## Abstract

We experimentally demonstrate coupled-resonator-induced-transparency (CRIT) phenomenon in ring-bus-ring (RBR) geometry synergistically integrated with Mach-Zehnder interferometer (MZI). The RBR consists of two detuned resonators indirectly coupled through a center bus waveguide. The transparency is obtained by increasing the light intercavity interaction through tailoring the RBR phase response while ensuring balanced MZI operation. In this work, a CRIT resonance with a quality factor of ~18,000 is demonstrated with cavity size detuning of ~0.035% and power coupling of ~60%, which are in good agreement with the theory.

©2011 Optical Society of America

## 1. Introduction

Micro-ring resonator is a versatile optical component in integrated optics useful for realizing functionalities such as filters, sensors, modulators, and switches due to its resonance property and its on-chip compatibility with other planar integrated optics devices. Recent findings have indicated that the phenomenon analogous to electromagnetically induced transparency (EIT) in atomic systems can also be found in the whispering-gallery mode resonators, commonly termed as coupled resonator-induced transparency (CRIT) [1]. Several examples of CRIT in various optical resonator systems have been demonstrated in a cascade of two indirectly coupled ring resonators [2] and two mutually coupled microspheres [3], with observation of slowing group velocities and storing light capabilities [4]. For the case of EIT, the transparency window is caused by the reduced absorption, due to the quantum destructive interference between the transitions from the two dressed states, into a common energy level [5]. Similarly, the CRIT works by means of coherent interference between the two resonating modes which produces optical transparency inside the absorption window. The spectral characteristics of CRIT can be seen from the steep and positive linear increase of the phase response, which renders a medium or system transparent over a narrow spectral range within an absorption line. In practice, it is challenging to detune optical cavity for controlling of the resonant interaction between the two optical pathways. For instance, the cascade of two-indirectly coupled resonators [2] requires the ~8nm perimeter difference between the two rings, which normally is very challenging to control experimentally. On the other hand, other existing configuration based on other coupled resonators [1,3] proposed two almost identical resonators but with different coupling strength and cavity losses. Although the coupling strength can be controlled in a passive manner, however, active tuning is required for controlling cavity losses, which adds complexity in device fabrication and design. In the previous work [6], we theoretically proposed that CRIT transmission can be generated in ring-bus-ring (RBR) geometry. The RBR geometry consists of a waveguide sandwiched by two indirectly coupled ring resonators. The uniqueness of the proposed geometry compared to other systems is in the use of tri-coupler instead of conventionally used directional coupler.

The unique characteristic of CRIT is marked by a rapid increase linear phase in between two phase discontinuities, which, in amplitude spectrum directly translates into a transparency window between two resonant dips. Therefore, in order to generate the CRIT spectrum, a resonator system should be designed in such a way that such phase discontinuity is made possible. In the two mutually coupled resonator systems [1], the phase discontinuity is obtained when one of the resonators is tuned to under-coupling situation, where the cavity loss dominates the coupling strength. On the other hand, in the cascade of two indirectly coupled resonators [2], the phase discontinuity naturally occurs in the phase response of the through transmission (because in lossless case the transmission is zero, which then gives phase discontinuity). In the former, the transparency is obtained by adjusting the resonance splitting in between two resonators, while in the latter, the transparency is obtained by adjusting the resonance detuning between the two resonators. In our proposed geometry, the phase discontinuity is created by changing the sign of RBRMZI transmittance, which is accomplished by interference amongst two resonant pathways from the RBR on one arm with the non-resonant (or indirect) pathway from another arm [6]. The CRIT absorption window is emulated by the destructive interference between the two RBR rings (similar to the two dressed states in the EIT), whereas the CRIT transparency condition is made possible by the rapid increase of the device phase response (similar to the rapid change of index of refraction in the EIT) which further translates into sharp and narrow optical transparency within the absorption line. This paper aims to verify the validity of our previous theoretical paper [6], through a set of experimental demonstrations based on the silicon-on-insulator technology [7].

The outline of this paper is given as follows: A brief theory is presented in Section 2, the experimental results and some discussions are presented in Section 3. Lastly, the conclusion is given in Section 4.

## 2. Theory

More complete theoretical work on RBR geometry has been done in Ref [6], however for the sake of clarity, RBR is briefly theoretically discussed here. Using the properties of tri-coupler [6], the transmittance of RBR geometry can be written as follows,

*r*

_{1}

*A*

_{1}), ring 2 (

*r*

_{2}

*A*

_{2}), and the mixture of both (

*r*

_{0}

*A*

_{1}

*A*

_{2}). The term

*r*

_{1,2}(

*t*

_{1,2}) corresponds to the self-coupling (cross-coupling) term for each rings and the term r

_{0}corresponds the effective self-coupling of the tri-coupler (i.e., the center bus waveguide), which is related to

*r*

_{0}=2

*r*

_{1,2}-1. The term

*A*

_{1,2}=

*a*

_{1,2}exp(-

*i*δ

_{1,2}) accounts for roundtrip loss and phase of each rings [6]. Similar to the RBR transmission, the phase response and the related build-up factors are determined by the cavity size detuning (γ=δ

_{2}/δ

_{1}=

*L*

_{2}/

*L*

_{1}) and the inter-cavity coupling strength (

*r*

_{1,2}). The MZI transmission when RBR is incorporated into one of the arm then can be written as,

*ϕ*

_{RBR}is the RBR phase response and

*ϕ*

_{B }is the lumped phase imbalance between the two MZI arms. Note that the MZI phase imbalance term

*ϕ*

_{B }is needed to take account of the experimental non-idealities such as coupling induced phase shift (CIPS) [8]. The origin of the phase discontinuity in CRIT can be traced directly from the cosine argument in the MZI phase term of Eq. (2) where the change of sign in the amplitude spectrum (

*t*

_{MZI}) is followed by the π phase jump in

*ϕ*

_{MZI}. It also follows that the transparency peak corresponds to the condition where the effective roundtrip phase (δ

_{1}+δ

_{2})/2 is a multiple integers of π as the light being equally distributed in both rings. Apart from the optical losses, the overall CRIT characteristic in the RBRMZI is determined by the following parameters: (1) cavity size detuning γ, (2) coupling strength

*r*

_{1,2}, and (3) MZI phase imbalance

*ϕ*

_{B}. In principle, the cavity size detuning determines the locations of the MZI phase discontinuities, i.e., the location of the ring 1 (R1) and ring 2 (R2) resonances. The coupling strength determines the resonance linewidth of both rings, whereas the MZI phase imbalance determines the degree of asymmetricity of the Fano-lineshape of the CRIT, due to the associated CIPS in the tri-coupler [8].

## 3. Experimental results and discussions

Figure 1
shows the fabricated RBRMZI devices where the dimensions of each components is given as follows. The 3dB couplers in the MZI section are based on multi-mode interferometers (MMI) with a nominal width of 3.5μm and a length of 11.5μm with I/O tapers to reduce insertion loss. The first ring has a radius of 5µm with a racetrack coupler length of *L _{C}*~6µm, giving a total circumference of ~43.42μm. It should be noted that the coupling strength is changed by adjusting the gap separation between the rings and the center waveguides. This is done to prevent the change of resonance wavelength as a result of changing the coupler length. The measurement methodologies are briefly outlined as follows. To facilitate fiber input/output (I/O) coupling, vertical grating couplers are fabricated at both ends of each device. The fibers are butt-coupled to the grating couplers at 10° off vertical. The device transmission is then measured with an amplified spontaneous emission (ASE) broadband light source (1.41 to 1.62 μm) and an optical spectrum analyzer (OSA).In this experiment, we explored the change of gap separation (

*g*) and cavity size detuning (γ). Here three values of γ is chosen, namely 0.95, 1.0, and 1.05, while the gap separation is varied to 150 nm and 200 nm, totaling to 6 devices. Note that the above values are nominal and experimentally the values may be slightly shifted due to fabrication imperfection. The devices are grouped in two groups: the first group (DUT01-03) is when the devices are cladded with air, while the second group (DUT04-06) is when the devices are cladded with i-Line resist. The curve-fitting strategy is described as follows. First, the initial guess of the group index is deduced from the free-spectral range (FSR), resonant wavelength, and the cavity length, i.e. λ

^{2}/(FSR ×

*L*

_{CAV}), which then is readjusted to match the closest resonance order. It is found that the resonance order is 129 and 119, for the first and second group, respectively. Second, the coupling strength (

*r*

_{1}=

*r*

_{2}) is obtained from independent fitting of the drop transmission of one-ring-two-bus (1R2B) devices on the same chip (using the same gap separation and coupler length). Third, the initial guess of the MZI phase imbalance is deduced from fitting the transmission of RBRMZI with symmetric rings (γ~1), which makes it easier since the resonance is characterized only by a single-ring. Fourth, by matching the relative separation between the two resonances over three free spectral ranges (FSR), it is possible to find a combination of group index and cavity size detuning that will fit the experimental results. The third and fourth step can be repeated for fine-adjustments until the fitting converges. The measurements of gap separations and obtained fittings are summarized in Table 1 . The cavity power cavity loss is ~1% which is responsible to the slight reduced transmission in the transparency peak. The reduction in transmission peak becomes more prominent in sharper and narrower transparency resonances, due to the dispersive nature at the transparency condition.

It should be emphasized that in symmetric RBR structures (γ = 1), the effect of CIPS cancels off each other so as to make the deviation of γ caused by CIPS to be very small (if not zero). This is because the rings are identical and receive the same amount of induced phase shift, making the size detuning to be the same as the original one. This idea is strongly supported by the experimental findings summarized in Table 1, where the possibly fitted γ in symmetric case (DUT02 and DUT05) can be of both signs, which is accompanied by the change of group index. This strongly indicates that deviation of γ is random and closely related with the change of group index. Thus, the deviation of γ is in principle absent from symmetric structures but in practice may present due to other non-idealities such as ring nonuniformity from fabrication imperfection [9]. The coupling of the first group is weaker than those of the second group even though the gap separation is smaller, which is an indicative of weaker index contrast in i-Line resist cladded devices in the second group. Moreover, it seems that the measurements of the high-contrast index of the bare silicon devices suffer more noise than the resist coated counterparts. This is attributable to stronger reflection in the I/O gratings due to higher index contrast in bare silicon devices, which gives additional loss in the measurement results.

Lastly, the advantage of the synergistic integration of RBR with MZI can also be seen from DUT 02 where a CRIT resonance with finesse value of ~70 (2.8 × higher) is achieved using relatively lower finesse rings ~25. For other cases like DUT 01, 03, 04, 06, the ring resonances are detuned further away form each other, resulting in weaker cavity interaction between the two resonators. Based on the fitting of the asymmetric Fano resonance, we estimate a lumped MZI arm phase imbalance of +0.35π for DUT 02 and −0.8π for DUT 05. The MZI phase imbalance of the asymmetric RBR counterparts is not far off from the symmetric ones. The general spectral responses in Fig. 2(b) (DUT 01 to 03) are characteristically an inverted version from those in Fig. 2(a) (DUT 04 to 06), due to ~π phase difference in the MZI phase imbalance between them (see Table 1). Apart from the measurement results shown in Fig. 2, we have done more device measurements and collected the Q-factors of the CRIT resonance in Fig. 3 . Based on the results, it is clear that the highest Q-factor is achieved when the designated γ is almost unity. This is consistent with our earlier point which states that the coupling induces phase shift is almost canceled in the symmetric RBR and a very slight deviation of cavity size detuning can give rise to very sharp CRIT resonance. Based on the gathered results, we estimate that ~0.035% cavity size deviation (with ~60% power coupling and ~1% cavity power loss) is sufficient for generating CRIT resonance with Q-factors more than 18,000.

To obtain better understanding of the design parameter variations, Fig. 4(a)
shows the theoretical contour plot of the calculated finesse and the calculated background envelope linewidth outside the transparency band, as a function of coupling strength and cavity size detuning, assuming lossless case and balanced MZI. Figure 4(b) shows the corresponding MZI transmission and the RBR phase response for three different cases (A to C). It is evident that by increasing the coupling strength, the CRIT resonance becomes more distinct as shown by the increased transparency finesse as the background envelope is suppressed. Case (A) in Fig. 4 shows the simulated case with r_{0} = +0.75 where the RBR phase jump of (2 × 2π) is derived mainly from the resonant phase contribution of the two rings which in turn results in stronger background envelope (Δδ_{1/2}/2π~0.1). This is to be contrasted to case (C) where r_{0} is negative (−0.75) and the finesse is increased by one order of magnitude (39 ×) [two order of magnitude means >100 × ]. Here, the RBR phase jump is dominated by a sharper non-resonant tri-coupler phase jump (4 × π/2) and is more localized towards the resonant order δ_{1}/2π = 121 [6] whereas the background linewidth outside the transparency is increased by 9 times (Δδ_{1/2}/2π~0.9). For completeness, we show an intermediate case (B) where *r*
_{0}~0 brings out a moderately high finesse value of ~274. The background envelope (Δδ_{1/2}/2π~0.5) is the most sinusoidal in comparison to other r_{0} values. Based on the trend, it is more desirable to operate with strong coupling condition (low finesse resonators) for obtaining the most optimized CRIT condition while ensuring balanced MZI.

## 4. Conclusion

We have demonstrated RBRMZI capable of generating narrow CRIT resonance by means of synergistic integration of the RBR geometry with the MZI device on SOI material platform. In contrast to other existing CRIT schemes, the CRIT in RBRMZI is generated through phase engineering facilitated by inter-pathway interference in RBR and MZI structure. This leads to CRIT or absorption using low-finesse resonators, which is qualitatively different from other existing schemes that require high-finesse resonators. We demonstrated a CRIT resonance with a Q-factor of ~18,000 using cavity size deviation of ~0.035% and power coupling of ~60%. It is interesting to note that similar transparency effect was also found in a plasmonic system with relatively similar geometry [10].

## Acknowledgments

This work is supported by Ministry of Education (ARC 16/07), National Research Foundation (NRF-G-CRP 2007-01), Singapore and Asian Office of Aerospace Research. The authors would like to thank Dr. Pieter Dumon for consolidating the SOI device fabrication and Mr. Zhang Yanbing for his kind assistance in device measurements.

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