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The performance of the phase-shifted superstructured fiber Bragg grating (SSFBG) for optical code (OC) recognition was investigated with different reflectivity as well as input pulse width. The auto-correlation peak (PA) and the ratios of PA to the maximum wing level (P/W) and cross-correlation level (P/C) were used to quantitatively evaluate the OC recognition performance. There is a conflict between obtaining high PA and high P/W and P/C ratios in high reflectivity regime. The approach of applying apodization technique to improve the performance in high reflectivity regime is proposed. The comparative experimental investigations with 127-chip 160-Gchip/s SSFBG are carried out to confirm the effectiveness of the proposed approach. Error-free transmission with multiplexing of two active users has been successfully achieved by the apodized SSFBG at a data rate of 1.25 Gbit/s.
©2004 Optical Society of America
1. Introduction
Optical code (OC) generation and recognition techniques have been primarily investigated for application in the optical code division multiple access (OCDMA) system to process the OC in the optical domain [1–3]. It has recently been noticed that OC labels have good prospect in versatile applications for OCDMA, optical burst switching (OBS) and optical packet switching (OPS) systems and will be able to play an important role in future Internet protocol (IP) over photonic networks [4–6]. There are a number of different OC generation/recognition schemes, which can be classified according to their operation principle as incoherent or coherent schemes, or according to their processing dimensions as one-dimensional (1-D), or two-dimensional (2-D) schemes. Figure 1 shows an illustration of these classifications.
The incoherent techniques, which work on an optical-power-intensity basis, process OCs in a unipolar (0,1) manner, which results in disadvantages such as small code size, low optical power and bandwidth efficiency, and poor correlation property [1–16]. In contrast, coherent techniques, which work on a field-amplitude basis, process OCs in a bipolar (-1, +1) manner all optically; thus, they are superior to incoherent techniques in the overall performance [3–7, 17–25]. On the other hand, OCs could be processed in either the time domain [1–8, 17–19] or the frequency domain [3–6, 9–11, 20–25] in 1-D schemes, and in the frequency and time domains simultaneously [12–16] in 2-D schemes.
The OC en/decoders are the most crucial components in these optical implementations. Techniques that have been adopted include fiber-optic delay lines (FODL) [1–3, 17–18], planar lightwave circuits (PLC) [4–6, 19], spatial light modulators (SLM) [9, 20–21], arrayed-waveguide grating (AWG) [10, 12–13], fiber Bragg gratings (FBG) [8, 11, 14–16, 22–25], holographic device [26], and micro-electromechanical systems (MEMS) [27]. Figure 1 shows their applications for different schemes.
Particularly, in the coherent time -spreading (TS) scheme, the OC is generated by spreading the coherent optical pulses in time, and the phase of the optical carrier is changed according to a specific bipolar signature pattern. It is similar to that in the electrical field, which has been studied quite extensively for radar and wireless CDMA communication applications. In this scheme, controlling the optical paths in the order fractions of optical wavelength is required to guarantee the optical pulses are coherently interfering with each other during the signal processing [3–4]. PLC that can satisfy this critical requirement has been applied as en/decoder [4–6]. However, PLC can not easily generate OC in the orders of a hundred-chips order long, because of the physical constraint of the silica substrate and design complexity, which will result in an inability to generate a large number of OCs, leading to poor system scalability. Given these fact, the FBG might be a powerful alternative.
The FBG has been developed into a critical component for many applications in fiber-optic communication and sensor systems [28–29]. A “superstructured” FBG (SSFBG) is defined as an FBG with a slowly varying refractive-index modulation profile imposed along its length [22, 30]. Furthermore, a full complex refractive-index modulation profile can be realized in an SSFBG by inserting phase shifts between different segments, as shown in Fig. 2(a). With an injection of a short optical pulse, this phase-shifted SSFBG can generate a series of coherent short optical pulses whose phases are determined by the pattern of the phase shifts in the SSFBG. If the lengths of all segments are all the same as Lchip and the refractive-index modulation is constant along the whole grating, the light can penetrate the whole grating length, and the individual segments of the grating contribute more or less equally to the reflected response. The phase-shifted SSFBG thus works as an optical transversal filter to generate a binary-phase-shift-key (BPSK) [22] or a quaternary-phase-shift-key (QPSK) [23] OC from its impulse response, and it can also perform correlation for OC recognition. Figures 2(b) and (c) illustrate the principles of BPSK OC generation and recognition respectively. This sort of phase-shifted SSFBG can be fabricated with a single short phase mask of length Lchip by continuous grating writing [22] or holographic techniques [25]. These techniques provide a high flexibility in producing different ultra-long optical code. High-precis ion phase control can be achieved as well for BPSK, QPSK or even more multiple phase level OC.
Fig. 2. Superstructured FBG with phase shifts for OC generation/recognition (a) Configuration, working principle for BPSK OC generation (b) and recognition (c).
However, previous investigations are based on the assumption of weakly coupled SSFBG [22, 23]. It has been suggested that the SSFBG should be with low reflectivity (peak reflectivity<20%) for OC generation/recognition to guarantee the Fourier-transform relationship between the spatial refractive-index modulation profile and the impulse response of the grating takes effect [22, 23]. The low reflectivity causes a high insertion loss of the en/decoder. This will be a critical issue in passive optical networks (PON), where the power budget is always very tight [31]. A compromise has to be made between the insertion loss and the recognition performance. However, there has been no quantitative investigation on the OC generation/recognition performance so far to determine the optimum reflectivity for SSFBG en/decoder. This paper will address on the above issues. In addition, the selection of a suitable code set for the SSFBG en/decoder, effects of input pulsewidth, impairments due to the wavelength drift and temperature deviation between the encoder and decoder will also be investigated.
2. Phase-shifted SSFBG and OC selection
The phase-shifted SSFBG OC en/decoder in Fig. 2(a) contains Nchip segments with length Lchip, where Nchip is the number of chips of the represented BPSK OC {ai: ai ∈(0,1), 0< i≤Nchip} and Lchip=Tchip/(2nc), Tchip is the temporal interval duration of the OC, n is the refractive index of the optical fiber, and c is velocity of light in vacuum. It is noteworthy that the SSFBG can’t discriminate a BPSK OC initiated with “1” from its complement code initialed with “-1” as shown in the bottom of Fig. 2(b). This would be a problem in electrical-signal processing such as wireless CDMA, where both the code processing and signal detection are based on the complex-form electrical field amplitude. However, as the optical signal detection is based on signal intensity instead of field amplitude, therefore, neglecting this OC representation degeneracy in the SSFBG en/decoder will not have any detrimental effect.
Various code sets used for wireless CDMA communications such as M sequence, Gold codes, Kasami code [32], have been adopted as the OCs [22–25]. In electrical field, the decoding process is to periodically correlate the encoded signal:
where {ai} and {bi} are two codes in a code set, . Therefore, these code sets are designed to have good periodic auto/cross-correlation properties. However, in the coherent OC generation/recognition with SSFBG, the OC recognition process does not perform the periodic correlation because the adjacent optical pulses are not coherent pulses. Therefore, the desired code sets should have good aperiodic correlation property instead of periodic correlation property, which is given by ai=0, if i>NChip in Eq. (1). It is still difficult to find a large number of available codes that have good aperiodic correlation property. A simple approach for our application is to select several code subsets from the original code set (e.g., Gold code), in which some specific aperiodic auto/cross-correlation criteria can be guaranteed. To quantitatively measure the aperiodic correlation property of an OC in coherent TS schemes, we introduce two parameters in this paper: one is the ratio of auto-correlation intensity peak over the maximum wing level (P/W ratio) as the measurement of the auto-correlation property, and another is the ratio of the peak over the maximum cross-correlation level (P/C ratio) for measuring the cross-correlation property. Table 1 lists several subsets of 127- and 511-chip Gold codes for different correlation criteria to illustrate this approach. To obtain the numbers in this table, we have calculated all the P/C and P/W ratios with all the codes in the code sets.
Table 1. Selection of OC subsets from 127-/511-chip Gold codes.
3. Performance of SSFBG en/decoder in different refractive -index regime and the improvement by apodization
Figure 3(a) is the calculated reflection spectrum of a weak SSFBG (peak reflectivity <-30 dB) with a 127-chip BPSK Gold code. Here, Lchip=0.64 mm, corresponding chip duration Tchip is about 6.4 ps, and maximum index modulation Δn0=1.0×10-6. The code is shown at the top of the figure as well. The transfer matrix method (TMM) is used here to model the phase-shifted SSFBG, while for the non-uniform gratings discussed below, piecewise uniform approach is used as well [28]. The input optical pulse is assumed to be transform-limited with Gaussian shape, whose spectrum is also plotted in Fig. 3(a). However, the variation of input pulsewidth will result in different correlation performance of the SSFBG en/decoder [33]. Figure 3(b) shows the calculated P/W and P/C ratios vs. the input pulsewidth for the 127-chip SSFBG. The P/C ratio is the average with 10 codes. The target ratios (approx. 37) are calculated directly by using the OC sequences. With shorter pulsewidth, the P/W and P/C ratios are closer to the target value, while the increase of the pulsewidth results in decrease of both the ratios. The shorter optical pulse therefore is more suitable for obtaining better correlation properties. However, the broad spectrum width will lower the frequency efficiency of the wavelength res ource. We need to make a compromise. In the calculations hereafter, we assume that the pulsewidth is approximately equal to Tchip, that is, 6.4 ps.
Fig. 3. Spectrum and performance of SSFBG with different input pulse width (a) Spectrum; (b) P/W and P/C ratios vs. input pulse width.
Figure 4 shows the calculated waveforms of the generated OC from 127-chip SSFBG encoders with various values of Δn0. The intensity of the generated OC is quite uniform with low Δn0, while with increasing Δn0, the waveform becomes more and more uneven and decays with time, and its tails (indicated by the arrows in the figures) become clearer. These waveform degradations are due to two factors: one is the increased loss because the encoded signal has to penetrate through the whole grating, and the other is the stronger multiple reflections between different grating segments.
To quantitatively investigate the OC processing performance of SSFBG in different Δn0 regime, we calculated power reflectivity, insertion loss (L in), and P/W and P/C ratios along with the auto-correlation peak value (PA) against Δn0. Figure 5 shows the results. The peak reflectivity of the spectra (Rf) was used as the measurement of the grating’s reflectivity in previous literatures [22–25], while the insertion loss Lin=-10 log(R) (R is the overall optical power reflectivity of the SSFBG) is the measurement of total optical-power loss. However, it is obvious that PA is more crucial in the case of OC recognition, so it is more informative in evaluating the performance of the SSFBG en/decoder. Table 2 shows the evaluation of SSFBG’s performance in different Δn0 regimes. It’s noteworthy that Rf increases (L in, P/W and P/C ratios decrease) with increasing Δn0 monotonically, while PA has a maximum value at Δn0≈7×10-5. Therefore, high P/W and P/C ratios and high Rf and PA (low Lin) can not been obtained simultaneously [31]. Another noteworthy fact is that the SSFBG in Regime III is not suitable for OC recognition as both the P/W and P/C ratios and PA decrease with increasing Δn0, although the insertion loss is low. Uniform SSFBG with low Rf therefore exhibits high P/W and P/C ratios but low PA value; on the contrary, high Rf lowers P/W and P/C but increases PA. A compromise between the P/W and P/C ratios and PA (Rf) should be made in regimes I and II to determine the optimum Δn0 value. This could be done by lowering the requirement of the P/W and P/C ratios to achieve higher PA and Rf. Using a longer OC in the SSFBG can get higher P/W and P/C ratios, therefore is easier to achieve higher PA and Rf [25].
Fig. 5. Performance of SSFBG en/decoder with different Δn0 (a) Power reflectivity, (b) P/W, P/C ratios and the auto-correlation peak value vs. Δn0..
Table 2. Performance of SSFBG in different Δn0 regime.
We previously proposed using a non-uniform profile of the refractive index along the whole grating length to mitigate the low reflectivity issue of SSFBG en/decoder [24, 31]. When the light signal is reflected by an SSFBG, the signal reflected from the far-end of the grating will experience more loss after penetrating through the whole grating than that from the near-end. Accordingly, the idea of using a non-uniform refractive index profile along the grating length is to compensate this loss properly. Here, we refer “apodization” to such non-uniform index profile. The simplest method is to balance the intensity of the reflected signals from the individual segments, it is similar as that in incoherent TS FBG encoders [8]. In Fig. 6, the monotonically increased profile marked as “AP-I” is one of the apodization profiles determined by this method. As indicated in Fig. 5, comparing to the uniform SSFBG with the same refractive index, the SSFBG with the AP-I profile has slightly improved P/W and P/C ratios and same value of PA. However, this method is effective only in low-Δn0 regime because the multiple reflections induced tails and, most importantly, the coherent coupling between the adjacent FBG segments are ignored in the calculation. Actually, it will completely fail if Δn0 is higher (in regime II) [31]. In Fig. 6, the profile indicated by AP-II was obtained by a try-and-error method [31]. With this apodization profile, the SSFBG exhibits high P/W as well as high PA values by maintaining P/C ratio as indicated in Fig. 5, while the average Δn0 is in higher part of regime II. Note that the improved P/W ratio and PA value even surpass the limits that a uniform SSFBG can attain, thus showing the significant improvement that the apoization technique can achieve.
4. Experimental investigation with 127-chip SSFBG
In this investigation, we prepared three groups of 127-chip 160-chip/s SSFBGs for comparison: the apodized SSFBG (AP), uniform LR and HR SSFBGs. Their refractive-index profiles are shown in Fig. 6. The AP-I type apodization was tested to show the feasibility and the effectiveness of the apodization technique. Figure 7 shows the measured spectra of the SSFBGs along with the calculation result. Two different 127-chip BPSK Gold code sequences, represented by GC-A and GC-B, were implemented in the prepared SSFBG. The patterns of these codes are shown at the top of Fig. 7.
Fig. 7. GC patterns and the measured (solid lines) and calculated (dashed lines) reflectivity spectrum (a) uniform LR samples, (b) uniform HR samples, and (c) AP samples.
For the LR SSFBG, Fig. 8(a) shows the close-up of the auto-correlation waveform measured by optical sampling oscilloscope (dots in the figure) as well as the calculated waveform (solid line). The measured pulsewidth is about 5.6 ps (input pulse width is about 2.3 ps), while the P/W ratio is about 13.3, which are in a good agreement with the theoretical predictions. The wavelength-deviation tolerance of the grating was evaluated in the experiment as well. The SSFBGs’ central wavelength was changed by electrically tuning the temperature of the package. The measured peak values of the auto-/cross-correlations with different central wavelength deviation between OC encoder and decoder are shown in Fig. 8(b) together with the simulation results. The measured temperature tolerance range is about ±0.3 °C, and the temperature stability of the package (±0.1 °C) is within this range.
Fig. 8. Performance of the uniform LR SSFBG en/decoder (a) auto-correlation waveform (dots: measured by optical sampling oscilloscope; solid line: calculated) (b) peak intensity of the auto-/cross-correlation (AC/CX) vs. temperature drift of the SSFBG OC decoder.
Table 3 summarizes the measured peak reflectivities Rf as well as the peak powers of the reflected signals Pen. The AP sample yields the highest reflectivity and optical power. The uniformity of Rf in the AP group is about 0.1 dB, whereas in the LR and HR groups, the uniformity is about 3dB and 0.2 dB, respectively. The improvement of the uniformity of the AP group is due to the fact that with the minimum controllable illumination, the UV-induced index change is smaller in the high-index-change regime (resulting in a higher precision of controlling the index change than that in the low-index-change regime) [34].
Table 3. Peak reflectivity of the different SSFBG samples.
The measured waveforms of the input pulse and the reflected signals from the OC encoders are shown in Fig. 9. As for the input pulse’s waveform, the ripples on the left ends of the waveforms, indicated by 1, are presumably caused by some reflections in the measurement equipment. The undershooting and overshooting after the auto-correlation peak, indicated by 2 and 3, respectively, are due to the detector’s impulse response. From Figs. 9(b) to (d), all results are measured under the same conditions and are comparable.
The encoded signal from the LR encoder has a uniform waveform with low intensity, while the waveform of the HR sample exhibits a decay from the beginning of the code, and higher intensity. The waveform from the AP sample shows an improved uniformity compared with the HR one, and has the highest intensity level among them.
Fig. 9. Waveforms of (a) input pulse, and generated OC-A signals from (b) LR sample, (c) HR sample, and (d) AP sample.
The measured auto- and cross-correlation waveforms are shown in Fig. 10. For the purpose of comparison, the intensity is normalized by the auto-correlation peaks. The maximum wings in the auto-correlation waveforms, which are indicated by 4 in the figures, are located in front of the auto-correlation peaks. It is difficult to estimate the exact P/W and P/C ratios in this experiment as the signal is detected by photodetector with 30-GHz bandwidth, which corresponds to 30 ps time resolution, and this precision is not good enough. However, qualitative comparison between them shows that t he P/W and P/C ratios are lower in the case of the HR samp le than in the case of the LR sample, while in the case of the AP sample, these ratios as well as the PA value are improved.
A transmission experiment was carried out to evaluate the overall BER performance of the SSFBG OC decoders. The experimental setup is shown in Fig. 11. The mode-locked fiber ring laser (MLFL) generates the 2.8 ps optical pulses at a repetition rate of 10 GHz with a central wavelength of 1549 nm. This signal is then modulated by the first electro-absorption modulator (EAM) into 1.25 Gb/s for transmission. The second EAM further modulates the signal by 223-1 pseudo-random binary sequence (PRBS). The data signal is then split into two arms, each with a different time delay, and encoded into GC-A and GC-B with OC encoders A and B via circulators, respectively. The time -delay difference between the two arms is set to be larger than the coherent length of the light source thus the signals from the two arms can be regarded as from different light sources. These signals are then combined and transmitted through a short length of optical fiber. At the receiver, the multiplexed signals are recognized by the OC decoder A and, finally, measured by the BER tester.
Fig. 11. Experimental setup of the BER measuring experiment with 2 MUX users (MLFL: mode locked fiber laser; EAM: electro-absorption modulator; LPF: low pass filter; ATT: Attenuator).
The measured BERs for the three groups of samples with and without multiplexing are shown in Fig. 12. In the case of single-user transmission (open marks in the figure), the AP group has the best receiver sensitivity, which is 1.7 dB less than the LR group and 3 dB less than the HR group for error-free transmission (BER<10-9). In the case of two-user multiplexing (filled marks in the figure), only the AP group can achieve error-free transmission. The power penalty to the single-user case is 3.8 dB, which is presumably due to the beat noise [7]. It is therefore concluded that, the AP group SSFBG en/decoder has better overall BER performance compared to the LR and HR group samples, which shows the effectiveness of the apodization technique.
5. Conclusion
The phase-shifted SSFBG is a promising device for coherent TS OC generation/recognition in OCDMA as well as OC-label based photonic MPLS [5] networks. The code sets used for wireless CDMA could be adopted as the OC. However, as the OC is required to have good aperiodic (instead of periodic) correlation properties, we need to further select subsets from the above code sets accordingly.
We use the P/W and P/C ratios and PA to quantitatively measure the OC recognition performance of the SSFBG in different reflectivity regimes. The relationship between Rf, L in, P/W and P/C ratios as well as PA vs. Δn 0 show the limitation of uniform SSFBG in high reflectivity regime. This is due to the loss and multiple reflections in the grating. We proposed an approach of adopting apodization technique to this issue. The proposed apodization profile significantly improves the OC recognition performance in terms of obtaining high P/W and P/C ratio as well as high PA simultaneously. This improvement means that the SSFBG can operate even with high reflectivity.
We carried out a comparative experimental investigation with 127-chip 160-Gchip/s SSFBGs : with apodization vs. without apodization. The apodized SSFBGs exhibited higher reflectivity as well as better correlation performance simultaneously. The apodized SSFBGs also had better BER performance in the transmission experiment with multiplexing of two active users. These performance improvements confirmed the effectiveness of the proposed approach. The wavelength deviation between the OC encoder and decoder was investigated as well. The temperature tolerance range is measured to be about ±0.3 °C agreeing with the theoretical calculation.
Acknowledg ments
The authors would like to thank for F. Kubota of NICT for his encouragement and Y. Tomiyama for his technical support.
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