Delay Measurement and SplitStep TimeDomain Analysis of Ring Resonator AllPass Filters
 Author: Kim Hyosuk, Ko Yoonyoung, Moon Hyunseung, Kim Jaeseong, Chung Youngchul
 Publish: Current Optics and Photonics Volume 18, Issue6, p766~771, 25 Dec 2014

ABSTRACT
Singlering allpass filters with various coupling ratios are designed, fabricated, and characterized to assess the validity of the splitstep timedomain modeling approach, which is considered for direct simulation of timedomain characteristics, such as optical delay, of various ring resonator devices. When the coupling ratio of the singlering allpass filter is 0.4 and 0.8, the delay time is measured to be about 145 and 42 ps respectively, which is comparable to the timedomain modeling results of 151 and 47 ps respectively. The measurements for two and threering allpass filters are also found to agree quite well with the simulation results. With these results it is confirmed that the splitstep timedomain model could be efficiently incorporated into an opticalcommunication simulation module for ring resonator delay components in an alloptical packet switching system.

KEYWORD
Optical delay , Slow light , Ring resonator , All pass filter , Timedomain modeling

I. INTRODUCTION
The demand for multimedia communication service is increasing beyond expectation, as video services through smart phones and wired subscriber networks are exploding. The increase of communication traffic in the enduser network requires wideband and smart fiberoptic backbone networks. In the backbone networks of the future, the packets will need to be alloptically routed, without the intervention of conversion between optical and electrical signals [1]. To realize alloptical routing networks, variable delay components are required for the buffering process. Ring resonator allpass filters (APFs) are good candidates for variable optical delay devices [25]. Even though several approaches in analytical and numerical analysis provide lots of information regarding the delay performance of ring resonator devices [5], the quality of delayed pulse shapes can be directly investigated through a timedomain analysis.
Recently, a splitstep largesignal timedomain modeling approach was reported, offering direct and easy analysis of pulse response of ring resonator delay devices [6]. In this paper, singlering APFs with various coupling ratios, tworing APFs, and threering APFs are designed, fabricated, and characterized to evaluate the effectiveness of the splitstep timedomain modeling. The measurement results are shown to agree fairly well with the timedomain modeling results, in terms of delay time and qualitive pulse shape, which confirms the usefulness of the splitstep timedomain modeling approach. Splitstep timedomain modeling can be efficiently incorporated into an advanced optical communication modeling tool, when the ring resonator delay devices are present in optical packet switching systems.
II. SPLITSTEP TIMEDOMAIN MODEL
A tworing resonator APF, shown in Fig. 1, is considered to illustrate the splitstep timedomain model (SSTDM) employed in this paper. In this model, the numerical solution of the timedependent coupledwave equation is found through a splitstep operator approach. The SSTDM consists of the numerical solution of the timedependent coupledwave equations for forward and reverse waves [6, 7].
The timedependent coupledwave equations can be numerically solved by dividing the bus and ring waveguides into a number of small subsections of equal length
△z , as shown in Fig. 2. In the simulation, the calculation in each section consists of two operations that are performed during the time interval corresponding to subsection (△z ) propagation.First, the forward/reverse waves in three waveguides (a bus and two ring waveguides) are updated to incorporate the attenuation and phase accumulation through a section in a time step. Then, the coupling effects between waveguides are taken into consideration. The appropriate boundary conditions in the bus and ring waveguides are applied at every time step. This approach can be extended as the number of coupled rings increases.
III. EXPERIMENTAL AND SIMULATION RESULTS FOR RING RESONATOR ALLPASS FILTERS
The top view of a fabricated singlering resonator APF is shown in Fig. 3. The waveguide core is filled with ZPU12 polymer (product of ChemOptics Co.), with equal width and height of 1.8 μm. LFR polymer (product of ChemOptics Co.) cladding material surrounds the core. The refractive indices of core and cladding near the wavelength of 1.55 μm are 1.48 and 1.37 respectively, which corresponds to a relative index difference of 7.4％. The dispersion of ZPU12 is −4.6×10^{−6} nm^{−1}, according to data from ChemOptics Co. The high index contrast between core and cladding results in strong optical confinement in the waveguide, so the ring resonator device can be made very compact by minimizing bending loss for quite a small ring radius [3]. Electrodes are evaporated on top of the ring resonators for thermal tuning of the resonance wavelength. The effective and group refractive indices of the straight polymer waveguide are 1.426504 and 1.435055 respectively. The radius of the curved waveguide in the ratrace track ring is 250 µm, which is large enough to provide neglible bending loss. In other words, the curved waveguide mode is well confined inside the core region, and the effective and group indices of the curved waveguide are found to be almost the same as those of the straight waveguide. Therefore, the same refractive index values are used both for the straight and curved waveguides in the following simulations. Including the straight waveguide length in the coupling region, the free spectral range is designed to be about 100 GHz, which corresponds to a roundtrip time of about 10 ps around the ring.
The shape of the ring resonator is a ratrace track composed of two semicircles of radius 250 µm plus two straight waveguides of length 213 µm. To investigate the effect of coupling ratio on the time delay characteristics, we designed and fabricated singlering APFs with different coupling ratios. The target coupling ratios of the busring couplers in the singlering APFs are 0.4, 0.5, 0.6, and 0.8 respectively. The various coupling ratios are achieved by adjusting the gap between the bus and the straight waveguides in the ratrace track. The gaps are designed to be 2.07 µm, 1.93 µm, 1.8 µm, and 1.58 µm respectively, to achieve the four coupling ratios. The fabrication process is as follows: The cladding material (LFR) is spincoated on a silicon wafer and baked for 30 minutes at a temperature of 200℃. The waveguide core regions are removed from the cladding polymer using photolithography and a dryetching process. The core polymer material (ZPU12) is filled by spincoating and hardened through UV irradiation and thermal curing, and then the polymer on top of the core region is removed using a plain dryetching process. Finally the 5.1μmthick cladding polymer is spincoated, baked, and cured to form the upper cladding [8].
The passthrough characteristics as a function of wavelength are measured and shown in Fig. 4 for coupling ratios of 0.4 and 0.8. The free spectral range is measured to be 0.82 nm, which corresponds to the fabricated ring resonator geometry. The setup for the pulse delay measurement is as follows: The optical waves from the tunable laser are modulated by a LiNbO_{3} modulator, to which an electrical pulse signal from a pulse pattern generator is applied. A TEpolarized pulse signal is launched into a singlering APF through a polarization controller. The FWHM (full width at half maximum) pulse width is about 230 ps. The optical pulse signal through the APF is amplified by an EDFA (ErbiumDoped Fiber Amplifier), and the time delay characteristics are measured using a DCA (Data Communication Analyzer), which can display the optical signal waveform directly with its builtin detector of bandwidth 20 GHz.
The delay measurement results for the APFs are shown in Fig. 5. During the measurement the wavelength is set to 1546.14 nm, at which the ring is nonresonant without current injection. The tuning current is applied to make the ring resonant, and the delay is observed. When the coupling ratio of the singlering APFs is 0.4, 0.5, 0.6, and 0.8, the delay times are measured to be about 145, 115, 86, and 42 ps respectively. In Fig. 5(a) the input optical pulse, as well as the output pulses in the nonresonant and resonant conditions, are displayed for comparison. The shape of the nonresonant output pulse is essentially the same as that of the input pulse. In the figure, the timing of the input pulse is shifted for comparison. Figure 6 shows the splitstep timedomain modeling results of the APFs having various coupling ratios. In the calculation, the propagation loss of the waveguide is assumed to be 1.5 dB/cm. The simulation time for a singlering APF is about 3 seconds when the subsection length
△z is set to be 10 µm, which is fast enough to be employed in the timedomain simulation module for the optical packet switching system. When the busring coupling ratios are 0.4, 0.5, 0.6, and 0.8, the time delays are observed to be 151, 123, 92, and 47 ps respectively, which agrees reasonably well with the experimental results. The measured shapes of the delayed pulses are qualitively similar to the timedomain simulation results.The APFs with two coupled rings and three coupled rings are also fabricated, to compare the delay measurement results with simulation results. The coupling ratio between the bus and ring waveguide is designed to be 0.5, for which the gap in the mask pattern is 1.93 µm. The coupling ratio between the rings in the tworing APF is designed to be 0.12, for which the gap in the mask pattern is 1.46 µm. In the threering APF (Fig. 8), the coupling ratio between the leftmost and the center rings is designed to be 0.12, and that between the center and rightmost rings 0.08, for which the gap is designed to be 1.73 µm. The geometry of the ring resonators is the same as that of the singlering APF discussed in the above. Photographs of the fabricated two and threering APFs are shown in Figs. 7 and 8 respectively; the measured delay characteristics are shown in Fig. 9. The delay times through the two and threering APFs are observed to be 238 and 330 ps respectively. The splitstep timedomain simulation results of the pulse delay characteristics through the two and threering APF are also shown in Fig. 10, and the delay times are observed to be 276 and 397 ps respectively, which corresponds reasonably well to the experemental results. Some discrepancy between experiment and simulation could be due to actual coupling ratios being slightly different from the nominal design values.
IV. CONCLUSIONS
We designed and fabricated polymer singlering APFs with various coupling ratios, as well as two and threering APFs, to evaluate the splitstep timedomain modeling approach, which is considered a beneficial tool to assess the passthrough characteristics of an optical pulse signal through the APFs.
The time delay is measured by tuning the resonance wavelength of the ring near the operating wavelength. When the coupling ratio of the singlering APF is 0.4, 0.5, 0.6, and 0.8, the delay is measured to be about 145, 115, 86, and 42 ps respectively. The measured delay times are quite comparable to the timedomain modeling results, which are 151, 123, 92, and 47 ps respectively. The delay times of the two and threering APFs are measured to be 238 and 330 ps, which are quite close to the simulation results of 276 and 397 ps respectively. The shape of the delayed pulses in the experiment also agrees well with that from simulation, confirming the accuracy of the splitstep timedomain modeling. The simulation time for a singlering APF is as short as about 3 seconds, which illustrates the efficiency of the model. From these experiments and simulations, the splitstep timedomain model exhibits the potential to be efficiently incorporated into a simulation tool for optical communcation, for the case of ring resonator delay devices in alloptical packet switching systems.

[FIG. 1.] A doublering APF, to illustrate the splitstep timedomain model.

[FIG. 2.] Conceptual configuration of the splitstep timedomain model for the doublering APF.

[FIG. 3.] Top view of a fabricated singlering resonator APF.

[FIG. 4.] Passthrough characteristics of a singlering resonator APF as a function of wavelength for coupling ratios of (a) 0.4 and (b) 0.8.

[FIG. 5.] Measured delay characteristics of the fabricated singlering APFs. The delay times are measured to be about 42, 86, 115, and 145 ps when the coupling ratios between bus and ring are (a) 0.8, (b) 0.6, (c) 0.5, and (d) 0.4 respectively.

[FIG. 6.] Simulation results of the singlering APFs with various coupling ratios. The delay times are about 47, 92, 123, and 151 ps when the coupling ratios between bus and ring are (a) 0.8, (b) 0.6, (c) 0.5, and (d) 0.4 respectively.

[FIG. 7.] Top view of a fabricated tworing APF.

[FIG. 8.] Top view of a fabricated threering APF.

[FIG. 9.] Measured delay characteristics through (a) a tworing and (b) a threering APF with all the rings in the resonant condition, compared to those with all the rings in the nonresonant condition. The delay times are measured to be 238 and 330 ps respectively.

[FIG. 10.] Splitstep timedomain simulation results of pulse delay characteristics through (a) a tworing and (b) a threering APF with all rings in the resonant condition, compared to those with all rings in the nonresonant condition. The delay times are 276 and 397 ps respectively.