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Abstract
A racetrack-shaped modulator, based on Double Injection method, has been recently presented able to provide multiple response shapes and exhibiting enhanced robustness to deviations in parameters. Fabrication process deviations that influence sensitive ingredients of ring-based modulators such as the ring's waveguide, couplers, and heat that is generated in Silicon Photonics devices due to carrier transport, can degrade the modulator extinction-ratio (ER) and optical modulation depth (OMD). The sensitivity of the, so-called, PIR20 configuration (Parameters-Insensitive Response with ER of 20 dB) to fabrication and temperature deviations is analyzed in detail. Comparison to other known modulators based on either a ring, MZI or Fabry-Pérot resonators, reveals that the PIR20 device is considerably less sensitive to deviations of these types.
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1. Introduction
The spreading of internet around the world leads to an ever-increasing demand for data transfer in long-haul communication links as well as short-range transport within data centers. To this end, a great deal of power consumption, space and overall solution efficiency can be improved by favoring integrated Silicon Photonics solutions over more conventional solutions. Their small footprint allows dense packing of multiple devices as well as a much desired large-scale integration with traditional microelectronics [1]. With integrated Silicon Photonics in mind, fabrication-related deviations that occur in either array level, or single-device level, can degrade the overall performance of the chip, and restrict the yield in mass production. Consequently, Electro-Optical (EO) components that constitute a photonic array, and are sensitive to fabrication deviations, still pose problems for large scale integration despite other advantages they might possess. Some recent estimates for basic fabrication deviations [2,3] in Silicon Photonics directional couplers, e.g., waveguide height, width and sidewall angle, indicate around ±10 nm deviation in coupling region. Mismatch of that magnitude may alter the splitting ratio by more than 10%, thus impacting the Extinction Ratio (ER) of the overall circuit by several up to few tens of decibels. In addition, even minor variations in the dimensions of the ring's waveguide may strongly detune the carrier wavelength of operation [4,5].
Another impairment that must be considered is the sensitivity of EO devices to temperature variations. When optical systems are expected to operate in a continuous manner, they are likely to experience temperature variations. For example, optical devices that are integrated with common electrical structures, PN, PIN diodes and MOS capacitors to name a few, are certainly exposed to the heat dissipated by these structures or side components that drive them, requiring (in many cases) active temperature control. In particular, resonance structures, such as ring-based modulators, observed to be extremely sensitive to these variations [6,7]. In general, a temperature change is equivalent to a wavelength shift. Since theoretical wavelength shift is ∼80 pm/°C, the temperature tolerance is within 0.1 °C for phase modulation architectures such as Quadrature Phase Shift Keying (QPSK) [8,9].
A recently introduced racetrack-shaped modulator [10,11] based on the principle of Double Injection is comprehensively analyzed in the following and critically compared to other alternative devices. It is specially configured (PIR20) to display enhanced resilience against critical parameter deviations, among other, to fabrication, wavelength and temperature variations. Specifically, potential improvement in temperature tolerance is shown to exceed previously reported figures [8,9] by more than one order of magnitude without resorting to materials outside standard Silicon Photonics.
For advanced modulation formats, such as 32 Quadrature Amplitude Modulation (QAM), optical Orthogonal Frequency Division Multiplexing (OFDM) and similar, ER higher than 20 dB is required [12–15]. The large ER is needed in order to increase the optical signal to noise ratio (OSNR), consequently, improving the bit-error-rate (BER). These formats are typically found in Data Centers interconnect applications, and whenever the reach requirements are limited to a few hundred km [12,13]. Therefore, our study is aimed at devices requiring higher performances, meaning optical modulation depths of at least 20 dB with Insertion Loss (IL) no greater than 3 dB.
2. PIR20 modulator introduction and analysis
The PIR20 modulator is based on a Double Injection (DI) architecture as depicted in Fig. 1(a). The DI consists of a racetrack-shaped ring resonator in an Add-Drop Filter (ADF) configuration, preceded by an optical splitter. Its operation can be described as follows: an optical wave entering the device is split by a coupler into two, not necessarily equal, waves that propagate through two waveguides towards the racetrack-shaped resonator. A portion of the power of each of the two waves is injected, via coupling, into the resonator (hence Double Injection) so that the two coupled waves travel inside the ring at the same direction. Since the injected waves are of the same wavelength, they interfere with each other inside the racetrack, and are mainly being manipulated by the coupling coefficients κ1, κ2 (but also via κ3).
Fig. 1. (a) Illustration of the PIR20 modulator (not to scale) based on the Double Injection method consisting of an input splitter and racetrack-shaped ring ADF resonator. It is driven by a common electrical structure. (b) PIR20 transmission (blue) and two additional transmissions with intended deviations in the ring's couplers (green, red). (c) PIR20 response shape vs. applied voltage.
A variety of optical transmissions, among them the PIR20, have been demonstrated based on the Double Injection architecture [10,16–20]. The corresponding devices have been analyzed at wavelengths around 1,550 nm and fabricated successfully in SOI platform, thus substantiating the versatile capabilities of the Double Injection approach. Herein, we carefully study and optimize the sensitivity of the PIR20 response to variations in the resonator's coupling ratios, waveguide dimensions, input wavelength and temperature. The modified PIR20 is optimized to attain much smaller device implementation size while maintaining adequate performance for modulation applications. These results are compared with well-known devices including ring notch and ADF modulators, MZI modulator and Fabry-Pérot modulator. All devices have been optimized to attain their best performance.
2.1 PIR20 response shape
We base the mathematical description of a DI resonator on Yariv's analytical model [21] originally intended for a ring resonator in ADF configuration. The main difference is that proper DI modeling requires that both Ei1 and Ei2 are non-zero, and have the same wavelength as both originate from a single input to the device. In steady state, the electromagnetic field of interest can be shown to obey [22]:
To analyze the various devices, a commercial mode-solver and circuit simulator for EO circuits [23] were used. The mode solver provides a 3D full-vector solution for the supported modes of the structure via the Galerkin procedure. By using the software analysis-tool we obtain profiles of waveguide structures, bus and directional couplers, with respect to various physical parameters. Later, these profiles were used by the circuit simulator to analyze the complete circuit. The circuit simulator models the directional couplers using Supermodes theory (both curved and parallel section are considered) and solves the steady state equations of the circuit. For coupling deviations, wavelength sensitivity and heat sensitivity analysis, the effective index profiles for the fundamental mode (TE polarity), neff, of the resonator's waveguide, and the related propagation constants of the directional couplers supermodes, βz, were described by
Fig. 2. (a) Illustration of the waveguide structures used for analyzing the circuits and their characteristics. In the analysis, the bus waveguides do not include electrical electrodes, while in practice, such electrodes may be used for calibration. (b) Deviation profiles (power transmission and phase) of coupling units for various devices: ring (blue) with radius 30 µm and passive loss of 55 dB/cm, racetrack (green) and MZI (red) with curvature radius (Rc), parallel section of 6 µm each and passive loss of 2.5 dB/cm. An effective coupling length of the curved section for the ring, racetrack and MZI coupler was around 2×11.6 µm, 2×4.7 µm and 2×3.6 µm, respectively. The mode-solver resolution was: Nx = Ny = 20 terms under the Slab-Modes basis (converging to the 4th digit in normalized index, b).
We first used the mode-solver to generate the dispersion profile, (2), for the fundamental mode of a practical rib-like waveguide structure. Due to the nature of the etching process, the sidewalls of the waveguide are rarely flat. Here we chose a trapezoidal waveguide with complementary error function (Erfc) decay profile in SOI platform. The waveguide has a 50 nm slab height to support integration with an electrical component such as a p-n diode or MOS capacitor. A typical p-n diode is the electrical control chosen for all circuits assuming to deplete carriers concentration of 2×1017 at -2.5 V [24]. The diode covers the resonator length excluding coupler regions. The presence of charged carriers produces additional loss, Δα(V), to the propagating mode and has been accounted for in the simulations.
Note that a maximum voltage of -2.5 V is applied to the circuits when producing spectrum transmissions and Optical Modulation Depth (OMD) behavior. The dispersion profile was then used by the circuit-level simulator that replicated the actual circuit, e.g., ring modulator. The circuit simulation assumes steady-state models such as (1). For the PIR20 device, a racetrack-based ADF circuit with both Ei1 and Ei2 present, was simulated. For the MZI, voltage was applied to the lower arm (θ2) while the upper arm was held constant. Push-pull configuration (i.e., ±1.25 V) requires the same device length and provided similar results. Common to all circuits were: |Ein|2 = 1mW/m2 and φτ,κ=0° when lumped couplers were used such as in Fig. 1(b) and in parts within Fig. 3. Lumped couplers, i.e. τ,κ=constant, may be applied to describe the behavior of a device in any platform, not necessarily just in silicon.
Fig. 3. Analysis of the sensitivity of OMD to variations in critical parameters due to fabrication deviations in both general and Silicon Photonics platforms. It is given for several circuits (top to bottom): Ring (Notch), Ring (ADF), MZI, Fabry-Pérot and PIR20. Common to all (except the ring notch device) is a typical passive waveguide loss of 2.5 dB/cm (note that the loss due to the presence of carrier conc. is taken into account too, Δα(V)) and T = 23°C. The maximum OMD (defined as in Fig. 1(c)) was calculated from devices spectrum at resolution of Δλ=0.001 nm.
Figure 1(b) depicts the steady-state intensity transfer function of the PIR20 modulator for two different scenarios representing coupling deviations due to fabrication process issues. A wideband notch-like profile with minimum ER in excess of 20 dB is observed even for coupling-coefficient deviations of 13%. For modulators, the OMD was chosen as a figure of merit (FoM) as it considers the attenuation of the signal with respect to two levels of voltages, representing either “on” state or “off” state [25]
where P denotes normalized optical power. Under applied voltage, the OMD and IL are measured at a fixed wavelength between the two states (0 V and -2.5 V), as depicted in Fig. 1(c). Another figure of merit, OMD penalty (ΔOMD), relates the maximum OMD throughout the spectrum and the OMD at very low modulation frequency [26] and is given in logarithmic units by Figure 2(a) shows the waveguide structures of the bus and resonator waveguides as well as the directional coupler units. The behavior of the coupler units comprising the optical structure of the various devices with respect to gap-width, parallel section length (L=), dispersion and temperature is depicted in Fig. 2(b).Note that the coupling powers are barely influenced by temperature variations as both symmetric and anti-symmetric Supermodes are equally exposed to it and their propagating index changes linearly for narrow spans (tens of degrees). However, the phase of the couplers does change with temperature spanning around 20° for couplers with a parallel section and around 4° without one.
2.2 Sensitivity analysis for fabrication deviations
To minimize the impact of fabrication deviations, and guarantee OMD greater than 20 dB, one must first identify the optimal splitting ratio (and working point) of the couplers. Figure 3 presents detailed analysis of the OMD associated with several devices in both general and Silicon Photonics platforms. The OMD is evaluated for coupler sensitivities, which is the most influential component in all circuits, as well as other parameters such as the waveguide loss (passive) parameter. With respect to coupler sensitives, the dashed rectangles shown in the subfigures represent the regions of coupling values within which all the points correspond to OMD greater than 20 dB. Note that the calculated OMD also satisfies IL no greater than 3 dB (The OMD was set to zero for IL larger than 3 dB). The physical parameters used for the devices and the resulting insensitivity ranges are seen in Fig. 4.
Fig. 4. Sensitivity analysis of OMD penalty and modulation bandwidth to variations in critical parameters due to fabrication deviations in Silicon Photonics platform. Given for several circuits (top to bottom): Ring (Notch), Ring (ADF), MZI, Fabry-Pérot and PIR20. The center point of the black rectangle in the subfigures may not fall exactly on the maximum OMD, i.e., ΔOMD = 0. Common to all is T = 23°C and a typical passive waveguide loss of 2.5 dB/cm (except ring notch).
To each device, the optimal OMD and IL were chosen between the two possible voltage states: 0 to -2.5 V or -2.5 to 0 V. Choosing the coupling parameters at the center of such a rectangle (meeting of the diagonals) provides an optimum splitting point. The physical sizes of the devices in Fig. 3, although are significantly different, were optimized to support modulation at 2.5 V. The radius of the ring notch modulator was initially chosen to 6 µm, similar to recent ring modulator reports [4,27,28]. However, simulations revealed that the insensitivities range for obtaining 20 dB attenuation were very limited. In addition, the small radius, which resulted in weak coupling, and naturally, required large Q factor for operation, yielded very low modulation speed, around 2 GHz. Therefore, to attain more typical bandwidth performance known to be realized by ring notch modulator and to extend the insensitivities range within the 20 dB ER requirement, the radius was increased to 30 µm and the passive waveguide loss was set to 55 dB/cm. It follows from the simulations that a conventional small-sized ring modulator, can hardly support advanced modulation formats. For the ADF ring modulator, however, the radius was set to a typical 20 µm [29,30].
The maximum modulation frequency, fQ, achievable by an optical structure is limited by the duration required for reaching steady state; but also, by the RC time of p-n diode, 1/fRC = 2πRC. The device 3 dB modulation bandwidth is expressed by [26]
For our waveguide structure and p-n diode, the junction capacitance is about 50 fF and the resistance is set to 50 ohm [25]. The RC time is therefore ∼2.5 ps, consequently, supporting 3 dB bandwidth of about 60 GHz. It is assumed that the input optical signal is narrow banded and the modulation is realized by properly driving the electrode of the device.Note that the transmission of a Fabry-Pérot circuit is equivalent to that of the drop port of a ring ADF circuit (peaks shape) [31]. The ring (notch and ADF) and Fabry-Pérot devices are typically aimed to work near the critical coupling regime (for enhanced OMD). Therefore, the passive waveguide loss substantially influences their sensitivity and was included in the analysis. Although, the PIR20 device is ring-based, it does not adhere to critical coupling condition; changes in the passive loss parameter mostly influence its IL. Consequently, since the PIR20 and MZI devices have an additional free parameter but are much less sensitive to the loss, they were tested against that parameter which mostly limits their insensitivity range: input splitting (|Ei1| or τ3) and variations between the arms (ΔL or Δθ), respectively. Thus, the left-hand side and middle columns in Fig. 3 show the sensitivity of the device to variations in the couplers only, while the right-hand side column shows the sensitivity to variations in the couplers and an additional parameter. Apparently, the additional parameter significantly decreases the insensitivity range for some of the devices. The transfer function of the cross-bar MZI is given by
It is evident from the results presented in Fig. 3 that the PIR20 is of the largest insensitivity range for couplers variations – about 26% (or 20 nm), around the nominal working point – twice that of the MZI – which indeed covers the discussed range of possible fabrication variances (±10 nm). Furthermore, it maintains larger OMD throughout the insensitivity range in average of 36 dB vs. 30 dB for MZI, ring ADF and ring notch modulators, and 24 dB for Fabry-Pérot modulator. While the ring notch and ADF devices exhibited limited insensitivity range, the Fabry-Pérot device proves to be more resilient to deviations. It is, however, prone to deviation when the passive waveguide loss, α, exceeds 3.5 dB/cm.
Due to the couplers’ dispersion, deviations in the couplings value shifts the resonance wavelength of the modulator from its nominal value (its value in case of no deviations). The OMD analysis (OMD (max)) in Fig. 3 assumed that the input wavelength can be tuned to the resonance wavelength within every deviation. In practice, the source wavelength is typically fixed in order to reduce costs and size required by ITU. Therefore, it is imperative to analyze the OMD in the case of fixed wavelength. Figure 4 presents the OMD penalty with respect to the resonance wavelength defined under no deviation in parameters, for every device. In addition, the 3 dB modulation bandwidth is also given. The black rectangles appearing in the subfigures represent a domain of coupling values such that all the points within the rectangle correspond to OMD greater than 20 dB (points with IL larger than 3 dB were omitted). Notice that the center point of these rectangles, which should be targeted in the design, do not necessarily fall on the center point obtained in the case of shifted resonances (Fig. 3).
Figure 4 reveals that the insensitivity range in case of fixed input wavelength decreased for all devices. The PIR20 and Fabry-Pérot modulators exhibit the best resiliency to deviations (twice that of the MZI) while the ring notch and ADF modulators appeared to be highly sensitive, and may require a tunable input source. The ring notch, ring ADF, MZI and PIR20 devices have a modulation bandwidth of tens of GHz while the Fabry-Pérot device is limited to just a few GHz. Increasing its bandwidth is possible when its Q factor is lowered; this, however, will deteriorate its OMD performance and may increase its IL. Nowadays modulators are expected to modulate at speed of at least 20 GHz, thus making the relatively insensitive Fabry-Pérot device a less appealing candidate for densely packed commercial modulators. Since the MZI is a single-pass circuit, its modulation speed is mostly limited by the electrical bandwidth.
The sensitivity of abovementioned modulators to wavelength variations is next studied. Variations in wavelengths may occur due to mismatch between the design or fabrication quality and the fixed wavelength of the input source. Furthermore, if the source is prone to temperature variations, its center wavelength may slightly drift [32]. In general, the source may emit a constant optical signal with bandwidth larger than a few mega-hertz. Figure 5 inspects the OMD and operational IL with respect to variations in optical input wavelength. The circuits’ parameters are set to the “mid-point” values of “fixed wavelength” as given in Fig. 4.
Fig. 5. Sensitivity analysis of the OMD and IL to variations in the input wavelength for several circuits: Ring (Notch), Ring (ADF), MZI, Fabry-Pérot and PIR20. The variations range were set around the resonance wavelength of each device (given in Fig. 4). The insensitive range, Δλ, is defined for OMD≥20 dB and IL≤3 dB (α=2.5 dB/cm, T = 23°C).
It is readily seen from Fig. 5 that the ring notch and ADF modulators, as well as the Fabry-Pérot modulator, are highly sensitive to the input wavelength variations and may support only narrow bandwidth optical input signal, BW∼1 GHz (Δλ<0.01 nm). The PIR20 modulator is more resilient to these variations and can support a wider variability in wavelength acceptance of optical input signal, BW∼10 GHz (Δλ=0.1 nm). The MZI modulator, being a symmetric non-resonance device, is hardly limited by this kind of variations.
In general, in cases where the fabrication quality limits the achievable OMD (i.e., OMD < 20 dB), in particular in ring-based modulators, the insensitivities range may naturally increase. Figure 6 presents the modulators insensitivity range to deviations in the couplers gap and input wavelength as a function of various OMD values under fixed wavelength (IL≤3 dB).
Fig. 6. Sensitivity analysis of the modulators to fabrication quality resulting with lower OMD values. (a) Insensitive range of the couplers gap. (b) Insensitive range of source input wavelength.
The resiliency of the ring ADF modulator barely improves with reduced OMD. For this device, variations in the couplers gap affecting both couplings amplitude and phase, drift its resonance frequency further reducing its OMD performance. For the ring notch, Fabry-Pérot and PIR20 modulators, the condition on the IL, i.e., IL≤3 dB, limits the step ascent behavior of the resiliency as the OMD decreases, as seen for the MZI modulator.
2.3 Temperature sensitivity analysis
For some materials, among them silicon [33], temperature variations can significantly affect their refractive index, and thus impact the propagating mode index. This, in turn, will change the transmission shape and properties of a modulator operating under applied voltage and set at a fixed wavelength. Since heat naturally spreads in the vicinity of its source, the couplers of an optical structure may be affected as well. Such an effect was observed experimentally even for the couplers of a MZI (cross-bar) modulator [34]. Therefore, both the resonator and its couplers are considered in the analysis the follows.
The temperature sensitivity analysis was carried out with all parameters analyzed in Fig. 4 set to “mid-point” values and the fixed wavelength set to the resonance wavelength given in the figure. Temperature variation, when it is monotonically increased, is expected to shift the transmission in the wavelength (or otherwise voltage) domain in one direction. However, such variations influence the couplers phase as well, yet in a non-monotonic fashion (as depicted in Fig. 2(b)). Consequently, the shift in the transmission is not necessarily monotonic.
The insensitivity range was chosen so as to guarantee at least 20 dB of OMD and IL below 3 dB. Figure 7 demonstrates the sensitivity behavior of several devices for temperature variations as a function of applied voltage. The OMD and the 3 dB modulation bandwidth of the modulators were analyzed for temperature variations in the range of 15°C to 35°C (res. 0.01°C).
Fig. 7. Sensitivity analysis of the OMD and modulation bandwidth to variations in temperature for several circuits: Ring (ADF), MZI, Fabry-Pérot and PIR20. The optical couplers are also influenced by the variations. OMD points with IL > 3 dB were set to zero.
The figure reveals that even though the PIR20 is ring-based, it can tolerate temperature variances of about 4°C. This is considerably better compared to the notch and ADF ring modulators, where even a minor variation in temperature (<0.6°C) reduces their OMD significantly. This result is of no surprise as the high sensitivity to temperature deviations of ring-based modulators have been widely studied and demonstrated [35] and farther observed experimentally [8].
In general, modulating at RF frequencies produces heat variations of a few degrees, thus a coarse temperature control may be sufficient for the PIR20 and MZI devices. Note that other electrical components such as drivers and converters may also produce heat levels that need also be considered.
The behavior of the 3 dB modulation bandwidth remains constant for all devices with values around the average given in Fig. 4. This can be expected since temperature variances influence mostly the phases of the waveguides (bus and couplers). This in turn can shift the resonance wavelength but does not influence the response near the resonance by much.
2.4 Waveguide sensitivity analysis
Considering large-scale integration, whether dense-WDM, complex logical circuits or stand-alone system-on-chip units, the entire wafer is expected to be utilized and yield is required to be high. The further they are placed from the center of the wafer, waveguide deviations are inevitable [4]. Major deviations include the waveguide's width, slab height and sidewall angle, radius or length of the resonator, and the coupling unit's phase and amplitude. Following [4], we focus our analysis on sidewall angle and coupling behavior.
One of the major inaccuracies in practical fabrication line, in particular while receding from the wafer center, is the uniformity of the etching depth. This affects not just the flatness of the waveguide sidewalls but also the slab height and base width. The latter directly influences the sidewall angle of the waveguide. Therefore, our analysis is carried out while both the base width and the slab height of the waveguide are modified when its sidewall angle is changed.
The waveguides chosen in this analysis, depicted in Fig. 2(a), have typical dimensions with a base width of 520 nm, slab height of 50 nm and a sidewall angle of 80°. Figure 8(a) inset shows that the difference in base width and slab height of the waveguide is about 6 nm and 0.6 nm each per 1° angle, respectively. This leads us to focus the analysis on variances of 1-2° about the center-point 80° (W = 520 nm, HSlab = 50 nm). It is interesting to note that the behavior of the couplers as function of the sidewall angle, Fig. 8(b), is very similar to their behavior for wavelength with an equivalence ratio of 1°≈10 nm (w.r.t Fig. 2(b)).
Fig. 8. Effect of waveguide variations in the sidewall angle for both the bus and coupling units. (a) Changes in neff of the propagating mode (green) as a function of sidewall angle. Waveguide's base-width (blue) and slab height (red) is given in the inset figure. (b) Couplers’ amplitude and phase behavior for ±0.5° sidewall angle variation about 80° for various devices: ring (blue) (R = 30 µm, α=55 dB/cm), racetrack (green) and MZI (red) (Rc = L==6 µm, α=2.5 dB/cm).
The deviations in sidewall angle are causing a significant change in the effective index of the propagating mode in the resonator waveguide, see Fig. 8(a). Consequently, the targeted resonance wavelength of the circuit (λRes of a deep (notch) or a peak) is shifted, thereby decreasing the OMD. This deviation does not influence much the couplers phase and hence the resonance shift, while it does indeed affect their amplitude which may result in an OMD degradation. Since the overall shift in resonance has a strong influence on the circuit performance, a figure of merit, dλRes/d∠ (or dλRes/dW), can characterize the resiliency of the modulator whilst still providing at least 20 dB OMD with IL smaller than 3 dB.
For the MZI, the couplers are accountable for most of the performance degradation if waveguide variances appear equally on both arms. In practice however, and in particular due to its large size, a fabricated MZI device may experience different variances on each arm that can further degrade its performances. Figure 9 provides sensitivity analysis of waveguide deviation with respect to both OMD (at λRes∠80°) and resonance shifts. In addition, the figure of merit proposed above is calculated for each modulator. Other circuit parameters are taken at “fixed wavelength” from Fig. 4. Note that the ring notch modulator exhibited extremely sensitive results and therefore omitted from the analysis.
Fig. 9. Sensitivity analysis of the OMD and resonance shifts, λRes, to variations in waveguide sidewall angle (res. 0.01°) for several circuits: Ring (ADF), MZI, Fabry-Pérot and PIR20. The optical couplers are influenced by the variations as well. Common to all: T = 23°C and center angle of 80°. OMD points with IL > 3 were nulled.
In general, it is desirable to achieve smaller resonance shifts and larger range of insensitivity to sidewall angles, and consequently, a smaller figure of merit. Even though the ring ADF and Fabry-Pérot devices have smaller resonance shifts than the PIR20, their insensitivity range (Δ∠) is much smaller. Since the MZI has a large insensitivity range, in which the resonance shift behaves nonlinearly as a function of the sidewall angle, an inspection of a range (close to the center-point 80° angle) equivalent to that of the PIR20 has been chosen to obtain a comparable figure of merit.
3. Conclusions
An EO modulator with improved insensitivity range to fabrication, input wavelength, and temperature variations was analyzed in depth. The modulator design, termed PIR20, is based on the Double Injection method and consists of a single ring resonator and p-n diode. It offers a minimum OMD of 20 dB with IL below 3 dB over a large bandwidth even if the coupling coefficients change by as much as 26% or 20 nm, and some resiliency to temperature variations (about 4°C). Analysis for waveguide deviations showed that the PIR20 can withstand about 0.05° (or 0.3 nm) variance in waveguide sidewall angle and still provide a 20 dB attenuation. A figure of merit has been suggested and used to evaluate the performance of several modulators. A comparison with well-known modulators based on either ring resonators, Fabry-Pérot or MZI, reveals that the PIR20 has better resiliency to the aforementioned variations and can therefore be considered as a viable candidate for large-scale integration. Table 1 summarizes the insensitivity range of all parameters analyzed in this article to each modulator in Silicon Photonics platform (under fixed wavelength).
Table 1. Insensitivity Range (OMD≥20dB, IL≤3dB) of Modulators Properties under Fixed Wavelength.
While MZI and Fabry-Pérot modulators demonstrate good resiliency in some of the parameters, the ring-based modulators, notch and ADF, were found to be highly sensitive to any one of the parameters analyzed.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper may be obtained from the authors upon request.
References
1. H. Subbaraman, X. Xu, A. Hosseini, X. Zhang, Y. Zhang, D. Kwong, and R. T. Chen, “Recent advances in silicon-based passive and active optical interconnects,” Opt. Express 23(3), 2487 (2015). [CrossRef]
2. A. Prinzen, J. Bolten, M. Waldow, and H. Kurz, “Study on fabrication tolerances of SOI based directional couplers and ring resonators,” Microelectron. Eng. 121, 51–54 (2014). [CrossRef]
3. J. Zhang, L. Han, B. P. P. Kuo, and S. Radic, “Broadband angled arbitrary ratio soi mmi couplers with enhanced fabrication tolerance,” J. Lightwave Technol. 38(20), 5748–5755 (2020). [CrossRef]
4. P. Sun, J. Hulme, T. Van Vaerenbergh, J. Rhim, D. Kielpinski, A. Seyedi, M. Fiorentino, R. G. Beausoleil, C. Baudot, F. Boeuf, and N. Vulliet, “Statistical Behavioral Models of Silicon Ring Resonators at a Commercial CMOS Foundry,” 2019 8th Annu. IEEE Photonics Soc. Opt. Interconnects Conf. OI 20192, 1–2 (2019).
5. M. R. Uddin, N. Lingas, B. Nakarmi, and Y. H. Won, “Waveguide side-wall angle dependant resonance of a Si micro ring-resonator,” 2015 11th Conf. Lasers Electro-Optics Pacific Rim, CLEO-PR 20152, 4–5 (2016).
6. M. Bahadori, A. Gazman, N. Janosik, S. Rumley, Z. Zhu, R. Polster, Q. Cheng, and K. Bergman, “Thermal Rectification of Integrated Microheaters for Microring Resonators in Silicon Photonics Platform,” J. Lightwave Technol. 36(3), 773–788 (2018). [CrossRef]
7. Z. Ying, Z. Wang, Z. Zhao, S. Dhar, D. Z. Pan, R. Soref, and R. T. Chen, “Comparison of microrings and microdisks for high-speed optical modulation in silicon photonics,” Appl. Phys. Lett. 112(11), 111108 (2018). [CrossRef]
8. P. Dong, C. Xie, L. L. Buhl, and Y. K. Chen, “Silicon microring modulators for advanced modulation formats,” Opt. Fiber Commun. Conf. OFC 20131, 1–3 (2013).
9. E. Ghillino, P. Mena, V. Curri, A. Carena, J. Patel, D. Richards, and R. Scarmozzino, “Simulation of silicon photonic coherent PM-QPSK transceivers using microring modulators,” Int. Conf. Transparent Opt. Networks19–22 (2014).
10. R. A. Cohen, O. Amrani, and S. Ruschin, “Response shaping with a silicon ring resonator via double injection,” Nat. Photonics 12(11), 706–712 (2018). [CrossRef]
11. R. A. Cohen, O. Amrani, and I. Ruschin, “Parameters-Insensitive Modulator for Optical Interconnect Systems Based on Double Injection,” 2019 8th Annu. IEEE Photonics Soc. Opt. Interconnects Conf. OI 20192019–2020 (2019).
12. J. Zhou, Q. Zhang, J. Wang, L. Zhu, and J. Hong, “Model and design of silicon photonic carrier-depletion Mach-Zehnder modulators for 400Gb/s and beyond PAM and QAM applications,” inProceedings of SPIE (2019), Vol. 1092318, p. 41.
13. J. C. Geyer, C. Doerr, M. Aydinlik, N. Nadarajah, A. Caballero, C. Rasmussen, and B. Mikkelsen, “Practical implementation of higher order modulation beyond 16-QAM,” Opt. Fiber Commun. Conf. OFC 20151–3 (2015).
14. T. Kawanishi, T. Sakamoto, and A. Chiba, “High-speed and presice lightwave modulation technologies,” 2009 14th Optoelectron. Commun. Conf. OECC 20091–2 (2009).
15. H. J. Kaur and M. L. Singh, “Modelling and Reporting Parameters of Optical OFDM System Using Different Modulation Techniques,” Opt. Photonics J. 03(02), 204–210 (2013). [CrossRef]
16. Y. Liu, A. Choudhary, D. Marpaung, and B. J. Eggleton, “Integrated microwave photonic filters,” Adv. Opt. Photonics 12(2), 485 (2020). [CrossRef]
17. X. Cao, S. Zheng, Y. Long, Z. Ruan, Y. Luo, and J. Wang, “Mesh-Structure-Enabled Programmable Multi-Task Photonic Signal Processor on a Silicon Chip,” ACS Photonics 10, 2658–2675 (2020). [CrossRef]
18. P. Zheng, X. Xu, G. Hu, R. Zhang, Y. Binfeng, and Y. Cui, “Integrated Multi-functional Optical Filter Based on a Self-coupled Microring Resonator Assisted MZI Structure,” J. Lightwave Technol. 39(5), 1429–1437 (2021). [CrossRef]
19. O. Daulay and E. Klein, “Reconfigurable Double-Injection Ring Resonator for Integrated Microwave Photonic Signal Processing,” in International Topical Meeting on Microwave Photonics (MWP) (IEEE, 2021), pp. 1–4.
20. O. Daulay, G. Liu, R. Botter, M. Hoekman, E. J. Klein, C. Roeloffzen, J. Capmany, and D. Marpaung, “Programmable Integrated Microwave Photonic Filter using a Modulation Transformer and a Double-Injection Ring Resonator,” in European Conference on Optical Communication (ECOC) (IEEE, 2021), pp. 1–4.
21. A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321 (2000). [CrossRef]
22. R. A. Cohen, O. Amrani, and S. Ruschin, “Linearized electro-optic silicon racetrack modulator based on double injection method,” in 2015 International Topical Meeting on Microwave Photonics, MWP 2015 - Conference Proceedings (2015).
23. Doctor Modes, Lord PICS, Software by Star Photonics, Single License (2021).
24. J. Ding, S. Member, R. Ji, L. Zhang, and L. Yang, “Electro-Optical Response Analysis of a 40 Gb / s Silicon Mach-Zehnder Optical Modulator,” J. Lightwave Technol. 31(14), 2434–2440 (2013). [CrossRef]
25. P. Dong, S. Liao, D. Feng, H. Liang, and D. Zheng, “Low Vpp, ultralow-energy, compact, high-speed silicon electro-optic modulator,” Opt. Express 17(25), 22484–22490 (2009). [CrossRef]
26. H. Yu, D. Ying, M. Pantouvaki, J. Van Campenhout, P. Absil, Y. Hao, J. Yang, and X. Jiang, “Trade-off between optical modulation amplitude and modulation bandwidth of silicon micro-ring modulators,” Opt. Express 22(12), 15178 (2014). [CrossRef]
27. Y. Tong, Z. Hu, X. Wu, S. Liu, L. Chang, A. Netherton, C. K. Chan, J. E. Bowers, and H. K. Tsang, “An Experimental Demonstration of 160-Gbit/s PAM-4 Using a Silicon Micro-Ring Modulator,” IEEE Photonics Technol. Lett. 32(2), 125–128 (2020). [CrossRef]
28. Y. Ban, J. Verbist, M. Vanhoecke, J. Bauwelinck, P. Verheyen, S. Lardenois, M. Pantouvaki, and J. Van Campenhout, “Low-Voltage 60Gb/s NRZ and 100Gb/s PAM4 O-Band Silicon Ring Modulator,” 2019 8th Annu. IEEE Photonics Soc. Opt. Interconnects Conf. OI 20192, 2019–2020 (2019).
29. Y. Hu, X. Xiao, H. Xu, X. Li, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “High-speed silicon modulator based on cascaded microring resonators,” Opt. Express 20(14), 15079 (2012). [CrossRef]
30. H. Jia, X. Fu, T. Zhou, L. Zhang, S. Yang, and L. Yang, “Mode-selective modulation by silicon microring resonators and mode multiplexers for on-chip optical interconnect,” Opt. Express 27(3), 2915 (2019). [CrossRef]
31. S. Meister, H. Rhee, A. Al-Saadi, B. A. Franke, S. Kupijai, C. Theiss, H. J. Eichler, D. Stolarek, H. H. Richter, L. Zimmermann, B. Tillack, M. Lesny, C. Meuer, C. Schubert, and U. Woggon, “High-speed Fabry-Pérot optical modulator in silicon with 3-µm diode,” J. Lightwave Technol. 33(4), 878–881 (2015). [CrossRef]
32. N. Yulianto, B. Widiyatmoko, and P. S. Priambodo, “Temperature Effect towards DFB Laser Wavelength on Microwave Generation Based on Two Optical Wave Mixing,” Int. J. Optoelectron. Eng. 5, 21–27 (2015). [CrossRef]
33. J. Komma, C. Schwarz, G. Hofmann, D. Heinert, and R. Nawrodt, “Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures,” Appl. Phys. Lett. 101, 041905 (2012). [CrossRef]
34. B. Guha, A. Gondarenko, and M. Lipson, “Minimizing temperature sensitivity of silicon Mach-Zehnder interferometers,” Opt. Express 18(3), 1879 (2010). [CrossRef]
35. K. Padmaraju and K. Bergman, “Resolving the thermal challenges for silicon microring resonator devices,” Nanophotonics 3(4-5), 269–281 (2014). [CrossRef]
