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Dispersion compensation is critical for high bitrate lightwave systems and reconfigurable optical networks, which will require tunable dispersion at the receiver to compensate the cumulative dispersion of different routes. Because of the large number of channels in dense WDM systems, periodic filters are advantageous compared to single channel devices, requiring a unique filter for every WDM channel. While there are several periodic compensators that rely on feedforward filters, such as cascaded Mach-Zehnder and phased array interferometers, we focus on optical allpass filters. Allpass filters are unique in their ability to provide a flexible phase response that can approximate any desired dispersion over a bandwidth which is large relative to the filter period and, in the limit of low feedback path losses, which is decoupled from the magnitude response. In contrast, feedforward filters must incur loss variation across the period to obtain dispersion across the passband. Thus, allpass filters are a natural choice for achieving low loss and extremely compact, dispersion compensating filters. Implementations in both planar waveguides and etalons with tunable reflectors are discussed, and system test results are reviewed.
Fig. 1. Allpass filter (a) basic ring resonator and (b) fully tunable design. (c) A tunable Gires-Tournois interferometer using an electrostatically controlled membrane.
Allpass filters, which ideally have lossless feedback paths, have a frequency-dependent phase response and unity magnitude response, such that no amplitude filtering occurs. The building blocks for optical allpass filters are the ring resonator and Gires-Tournois interferometer shown in Fig. 1(a-c). The group delay depends on the coupling kr into the feedback path and has a maximum on-resonance [1#]. The resonant frequency can be translated a full period by varying the feedback optical path length over one wavelength; this variation is represented by the phase change fr. The filter period, or free spectral range (FSR), is inversely related to the feedback path delay (T). The dispersion scales as T2, but the bandwidth scales as 1/T. For a single-stage filter and fixed FSR, the coupling can be varied to achieve a large dispersion, but only at the expense of limiting the bandwidth over which the dispersion is roughly constant. By cascading multiple stages, a desired dispersion is achieved over a large portion of the filter period as shown in Fig. 2a [#2]. The opposite sign of dispersion is achieved by reversing the order of the resonant frequencies. If wavelength-dependent coupling into the feedback path is introduced, the delay slope from period-to-period is varied and a dispersion slope compensator results. In addition to dispersion compensation, allpass filters are building blocks for many other filter applications as well .
Fig. 2. (a) Multistage simulated filter response showing contributions of individual stages to the overall delay. (b) Measured group delay for a 4-stage ring resonator filter demonstrating dispersion tuning from Ð2000 ps/nm to Ð500 ps/nm.
Very compact, fully tunable ring resonators have been fabricated using planar waveguides. Many stages are easily cascaded, and tunability is achieved via thermo-optic phase shifters. Both the feedback coupling and resonant frequency are tuned with phase shifters as shown in Fig. 1b, which incorporates a Mach-Zehnder interferometer (MZI) in the ring [#3]. If the arms of the MZI are not crossed, an asymmetric MZI is formed, which provides wavelength-dependent coupling useful for dispersion slope compensation. A large, continuous dispersion tuning range (±2000 ps/nm) was recently demonstrated on a four-stage, silica-on-silicon planar waveguide compensator . A core-to-cladding index contrast of 2% and a minimum bend radius of 1 mm were used. The roundtrip loss was 0.7 dB/ring, and the waveguide-to-standard singlemode fiber (SSMF) coupling loss was 0.8 dB/facet, which could be improved, for example, by coupling to high numerical aperture fiber instead. The ring loss introduces a loss variation across the period with the peak loss occurring coincident with the maximum delay. The magnitude and group delay response were measured at various heater powers and input to an algorithm that determines the required heater settings for a desired dispersion given requirements on the bandwidth utilization and maximum allowable group delay ripple. A large dispersion tuning range is demonstrated in Fig. 2b for a passband of 16 GHz, or 60% bandwidth utilization. Even larger bandwidth utilizations can be achieved by changing the heater settings, with the only limit being a tradeoff in peak dispersion or group delay ripple. The FSR is increased by implementing tighter bend radii.
System tests were performed using the filter to compensate a 100 km span of SSMF (+1700 ps/nm). A single tunable laser source was externally modulated with a 10 Gb/s NRZ signal (PRBS=231-1). The filter was used both as a pre-compensator and post-compensator with equal results. The polarization into the filter was controlled in either case due to the waveguide birefringence, which causes polarization mode dispersion (PMD). To test the filters wavelength tolerance, the laser was tuned across one filter period. The system penalty remained below 1 dB over 30% of the FSR. Then, the laser was tuned to adjacent periods of the device. Over a range of 17 nm (93 periods), which was limited by the optical amplifiers gain bandwidth, the filter compensated the dispersion with a penalty of < 1dB.
For etalon-based implementations, tunability has been achieved using an electrostatically-actuated membrane for the partial reflector [5#] as shown in Fig. 1c and thermal tuning of the resonant wavelength. A two-stage allpass filter was demonstrated with a 100GHz FSR, +/-100 ps/nm tuning range and a 50 GHz passband width. Etalon approaches offer a path to low PMD devices without polarization diversity, but are more challenging to scale in terms of number of stages. A tunable thin film dispersion slope compensating filters has been demonstrated recently [6#]. In this case, multiple passes are made through a given set of cavities to increase the effective number of stages.
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