Optimally-designed single fiber Bragg grating filter scheme for RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion

Hui Cao; Xuewen Shu; Javid Atai; Adenowo Gbadebo; Bangyun Xiong; Ting Fan; HaiShu Tang; Weili Yang; Yu Yu

doi:10.1364/OE.22.030442

1. Introduction

Future all-optical networks may be required to support a variety of modulation and data formats. Two standard data formats that are fairly mature and widespread in current optical transmission systems are the return-to-zero (RZ) and non-return-to-zero (NRZ) formats. Various all-optical conversion schemes from RZ to NRZ have been demonstrated to provide an important interface technology at the nodes of wavelength division multiplexing (WDM) and optical time division multiplexing (OTDM) networks [1, 2]. These conversion schemes can be classified into two categories, namely the time-domain waveform processing and frequency domain spectrum tailoring. The time domain approach is based on a variety of optical nonlinear effects and devices, including four-wave mixing, phase modulation, cross phase modulation, cross gain modulation, cross gain compression, gain clamp effect [3, 4], highly nonlinear optical fiber [5], photonic crystal fiber [6], active Michelson interferometer [7], nonlinear optical fiber loop mirror [8, 9]. The frequency domain approach utilizes the linear filtering process to suppress sidebands of RZ spectra and narrow frequency spectrum to broaden the pulse in time domain. The reported methods include spectral line-by-line pulse shaping technology [10], optical fiber delay interferometer (DI) (or Mach–Zehnder interference, or uniform fiber Bragg grating (FBG)) cascaded narrow-band filter based conversion technology [11–17], silicon microring resonator (or silicon-based DI) and arrayed waveguide grating (AWG) based conversion technology [18, 19].

Generally, the spectrum tailoring based converter is all-passive and very attractive compared with active-operation device, thanks to its advantages of simple structure, high cost performance and stable performance. However, there are many drawbacks of the reported spectrum tailoring schemes. First, these schemes cannot guarantee the best conversion results since these schemes use off-the-shelf filters rather than an optimally-designed one. Second, at least two filters are required in such schemes to fulfill the format conversion. For example, both microring resonator and DI are comb filters whose periods are determined by the free spectral range (FSR). As a result, to perform format conversion, these devices need to be combined with another band-pass filter. Additionally, in the case of DI cascaded filter scheme, the pattern effects are present for any duty cycle and they are more conspicuous for larger duty cycles such as 50% and 67%. The last but not the least, many reported schemes are limited to RZ on-off keying (RZ-OOK) to NRZ on-off keying (NRZ-OOK) or/and RZ differential phase shift keying (RZ-DPSK) to NRZ differential phase shift keying (NRZ-DPSK) format conversion, and, to the best of our knowledge, there are no reports on using the same device to fulfill RZ-OOK to NRZ-OOK, RZ-DPSK to NRZ-DPSK and RZ differential quadrature phase shift keying (RZ-DQPSK) to NRZ differential quadrature phase shift keying (NRZ-DQPSK) format conversion.

In this paper, we rigorously analyze the FBG-based RZ to NRZ format conversion by means of the linear time-invariant theory. This approach is then used to propose a novel RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK conversion scheme based on a single optimally-designed FBG. The spectral response of this FBG is designed according to the algebraic difference of the optical spectra of isolated NRZ and RZ pulses. Further, the filter order is optimized to maximize the Q-factor of the converted NRZ signals. Numerical investigations show that the optimally-designed FBG is capable of converting the input RZ-OOK/DPSK/DQPSK signals with different duty cycles to NRZ-OOK/DPSK/DQPSK signals with high Q-factor. Moreover, in our proposed scheme, the pattern effects are efficiently mitigated compared with previously reported schemes. Finally, experimental demonstration of RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK conversion with the proposed scheme is presented.

2. Frequency-domain analysis

Taking RZ-OOK to NRZ-OOK format conversion as an example, the schematic diagram of the FBG-based RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion is shown in Fig. 1. The RZ-OOK signal are coupled into the FBG via the first port of the optical circulator and reflected back by the FBG via the second port. In the process of reflection, the spectra of RZ-OOK signal are linearly tailored by the reflection spectra of the FBG to produce the output signal characterized by the spectra of NRZ-OOK signal. The converted NRZ-OOK signal is outputted from the third port of the optical circulator.

Fig. 1 Schematic diagram of the FBG-based RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion (In the case of RZ-OOK to NRZ-OOK).

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Since RZ-OOK/DPSK/DQPSK data can be constructed from convolution of the RZ-OOK/DPSK/DQPSK signal with a series of delta functions representing data in the time domain, and that the FBG-based filtering is a linear process, the FBG-based RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format converter can be analyzed using linear time-invariant system theory. Thus, the complex problem of converting random RZ-OOK/DPSK/DQPSK stream to NRZ-OOK/DPSK/DQPSK stream can be reduced to constructing an appropriate transfer function for the FBG filter. This process is described below.

In principle, the time-domain electric field of the RZ-OOK/DPSK/DQPSK modulated optical signal can be expressed as

E_{R Z} (t) = \sum_{k = - \infty}^{+ \infty} [b_{k} \cdot P_{R Z} (t)] * δ (t - k T_{P}) \cdot \exp (j ω_{c} t)

where

b_{k}

is the encoded and transmitted data stream (

b_{k} \in [0, 1]

,

b_{k} \in [- 1, 1]

and

b_{k} \in [\exp (i π / 4), \exp (i 3 π / 4), \exp (5 π / 4), \exp (i 7 π / 4)]

for OOK, DPSK and DQPSK, respectively) [2, 20],

T_{P}

is the interval between pulses, and

ω_{c}

is the carrier angular frequency and

P_{R Z} (t)

is the shape of the isolated RZ-OOK/DPSK/DQPSK pulse. Note that the shapes of the isolated RZ-OOK, RZ-DPSK and RZ-DQPSK pulses are identical because in DPSK and DQPSK only the phase is used to encode information. Denoting the impulse response of the format converter as

h (t) \cdot \exp (j ω_{c} t)

, for RZ input, the output electric field can be calculated in terms of the input electric field and the impulse response as follows:

E_{o u t} (t) = E_{R Z} (t) * [h (t) \cdot \exp (j ω_{c} t)]

where * denotes the convolution operation. Similarly, the electric field of the NRZ-OOK/DPSK/DQPSK modulated optical signal, with the same encoded and transmitted data stream

b_{k}

as Eq. (1), can be written as

E_{N R Z} (t) = \sum_{k = - \infty}^{+ \infty} [b_{k} \cdot P_{N R Z} (t)] * δ (t - k T_{P}) \cdot \exp (j ω_{c} t)

where

P_{N R Z} (t)

is the shape of the isolated NRZ-OOK/DPSK/DQPSK pulse and other parameters are the same as in Eq. (1) (note that the shapes of the isolated NRZ-OOK, NRZ-DPSK and NRZ-DQPSK pulses are identical). Equations (1)-(3) yield the following impulse response for the RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format converter:

[P_{R Z} (t) \cdot \exp (j ω_{c} t)] * [h (t) \cdot \exp (j ω_{c} t)] = P_{N R Z} (t) \cdot \exp (j ω_{c} t) .

Application of the convolution theorem to Eq. (4) leads to

{\hat{P}}_{R Z} (ω - ω_{c}) \cdot \hat{H} (ω - ω_{c}) = {\hat{P}}_{N R Z} (ω - ω_{c}),

where

{\hat{P}}_{R Z} (ω - ω_{c}), \hat{H} (ω - ω_{c}) and {\hat{P}}_{N R Z} (ω - ω_{c})

are the Fourier transforms of

P_{R Z} (t) \cdot \exp (j ω_{c} t)

,

h (t) \cdot \exp (j ω_{c} t)

and

P_{N R Z} (t) \cdot \exp (j ω_{c} t)

, respectively.

\hat{H} (ω - ω_{c})

denotes the transfer function, namely, the system frequency response of the format converter. Rewriting Eq. (5) in decibels yields

{\hat{H}}_{d B} (ω - ω_{c}) = {\hat{P}}_{N R Z, d B} (ω - ω_{c}) - {\hat{P}}_{R Z, d B} (ω - ω_{c}),

where subscript dB denotes the logarithmic unit, calculated according to

F_{d B} (ω - ω_{c}) = 10 \cdot \log_{10} [F (ω - ω_{c})]

,

F = \hat{H}, {\hat{P}}_{N R Z}, and {\hat{P}}_{R Z}

.

The filter described by Eq. (6) is defined as the first-order filter. Higher-order filters are typically implemented as serially-cascaded first-order filters. The transfer function of the n^th-order filter can be calculated by multiplying the transfer function of the first-order filter by the ordinal number n. Therefore, the transfer function of the n^th-order filter is

{\hat{H}}_{}^{n^{t h}}_{d B} (ω - ω_{c}) = n \cdot {\hat{H}}_{d B} (ω - ω_{c}) \begin{matrix} n > 0 \end{matrix}

It should be pointed out that the ordinal number n is not necessarily an integer. Equation (7) describes the fundamental principle for FBG spectral response design, where the ordinal number n is free to be optimized.

3. FBG-based filter design

Taking 40-Gbit/s RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion as an example, the optimal design of FBG-based filter is demonstrated. Specifically, considering an RZ-OOK/DPSK/DQPSK signal with 50% duty cycle, and noting that the shapes of isolated RZ pulse and NRZ pulse are independent on OOK, DPSK or DQPSK modulations, we can write the time-domain electric field waveforms for isolated RZ-OOK/DPSK/DQPSK pulse and isolated raised-cosine NRZ-OOK/DPSK/DQPSK pulse as follows [20],

P_{50} (t) = {\begin{matrix} \frac{1}{\sqrt{E_{50}}} \sin {\frac{π}{4} [1 + \cos (\frac{2 π t}{T_{p}})]}, | t | \leq \frac{T_{p}}{2} \\ 0, | t | > \frac{T_{p}}{2} \end{matrix}

P_{N R Z} (t) = {\begin{matrix} \frac{1}{\sqrt{E_{N R Z}}}, | t | < (1 - β) \frac{T_{P}}{2} \\ 0, | t | \geq (1 + β) \frac{T_{P}}{2} \\ \frac{1}{2 \sqrt{E_{N R Z}}} [1 - \sin (\frac{π | t | - \frac{T_{P}}{2}}{β T_{P}})], otherwise \end{matrix}

where

β

is the roll-off factor,

T_{P}

is the interval between pulses and the pulse energies

E_{50}

and

E_{N R Z}

are given by

E_{50} = \int_{- \infty}^{+ \infty} P_{50}^{2} (t) d t; E_{N R Z} = \int_{- \infty}^{+ \infty} P_{N R Z}^{2} (t) d t .

Given

T_{P} = 25 p s

,

β = 0.2

and the wavelength of the carrier

λ_{c} = 1550.12 n m

, Fig. 2 shows the amplitude of the spectra of

P_{50} (t) \cdot \exp (j ω_{c} t)

and

P_{N R Z} (t) \cdot \exp (j ω_{c} t)

, and their algebraic difference, namely, the ideal transfer function of the first-order filter.

Fig. 2 The amplitudes of the spectra of the isolated RZ-OOK/DPSK/DQPSK pulse with 50% duty cycle (green curve), the isolated NRZ-OOK/DPSK/DQPSK pulse (blue curve), for $T_{P} = 25 p s$ , the wavelength of the carrier $λ_{c} = 1550.12 n m$ , and $β = 0.2$ . The red curve is their algebraic difference (i.e. the ideal transfer function of the first-order filter).

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The ideal transfer function (i.e. the red curve in Fig. 2) is symmetrical but complex. In particular, for some higher frequency components that are out of the NRZ-OOK/DPSK/DQPSK spectra main-lobe bandwidth of $| ω - ω_{c} | \leq \frac{2 π}{T_{p}}$ (or $| λ - λ_{c} | \leq 0.32 n m$ at bit rate of 40-Gbit/s), the value of the transfer function is greater than 0-dB, which is obviously impossible to be fulfilled by a passive filter. Fortunately, many reported studies have indicated that we should concentrate on the in band filtering rather than out of band filtering because most of the NRZ-OOK/DPSK/DQPSK signal power is in the range $| ω - ω_{c} | \leq \frac{2 π}{T_{p}}$ [12–14, 18–20]. Thus, it is reasonable to set a uniform attenuation (say, 25-dB) for out-of-band components, and eventually construct a band-pass filter as routinely done in the reported schemes [11–14,18,19]. Moreover, it is also necessary to set a physically realizable minimum reflectivity (say, 25-dB, the same as above) in the pass band. Taken together, the simplified transfer function of the first-order FBG filter is given by

{\hat{H}}_{}^{1^{s t}}_{d B, F B G} (ω - ω_{c}) = {\begin{matrix} \max [{\hat{H}}_{d B} (ω - ω_{c}), - 25], | ω - ω_{c} | \leq \frac{2 π}{T_{p}} \\ - 25, | ω - ω_{c} | > \frac{2 π}{T_{p}} \end{matrix}

where

{\hat{H}}_{}^{1^{s t}}_{d B, F B G} (ω - ω_{c})

describes the reflectivity spectra of the first-order FBG filter. More generally, for the n^th-order FBG filter,

{\hat{H}}_{}^{n^{t h}}_{d B, F B G} (ω - ω_{c}) = {\begin{matrix} \max [n \cdot {\hat{H}}_{d B} (ω - ω_{c}), - 25], | ω - ω_{c} | \leq \frac{2 π}{T_{p}} \\ - 25, | ω - ω_{c} | > \frac{2 π}{T_{p}} \end{matrix} \begin{matrix} n > 0 \end{matrix}

It is worth noting that the n^th-order FBG filter is based on one FBG rather than n FBGs. Therefore, the maximum isolation is fixed to 25-dB for any filter of order. Figure 3 displays the reflectivity spectra of the n^th-order FBG filters calculated using Eq. (12) for different values of n. A noteworthy feature shown in Fig. 3 is that the higher the order of the filter, the narrower is the 3-dB bandwidth. It is interesting that the spectral response of the DI scheme is very close to that of the 2.97th-order FBG filter.

Fig. 3 Comparison the ideal transfer function with the reflectivity spectra of the n^th-order FBG filters, with $n = 0.5, 1, 2, 2 .97 and 4 .$

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As pointed out earlier, among all the n^th-order FBG filters, the first-order FBG filter is not necessarily the best one, since ${\hat{H}}_{}^{1^{s t}}_{d B, F B G} (ω - ω_{c})$ is different from ${\hat{H}}_{}^{1^{s t}}_{d B} (ω - ω_{c})$ as shown in Eqs. (7) and (11). To further investigate the effect of ordinal number on format conversion, we calculate the Q-factor of the converted NRZ-OOK signal with the ordinal number n ranging from 0.5 to 4. The results are plotted in Fig. 4, where the insert (a) is the standard deviations of the marks and spaces rail of the NRZ-OOK signal. Figure 4 shows that the 2.07th-order filter presents the minimum standard deviations and the maximum Q-factor. Hence, we chose ${\hat{H}}_{}^{{2.07}^{t h}}_{d B, F B G} (ω - ω_{c})$ as the optimal designed reflectivity spectra of FBG, with 3-dB bandwidth of 0.46 nm and 25-dB bandwidth of 0.64 nm as is shown in the insert (b) of Fig. 4. As analyzed above, this 2.07th-order filter is the best one for RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion. Note that, the 2.97th-order filter, which is very similar to the DI scheme, has a Q-factor of 11.1.

Fig. 4 Variation of the Q-factor of the converted NRZ-OOK signal with filter order. The insert (a) is the standard deviations of the marks and spaces rail of the NRZ-OOK signal, and the insert (b) shows the reflectivity spectra of 2.07th-order FBG.

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In order to verify this FBG is physically realizable, we employ layer peeling method [21,22] to synthesize the reflectivity spectra of the optimally-designed FBG. Figure 5(a) shows the synthesized grating with the grating length of 4 cm. As is shown in Fig. 5(a), the maximum refractive index modulation of $2.23 \times 10^{- 4}$ and the maximum local chirp of −0.27 nm are well within the practically realizable range. Furthermore, in Fig. 5(b), we plot the simulated reflection spectra of the designed FBG with transfer matrix method. It is clear that the simulated reflection spectra (the dotted blue line) are in excellent agreement with the target reflection spectra (the solid red line).

Fig. 5 Structure and reflection spectra of the synthesized FBG filter used for 40-Gbit/s RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion. (a) Synthesized index modulation (the green line) and local chirp (the blue line). (b) Simulated reflection spectra (the dotted blue line) and target reflection spectra (the solid red line).

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4. RZ-OOK to NRZ-OOK format conversion simulation and discussion

In this section we investigate the performances of the FBG based RZ-OOK to NRZ-OOK format converter and compare it with the previously reported results.

Given the carrier wavelength of 1550.12 nm, we simulate the operation of designed FBG based optical filter for single channel RZ-OOK to NRZ-OOK format conversion in the case of a pseudo-random binary sequence (PRBS) of length 2³¹-1 bits with different duty cycles. Figure 6 shows the simulation results at a bit rate of 40-Gbit/s with duty cycles of 20%, 33%, 50% and 67%. It should be noted that we only consider the duty cycles rather than the polarity of electric field waveforms. Therefore, the unipolar electric field waveforms are necessary for all 4 duty cycles in simulation. Figures 6(a)-6(c) show the waveforms, power spectra and eye diagrams of the input RZ-OOK signals, respectively, while Figs. 6(d)-6(f) depict the corresponding profiles of the output NRZ-OOK signals. In Fig. 6(a), the RZ-OOK waveforms with different duty cycles are normalized according to Eq. (10) to have unit energy over the symbol period. It is shown in Fig. 6(d) that the RZ-OOK pulses have been broadened to NRZ-OOK pulses via the filtering introduced by the optimal designed FBG. As is shown in Fig. 6(f), for four different duty cycles, all the eye diagrams are very clean and open.

Fig. 6 Simulated waveforms, power spectra and eye diagrams of (a)-(c) the input RZ-OOK signals, (d)-(f) the corresponding output NRZ-OOK signals by the proposed filter, and (g)-(i) the corresponding output NRZ-OOK signals by DI based filter, for four different duty cycles (20%, 33%, 50% and 67%), with all the curves in the same sub-figure shifted up and down for clarity.

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To better appreciate the superior performance of the FBG based format converter, in Figs. 6(g)-6(i), we plot the simulation results of the reported DI cascaded filter scheme, where a DI with 80-GHz free spectral range (FSR) is cascaded by a filter with 3-dB bandwidth of 0.6 nm for 40-Gbit/s RZ-OOK to NRZ-OOK format conversion. As is shown in Fig. 6(g), in the case of 50% and 67% duty cycles pattern effects appear in the waveforms. That is, a single “1” bit has lower peak power than the several consecutive “1” bits (This is also shown in Fig. 2 of [12] by Y. Yu et al.). Figure 6(i) demonstrates that this effect seriously decreases the Q-factor of the output NRZ-OOK signal. However, our FBG based format converter can efficiently reduce the pattern effects and greatly increase the Q-factor. In particular, comparing Fig. 6(f) with Fig. 6(i), the Q-factors for our FBG-based scheme are significantly higher than the DI scheme. Physically, the pattern effects observed for the high duty cycles in the DI scheme can be attributed to the high-frequency components being excessively suppressed. As is shown in Fig. 6(b), the smaller the duty cycle, the flatter are the spectra of RZ-OOK signals. As a result, the proportions of the high-frequency components in the main lobe ( $1550.12 \pm 0.32 n m$ ) increase as the duty cycle decrease.

The reduction of the pattern effects in our FBG based scheme originates from the well-designed spectra with moderate high-frequency suppression. This can be verified by comparing the spectral response of the proposed FBG scheme and the reported DI scheme.

The overall spectral response of the DI scheme with a filter with 3-dB bandwidth of 0.6 nm can be expressed as

R (λ) = \frac{1}{2} {1 + \cos [2 π c (\frac{1}{λ} - \frac{1}{λ_{c}}) Δ t]} \exp {- \ln (2) {[\frac{2 (λ - λ_{c})}{0.6}]}^{2}}

where

c

is the velocity of light in vacuum,

Δ t = 0.0125 n s

for 80GHz FSR,

λ_{c}

is the carrier wavelength of RZ-OOK signal. In Fig. 7, we plot the spectra response of the proposed 2.07th-order FBG filter and the DI based filter as well as their algebraic difference. As shown in Fig. 7, from the point of view of the spectrum, the proposed FBG filter is flatter than the DI based filter and essentially possesses moderate high-frequency suppression. The dotted line in Fig. 7 shows that the depths of high-frequency suppression have been significantly reduced. The maximal reduction is close to 10-dB compared with the DI based filter. As can be seen from Fig. 6(d), the pattern effects are perfectly suppressed in the cases of 33% and 50% duty cycles where the peak powers of a single “1” bit and the several consecutive “1” bits are similar. On the other hand, minor pattern effects exist for 20% and 67% duty cycles, i.e. the peak powers of single “1” bit are slightly greater than the several consecutive “1” bits. On the basis of these results, it can be concluded that the proposed 2.07th-order FBG filter has superior characteristics compared with the DI scheme.

Fig. 7 The power spectral response of the proposed 2.07th-order FBG filter (the solid green line) and the DI based filter (the solid red line), and their algebraic difference (the dotted blue line).

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As for the operational tolerances of this scheme, we consider the detuning of the central wavelength of FBG reflection band. The central wavelength may be detuned from the carrier wavelength due to fabrication process, variations of temperature or pressure. Alternatively, the carrier wavelength of the transport system may change slightly from time to time. Figure 8 shows the Q-factor as a function of the filter wavelength detuning. It is interesting to note that in Fig. 8 each Q-factor curve has a flat top around the center (approximately within ± 0.02nm depending on the duty cycle). In this range, the Q-factor is insensitive to the detuning of the central wavelength. Supposing a detuning of 0.032 nm (i.e. 5% of the bandwidth of FBG reflection spectra), the inserts (a)-(c) show corresponding waveform, power spectra and eye diagrams of the output NRZ-OOK signal, respectively. It is clear that the performance of 0.032 nm-detuning filters is still acceptable with the Q-factor being greater than 16 for four different duty cycles. In particular, in the case of 67% duty cycle, the performance is enhanced due to partial mitigation of the excessive high-frequency suppression. Compared with Fig. 6(i), the performance shown in the insert (c) of Fig. 8 is better than that of the DI scheme, except in the case of 20% duty cycle. As expected, an over-detuning can obviously degrade the performance due to the fact that it can result in the carrier being overfiltered as well as the first order spectra spike being underfiltered and therefore seriously affect format conversions. We would also point out here that such a problem may be solved by packaging the FBG with either thermal package or mechanical package so that its central wavelength can be dynamically adjusted and controlled (thermally or mechanically) to ensure the conversion function.

Fig. 8 Q-factor as a function of the filter detuning for four different duty cycles (20%, 33%, 50% and 67%). Inserts (a), (b) and (c) are the simulated waveforms, power spectra and eye diagrams of the output NRZ-OOK signals with the filter detuning of 0.032nm, respectively.

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As regards the impact of bit rate on the proposed filter design, according to Eq. (12), the bandwidth of the designed FBG is proportional to the bit rate. For instance, for the RZ-OOK signals with higher bit rates, such as 80- or 100-Gbit/s, the bandwidth of designed FBG should be 1.28 nm or 1.6 nm, respectively. Such FBGs are even easier to be designed and fabricated compared with the one considered here (i.e. 0.64 nm in the case of 40-Gbit/s). On the other hand, in the case of 20- or 10-Gbit/s, the bandwidth of the designed FBG should be 0.32 nm or 0.16 nm, respectively. Although such FBGs can readily be designed, their fabrication is somewhat more difficult than the ones with higher bandwidth mainly because of the issues related to controlling the bandwidth for the rising and falling edges.

5. RZ-DPSK to NRZ-DPSK format conversion simulation and discussion

The optimally-designed FBG in Section 3 can also be used to convert 40-Gbit/s RZ-DPSK signals to the corresponding NRZ-DPSK signals. Figure 9 shows the simulation results at a bit rate of 40-Gbit/s for duty cycles of 20%, 33%, 50% and 67%. Figures 9(a)-9(c) show the waveforms, power spectra and eye diagrams of the input RZ-DPSK signals, respectively, while Figs. 9(d)-9(f) depict the corresponding profiles of the output NRZ-DPSK signals. In Fig. 9(a), the RZ-DPSK waveforms with different duty cycles are normalized to have unit energy over the symbol period. As shown in Fig. 9(f), all the eye diagrams for four different duty cycles are very clean and open.

Fig. 9 Simulated waveforms, power spectra and eye diagrams for four different duty cycles (20%, 33%, 50% and 67%). (a)-(c) the input RZ-DPSK signals; (d)-(f) the output NRZ-DPSK signals generated by the FBG-based filter; (g)-(i) the output NRZ-DPSK signals generated by DI-based filter.

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In order to compare our FBG-based scheme with the DI cascaded filter scheme, in Figs. 9(g)-9(i), we plot the simulation results of the DI cascaded filter scheme (specified by Eq. (13)) for 40-Gbit/s RZ-DPSK to NRZ-DPSK format conversion. As is shown in Fig. 9(g), in the cases of 50% and 67% duty cycles, pattern effects appear in the waveforms. Correspondingly, in Fig. 9(i), the central part of the upper eyelid of the eye diagrams is thickening with the increase of duty cycles. The constellation diagrams of the DPSK signals are shown in Fig. 10, indicating the phase alternation between “0” and “π” in DPSK pulse trains. Figures 10(a)-10(d), 10(e)-10(h) and 10(i)-10(l) are the constellations of the original RZ-DPSK, the FBG-converted NRZ-DPSK and the DI-converted NRZ-DPSK signals, respectively. In Fig. 10, starting from the left, the columns one to four correspond to 20%, 33%, 50% and 67% duty cycles, respectively. It is noteworthy that no significant constellation degradation is present in Figs. 10(e)-10(h). On the other hand, in Figs. 10(i)-10(l), constellation dispersion is clearly observable and it increases significantly with the increase of the duty cycle.

Fig. 10 Simulated constellation diagrams for different duty cycles (starting from the left, columns one to four correspond to 20%, 33%, 50% and 67% duty cycles, respectively). (a)-(d) the input RZ-DPSK signals; (e)-(h) the output NRZ-DPSK signals generated by the FBG-based filter; and (i)-(l) the output NRZ-DPSK signals generated by DI based filter.

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Figure 11 shows the demodulated Alternative Mark Inversion (AMI) signals and Dual Binary(DB)signals outputted from a one-bit-delay Mach-Zehnder delay interferometer (MZDI) which serves as the DPSK demodulator [2, 23]. To compare our FBG-based scheme with the DI scheme, the NRZ-DPSK signals shown in Fig. 9 are inputted to the DPSK demodulator and the outputs are compared. Using the FBG-generated NRZ-DPSK signals (i.e. Figure 9(d)) as the input, the AMI [DB] signals outputted by the demodulator are shown in Figs. 11(a), 11(b) [Figs. 11(e) and 11(f)]. Similarly, Figs. 11(c) and (d) and 11(g) and (h) show the corresponding outputs in the case of DI-generated NRZ-DPSK input (i.e. Figure 9(g)). A remarkable feature shown in Fig. 11 is that the demodulated FBG-generated NRZ-DPSK signal gives rise to a higher Q-factor than that for the DI-generated NRZ-DPSK.

Fig. 11 Simulated waveforms and eye diagrams for four different duty cycles (20%, 33%, 50% and 67%). (a)-(b) and (e)-(f) show the demodulated AMI and DB signals for the FBG-generated NRZ-DPSK, respectively; (c)-(d) and (g)-(h) are the demodulated AMI signals and DB signals for the DI-generated NRZ-DPSK, respectively.

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6. RZ-DQPSK to NRZ-DQPSK format conversion simulation and discussion

DQPSK is a spectrally efficient modulation format in which two bits per symbol are encoded by multiplexing I (in-phase) and Q (quadrature) signals on a single wavelength [23–26]. In this Section, we will again use the optimally-designed FBG in Section 3 to convert a 40- Gbaud/s (PRBS of length 2³¹-1) RZ-DQPSK signal at 1550.12 nm to the NRZ-DQPSK format. The results of the simulations for duty cycles of 20%, 33%, 50% and 67% are presented in Fig. 12. Figures 12(a)-12(c) show the waveforms, power spectra and eye diagrams of the input RZ-DQPSK signals, respectively. Figures 12(d)-12(f) depict the output NRZ-DQPSK signals using our FBG scheme. As are shown in Fig. 12(a) and Fig. 9(a), the waveforms of RZ-DQPSK and RZ-DPSK are identical because both DPSK and DQPSK are constant-amplitude formats. It should be noted that although the shape of the RZ-DQPSK power spectra is identical to that of RZ-DPSK, the RZ-DQPSK power spectra are compressed in frequency by a factor of two due to two bits encoded per symbol [2]. Figure 12(f) shows that all the eye diagrams for four different duty cycles are very clean and open.

Fig. 12 Simulated waveforms, power spectra and eye diagrams for four different duty cycles (20%, 33%, 50% and 67%). (a)-(c) the input RZ-DQPSK signals; (d)-(f) the output NRZ-DQPSK signals generated by the FBG-based filter; (g)-(i) the output NRZ-DQPSK signals generated by DI-based filter.

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Once again, we compare our scheme with the DI cascaded filter scheme. In Figs. 12(g)-12(i), we present the simulation results of the DI cascaded filter (specified by Eq. (13)) scheme for 40- Gbaud/s RZ-DQPSK to NRZ-DQPSK format conversion. As is shown in Fig. 12(i), the central part of the upper eyelid of the eye diagrams is thickening with the increase of duty cycles. We further depict the constellation diagrams of the DQPSK signals in Fig. 13, where Figs. 13(a)-13(d), 13(e)-13(h), and 13(i)-13(l) are the constellations of original RZ-DQPSK, FBG-generated NRZ-DQPSK signal and DI-generated NRZ-DQPSK signal, respectively. Starting from the left, columns one to four correspond to 20%, 33%, 50% and 67% duty cycles, respectively. Figure 13 indicates the phase alternation among “π/4”, “3π/4”, “5π/4” and “7π/4” in DQPSK pulse trains. Similar to the case of DPSK, constellation dispersion in Figs. 13(i)-13(l) increases significantly with the increase of duty cycle, and is more serious than that of Figs. 13(e)-13(h). It is worth noting that in the case of DQPSK, constellations disperse along both the phase and amplitude directions rather than only along the amplitude direction as presented in the case of DPSK.

Fig. 13 Simulated constellation diagrams for different duty cycles (starting from the left, columns one to four correspond to 20%, 33%, 50% and 67% duty cycles, respectively). (a)-(d) the input RZ-DQPSK signals; (e)-(h) the output NRZ-DQPSK signals generated by the FBG-based filter; and (i)-(l) the output NRZ-DQPSK signals generated by DI-based filter.

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As is well known, the NRZ-DQPSK signal can be demodulated using two one-symbol-period-delay MZDIs arranged in parallel with a relative phase shift of π/4 and -π/4 for upper and lower branches, respectively, and detected by two balanced receivers to present I and Q components [23, 27].

Figures 14(a) and 14(b) [Figs. 14(e) and 14(f)] depict the waveforms and eye diagrams of the demodulated I[Q] components using the FBG-generated NRZ-DQPSK signal (i.e. Fig. 12(d)) as the input of the DQPSK demodulator. Similarly, Figs. 14(c)-14(d) and 14(g)-14(h) present the corresponding outputs in the case of DI-generated NRZ-DQPSK signal. Once again, it is found that the demodulated FBG-generated signals result in higher Q-factors than those of the DI-generated ones.

Fig. 14 Simulated waveforms and eye diagrams for four different duty cycles (20%, 33%, 50% and 67%). (a)-(b) and (e)-(f) show the I and Q components for the FBG-generated NRZ-DQPSK, respectively; (c)-(d) and (g)-(h) are the I and Q components for the DI-generated NRZ-DQPSK, respectively.

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8. Experimental results and discussion

To experimentally demonstrate the single FBG-based RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion, we fabricated a FBG that is optimally designed for 40-Gbit/s (40-Gbaud/s in case of DQPSK) format conversion, with the central wavelength of 1550.12 nm, bandwidth of 0.64 nm and 30-dB isolation. The FBG was fabricated in hydrogen-loaded standard optical fiber (SMF28) with a UV laser direct-writing system. The grating structure was then stabilized by annealing at 80°C for 60 hours after the fabrication. As is shown in Fig. 15, the theoretical and the measured spectra agree very well and differ slightly in the long wavelength side.

Fig. 15 Measured spectra and optimal designed spectra of the fabricated FBG.

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To demonstrate the proof of concept, we only discuss the experimental results for the case of 40 Gbit/s RZ-OOK with 33% duty cycle. The experimental setup is shown in Fig. 16. The SHF optical communication system is employed to generate the RZ-OOK signal with wavelength of 1550.12 nm (the same wavelength as the peak reflection wavelength of the fabricated FBG). By controlling the modulation parameters, 40-Gbit/s RZ-OOK signals (PRBS 2³¹-1) with 33% duty cycle can be achieved. The signal power can be controlled by the subsequent erbium doped fiber amplifier (EDFA) and an attenuator (ATT). Using a circulator, the signals are coupled to the FBG and the converted signals are coupled out to be analyzed by the communication signal analyzer (CSA), the optical spectrum analyzer (OSA) and the Error analyzer, respectively.

Fig. 16 Experimental setup for RZ-OOK to NRZ-OOK format conversion.

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Figure 17 shows the experimental results of RZ-OOK to NRZ-OOK conversion. The spectra of the RZ-OOK signal (blue line), the fabricated FBG (dashed green line) and the NRZ-OOK signal (red line) are shown in Fig. 17(a). It can be seen that the first-order sidebands of converted NRZ-OOK spectra are suppressed near 30-dB by the fabricated FBG compared with the RZ-OOK spectra. Figures 17(b) and 17(c) [Figs. 17(d) and 17(e)] are the eye diagrams and the waveform of the RZ-OOK [NRZ-OOK] signals, respectively. As is shown in Fig. 17(e), the RZ-OOK pulses have been broadened to corresponding NRZ-OOK pulses owing to the filtering introduced by the fabricated FBG. Due to the all-passive format converter, no additional noise is introduced in the conversion. The eye diagrams of the converted NRZ-OOK are clear and open. Also, as is shown in the NRZ-OOK waveform, the pattern effects are negligible. Furthermore, flatter ‘0’ bits are presented in the NRZ-OOK waveform thanks to the filtering of chirps in the RZ-OOK waveform by the fabricated FBG.

Fig. 17 Experimental results of RZ-OOK to NRZ-OOK format conversion. (a) Measured optical spectra; (b)-(c) and (d)-(e) are the measured waveform and eye diagrams of RZ-OOK and NRZ-OOK, respectively.

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The BER and power penalty measurement results are shown in Fig. 18. Figure 18(a) shows that the power penalty induced by the conversion is about 0.7-dB. This is an improvement compared with 2.2-dB that is reported in [12]. To investigate the operational tolerances of this fabricated FBG, the power penalties for different wavelength detunings are measured (at BER of 10⁻⁹ level). The measured results and corresponding eye diagrams are shown in Fig. 18(b). When the offset of the carrier wavelength varies from −0.04nm to 0.04nm away from the central wavelength of the fabricated FBG, the power penalties are limited in 1.5 dB. On the basis of these experimental results, it can be concluded that the fabricated FBG filter presents a good-performance format conversion.

Fig. 18 Measured BER and power penalty. (a) BER measurements for original RZ-OOK signal and converted NRZ-OOK signal; (b) Measured power penalty.

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To experimentally demonstrate RZ-DPSK/DQPSK to NRZ-DPSK/DQPSK format conversion with the same fabricated FBG, we replace the RZ-OOK generator in Fig. 16 with RZ-DPSK generator and RZ-DQPSK generator, respectively. Figures 19 and 20 show the measured optical spectra, waveform and eye diagrams of DPSK and DQPSK modes, respectively. It is shown in Figs. 19(e) and 20(e) that the RZ- DPSK/DQPSK pulses have been broadened to NRZ- DPSK/DQPSK pulses via the filtering introduced by the same fabricated FBG. Furthermore, the NRZ-DPSK waveform is featured with one-level intensity dip where there is a π optical phase shift between adjacent bits. On the other hand, the NRZ-DQPSK waveform is characterized with two-level intensity dips since it contains more phase-shift information. These observations agree well with the simulation results presented in Figs. 9(d) and 12(d). From the point of view of the eye diagrams, there is no “0” level in both NRZ-DPSK and NRZ-DQPSK eye diagrams because of their constant envelope (without “0” pulses, for optical power appears in each bit slot). Again this coincides well with the simulation results in Figs. 9(f) and 12(f). One can, therefore, conclude that both RZ-DPSK to NRZ-DPSK and RZ-DQPSK to NRZ-DQPSK format conversions are successfully fulfilled with the same fabricated FBG.

Fig. 19 Experimental results of RZ-DPSK to NRZ-DPSK format conversion. (a) Measured optical spectra; (b)-(c) and (d)-(e) are the measured waveform and eye diagrams of RZ-DPSK and NRZ-DPSK, respectively.

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Fig. 20 Experimental results of RZ-DQPSK to NRZ-DQPSK format conversion. (a) Measured optical spectra; (b)-(c) and (d)-(e) are the measured waveform and eye diagrams of RZ-DQPSK and NRZ-DQPSK, respectively.

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It should be point out that the eye diagrams of the converted NRZ-DQPSK signals are not very clear and open. This is due the fact that the eye diagrams of the original RZ- DQPSK signals are degraded compared with those of RZ-OOK signals (i.e. The upper eyelid of the eye diagrams is thicker than that of the eye diagrams of RZ-OOK signals, as is shown in Figs. 17(b) and 20(b)). It should be noted that the RZ- DQPSK eye diagram degradation arises from the limitations of the RZ-DQPSK generator used in this experiment. However, this restriction does not prevent the demonstration of RZ-DQPSK to NRZ- DQPSK format conversion.

9. Conclusion

We have proposed and experimentally demonstrated a novel optimally-designed single fiber-Bragg grating (FBG) filter scheme for RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion. Employing the linear time-invariant system theory, the complex problem of converting random RZ stream to NRZ stream is reduced to constructing an appropriate transfer function for the FBG filter. Furthermore, theoretical analysis shows that the spectral response of the FBG can be constructed based on the algebraic difference between optical spectra of isolated NRZ-OOK and RZ-OOK pulses. The filter order is optimized for the maximum Q-factor of the output NRZ-OOK signals. Based on the optimal designed 2.07th-order filter, format conversions from RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK are investigated. Simulation results consistently show superior performance for our FBG scheme than DI cascaded filter scheme. Experimental results show that such an optimally-designed single FBG filter can efficiently reduce the pattern effects, and results in a significant improvement in power penalty compared with previously reported delay interferometer scheme.

Acknowledgments

The authors thank Dr. Jie Hou and Dr. Mengyuan Ye of Huazhong University of Science and Technology for helpful discussions. This research was conducted during Dr Hui Cao’s visit to Wuhan National Laboratory for Optoelectronics & School of Optoelectronic Science and Engineering, Huazhong University of Science and Technology (July 2013 – June 2014), and was supported by the National Natural Science Foundation of China (grant 61178030), the Natural Science Foundation of Guangdong Province, China (grant S201101000122), the Fundamental Research Funds for the Central Universities, China (HUST: 2013TS047), and the Fundamental Research Funds of Foshan University.

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Optimally-designed single fiber Bragg grating filter scheme for RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion

Abstract

1. Introduction

2. Frequency-domain analysis

3. FBG-based filter design

4. RZ-OOK to NRZ-OOK format conversion simulation and discussion

5. RZ-DPSK to NRZ-DPSK format conversion simulation and discussion

6. RZ-DQPSK to NRZ-DQPSK format conversion simulation and discussion

8. Experimental results and discussion

9. Conclusion

Acknowledgments

References and links

Cited By

Figures (20)

Equations (13)

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