Ultra-wide band signal generation using a coupling-tunable silicon microring resonator

: U ltra-wide band signal generation using a silicon microring resonator tuned to an NRZ-DPSK modulated optical carrier is proposed and demonstrated. The scheme is shown to enable the generation of UWB signals with switchable polarity and tunable bandwidth by simply tuning the coupling regions of the microring resonator. Monocycle pulses with both negative and positive polarities are successfully synthesized experimentally.


Introduction
Ultra-wide band (UWB) over fiber is a promising technique to overcome the inherent limited propagation range of traditional electrical UWB signals in high data rate wireless applications [1]. As a consequence, the photonic generation of UWB signals has been a very active area of research over the past few years, and numerous techniques have been suggested and demonstrated [2][3][4][5][6]. One of the principles underlying a number of those techniques is to perform phase modulation of an optical carrier with Gaussian pulses, followed by phase-tointensity modulation (PM-to-IM) conversion using a frequency discriminator or a dispersive element [2,3]. PM-to-IM conversion can be achieved using the slopes of the transfer functions of optical filters, and the use of a Mach-Zehnder interferometer (MZI) [7], a silicon microring resonator (MRR) [8,9], and a microfibre ring resonator [10] have enabled the synthesis of UWB waveforms with adjustable polarity. However, the previously quoted methods rely on the generation of Gaussian electrical pulses, which may not be available from conventional electronic circuits. Recently, the use of a nonlinear optical loop mirror [11] and two-photon absorption in a silicon waveguide [6] have been demonstrated, showing the ability to synthesize UWB signals with tunable bandwidth.
In this paper, we propose to use phase modulation with standard non return-to-zero (NRZ) electronics in a Mach-Zehnder modulator (MZM) and to exploit the simultaneous phase shifts and intensity dips of an NRZ differential phase-shift keying (NRZ-DPSK) signal to generate an UWB signal after filtering by a silicon add-drop MRR whose resonance is tuned to the center frequency of the signal. We emphasise that this method is different from previously demonstrated techniques making use of Gaussian phase modulation followed by frequency discrimination such as in [8,9]. We show that, by proper adjustment of the coupling coefficients of the MRR, monocycle pulses with both negative and positive polarities can be obtained. Furthermore, the bandwidth of the UWB signal can be easily tuned by tuning the coupling coefficients of the MRR. We demonstrate the concept experimentally using a specially designed and fabricated silicon MRR.

Principle of the method
The principle of the method is depicted schematically in Fig. 1. A continuous wave (CW) laser is modulated in the NRZ-DPSK format in an MZM. The modulation results in intensity dips each time the phase of the signal is flipped between 0 and π. The modulated signal is then input to a silicon microring resonator in add-drop configuration (therefore with two coupling regions). In the proposed method, the CW laser needs to be tuned to a resonance frequency of the MRR. The output of the through port of the MRR is finally detected in a photodiode (PD). When the carrier wavelength of the NRZ-DPSK signal is tuned to a resonance, the MRR through output field E t can be expressed in the time domain as  where E in (t) is the electric field of the input NRZ-DPSK signal and a and T are the field roundtrip transmission coefficient and roundtrip time of the MRR, respectively. r 1 and r 2 are the field transmission coefficients of the through and drop coupling regions, respectively, with the corresponding field coupling coefficients κ 1 and κ 2 satisfying r 2 1 + κ 2 1 = 1 and r 2 2 + κ 2 2 = 1 for lossless coupling. According to Eq. (1), it can be found that an overshoot followed by a dip, or a dip followed by an overshoot can be obtained each time an intensity dip of the NRZ-DPSK signal is input to the MRR if r 1 < ar 2 or r 1 > ar 2 , respectively. In addition, by adjusting the coupling coefficients κ 1 and κ 2 at the through and drop couplers of the resonator, respectively, the amplitudes of the overshoots and dips with respect to the average signal level (A 1 and A 2 , respectively, as defined in Fig. 1) can be equalized, resulting in a typical monocycle pulse shape as simulated in Figs. 2(a) and 2(b). The values of the optimum coupling coefficients depend on the fall and rise times of the intensity dips of the NRZ-DPSK modulated signal, and therefore on the electrical driving signal rise time and modulator bandwidth. This point is illustrated in Fig. 2(c), which represents the combination of values of κ 2 1 and κ 2 2 for which A 1 = A 2 for three signal rise times of 50 ps, 100 ps and 200 ps, respectively. It can be seen that, for each value of the rise time of the phase modulating signal, two sets of κ 2 1 , κ 2 2 parameters that equalize A 1 and A 2 can be found. Each set corresponds to a given polarity of the monocycle pulse, as illustrated in Fig. 2(c). Consequently, optimization of the UWB waveform requires MRRs with tunable coupling coefficients. To obtain a monocycle with higher radio frequency (RF) power, a higher peak-to-peak power (A 1 +A 2 ) is preferred. Figure 2(d) shows the normalized peak-topeak power as a function of the MRR through and drop power coupling coefficients κ 2 1 and κ 2 2 in case the rise time of the electrical driving signal is 200 ps. The combinations of κ 2 1 and κ 2 2 equalizing A 1 and A 2 for this rise time are also reproduced for reference with black curves.
One can find that, as κ 2 2 decreases, a higher peak-to-peak amplitude will be obtained for the generated monocycle pulses. Figure 3 analyzes how the 10 dB bandwidth and peak frequency of the generated UWB spectra evolve as a function of power coupling coefficient κ 2 2 for both positive and negative polarities of the monocycle pulse and for different electrical signal rise time values. One can find that, as κ 2 2 increases, both the 10 dB bandwidth and peak frequency increase for both generated positive and negative polarity UWB signals, as shown in Figs. 3(a) and 3(b). This is because, as κ 2 2 increases, the Q value of the MRR decreases, leading to a shorter photon lifetime and consequently shorter overshoot of the generated UWB signal and larger 10 dB bandwidth. The tunable ranges of both 10 dB bandwidth and peak frequency increase as the electrical driving signal rise time decreases. For different electrical driving signal rise times, both positive and negative polarity UWB signals exhibit a high fractional bandwidth around 130%, as shown in Fig. 3(c), which meets the Federal Communications Commission (FCC) requirement of 20% [12].

Fabricated device
In order to test this new concept, a silicon MRR with adjustable through and drop power coupling coefficients was designed and fabricated. The tunability of the coupling coefficients is achieved by two MZI structures which act as through and drop couplers. Thermal tuning enables to control the relative phase shifts between the two arms of each MZI, and consequently the power coupling ratio between the ring and the input and drop waveguides. The device was fabricated on a silicon-on-insulator (SOI) wafer with top silicon thickness of 250 nm and buried silicon oxide of 3 µm. The fabrication process is identical to the one described in details in [13]. Figure 4(a) shows a picture of the fabricated device. The waveguides are 435 nm wide and covered with 600 nm benzocyclobutene (BCB) as top cladding layer. A coupling gap of 248 nm is introduced in each coupling region of the MZIs, as shown in Fig. 4(b). Three heaters (100 nm thick titanium with 5 nm thick gold) are deposited on top of part of the ring waveguide and of one of the arms in each of the MZI structures in order to perform thermal tuning of the resonance wavelength and the MRR coupling coefficients. The device operates in the transverse magnetic (TM) mode and has a free-spectral range (FSR) of 100 GHz. The input and output silicon waveguides are inversely tapered to 45 nm, as shown in Fig. 4(c), and covered by a polymer (SU8 2005) waveguide to form a nano-coupler to improve the coupling loss to tapered fibres. The insertion loss is measured to be 10.5 dB for the TM mode before heating the two coupling regions. The high insertion loss is potentially due to optical power leakage to the metal heater above the waveguide. It could be improved by increasing the thickness of the BCB layer.

Experimental demonstration
The fabricated device was used in an UWB generation experiment at 1.25 Gbit/s. The experimental set-up is shown in Fig. 5. The electrical signals driving an MZM biased at a transmission minimum in push-pull mode were generated at 1.25 Gbit/s by programming a 40 Gbit/s bit pattern generator, hence resulting in fast rise and fall times. Low pass filtering of the driving signals with a 4 th order Bessel filter having a 7.5 GHz cut-off frequency was performed in order to in- crease their rise time to ∼50 ps. It should be pointed out that this filtering is required by the fast rise time of the electronics available in our laboratory. In practice the proposed method will directly accommodate the rise times of lower speed signal generation electronics compatible with UWB applications. Similarly, the choice of the 1.25 GHz frequency is a consequence of available equipment but the concept is straightforward to implement at lower repetition rates. The optical signal was amplified by an erbium-doped fiber amplifier (EDFA). Afterwards, its state-of-polarization was aligned to the TM mode by a polarization controller (PC) and input to the chip with an input power of about 18 dBm. The output signals from the MRR were amplified by another EDFA and detected with a high-speed photodiode with cut-off frequency of 45 GHz. Figure 6 shows the experimental results for the generation of UWB signals with both negative and positive polarities. The CW laser was precisely tuned to a resonance of the MRR, as shown in the optical spectra of Figs. 6(a) and 6(d). The power coupling coefficients of the through and drop couplers of the MRR were thermally tuned to obtain the balanced monocycle pulses of Figs. 6(b) and 6(e). Figures 6(c) and 6(f) show the radio-frequency spectra of the UWB signal after photodetection for generated UWB signals of negative and positive polarities, respectively. The MRR insertion loss increases when the polarity is tuned from negative to positive, as shown in Figs. 6(a) and 6(d). This is due to the fact that higher coupling coefficients are used in order to balance the generated monocycle pulses, which further results in narrower UWB pulses (see Fig. 6(e)) and broader RF spectra (see Fig. 6(f)). The independent settings of κ 1 and κ 2 offer a large degree of flexibility to tune the UWB waveform and the resulting radio-frequency spectrum.

Discussion
Due to the short electrical rise time of the driving signals used in our experimental demonstration, the measured RF spectra shown in Figs. 6(c) and 6(f) have broad bandwidths compared with the FCC mask. In order to map the FCC mask, a microwave filter could be used to tailor the RF spectrum [17]. Otherwise, a slower rise time is needed and more complex pulse shapes would be required [14]. Figure 6 shows a simulated typical UWB monocycle pulse (detailed in Fig. 7(a)) generated by our proposed MRR method and the corresponding RF spectrum (see Fig. 7(b)) with κ 2 1 = 0.462, κ 2 2 = 0.015 and rise time of 100 ps. A Gaussian monocycle pulse obtained by first order differentiation of a Gaussian pulse and having the same time delay between the peak and dip as the MRR-generated monocycle, as well as its calculated RF spectrum, are also shown for comparison. The RF spectrum of the MRR-generated UWB monocycle pulse appears to be more compliant with the FCC mask than that of the Gaussian monocycle. Once such a monocycle pulse has been synthesized, more complex pulse shapes could be obtained by cascading additional MRRs, as demonstrated in [9].  Using the proposed technique, a compact UWB signal generator could potentially be realised by monolithically integrating the coupling-tunable silicon MRR with a silicon MZM [15] and germanium detectors [16] on a single chip.

Conclusion
A novel method to generate an UWB signal using a silicon MRR and a phase modulated signal generated using conventional NRZ electronics in a Mach-Zehnder modulator has been proposed and demonstrated. It has been shown that proper adjustment of the coupling coefficients of the add-drop MRR enables the synthesis of high-quality monocycle pulses with tunable bandwidth. A stable and compact silicon-on-insulator MRR with 100 GHz FSR and tunable coupling coefficients has been specially designed and fabricated for this application. The fabricated device was applied to the generation of an UWB signal at 1.25 Gbit/s with both negative and positive polarities.