the resonance wavelength keeps constant while the bandwidth is tuned. To tune the resonance wavelength, the same phase shift change can be introduced to the two MZI arms simultaneously. In this way, the transmission phase shift can be changed while

*θ*keeps constant. Thus, the resonance wavelength can be tuned while the bandwidth remains invariant. When the device is configured as a second-order filter, the resonance wavelength tuning of the device might be more power-efficient compared to that of the second-order filter consisting of two coupled microrings. This is because in the demonstrated resonator structure, both the clockwise and counterclockwise modes, which share the same physical cavity, can be tuned simultaneously. However, in the second-order filter consisting of two coupled microrings, each ring resonator needs to be tuned to shift its resonance wavelength to the desired location.

_{d}With the tunability in resonance spacing, bandwidth and resonance wavelength, and reconfigurability in filter response, the demonstrated resonator structure is promising for applications in reconfigurable optical filtering. Besides, the device has potential to be used as a microwave photonic notch filter with double-sideband intensity modulation. By locating the optical carrier at the center of two splitting supermodes and tuning the resonance splitting, the central frequency of the microwave notch filter is tunable. Compared to the previously reported solutions based on two cascaded microrings [24], only a single microring resonator is used and continuous tuning of the central frequency can be achieved.

## 5. Summary

In conclusion, we have demonstrated a resonance spacing-tunable single ring resonator device by incorporating a MZI-loop mirror. Based on the ATS effect, the spacing between two adjacent resonances can be tuned by controlling the coupling strength between the two counter-propagating degenerate modes in the resonator. By integrating microheaters on the arms of MZI, the tuning of resonance spacing from zero to the FSR of the resonator (1.17 nm) is experimentally achieved within 9.82 mW power dissipation in the microheater. To the best of our knowledge, this is the first demonstration of the tuning of resonance spacing over the whole FSR. The device is expected to have potential applications in reconfigurable optical filtering and microwave photonics.

## Acknowledgments

This work was partly supported by the Major State Basic Research Development Program of China (grant 2013CB632104 and 2013CB933303), the National Natural Science Foundation of China (grant 61335002 and 61177049), the National High Technology Research and Development Program of China (grant 2015AA016904), and the Program for New Century Excellent Talents in Ministry of Education of China (grant NCET-12-0218).

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