1. Introduction

Advanced modulation formats that involve optical phase modulation have become attractive alternatives to on-off keying (OOK) in optical communications because of their potential to increase the spectral efficiency and receiver sensitivity [1, 2]. The most simple phase modulation format is binary phase-shift keying (BPSK), where the data is encoded as 0 and π radian phase-shifts on the optical carrier. BPSK offers a relative ∼3-dB boost in receiver sensitivity and a lower vulnerability to fiber nonlinearities compared to OOK [1, 2]. In differential binary phase-shift keying (DPSK), information is encoded as phase differences between successive bits. Optical BPSK signals can be generated either with a phase modulator or with a Mach-Zehnder interferometer (MZI) modulator as illustrated in Figs. 1(a) and 1(b). Driving a MZI in a push-pull manner through the zero transmission point causes a π radian phase flip [1, 2]. The advantages of using a MZI over a phase modulator for BPSK are a chirp-free output (except at the phase flip), a π phase flip that is independent of the voltage swing, and an improved tolerance to drive signal imperfections (e.g., due to limited bandwidth or over/undershoot) [1, 2]. Drive signal imperfections affect the intensity, but the fluctuations are compressed by the MZI nonlinear transfer characteristic when the ‘0’ and ‘1’ symbols are positioned near the transmission peaks as shown in Fig. 1(b).

 

Fig. 1 Illustrations of BPSK modulation using (a) a phase modulator, (b) a MZI modulator, (c) an intracavity-modulated microring, and (d) a coupling-modulated microring. The illustrations show the similarities between MZI modulators and coupling-modulated microrings, as well as the similarities between phase modulators and intracavity-modulated microrings. Constellation diagrams and output intensity (|T|²) and phase (∠T) versus applied phase-shift (Δθ) are shown. For the intracavity-modulated microring, the input wavelength is on resonance for Δθ = 0; modulating Δθ shifts the resonance wavelength. For the coupling-modulated microring, the input wavelength is on resonance, and the drop port coupler is modulated; the ‘1’ and ‘0’ symbols correspond to the two critical coupling conditions.

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Microring modulators have the potential of reducing the size and power consumption of traditional single-pass modulators, such as phase modulators or MZIs [3–10]. Recently, BPSK modulation using a single microring was proposed [11] and demonstrated [12, 13]. Using a microring-enhanced MZI, quadrature phase-shift keying modulation (QPSK) has also been proposed and demonstrated [14, 15]. In these works, the refractive index in an over-coupled microring was modulated to spectrally shift the resonance relative to the input wavelength [Fig. 1(c)]. This “intracavity modulation” of the microring produces a time-varying phase-shift and achieves BPSK modulation analogous to a phase modulator. The optical output is continuously chirped and is less tolerant to drive signal imperfections. Moreover, because near unity transmission requires strong over-coupling, hence large linewidths, there exists a fundamental trade-off between the efficiency and insertion loss.

In this work, we propose a microring BPSK modulator based on coupling modulation and demonstrate the concept in silicon-on-insulator (SOI). The purpose of this demonstration is to verify that coupling modulation can result in BPSK outputs. A preliminary report of this work was presented in [16]. In coupling modulation, the coupling coefficient between the microring and the input/output bus waveguide is modulated rather than the intracavity index or loss [17–19]. Even though coupling modulation can circumvent the cavity linewidth limitation to the modulation rate of resonators, here, we focus on the “quasi-static” regime, where the modulation rate is within the cavity linewidth [18, 20]. As illustrated in Fig. 1, the operation of the coupling-modulated microring for BPSK is analogous to that of a MZI. Thus, the benefits of coupling-modulated microrings for BPSK over existing intracavity-modulated microrings are akin to the benefits of a MZI for BPSK over a phase modulator (i.e., lower chirp and improved tolerance to drive signal imperfections).

2. Principle of operation

The operation of the proposed device is summarized in Fig. 1(d) and the device schematic is shown in Fig. 2. The microring is in an add-drop configuration where the waveguide-ring couplers for the “through” and “drop” ports are tunable 2 × 2 MZI-couplers. In Fig. 1(d) and the experimental demonstration in Section 3, we focus on high-speed modulation of the drop port coupler, but our analysis below shows that modulation of either the through or drop port coupler can result in BPSK modulation.

 

Fig. 2 Schematic of a coupling-modulated microring for BPSK. The microring is in an add-drop configuration with MZI-couplers at the through and drop sides. Either MZI-coupler can be modulated through its zero transmission point to achieve BPSK. Here, only the MZI-coupler at the drop side is modulated, and the MZI-coupler on the through side acts as a tunable coupler. This configuration matches the experimentally demonstrated device.

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Since the device will operate in the quasi-static regime, we can analyze its operation using the steady-state transmission coefficients. The field transmission coefficients at the drop and through ports of the microring are, respectively,

Intuitively, T_drop in Eq. (1a) is simply the modulation of the coupling coefficients, κ₁ or κ₂, multiplied by the large circulating field amplitude. If we use 2 × 2 MZI-couplers at the through and drop ports as in Fig. 2 [21,22], BPSK modulation of either MZI-coupler results in a BPSK modulation of T_drop with the same properties as a MZI. To describe this more rigorously, we write the through- and cross-coupling coefficients of the push-pull driven MZI-coupler as

From Eq. (1a), if either κ₁ or κ₂ changes sign while ϕ, a, and σ_1,2 are constant, then the optical output at the drop port would exhibit a phase-flip of π radians. This can be accomplished by modulating Δθ₁ or Δθ₂ in the MZI-coupler between positive and negative values such that κ₁ or κ₂ is driven through the zero transmission point. For BPSK modulation, κ₁ or κ₂ should swing between two values of equal magnitude and opposite sign, and σ₁ or σ₂ would swing between two identical values. The drop port transmission is the highest when the intracavity field amplitude is maximum, which is at the critical coupling condition, when T_thru = 0 on resonance, i.e., σ₁ = aσ₂. Therefore, for low insertion losses, κ₁ or κ₂ should be modulated between the two values that lead to critical coupling, i.e., the drop port MZI-coupler is modulated between ${\kappa }_2=\pm \sqrt{1-{\sigma }_1^2/a^2}$ or the through port MZI-coupler is modulated between ${\kappa }_1=\pm \sqrt{1-a^2{\sigma }_2^2}$. Modulating κ₂ between the two critical coupling values is illustrated in Fig. 1(d). Similar to a MZI, drive signal imperfections would not affect the phase-shift and the output intensity would be more tolerant to the drive signal imperfections because the transmission reaches local maxima at κ₂ values for critical coupling.

When either MZI-coupler is driven between the two values for κ₂ or κ₁ that lead to critical coupling, the phase-shifts, Δθ₁ or Δθ₂, required for the modulation are reduced compared to that of the MZI-coupler modulator alone by factors of

As an aside, efficient BPSK is not possible at the through port. From Eq. (1b), T_thru depends on σ_1,2 and not κ_1,2, and from Eq. (3), σ_1,2 does not change signs in microrings with reasonable finesse. To use the microring for DPSK modulation at the through port, the MZI-couplers would need to be biased at |σ_1,2| ≈ 0 and |κ_1,2| ≈ 1, and thus, the energy stored in the microring and the modulator efficiency would be low.

3. Experimental demonstration

Figure 3(a) shows an optical microscope image of the fabricated silicon coupling-modulated microring used for a proof-of-concept demonstration of the proposed design. The modulation drive signal is applied to the drop port MZI-coupler, and the through port MZI-coupler is only for tuning and is not compatible with high-speed modulation. The device was fabricated in the IBM Silicon CMOS Integrated Nanophotonics process [25].

 

Fig. 3 (a) Optical micrograph of the fabricated device. The thermal tuners are 50 μm long, and the PN diode phase-shifters are 200 μm long. PN diode phase-shifters are only present in the MZI-coupler at the drop side. (b) Measured transmission spectra at the through (thru) and drop ports. The thermal tuners were set for critical coupling with a drop port transmission of 30% on-resonance relative to the off-resonance through port transmission.

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The coupling coefficients at the through and drop ports of the microring were biased using the thermal tuners in the 2 × 2 MZI-couplers, while PN diode phase-shifters were included only in the MZI-coupler at the drop port. The PN diode phase-shifters and thermal tuners were 200 μm and 50 μm long, respectively. The MZI-couplers enable the independent tuning of the resonance wavelength and coupling coefficients [20, 23]. When the drop port was tuned to κ₂ = 0 and the through port was tuned to critical coupling, the full-width at half maximum linewidth of the microring at the through port was about 19.6 GHz, resulting in a cavity quality factor of Q ≈ 10⁴. The free spectral range of the microring was 92 GHz, so the finesse was about 5. Figure 3(b) shows the measured through and drop port transmission spectra of the microring when κ₁ and κ₂ were tuned to critical coupling with 30% power transmission on-resonance at the drop port relative to the off-resonance through port power.

To demonstrate DPSK modulation, the PN diode phase-shifters were forward-biased at 0.25 V and driven in a push-pull configuration. Non-return-to zero (NRZ) PRBS 2³¹ − 1 voltage signals with a 16 – 18 dB single-tap pre-emphasis and maximum swings of 1.6 V_pp were applied to each of the PN diode phase-shifters. The optical input was TE-polarized, resonant, and at a wavelength of about 1535 nm. The optical output from the drop port was demodulated using a fiber delay line interferometer. An interferometer with a delay of about 200 ps was used to demodulate the output at 5 Gb/s, and an interferometer with a delay of about 100 ps was used for the 10 Gb/s output. The DPSK modulated and demodulated optical signals were amplified using an erbium doped fiber amplifier, bandpass filtered (0.8 nm full-width at half-maximum bandwidth), and detected by a digital communications analyzer with a 28 Gb/s optical module.

Figure 4 shows the eye diagrams before and after the demodulator. The purpose of these measurements is to confirm DPSK modulation. The measured eye diagrams are characteristic of NRZ-DPSK modulation using MZIs [1]. Because κ₂ was driven through its zero transmission point, a lower rail is absent in the eye diagrams before the demodulator. The destructive port of the delay line demodulator produces the alternate mark inversion (AMI) [1]. The bottom rail is due to destructive interference of consecutive bits with the same phase, and the pulses are due to constructive interference of phase-flipped consecutive bits. In contrast, the eye diagrams of the demodulator constructive port have a top rail from constructive interference of successive bits of the same phase and a bottom rail from destructive interference of phase-flipped consecutive bits. Overall, the open eye diagrams at both demodulator outputs confirm that the coupling-modulated microring produced DPSK signals.

 

Fig. 4 Measured eye diagrams of the DPSK microring modulator at 5 and 10 Gb/s before and after the fiber delay line interferometer demodulator. The open eye diagrams with large extinction ratios confirm DPSK operation. The drive signals were NRZ PRBS 2³¹ − 1. The vertical scales differ between the 5 and 10 Gb/s eye diagrams and between the DPSK modulated and demodulated eye diagrams; accurate amplitude comparisons between the eye diagrams are difficult due to the different fiber paths and losses for each set of measurements.

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Even with open eye diagrams at the demodulator outputs, phase errors may be present and the phase difference between the two DPSK symbols may not be exactly π radians. The extinction ratio of the constructive port eye diagram is an indication of the phase errors in the DPSK signal, i.e., a 0 bottom rail requires perfect destructive interference (π radian phase-shift) between consecutive bits. We can calculate an upper-bound on the phase error by assuming the finite extinction ratio at the constructive port is entirely due to phase errors in the DPSK signal, and not the finite extinction ratio of the demodulator or any optical intensity fluctuations. The constructive port eye diagrams in Fig. 4 exhibit extinction ratios > 15 dB, which corresponds to a worst-case phase error of 0.11π radians between the two DPSK symbols. The phase error may be caused by a residual modulation of the resonance wavelength due to the nonlinear electrical response of the forward-biased PN diodes, which would result in deviation from ideal push-pull modulation. Reverse-biased PN junctions would provide more ideal push-pull modulation due to their more linear electrical response.

Due to the low finesse of the microring and the non-optimized PN diode phase-shifters, the swing in the optical power before the demodulator at 5 and 10 Gb/s was only about 30% and 10% of the off-resonance through port transmittance, respectively. The small swing is not an inherent characteristic of this microring DPSK modulator design. As shown in Eq. (1), |T_drop| → 1 on-resonance as a and |σ_1,2| approach unity. Reducing the size of the ring and the intracavity losses would increase the output transmission swing, since the drop port insertion loss decreases and the modulation efficiency increases with the finesse. An obvious approach to increase the finesse is to reduce the length of waveguide sections that do not contribute to modulation. First, the microring could be reconfigured to eliminate the long passive waveguide sections adjacent to the through port coupler in Fig. 3(a). Second, the tunable through port coupler could be replaced with a significantly smaller, fixed, directional coupler. Tunability of the through port coupling may not be necessary if the device is designed carefully and the fabrication variation is not too large [26].

4. Conclusion

We have proposed a new type of BPSK/DPSK microring modulator that operates by the phase-flip of the MZI-coupler. The proposed device was demonstrated in silicon and operated at 10 Gb/s. DPSK modulation was confirmed by eye diagram measurements of the output signal before and after a delay line interferometer demodulator. The modulation efficiency and insertion loss of the device can be improved by reducing the size of the microring and increasing the PN diode phase-shifter efficiency. The design can be extended to higher order phase modulation formats, such as quadrature phase-shift keying (QPSK), by inserting a coupling-modulated microring BPSK modulator into each arm of a MZI, with a relative phase-shift of π/2 radians between them. This concept can also be extended to lasers to produce coupling-modulated lasers with BPSK outputs [27].