## Abstract

High speed coupling-modulation of a microring-based light drop structure is proposed, which removes severe signal distortion due to intracavity energy depletion and separates the modulation speed from the resonator linewidth restriction. Extinction ratio improvement from <1 dB to >20 dB with 40 Gb/s non-return-to-zero (NRZ) signals is obtained with 25 times smaller drive voltage. The tolerance to active ring propagation loss is increased from 5 dB/cm to over 25 dB/cm with less than 5% modulation bandwidth reduction. The possibility of obtaining 160 Gb/s NRZ signal with no more than 4 V drive voltage and less than 5 dB insertion loss is highlighted.

©2012 Optical Society of America

## 1. Introduction

Optical modulation is one of the most important functions of any optical communication system. Compared to Mach-Zehnder-Modulators (MZMs) [1], microring modulators enable larger scale integration, small capacitance and lower power consumption [2–5]. The figures of merit are operating bandwidth, signal quality and drive voltage [6–9].

Very recent progress has shown that RC constant as short as 1 ps can be achieved by using compact silicon-micro-resonator-based active elements [9]. Currently the fundamental limitation to the silicon micro resonator modulator's speed comes mainly from the optical domain. Typically, the intrinsic bandwidth of a single ring modulator (SRM) is limited by its photon lifetime which determines the speed that light is coupled in/out of the cavity. The photon lifetime limits the achievable modulation bandwidth to the resonance linewidth when the resonance shift is typically comparable to the resonance linewidth. The speed of most recent silicon micro-resonators-based modulators is limited within 10~20 GHz [6–9] due to the strict requirement on power consumption [10]. The modulator described in [11] is able to enhance bandwidth compared to an SRM by 80% but relies on low propagation loss in a small radius active ring, which is quite challenging. Recently, a theory of coupling modulation [12–15] was proposed for achieving very high bandwidth that is not constrained by photon lifetime, in which the waveguide-ring coupling in a single ring notch filter is modulated (defined here as a ‘notch design’, shown in Fig. 1(a) ). However, a few critical drawbacks exist in this design: (1) a long ‘1’ pattern leads to intra-cavity energy depletion, which removes the stable energy amplitude and induces severe pattern dependence; (2) relatively long arms of several hundred micrometers are needed to implement the coupling structure, which leads to a considerable capacitive loading [1,16]. Although the design proposed in [17] can help relieve the intra-cavity energy fluctuation problem in [14], it generates another two new problems: (1) compared to the notch design, it asks for two (instead of one) composite interferometers with the exactly the same structure to each other, which greatly increases the structure complexity; (2) since the design counts on extremely high cavity energy density to allow for small coupling modulation and short phase shifters, nearly lossless 3 dB couplers and phase shifters are demanded to implement the design, which is extremely challenging. A novel and practical modulation scheme is required to separate the bandwidth from the photon lifetime restriction, remove pattern dependence, reduce the RC time constant and ease the requirement on active element intrinsic loss.

In this paper, a light drop structure (Fig. 1(b)) is proposed in which one waveguide couples CW light into the large ring resonator and the coupling between the large ring and another waveguide is modulated with a small amplitude by using one composite interferometer. Compared to the notch design (Fig. 1(a)), CW light coupling into the large ring is not interrupted by the signal modulation. As a result, the light dissipation in the large ring is compensated by continuous input of CW light and the intracavity energy remains relatively stable instead of depleting. The severe intracavity energy fluctuation inherent to the notch design is removed by the proposed design, and the extinction ratio is improved from <1 dB to >20 dB with a factor of 25 smaller drive voltage. Two low Q ring phase shifters are used in the push-pull configuration to allow for both very small capacitance and high response speed in optical domain. The ring phase shifter’s cavity Q is intentionally chosen to make its photon lifetime no more than the RC constant. Non-return-to-zero (NRZ) signals with performance comparable to that of MZMs at 40 Gb/s is obtained with 0.4 V drive voltage. As the RC constant scales down to 1 ps, up to 160 Gb/s NRZ signal can be achieved with no more than 4 V drive voltage and < 5 dB insertion loss. The speed is independent of the large ring’s linewidth and mainly dominated by the RC constant. The performance is comparable to the MZM driven with the same voltage. Compared to [11], the tolerance to active ring propagation loss is increased from 5 dB/cm to over 25 dB/cm with less than 5% modulation bandwidth change.

As shown in Fig. 1(a), in the notch design, the energy amplitude inside the resonator is assumed to be constant due to the long photon lifetime enabled by the extremely high cavity Q. The ring-waveguide coupling is modulated to control the destructive interference between the CW light in waveguide and the light coupled out of the cavity, thus the modulation speed depends only on the bandwidth of the composite coupler (inside dashed line region) which is presented in [14]. The modulation of the coupling coefficient is achieved by a push-pull configuration with equal but reverse phase shifts on the upper and lower arms. However, for long NRZ ‘1’ pattern, the signal pulse width is comparable to the photon lifetime. Since the coupling is 0 during this time, the intra-cavity energy may deplete, which contradicts the constant energy amplitude assumption [14] and leads to severe pattern dependence.

As shown in Fig. 1(b), a light drop structure is proposed in which one waveguide couples CW light into the large ring resonator and the coupling between the large ring and another waveguide is switched via the composite coupler inside the dash line region. Both the large ring and the waveguides are passive components. The signal is generated by modulating the upper waveguide-to-large ring coupling using the ‘composite interferometer’ in the dashed line region in Fig. 1(b), in which two very low cavity Q ring phase shifters are used in push-pull configuration. The proposed modulator features the following important advantages: (1) since CW light is coupled continuously from the lower waveguide to the large ring resonator, the CW light coupling is not disturbed by the coupling modulation and the intra-cavity energy depletion is avoided; (2) since compact ring phase shifters are used, short RC constant can be obtained; (3) the ring phase shifters linewidth is around 160 GHz and photon lifetime is chose as 1 ps to be no larger than the RC constant, which allows for high coupler response speed; (3) due to relatively high cavity Q of the large ring and ring enhancement of the ring phase shifter, small coupling modulation is implemented with modest drive voltage to obtain signals with moderate insertion loss, enabling good signal quality and small drive power; (4) because signals are generated by light drop instead of destructive interference, the signal is purely 0 when the upper waveguide-ring coupling is 0, which enables a high extinction ratio;

## 2. Operating principles of proposed design

To describe the operating principles of the proposed design, it is necessary to introduce the “notch” design of Fig. 1(a) for first. As shown in Fig. 2
, the coupling region in Fig. 1(a), can be seen as a ‘composite interferometer’. The transfer function between a_{4}, b_{4} and a_{1}, b_{1} are derived as [3,12].

*t*

_{1},

*κ*

_{1},

*t*

_{2}, and

*κ*

_{2}refers to the reflectivity coefficient, amplitude coupling coefficient of the left 3 dB coupler, the reflectivity coefficient, amplitude coupling coefficient of the right 3 dB coupler; γ(< 1) is the amplitude transmission of the phase shifter; the phase shift in upper and lower arms are ±

*θ*/2;

*t*and

*κ*are the reflectivity coefficient and amplitude coupling coefficient of the whole composite interferometer. There is a π phase difference between the upper arm and the lower arm. As shown in Eq. (2), the coupling

*κ*can be controlled by the equal but reverse phase shift ±

*θ*/2 in the upper and lower arms, i.e. push-pull operation.

According to [11,18,19], the dynamic equations for notch design in Fig. 1(a) are

*a*(t)|

^{2}is the intracavity energy of the ring resonator and

*A*(t) is the time-varying amplitude of

*a*(t),

*ω*and

*ω*

_{r}are the carrier wave angular frequency and the resonance angular frequency of the ring;

*μ*

_{1}

^{2}= k

_{1}

^{2}

*V*

_{g1}/2πR

_{1}= 2/τ

_{e1}; k

_{1}is the large ring and the waveguide amplitude coupling coefficient and

*V*

_{g1}is the group velocity inside the large ring; 1/τ

_{e1}and 1/τ

_{p}are the amplitude decay rate due to the phase shifter, including power coupling from the large ring into the waveguide (1/τ

_{e1}) and the power loss induced by the phase shifter (1/τ

_{p}). 1/τ

_{l}is the amplitude decaying rate due to the loss in the passive part of the large ring. k

_{1}is modulated to generate signals. R

_{1}is the radius of the large ring.

*E*and

_{in}= E_{in0}e^{−jωt}*E*represent the input CW and modulated signal respectively. Substitute Eq. (3c) into Eq. (3a) and let

_{out}= E_{out0}e^{−jωt}*ω*

_{r}=

*ω*,

Signals are obtained by the cancellation between the light coupled-out of the cavity and CW light in the waveguide. As *μ*_{1} = 0, no light is coupled into the waveguide to cancel the CW light and signal ‘1’ is generated. However, in this time period, no CW light is coupled into the cavity either. The Eq. (4a) changes into

_{p}+ 1/τ

_{l})

^{−1}. For NRZ signals at a bit rate beyond the resonator linewidth and for a continuous ‘1’ pattern with a length comparable to (1/τ

_{p}+ 1/τ

_{l})

^{−1}, the intra-cavity energy amplitude will be depleted and severe signal pattern dependence will occur. These conditions will result in unacceptably low signal quality.

For the design in (Fig. 1(b)), after cancelling *e ^{−jωt}* and making the CW light frequency equal to the large ring resonance frequency, the dynamic equations are

*A*′(t) is the intra-cavity energy amplitude inside the large ring, k

_{1}′ and k

_{2}′ are the amplitude coupling coefficient between the large ring and the upper waveguide and that between large ring and the lower waveguide, respectively.

*μ*′

_{1}

^{2}= k

_{1}′

^{2}

*V*′

_{g1}/2πR′

_{1}= 2/τ′

_{e1}.

*μ*′

_{2}

^{2}= k

_{2}′

^{2}

*V*′

_{g1}/2πR′

_{1}= 2/τ′

_{e2}.

*V*′

_{g1}is the group velocity in the large ring. R′

_{1}is the large ring’s radius.

*μ*′

_{1}is switched between zero and non-zero to generate signals. 1/τ′

_{e1}, 1/τ′

_{p}are the amplitude decaying rate due to the phase shifter, including power coupling from the large ring into the waveguide (1/τ′

_{e1}) and the power loss due to the phase shifter (1/τ′

_{p}). 1/τ′

_{l}and 1/τ′

_{e2}are the amplitude decay rates due to the intrinsic loss in the passive large ring waveguide and the power coupling from the large ring into the lower waveguide, respectively. Two ring phase shifters are simulated with push-pull operation to generate phase change ±

*θ*/2. Both of the two ring phase shifters are designed to have cavity Q of 1200 with 160 GHz linewidth and photon lifetime no more than 1 ps. They are heavily over-coupled to the arms. Their modeling essentially follows our previous work in [18]. The CW light coupling (

*μ*′

_{2}) into the large ring cavity is time-independent since the coupling from lower waveguide to large ring is passive. This is different from notch design.

*μ*′

_{1}is modulated to generate signals.

As *μ*′_{1}≠ 0,

As *μ*′_{1} = 0,

*A*′(t) is fixed at a non-zero value, because light is coupled into the large ring cavity via

*μ*′

_{2}continuously and compensates the dissipated intracavity energy. This is entirely different from the notch design. The intracavity energy reaches a dynamic balance state. Hence, as

*μ*′

_{1}is modulated, the energy amplitude switches between two non-zero values,

_{${A}^{\prime}(t)=\frac{j{{\mu}^{\prime}}_{2}{E}_{in0}}{\left[\left(\frac{1}{{{\tau}^{\prime}}_{e1}}+\frac{1}{{{\tau}^{\prime}}_{p}}\right)+\frac{1}{{{\tau}^{\prime}}_{l}}+\frac{1}{{{\tau}^{\prime}}_{e2}}\right]}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{and}\text{\hspace{0.17em}}{A}^{\prime}(t)=\frac{j{{\mu}^{\prime}}_{2}{E}_{in0}}{\left[\frac{1}{{{\tau}^{\prime}}_{p}}+\frac{1}{{{\tau}^{\prime}}_{l}}+\frac{1}{{{\tau}^{\prime}}_{e2}}\right]}.$}The energy amplitude fluctuation ratio is

According to (6-b), |E_{out}|^{2} is purely zero as *μ*′_{1} is 0. Therefore, high extinction ratio signals can be obtained even when *μ*′_{1}^{2} switches between 0 and a value that is small compared to (1/τ′_{p} + 1/τ′_{l} + 1/τ′_{e2}). Notice that *μ*′_{1}^{2} = 2/τ′_{e1}, small *μ*′_{1}^{2} amplitude makes the energy amplitude fluctuation ratio in Eq. (11) tend to 1, indicating relatively stable intra-cavity energy amplitude.

## 3. Results

In our simulations, the large ring radius in Fig. 1(b) is set equal to the ring radius in Fig. 1(a) and a large radius of 64.8 μm is used to achieve large cavity Q and narrow linewidth, corresponding to a FSR of 287 GHz. In Fig. 1(b), the power coupling coefficient between the lower waveguide and the large ring is 0.1089. The cavity Q of Fig. 1(a) is calculated to be around 68,000 and linewidth is 3 GHz. For Fig. 1(b), they are 19,000 and 10 GHz respectively. The cavity Q of the large ring in Fig. 1(b) is lower because the ring phase shifters introduce higher loss than the active arms in Fig. 1(a). The propagation loss is set as 1 dB/cm [20] in passive rings/waveguides in Figs. 1(a) and 1(b) (not in phase shifters). The arm length in Fig. 1(a) is chosen to be 100 μm for the notch design, based on [3,14,15]. The ring phase shifters radii in Fig. 1(b) are both 5.4 μm. The ring resonator phase shifters are heavily over-coupled to the short waveguides. Their cavity Q is 1200 (linewidth = 160 GHz) and roundtrip loss coefficient is 0.9961. The low quality factor of coupling is shown to be realizable in [21,22]. Among forward biased p-i-n junctions, reverse biased p-n junctions, and sub-micrometer MOS structures, sub-micrometer MOS structure enables modulator designs with both high modulation efficiency and high speed [9,23,24]. Here an MOS structure is simulated to realize electro-optic modulation. A time constant τ of 5.68 ps is chosen for the carrier density to fall to 1/e of its peak and a V_{π}∙L of 1.6 V∙cm is assumed, which follows reported structures [1,23]. Actually, since our ring phase shifter’s perimeter is tens of times shorter than the phase shifter length in [23], significantly smaller RC constant could be obtained. For straight-waveguide-based phase-shifters in the notch design and the ring phase shifters in our design, a propagation loss of 10 dB/cm is assumed [1,23]. 10 V drive voltage is needed to achieve critical coupling in the notch design. In our model, a laser with a linewidth of 100 KHz is used, with output power of 1 mW. A square-wave voltage signal providing a non-return-to-zero (NRZ) pseudo-random-bit- sequence (PRBS) is used as the drive signal. The receiver sensitivity is −17.9 dBm for a bit error rate at 10^{−9} at 40 Gb/s. To observe the pattern dependence induced signal degradation, erbum doped fiber amplifier simulation models are used to maintain the same received power. An optical filter with 4 × bit-rate bandwidth is used before the receivers to remove optical noise.

Figures 3(a) and 3(b) show the simulated coupling, intra cavity energy amplitude and the signal power over time of both designs at the bit-rate of 40 Gb/s in NRZ format. The insertion loss of the notch design is less than 1 dB. The insertion loss of the proposed design depends on the drive voltage. When drive voltage is 2.6 V, the insertion loss (signal peak power over laser power) is less than 5 dB. Here, to avoid strong signal overshoots, a drive voltage of 1V is used. Figures 3(a) and 3(b) are drawn with the same time scale at the same received power, by assuming that the propagation loss of the large ring passive waveguide is 1dB/cm. In Fig. 3(a), the energy amplitude in the notch design is almost depleted during a continuous long '1' signal pattern in which the coupling is zero, and consequently the signal suffers from non-uniform ‘0’ patterns. Contrary to the notch design, as shown in Fig. 3(b), the energy amplitude in the large ring in Fig. 1(b) fluctuates in a very small range and nearly uniform ‘0’ /’1’ signal patterns are generated. Figures 3(c) and 3(d) show the energy amplitude fluctuation and the extinction ratio of both designs over the propagation loss of the passive waveguide in the large ring. In Fig. 3(c), the intracavity energy amplitude is shown to change greatly, with energy amplitude ratio of 9 to 12 dB. And this intense change is independent of the passive ring waveguide loss because the active arm loss dominates the roundtrip loss and the photon lifetime of the ring resonator is limited. In Fig. 3(d), the energy amplitude fluctuates by less than 1 dB and the exctination ratio is improved by 20 dB, compared to the notch design.

Since our research focuses on enhancing the modulation speed in optical domain, we scan the RC constant from 6 ps to 1 ps and examine the modulator’s 3 dB bandwidth. Here we examined two cases: (1) the ring phase shifter’s resonance is exactly the same with the laser frequency and the main cavity resonance, i.e. 0 offset; (2) the upper and lower ring phase shifter’s resonance is ± 80 GHz off from the laser frequency and the main cavity resonance, i.e. half linewidth offset. For both cases, the phase difference between the upper and the lower phase shifters is assumed to be biased at (2m + 1)π. The drive voltage is 2.5 V. As shown in Fig. 4(a) , as the RC constant varies from 6 ps to 2 ps, the modulator’s 3 dB bandwidth grows nearly linearly along with the RC cutoff frequency (dotted line). As the RC constant decreases to 1 ps, a 3dB modulation bandwidth is lower than the RC cutoff frequency since it comes to receive the influence of the ring phase shifter’s cavity dynamics. Despite this, 3 dB bandwidth as high as 98 GHz can be obtained for the 0 offset case and 122 GHz for the half linewidth offset case. In both cases, the modulation speed is independent of the main cavity’s linewidth (around 10 GHz). It is found that the 3 dB bandwidth is higher for the half linewidth offset case because the ring phase shifter receives less influence from cavity dynamics, as discussed in [25]. In contrast, the coupled ring design in [11] can only achieve a bandwidth as 47 GHz even the RC constant is 1 ps, because its speed is limited by its cavity linewidth (20 GHz). The influence of the propagation loss inside the ring resonator on 3 dB bandwidth is compared between this design and our previous design in [11] in Fig. 4(b). A RC constant of 1 ps is assumed for the active rings in two cases. The 3 dB bandwidth decreases from 72 GHz to 54 GHz as the loss increases from 5 dB/cm to 30 dB/cm with our previous design in [11] when a drive voltage of 5 V is used. On the contrary, the 3dB bandwidth of the proposed modulator changes from 124 GHz to 118 GHz for the half linewidth offset case and from 98 GHz to 94 GHz for the 0 offset case. The modulation bandwidth of the proposed modulator changes no more than 5%. This high tolerance to the intrinsic loss allows for higher doping concentration, which implies short RC constant and higher electro-optic modulation efficiency [26]. For instance, the intrinsic loss in [9] is around 20 dB/cm, in which a RC constant of 1 ps is presented.

The system performance of the proposed modulator is examined. 40 Gb/s NRZ signal BER curves are presented in Fig. 5(a)
. A traditional Mach-Zehnder Modulator (MZM) with V_{π} voltage of 5 V is used as the benchmark. A single ring modulator with 40 GHz linewidth (nearly critical coupling with roundtrip loss of 0.9781 and reflection reflectivity coefficient of 0.9819, same radius, RC constant of 5.68 ps and same V_{π}∙L with the active rings in Fig. 1(b)) driven by 0.4 V is compared to the proposed modulator as well. As shown in Fig. 5(a), the proposed modulator shows performance comparable to the MZM, though nearly 2 dB power penalty is observed. On the contrary, neither the notch design driven by 10 V nor the SRM driven by 0.4 V is capable of 40 Gb/s NRZ signals with acceptable quality, due to the poor extinction ratio. Compared to a SRM design that requires a resonance shift comparable to the bit rate (40 GHz), this design needs a resonance shift as small as 1/20 of 40 GHz to achieve good signal quality. In Fig. 5(b), with a RC constant of 5.68 ps, the power penalty of the notch design modulator and the proposed modulator (0 offset) are compared over different bit-rates for NRZ signal format referenced to a MZM. Within a power penalty of 2 dB, the proposed modulator can achieve NRZ modulation up to 4 times the linewidth (‘B’ point in Fig. 5(b)). This 2 dB power penalty is due to the 29 GHz response speed (Fig. 4(a)) and the low drive voltage of the proposed modulator. For comparison, the notch design shows power penalty no more than 2dB only when the bit rate is lower than the linewidth (‘A’ point) [16]. In Fig. 5(c), with a RC constant of 1 ps, the power penalty of the notch design modulator and the proposed modulator are compared over different bit-rates for NRZ signal format referenced to a MZM. Within a power penalty of 4 dB, the proposed modulator can achieve NRZ modulation up to 12 times of the linewidth (‘B’ point in Fig. 5(c)) for the 0 offset case and 16 times of the linewidth for the half linewidth offset case. The response speed is independent on the main cavity linewidth but mainly determined by the RC constant. Nevertheless, for the half linewidth offset case, a drive voltage of 4 V will be needed to obtain insertion loss no more than 5 dB, because the smaller phase change obtained compared to the 0 offset case. The notch design can achieve bit rate only 1.6 times of its linewidth (‘A’ point) even 1 ps RC constant is given and 4 dB power penalty is allowed. It is shown that, the proposed design performs a little bit worse with 2.5 V drive voltage at low speed than it does with 0.4 V drive voltage and 5.68 ps RC constant. It is mainly due to the signal overshoots.

## 4. Model accuracy

In addition to the dynamic equation model utilized here, another dynamic modulation model, known as the time dependent model [14] can be used to study the performance of the notch design and the proposed modulator. To check the accuracy of our model, the notch design modulator was simulated using both modeling methods. Figure 6 shows 40 Gb/s RZ signals obtained with the notch design modulator using the time dependent model and our dynamic equations model. The data are simulated with the same simulation parameters and structure parameters. The signal pulses obtained with the two models agree with each other according to Fig. 6. The difference is less than 1%, nearly negligible.

## 5. Discussion and conclusion

It is noticed that the modulator’s response speed receives the influence of the ring phase shifter’s cavity dynamics as the RC constant drops to 1 ps. This influence could be removed by using lower Q ring phase shifters or biasing the ring phase shifter’s resonance a little more off the laser and main cavity’s resonance. Essentially, the modulation speed is dominated by the RC constant of the ring phase shifters.

According to [23], we estimated the capacitance of our ring phase shifter to be around 60 fF. If an insertion loss less than 5 dB is required, a drive voltage of 2.6 V will be needed for the 0 offset case and the power consumption be 304.2 fJ/bit, according to the Eq. (12) given by [23].

It can be greatly reduced by tens of times if a MOS depletion structure is used, as proved in [9].

Resonance alignment of multiple rings by thermal tuning has been demonstrated in our recent paper [27] and the thermal tuning to the upper and lower arms of the composite interferometer has also been demonstrated in [6]. These progresses have shown that alignment of the resonances between the ring phase shifters and the large ring can be achieved by employing current technology.

In conclusion, a silicon microring-based coupling modulator with light drop structure is proposed by using a light drop structure to remove the modulation speed limitation from the optical domain. The critical problem of severe cavity energy fluctuation with the notch-design-based coupling modulator is solved. The modulator’s response speed is dominated by the coupler’s RC constant and independent of the main cavity linewidth. It is shown that up to 160 Gb/s NRZ signal with no more than 4 V drive voltage and less than 5 dB insertion loss can be obtained as the RC constant scales down to 1 ps. Great tolerance to the active element’s intrinsic loss is achieved.

## Acknowledgments

Sincerely, we thank Dr. Willner’s great help with the simulations during Yunchu’s studies.

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