A novel all-optical transversal filter with negative coefficients and tap doubling is proposed and experimentally demonstrated. Based on polarization modulation using the anisotropy of the electro-optic coefficient of LiNbO3 crystals, negative and positive coefficients are simultaneously generated. Tap doubling is also achieved by using wavelength- and polarization-dependent time delays in fiber. Due to the orthogonal polarity between the two coefficients of each wavelength, the proposed filter is free from coherent interference and the synthesis of filter taps is performed in the optical domain. The experimental results demonstrated that stable 6-tap bandpass filter characteristics can be obtained by using only three optical sources.
©2007 Optical Society of America
Photonic microwave filters (PMFs) have attracted great interest because incoming radio frequency (RF) signals can be processed in the optical domain with the advantages of wide bandwidth, immunity to electromagnetic interference, and low losses [1–2]. These PMFs have mostly been studied based on a transversal filter structure using a tapped fiber delay line. In this structure, the signal at each tap along this delay line is weighted by the appropriate coefficient, and the resulting products are summed to form the output. Therefore, filter characteristics depend on how many taps are being used and the coefficients available. Consequently, the number of filter taps limits the filter shapes achievable. Furthermore, to suppress resonant peaks around the baseband, coefficients with negative values (the inverse form of the positive value) are required.
One easy way to increase the number of taps is to use a corresponding number of optical sources with different wavelengths [3–4]. However, it increases the system cost. For this reason, spectrum-sliced optical sources using the amplified spontaneous emission noise of an erbium-doped fiber amplifier (EDFA) , and a super-electroluminescent diode (SLED)  have been introduced. Although these methods can reduce the filter cost, more effective filter structures exist to increase filter taps without increasing the number of optical wavelengths. As one approach, Vidal et al.  proposed an efficient wavelength division multiplexing (WDM) transversal filter architecture that increased the number of filter taps by reusing optical carriers based on a time division multiplexing technique. However, the filter taps were synthesized in the electrical domain to avoid interference between reused optical carriers. As a result, the bandwidth of the filter was limited by that of electronic components and careful path balance had to be maintained after OE conversion even though negative coefficients could be realized using a differential detection method such as reported in Sales et al. .
In this paper, we propose and experimentally demonstrate a novel all-optical transversal filter with not only negative coefficients but also tap doubling, wherein tap doubling means that the number of filter taps is doubled without increasing the number of optical wavelengths. This tap doubling was achieved by using wavelength- and polarization-dependent time delays while propagating through the fiber. Also, negative and positive coefficients were simultaneously generated by well known polarization modulation technique using the anisotropy of the electro-optic coefficient of LiNbO3 crystals [9–10]. The proposed filter, due to the orthogonal polarity between the two coefficients of each wavelength, is free from coherent interference.
2. Principle of the filter operation
Figure 1 illustrates the principle of operation used to implement positive and negative coefficients based on polarization modulation. A continuous-wave (CW) input beam is launched at 45° with respect to the principal axis of the LiNbO3 crystal. After passing through the crystal, the polarization state of the input beam is rotated depending on the applied voltage level due to the anisotropy of the electro-optic coefficient of the crystal [9–10]. For example, the polarization state of the input beam does not change when no voltage is applied to the crystal. However, the polarization state is rotated up to 90° when a switching voltage (Vπ) is applied. To confirm this operation, a 10-GHz RF signal was applied to the crystal and the outputs were measured with a sampling oscilloscope. In this measurement, commercial LiNbO3 based phase modulator (Vπ = 4.8 V) was used as a crystal and RF signal of 1.5 Vπ is driven to compensate residual phase shift in nx direction [9–10]. As shown in Fig. 1, the non-inverted and inverted RF signals were observed when the transmission axis of the tunable linear polarizer (TLP) was in ‘state A’ or ‘state B’, respectively. This means that these signals can be used as the positive and negative coefficients for a transversal filter. If the optical time delay between the positive and negative coefficients is applied properly, as reported in Oh et al. , the notch filter characteristic can be easily obtained.
3. Description of the multi-tap transversal filter architecture
Figure 2(a) illustrates a direct form realization of the transversal filter having a cascade form of basic notch filters. The transfer response, the output of the transversal filter, is given by
where a is the filter coefficient, N is the number of taps, and f is the electrical frequency. Odd-term coefficients (a 2k-1) are 1 and even-term coefficients (a 2k) are -1, due to polarization modulation. In the proposed transversal filter design, the most important part is how to implement the uniform time delay between filter coefficients.
Figure 2(b) illustrates a functional block diagram used to realize a multi-tap transversal filter. CW optical beams are launched by WDM sources. These beams are polarization-modulated using a RF signal. As a result, two polarized signals for each wavelength are generated and have an inverted pattern relative to each other as shown in A of Fig. 2(c), where M(=N/2) is the number of optical sources, and λ̅i represents the inverted form of the signal carried on the i-th wavelength. This method has an effect of doubling the number of taps. Subsequently, the time delay of 2Td is introduced between adjacent wavelengths by passing through a dispersive medium such as a standard single-mode fiber , or a high dispersion fiber . These media induce a wavelength-dependent time delay between wavelengths and the delay value can be controlled by adjusting the length of the medium. The wavelength-dependent time delay inside a fiber is inherently very small, and therefore, a long length of fiber is necessary to obtain the proper time delay, 2Td. Using the polarization modulation approach, the output has double sidebands and becomes weak to chromatic dispersion, especially, for the long length of fiber compared to single sideband modulation using a dual drive Mach-Zehnder modulator . For this reason, it is more useful to use such a method that takes a different path depending on the wavelength value. In our experiment, we implemented it by using a wavelength-selective coupler and mirror-coated fibers. The time relationship following a wavelength-dependent time delay is depicted in B of Fig. 2(c). Finally, a basic time delay, Td, is introduced between positive and negative coefficients of each wavelength using a polarization-dependent time delay. This can easily be implemented by making the signals propagate through a high birefringence (Hi-Bi) fiber. These signals undergo a polarization-dependent time delay while propagating through a fiber due to the difference in propagation velocity along the fast and slow axes. This delay can also be controlled by adjusting the length such that the polarization-dependent time delay is half of the wavelength-dependent time delay. In this manner, a uniform time delay can be realized between filter coefficients, such as illustrated in C of Fig. 2(c). This tap doubling method is achieved in the optical domain and is free from the electrical bandwidth limitation.
4. Experiment and Results
The experimental setup for testing the feasibility of the proposed filter is shown in Fig. 3. Three distributed feedback lasers with a 10 MHz linewidth (LD1: λ1=1547.2 nm, LD2: λ2 = 1548.8nm, LD3: λ3=1550.4nm) were used to implement the 6-tap filter. A LiNbO3-based phase modulator (PM) with an 8-GHz 3-dB down optical bandwidth was employed as a polarization modulator. Each polarization state of optical sources was adjusted by polarization controllers (PC1∼PC3). These beams were fed to the PM at 45° with respect to the principal axis, as described in Fig. 1, and then were polarization-modulated through the PM with a RF signal of 1.5 Vπ which was swept from 300 kHz to 3.5 GHz. The output from the PM was amplified by an erbium-doped fiber amplifier to compensate for the insertion loss of the optical circulator (OC), the arrayed waveguide grating (AWG) and optical mirrors (M1, M2, M3). After propagating the OC and AWG, a time delay of 2Td was given between two adjacent wavelengths. In this setup, the employed optical path difference was 13 cm. By considering the round trip time due to optical mirrors, the delay time was 1.26 ns. After that, the reflected and time-delayed beams were wavelength-multiplexed by the same AWG. To achieve the polarization-dependent time delay, a 500-m length of Hi-Bi fiber with a beat length of 4.1-mm at 1550 nm was used. At this Hi-Bi fiber, the polarization-dependent time delay was approximately 0.63 ns which were half of the value of the wavelength-dependent time delay. The PC4 was used to match the polarization state of the inverted and non-inverted beams into the slow and fast axes of the Hi-Bi fiber, respectively. Finally, the output of the Hi-Bi fiber was detected by a photodiode and the filter response was observed by a network analyzer.
To check the states of polarization-modulated signals after wavelength-dependent time delay, we measured it with respect to three different source wavelengths (λ1, λ2, λ3). For this measurement, TLP was used after OC, and 1-Gb/s digital patterns of ‘10111100’ were employed to clearly show the each time-delayed signal. When TLP is fixed to transmit non-inverted /inverted signals, three different signals were obtained with same amplitude level and time delay of 2Td (= 1.26 ns) as shown in Figs. 4(a) and 4(b), respectively. From these results, we can know that optical signals after wavelength-dependent time delay have almost same polarization states. This is due to the relatively small optical path difference between wavelengths compare to beat length (about 40 m, ) of conventional single mode fiber. Therefore, after wavelength-dependent time delay, one polarization controller (PC4) can be used for polarization-dependent time delay (Hi-Bi fiber).
Figure 5 shows the optical spectrum of three wavelengths after the polarization-dependent time delay. The amplitudes were adjusted to be equal to each other. No amplitude fluctuation due to optically coherent interference was observed.
Figure 6 shows the transfer responses of the implemented transversal filters with an increase in the number of optical sources from one to three. The solid lines represent experimental results and dotted lines depict theoretical results, where the experimental results of (a), (b), and (c) were obtained from one, two, and three optical sources and, on the other hand, the theoretical results from the simulation with two, four, and six sources. The measured response function was well-matched to the theoretical results. As expected, the obtained transfer responses present the tap doubling bandpass filter characteristic compared to the number of sources and the measured FSR (= 1/Td) was about 1.6 GHz. The filter coefficients of Figs. 6(a), 6(b), and 6(c) correspond to [1, -1], [1, -1, 1, -1], and [1, -1, 1, -1, 1, -1], respectively. Due to negative coefficients, no resonance in filter characteristics was observed at the baseband. Also, the filter was very stable despite the large coherence length of optical sources because two linear orthogonal polarization modes of each wavelength were well preserved until reaching the PD.
It is noteworthy that the wavelength-dependent time delay using AWG and optical mirrors could be integrated into planar waveguide circuits as a compact component. Also, the wavelength-dependent time delay could be realized by exploiting FBG arrays with the proper spacing between fiber gratings, corresponding to a time delay of Td.
We proposed and experimentally demonstrated a novel all-optical transversal filter with negative and positive coefficients based on polarization modulation. The combination of wavelength- and polarization-dependent time delay effectively gives the optical time delay between filter taps, so tap doubling is successfully achieved. Due to orthogonal polarity between the two coefficients of each wavelength, the proposed filter was free from coherent interference and the synthesis of filter taps was performed in the optical domain. This technique will be useful for enhancing filter performance by tap doubling in a conventional WDM-based transversal filter. From the measured frequency response, a stable 6-tap bandpass filter characteristic having an FSR of 1.6 GHz was obtained by using only three optical sources.
This research was partially supported by grant No. R01-2006-000-11088-0 from KOSEF and grant No. B1220-0601-0014 from IITA.
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