1. Introduction

Compact, efficient, silicon-on-insulator (SOI) optical transmitters with monolithically integrated CMOS drive circuitry are foreseen as critical components within future on-chip optical interconnects [1–3]. As conventional CMOS scaling continues to drive individual transistors to decreasing dimensions, the operating voltages are also being decreased in order to prevent device breakdown and reduce power consumption [4]. Therefore, designing optical modulators capable of being driven directly by digital CMOS signals with amplitude below 1 Volt, without any intervening electronic amplifier stages, is of practical importance.

Electrooptic modulators based on free carrier dispersion [5] in high quality factor (Q) silicon microring resonators [6–8] and Mach-Zehnder interferometers [9–13] with embedded p-i-n or p-n diodes have been previously demonstrated. While some of these devices have been designed to occupy an ultra-compact footprint less than 0.001 mm² [6–10], the drive voltages required for operation are presently quite high, on the order of 3 to 16 V peak-to-peak. Therefore, additional research is required to identify ideal modulator devices capable of operating at reduced voltages, while maintaining high-speed operation and an ultra-compact footprint. In this work we present a high-sensitivity optical modulator design which illustrates a route to a large reduction of the ON-OFF switching voltage, within a CMOS-compatible platform.

2. Design and fabrication

The series of schematics in Fig. 1 serves to explain the evolution of the novel modulator design presented here. First, Fig. 1(a) depicts a racetrack resonator side-coupled to an input-output bus waveguide through a generic coupling region as shown within the dashed red box. The racetrack is referred to as the “amplitude resonator,” for the attenuation it produces at the output port as discussed below.

The optical coupler can be characterized by coefficients |t|² and |κ|², which describe the transmission and cross-coupling of optical power, respectively [14]. Together with parameters describing the circulation losses (1-α²) and round-trip phase (exp(iθ)) within the amplitude resonator, straightforward analysis of the characteristics of this generic system reveals an operating point at which the on-resonance (θ=2mπ, m integer) optical power transmitted from input to output is identically zero. This point, referred to as critical coupling [14, 15], is the result of perfect destructive interference in the output waveguide, and is useful for optical amplitude modulation.

 

Fig. 1. Schematic illustrations of various modulators based on control of waveguide-resonator coupling. (a) Side-coupled racetrack resonator interacting with a bus waveguide via a generalized variable power coupler, (b) single amplitude resonator (SAR) modulator, (c) paired amplitude phase resonator (PAPR) modulator.

Download Full Size | PDF

Critical coupling occurs when the power coupled into the amplitude resonator is exactly equal to the round-trip resonator loss, given by |κ|²=1-α². Within the regime of under-coupling defined by 0 ≤|κ|²≤1-α², the on-resonance transmission can be changed dramatically via small changes in the coupling coefficient |κ|², rapidly increasing from zero transmission at critical coupling to unity transmission at zero coupling. Therefore, study of the generalized system has led to development of a class of devices in which variable control of waveguide-resonator coupling, as indicated by the “control terminal” in Fig. 1(a), is exploited to produce ON-OFF optical modulation with high extinction [16–18]. This mode of operation has the advantage that achieving critical coupling, and accordingly a high extinction ratio, can be assured by adjusting the external bias conditions of the modulator after it is fabricated. Because tuning into critical coupling is fundamentally “built-in” to the operation of the device, control of the exact loss and coupling parameters from design to fabrication is not required, making this class of optical modulators intrinsically tolerant to variations in the fabrication process. In contrast, for microring modulators which have a fixed waveguide-resonator coupling coefficient and operate by scanning the resonance wavelength [6, 7], the extinction ratio is very sensitive to fabrication accuracy. Particularly for high index contrast waveguides such as SOI nanophotonic wires, it is known that even nanometer-scale variations in the dimensions of the waveguides and coupling gaps [19] can have a large impact upon the uniformity and reproducibility of the extinction ratio across a set of optical modulators.

One specific implementation of an optical modulator exploiting controlled waveguide-resonator coupling is illustrated in Fig. 1(b), as was previously suggested in reference [16]. In this device, the generic variable coupling region within the dashed red box is replaced with a Mach-Zehnder interferometer (MZI), assembled from two 3 dB directional couplers and a phase shifter, which may be controlled by a voltage signal, for example. Manipulation of the phase Δϕ at the control terminal produces a sinusoidal variation of the coupling coefficient |κ|², with all possible coupling values 0≤|κ|²≤1 being achieved across a relative phase shift of Δϕ=π. Using the phase Δϕ to switch the amplitude resonator in and out of critical coupling in this device (referred to here as a “single amplitude resonator” (SAR) modulator) has been shown to result in a significant reduction (~10x) in the relative phase shift required for ON-OFF modulation in comparison with the conventional MZI (i.e., having no resonator) [16, 17]. Since the phase shift is generally proportional to an applied voltage, as in the case of recently demonstrated SOI electrooptic devices [6, 7, 9–13], a similar reduction in the necessary drive voltage can be expected.

The novel device introduced here, illustrated in Fig. 1(c), further extends and improves upon the concept of optical modulation using controlled waveguide-resonator coupling. In this case, a ring-enhanced Mach-Zehnder interferometer (REMZI) [20–22] is incorporated as the variable coupler device within the red dashed box. Within the REMZI coupler, light traveling through the upper arm of the MZI experiences a highly nonlinear π effective phase shift in the vicinity of the resonances of the (over-coupled and ideally lossless) side-coupled “phase resonator” [21–23]. The coupling coefficient to the phase resonator is labeled as |κ₂|². Now, tuning an input laser beam into resonance with one of the amplitude resonances, and using the control terminal Δϕ to spectrally scan the phase resonator near the same wavelength, the coupling |κ₁|² to the amplitude resonator can be rapidly tuned in and out of critical coupling for efficient ON-OFF modulation, while requiring only a small fraction of the relative phase change Δϕ (or drive voltage) needed in the case of the SAR device. In fact, when these paired amplitude and phase resonators are tuned into resonance with one another, a modal anti-crossing results, near which the transmitted output power becomes an extremely sensitive function of the control phase Δϕ. The design shown in Fig. 1(c) will thus be referred to as the “paired amplitude phase resonator” (PAPR) modulator.

In summary, while the SAR modulator studied previously benefits from resonant enhancement of the modulation response via the amplitude resonator, this new PAPR configuration introduces an additional degree of resonantly enhanced control of the coupling coefficient |κ₁|², via the phase resonator. Experimental verification of the design concepts discussed above is performed by fabricating PAPR and SAR modulators using silicon nanophotonic wire waveguides, as shown in the optical micrographs in Fig. 2(a) and Fig. 2(b), respectively. These devices are fabricated on a SOI wafer with 220 nm thick silicon and a 2 µm thick buried oxide layer. The nanophotonic waveguides are nominally 500 nm wide, and the racetrack resonators are designed with a bending radius of 6.5 µm. The 3 dB multimode restricted interference (MMI) couplers [24] within the MZI sections are designed with a width of 3 µm and a length of 10 µm, as shown in the scanning electron microscope (SEM) image inset in Fig. 2(b). The directional coupler section in the PAPR phase resonator is 7 µm long with a 200 nm gap between the waveguides. A directional coupler was used in the case of the phase resonator in order to ensure the lowest possible loss within the coupling section. The MMI couplers were chosen for their large fabrication tolerances and broadband 3 dB coupling performance, to achieve balanced MZI operation.

The fabricated PAPR and SAR modulators occupy footprints of approximately 0.003 mm2 and 0.0027 mm², respectively. While no attempt has been made to optimize the footprint of either device in Fig. 2, it is clear that the additional area occupied by the phase resonator makes the PAPR design only fractionally larger than the SAR modulator, while offering superior modulation characteristics, as will be further discussed below. The PAPR footprint may be reduced to less than 0.001 mm² by straightforward adjustment of the layout.

 

Fig. 2. Optical microscope images of fabricated SOI modulator devices. (a) Paired amplitude phase resonator (PAPR) modulator, (b) single amplitude resonator (SAR) modulator. Red circles indicate “control terminal” locations at which an Ar-ion pump laser is focused for optical injection of free carriers. Inset: SEM image of the 3 dB multimode interference coupler.

Download Full Size | PDF

Electron beam lithography followed by a series of reactive ion etching steps is used to pattern the devices, as has been previously described in reference [25]. In order to achieve efficient on-chip coupling between the sub-micron waveguides and tapered lensed optical fibers, polymer spotsize converters were formed over SOI inverted tapers [26], and device chips were cleaved for testing.

3. Experimental results and discussion

The spectral transmission characteristics of the PAPR modulator (Fig. 2(a)) near λ=1550 nm are characterized using a broadband LED light source polarized to excite the TE guided mode, and an optical spectrum analyzer. Manipulation of the control phase Δϕ (i.e. the spectral position of the phase resonance) is accomplished via free carrier dispersion [5], using a CW Ar-ion pump laser operating at 488 nm to optically inject electron-hole pairs within the silicon waveguide. The laser is fiber-coupled and focused through an optical microscope, to a spot of ~2 µm diameter over the phase resonator, as indicated by the red circle in Fig. 2(a).

Fig. 3 illustrates the operation of the PAPR modulator with a series of transmission spectra, in which the phase resonator is sequentially blue-shifted into and through the amplitude resonance, located at zero spectral detuning. At zero incident Ar-ion power (bottom spectrum), the loaded Q factors of the phase and amplitude resonances are ~17000 and ~4000, respectively. The free spectral ranges of the phase and amplitude resonances are 9.9 nm and 2.7 nm. As the pump laser power is increased from zero to the order of several mW, the phase and amplitude resonances couple and interact. Near the joint-resonance condition, transmission at the initially weak amplitude resonance (ON state) is rapidly attenuated as the scanning phase resonator produces the coefficient |κ₁|² necessary for critical coupling (OFF state). When the Ar-ion pump power is increased even further, the phase resonance completely de-couples from the amplitude resonance, and the transmitted power is restored back to its original state. The observed broadening of the phase resonance at high pump power is caused by absorption from the optically injected free carriers.

 

Fig. 3. Series of PAPR modulator transmission spectra, obtained as a function of increasing Ar-ion pump laser power incident upon the phase resonator. Interaction with the phase resonance results in large modulation of transmission at the amplitude resonance. Spectra are vertically offset from one another for visibility.

Download Full Size | PDF

The modulation of the transmitted power (at zero detuning in Fig. 3) in response to the Ar-ion pump power is examined more closely, and is plotted using the red curve in Fig. 4(a). This plot shows a region in which the relative transmission is sharply attenuated by 14 dB for a small change in the incident pump power. This region defines an ideal operating window for ON-OFF modulation, and occurs as a result of critical coupling near joint amplitude-phase resonance. In order to make a comparison of the PAPR modulator with the previously studied SAR design, a series of transmission spectra similar to those shown in Fig. 3 were obtained for the SAR device. In this case, the Ar-ion pump laser was used to inject free carriers at the control terminal location illustrated by the red circle in Fig. 2(b). The transmitted power at zero detuning from the SAR amplitude resonance is plotted in Fig. 4(a) using the black curve. Within the same modulation window, the relative transmission through the SAR modulator decreases by only 1 dB.

Comparison of the relative performance of these two designs can be made through the modulation sensitivity, which is defined as the average attenuation per unit change in the Ar-ion pump power, within the modulation window shown in Fig. 4(a). The data illustrates that for the same change in the free carrier-induced phase shift Δϕ (or drive voltage), the PAPR modulator demonstrates a 25x improvement in the modulation sensitivity over the SAR design. In contrast to recent studies of silicon electrooptic modulators where ON-OFF drive voltages on the order of 3 to 16 V peak-to-peak have been required [6–13], the highly enhanced sensitivity exhibited by the PAPR device has the potential to enable a modulation swing as small as 0.12 V. This voltage reduction would eliminate the need for driver amplifiers, and enable on-chip modulators to be driven directly by digital CMOS signals.

 

Fig. 4. (a) Comparison of relative transmission at zero detuning through the PAPR and SAR modulator devices, as a function of incident Ar laser power. (b) Temporal modulation of transmission through a PAPR device. Inset: Rapid signal attenuation occurs with a fall time of ~60 ps.

Download Full Size | PDF

Finally, in order to demonstrate the viability of the PAPR device under high-speed modulation conditions, the Ar-ion pump laser focused onto the phase resonator is replaced by a mode-locked Ti:sapphire laser, emitting ~150 fs pulses at a center wavelength of 780 nm. A CW tunable laser operating near 1550 nm is coupled into the device and tuned to the amplitude resonance at the zero detuning point shown in Fig. 3. The optical output is amplified by an erbium doped fiber amplifier (EDFA), and detected using a 20 GHz InGaAs receiver connected to a digital communications analyzer (DCA) module with 20 GHz electrical bandwidth. The free carriers generated by each Ti:sapphire laser pulse blue-shift the phase resonance, resulting in strong attenuation of the transmitted signal with a fall time of approximately 60 ps, as shown in Fig. 4(b). While transmission through the device recovers with a longer exponential time constant of ~5 ns, as governed by the recombination of photogenerated free carriers, this is not a fundamental limitation. Within an active implementation of the PAPR modulator incorporating a p-i-n junction, a reverse bias field may be applied to sweep the carriers out of the phase resonator on time scales as short as 10 ps [27]. Therefore, despite the higher-order resonant nature of the PAPR design, the measured 60 ps fall time illustrates that high-speed modulation at rates up to 10 Gb/s [28] should be possible. The intrinsic modulation bandwidth limitation is set by the photon lifetime of the jointly resonant mode of the amplitude and phase resonators. Depending upon the specific application, it is possible to trade off the maximum speed against the modulation sensitivity enhancement, through appropriate design of the amplitude and phase resonator quality factors [8].

4. Anti-crossing behavior

As described in Section 2, the PAPR modulator can be modeled as a side-coupled amplitude resonator which uses a REMZI as a “variable coupler”. Analytical expressions [14, 16, 21, 22] describing both the transmitted power and phase of light passing through the amplitude and phase resonators are used to predict the output transmission characteristics of the PAPR device.

Although we are unable to accurately extract independently the round-trip losses (α ₁ and α2) and coupling coefficients (|κ₁|² and |κ₂|²) of both the amplitude and phase resonators respectively, in the following section we illustrate the qualitative characteristics of the PAPR device numerically. As input parameters for the model, the phase resonator is assumed to be lossless (α₂=1) for a phase-only response, and has a coupling coefficient |κ₂|²=0.0975. The amplitude resonator has a small degree of loss (α₁=0.95), and its coupling coefficient |κ₁|² is controlled by the spectral position of the phase resonator.

The simulated transmission map shown in Fig. 5 plots the normalized output power as a function of the spectral detuning between the amplitude and phase resonances. The amplitude resonance remains fixed, while the location of the phase resonance is manipulated via the control terminal Δϕ, using a “simulated” Ar-ion pump laser. At zero Ar laser power, the phase resonance is initially red detuned far from the amplitude resonance. As the laser power increases, the phase resonance is blue-shifted through the amplitude resonance. Particularly interesting anti-crossing behavior occurs when the amplitude and phase resonances are coincident with one another. The transmission map shows that the transmitted power is rapidly modulated from ON to OFF near the two blue-colored regions adjacent to the anti-crossing. Within these regions, control of the PAPR phase resonator induces critical coupling to the amplitude resonator. For an input laser tuned to one of these critical coupling points, high contrast modulation can be produced by small changes in the incident Ar pump power, or an equivalent voltage signal.

 

Fig. 5. Simulated PAPR transmission map, showing anti-crossing behavior near the joint amplitude-phase resonance condition. The colorbar on the right labels the normalized transmitted power.

Download Full Size | PDF

For practical devices, such as the SOI PAPR modulators demonstrated above, the phase resonator generally has non-zero loss. In this case, anti-crossing behavior qualitatively similar to that shown in Fig. 5 also occurs. However, as the experiments in Fig. 3 illustrate, the anti-crossing region becomes blurred and more difficult to resolve. In addition, the spectral width of the critical coupling features broadens. Therefore, an increase in the phase resonator loss results in degradation of the modulation sensitivity enhancement. Nevertheless, the comparison of the SAR and PAPR modulator devices in Fig. 4(a) illustrates that significant gains in sensitivity are achieved with the PAPR design introduced here.

The interaction of the amplitude and phase resonators producing the anti-crossing is related to the coupled microring optical interference mechanisms observed in [29, 30], which were explained in analogy to EIT. The region of high transmission at the center of the anti-crossing has similar features with those observed in these previous experiments.

5. Conclusions

The novel PAPR modulator design presented here uses paired microring resonators with independent amplitude and phase functionality to achieve enhanced modulation sensitivity near the critical coupling condition. These improved operating characteristics occur in the vicinity of an anti-crossing between the amplitude and phase resonators. PAPR devices are fabricated using silicon nanophotonic waveguides, and are tuned by optical injection of free carriers to study their transmission and temporal response characteristics. These modulators exhibit an extinction of 14 dB, a response time of 60 ps, and have a footprint of 0.003 mm2. The PAPR design shows a 25x improvement in modulation sensitivity when compared with the previously studied SAR modulator. This increased sensitivity may be used to enable high-speed, sub-1V modulators driven directly by low-voltage digital CMOS drive electronics.