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Parametric tunable dispersion compensator (P-TDC), which allows format-independent operation owing to seamlessly wide bandwidth, is expected to be one of the key building blocks of the future ultra-high speed optical network. In this paper, a design of ultra-wide band P-TDC is presented showing that bandwidth over 2.5 THz can be achieved by compensating the chromatic dispersion up to the 4th order without employing additional method. In order to demonstrate the potential application of P-TDC in the Tbit/s optical time division multiplexing transmissions, 400 fs optical pulses were successfully transmitted through a dispersion managed 6-km DSF fiber span.
©2011 Optical Society of America
1. Introduction
Future high-speed optical networks with symbol rates exceeding 160 Gbit/s require wideband and fast tunable chromatic dispersion (CD) compensators [1]. As the tolerance for the dispersion decreases rapidly with the square of the symbol rate, compensation of high-order dispersion is required in the Tbaud optical time division multiplexing (OTDM) transmission with femtosecond optical pulses. The management of high-order dispersion is also an important issue in the generation and preparation of femtosecond pulses [2]. Although dispersion up to the third order can be compensated by combining optical fibers with different dispersion properties such as single-mode fiber (SMF) and dispersion-compensating fiber (DCF) in the link, an additional method needs to be employed for the compensation of the fourth order dispersion (FOD). Up to now, compensation of FOD has been achieved in the non-tunable scheme in the 1.28-Tbit/s OTDM transmission over 70-km fiber link by using the phase modulation method [3] or in the 640-Gbit/s OTDM transmission over 100-km SMF link by mid-span spectral inversion (MSSI) with wavelength transparent conjugation [4].
Among the tunable CD compensators, parametric tunable dispersion compensator (P-TDC), which comprises a phase preserving frequency converter together with frequency dependent dispersive media, is particularly attractive because it is free from the tradeoff between the amount of dispersion and the bandwidth, and allows fast dispersion tuning on the order of μs [5,6]. In principle, P-TDC can compensate for FOD as well as second order dispersion (SOD) and third order dispersion (TOD) without using additional device. This suggests the usefulness of P-TDC in the Tbit/s OTDM transmissions or in the chirp control of femtosecond laser pulses including the use in the chirped pulse amplification (CPA) [7]. We have, so far, verified wide bandwidth of P-TDC over 1 THz in the experiment using 2.7 ps optical pulses [5]. The usefulness of P-TDC was also demonstrated for OTDM transmissions at 172 Gbit/s [8]. The principle of P-TDC was later expanded to the idea of simultaneous control of delay and dispersion [9], by which microsecond optical delays were achieved with the record delay-bandwidth products [10,11]. While wide bandwidth of P-TDC has been well recognized, it has never been applied to femtosecond pulses.
In this paper, we present the performance of P-TDC applied to sub-picosecond pulses. First, we the present basic design issue of ultra-wideband P-TDC with the perfect compensation of FOD. Then, we present transmission characteristics of 400-fs optical pulses through a 6-km dispersion shifted fiber (DSF), concatenated with a P-TDC in nearly optimum configuration.
2. The Impact of Higher Order Dispersion on the Pulse Propagation
In general, DSF is more suitable than SMF for the transmission of optical pulses in the sense that its dispersion is close to zero at 1.5 μm. However, higher order dispersion of DSF still limits the transmission of sub-picosecond pulses. Figure 1 shows the output waveforms when a sub-picosecond pulse propagates through a DSF with or without CD compensation. The calculation was made for Gaussian pulses with different pulse widths of 100 fs, 200 fs and 400 fs. The center wavelength of the input pulse and the zero-dispersion wavelength of DSF are 1535 nm and 1546 nm, respectively. Figure 1(a) shows the output waveforms from a 100-m DSF for which no CD compensation is performed. Figure 1(b) shows the waveforms from a 100-m DSF for which only SOD is compensated. It is seen that TOD of a 100-m DSF seriously distorts the pulse shape. Figure 1(c) shows the waveforms after transmitting through a 6-km DSF for which both SOD and TOD are compensated. It is seen that pulses narrower than 200 fs are stretched symmetrically and entail pedestals by FOD.
Fig. 1 The output waveform of sub-picosecond Gaussian pulses after transmission through a DSF with or without CD compensation. τ in: Input pulse width. (a) 100-m DSF without CD compensation, (b) 100-m DSF with SOD compensation, (c) 6-km DSF with compensation of SOD and TOD.
P-TDC enables dispersion compensation up to 4th order without employing additional device such as phase modulator, while facilitating a tunability of SOD. Since compensation of TOD and FOD relies on the careful arrangement of optical fibers, optimum performance of P-TDC is obtained at the designed input wavelength. When the dispersion of an optical fiber is compensated up to 4th order, zero dispersion is obtained in a range over ~30 nm. There is a tolerance of this range for the varying input wavelength, although the tuning range decreases with the offset from the designed wavelength. For example, a tolerance of ± 5 nm exists for 400 fs pulse.
3.Theory
The details of the principle of P-TDC are described in [5]. In P-TDC, signal passes two dispersive mediums with a moderate dispersion slope and phase preserving frequency conversion takes place in between them. The wideband frequency conversion, which is accompanied by spectral inversion (type-1) or non-inversion (type-2), is, for example, performed through four-wave mixing (FWM) process in a highly nonlinear fiber (HNLF) [12]. In the design of ultra-wide band P-TDC, the type-1 scheme provides more flexibility than the type-2 scheme owing to the effect of spectral inversion (SI). Therefore, we focus our attention on the type-1 scheme, whose configuration and operating principle are shown in Fig. 1. To make the argument simple, the transmission line whose dispersion is to be compensated is included as a part of the first dispersive medium in Fig. 2 . In this scheme, CD compensation is achieved by controlling the signal frequency in the second dispersive medium so that the effective dispersion of the system is maintained to zero.
Fig. 2 The configuration and operating principle of P-TDC. FC/SI: Frequency converter with spectral inversion.
If we define normalized amplitude u(z, t) and ignore nonlinear effects, pulse propagation through a dispersive medium is described by [13]
where β k is k-th order dispersion. If the input pulse shape u in(t) is given, the solution of Eq. (1) is given by the Fourier inverse transform aswhere L is the length of the medium, is the Fourier transform of uin (t) andWe note that ω is the frequency offset from the central frequency of the pulse. Using this solution successively and applying a transformation ω → -ω for the first dispersive medium, the pulse shape after transmitting the system shown in Fig. 1, uout (t), is given aswhere is given byHere, Li is the length of the i-th dispersive medium and is the k-th order dispersion defined around the signal frequency in the i-th dispersive medium. In the case when the system includes optical components that modify signal spectrum, their effect can be included using their transfer function and the output pulse shape is given bywhere plus and minus sign of applies for the optical components in the second and first dispersive medium, respectively.From Eq. (5), the effective dispersion of the system is obtained as
Equation (7) shows that the dispersion of even orders are cancelled. The illustration in Fig. 1 shows the ideal case, where the two dispersive media have symmetric dispersion profiles with respect to the conversion frequency. In this case, the effective dispersion vanishes completely, because holds for all k.4. Design Concept for Ultra-Wide Band P-TDC
Here, we present the basic concept for designing ultra-wide band P-TDC and apply it to a DSF of 6 km for the transmission of sub-picosecond pulses. DSF was chosen as the transmission line, because CD compensation of DSF is not feasible compared to other fibers due to large relative dispersion slope (RDS) [5]. As the dispersive media, we can use several kinds of fibers that are commonly used in the optical telecommunication. Figure 3(a) shows the typical dispersion profiles of the SMF, DSF and DCF together with measured dispersion properties. Since DCF is designed to compensate for SOD and TOD of an SMF simultaneously, by adding a proper length of DCF to an SMF, we can obtain a quadratic dispersion profile where FOD is dominant with a total suppression of SOD and TOD. Such a fiber pair is available to compensate for the FOD of a DSF. As the example of such special combination of optical fibers, Fig. 3(b) and 3(c) show a quadratic dispersion profile, which is obtained from a combination of “1-km SMF and 153-m DCF” and a linear dispersion profile, which is obtained from a combination of “1-km DSF, 500-m SMF and 75-m DCF”, respectively. In principle, by properly arranging SMF, DSF and DCF, we can freely tailor dispersion profile of a system up to the 4th order.
Fig. 3 (a) Typical dispersion profile of SMF, DSF and DCF. (b) Quadratic dispersion profile obtained from a combination of “1-km SMF and 153-m DCF”. (c) Linear dispersion profile obtained from a combination of “1-km DSF, 500-m SMF and 75-m DCF”.
P-TDC with maximum bandwidth is obtained by arranging optical fibers so that the effective dispersion given by Eq. (7) becomes zero up to the 4th order. This is possible owing to the negative sign of the second term. If this sign was positive, effective FOD could not be zero, because the sign of is same for all the fibers. This design concept is true for the compensation scheme by MSSI [4], whose principle is similar to P-TDC and can be explained using the same diagram in Fig. 1. In the wavelength transparent MSSI, signal wavelength and dispersion property are same in the two dispersive media and effective dispersion becomes zero if is zero for odd number of k. Therefore, CD compensation up to the 4th order can be achieved simply by compensating the dispersion slope, although dispersion tunability is not obtained in this scheme.
Figure 4 presents the example of P-TDC designed for a 6-km DSF using three kinds of optical fibers whose characteristics are shown in Fig. 3(a). The 6-km DSF together with a 3.6-km SMF and a 980-m DCF comprises the first dispersive medium and a 430-m DCF comprises the second dispersive medium. The frequency conversion with SI can be performed by a degenerate FWM. Figure 5(a) shows the effective dispersion profile calculated for several converted wavelengths when the input signal is centered at 1535 nm together with the dispersion profile of 6-km DSF. At the converted wavelength of 1554.6 nm, zero dispersion is obtained in a frequency range over 2.5 THz owing to the dispersion compensation up to the 4th order. It is seen from Fig. 5(a) that effective TOD deviates from zero as the converted wavelength departs from 1554.6 nm. However, the amount of deviation is very small compared to the dispersion slope of DSF and has negligible effect on the performance of P-TDC. Figure 5(b) shows the variation of output pulse width calculated for Gaussian pulses with a width of 100 fs and 400 fs. It is shown that input pulse width is restored at the converted wavelength of 1554.6 nm for both input pulse widths.
Fig. 5 (a) Effective dispersion calculated for several converted wavelengths (input signal: 1535 nm) and the dispersion of DSF. (b) Output pulse width estimated for Gaussian pulses with a width of 100 fs (blue) and 400 fs (red).
We verified the performance of this P-TDC theoretically by simulating the transmission of 100 fs pulses. Figure 6 shows the output waveform obtained at the converted wavelength of 1554.6 nm. For comparison, waveform that is obtained when the dispersion compensation is performed only up to the 3rd order is also shown in the figure. It is confirmed that optimally designed P-TDC enables transmission of 100 fs pulses through a 6-km DSF, whereas dispersion compensation up to the 3rd order is not sufficient.
Fig. 6 Waveforms of 100-fs Gaussian pulse after transmission of 6-km-DSF with optimally arranged P-TDC (solid curve) and CD compensation up to the 3rd order (dashed curve).
5. Experiment and Results
In the experiment to study transmission characteristics of sub-picosecond pulses, we arranged a P-TDC for a 6-km DSF span using off-the-shelf optical fibers. The pulse width after transmission was measured for various conversion frequencies and compared with theoretical estimations. Owing to the limitation of available fibers, ideal P-TDC mentioned in the previous section could not be tested. Instead, P-TDC in a nearly optimum configuration was arranged for 6-km DSF. Figure 7 presents the experimental setup. As shown in Fig. 6, the CD of 6-km DSF was compensated only by a 426-m DCF. The dispersion property of the used DSF and DCF are given in the inset of Fig. 3(a). After the transmission of 6-km DSF, signal passed through 426-m DCF twice before and after the frequency conversion. In this setup, effective TOD was almost entirely suppressed and FOD of the DCF was cancelled out in the double pass configuration. Figure 8 shows the dispersion profile of the system calculated for several converted wavelengths when the input signal is centered at 1535 nm. Compared to the ideal case, the dispersion profile is less uniform due to the uncompensated FOD of the DSF. However, nearly zero dispersion is realized in the frequency range over 1.5 THz at the converted wavelength of 1555 nm. The residual FOD, which was −0.0014 ps4, is estimated to have very small effect on the transmission of 400 fs pulse as shown in Fig. 1(c).
Fig. 7 Experimental setup and dispersion property of the used fibers. TL: Tunable CW-laser, PC: Polarization controller, FC: Frequency converter, F: Optical bandpass filter, HNLF; Highly nonlinear fiber, AC: auto-correlator.
A pulse train with a repetition rate of 43 GHz and central wavelength of 1535 nm was generated from a fiber based pulse source, which consisted of an intensity-modulated CW laser and a comb-like profile fiber compressor [14]. The output power of the pulse source was attenuated to −6 dBm and launched into the 6-km DSF. The input pulse shape had sech2 profile with a width (FWHM) of 400 fs. Figure 9(a) and 9(b) show the auto-correlation trace and the spectrum of the input pulse, respectively. The observed spectrum, which was fitted well by a sech2 profile with a width (FWHM) of 6.7 nm, was used as in the calculation of output pulse shape. In the frequency converter (FC), the signal was amplified to 13 dBm by a gain-flattened EDFA, which is followed by a band-pass filter (BPF) with 16 nm bandwidth for ASE rejection, and mixed with a pump laser of 20 dBm through a 3 dB coupler for the degenerate FWM in a HNLF. The HNLF was 100 m long and had a uniform conversion efficiency of −19 dB for the converted wavelength of 1545 nm ~1565 nm. After the HNLF, the converted signal was selected using another BPF with 16 nm bandwidth. Polarization controllers (PC) were used to adjust the polarization of the signal through the fiber. The output pulse was amplified to 6 dBm for the pulse width measurement using an auto-correlator (AC). When the signal power after FC was too small, the AC trace did not reflect the pulse shape correctly and measurement became inaccurate. To avoid this, signal power was amplified to 13 dBm before FWM in FC. There was a small deviation of the output pulse shape from sech2 profile. However, we estimated the pulse width from the AC trace assuming a sech2 profile in order to keep consistency with the measurement for the input pulse.
Fig. 9 The auto-correlation trace (a) and spectra of the input pulse (b). The curve in fig. (b) is a theoretical fit to the data.
Figure 10 shows the output pulse width measured for several converted wavelength together with theoretical values. The minimum pulse width of 480 fs was obtained at the converted wavelength of 1555.3 nm.
Fig. 10 Output pulse width measured for various conversed wavelength. Two curves show the theoretical estimations made with (bold) or without (dash) including the effect of EDFA and bandpass filter. Inset shows the AC traces for input and restored pulse.
6. Discussions
The experiment showed that the pulse after compensation was slightly broader than the input pulse. The slight broadening could be caused by the effects that appear in the optical fiber such as polarization mode dispersion (PMD) or self phase modulation (SPM). These possibilities were, however, excluded by the following observations. When we varied the power or the polarization of the signal, only very small change was observed in the restored pulse width. In another measurement performed using a similar setup, where the length of DSF and DCF was reduced by a factor of twelve, almost same width was obtained for the restored pulse. These observations imply that the slight pulse broadening was caused by FC rather than the effects in the optical fiber.
We found that limited bandwidth of the BPF and the EDFA which are used in the FC could slightly broaden the restored pulse. The BPFs, which had a flat-top profile with sharp edge, rejected small portion of the signal spectrum lying outside its 16 nm pass band. The non-uniform gain profile of the EDFA also slightly reduced the width of signal spectrum. In the theory, those spectral shaping effects were included by putting in Eq. (6), where and are the transfer function of the filter and the EDFA, respectively. For the filter, we assumed a rectangular window given by
where B filter( = 2π × 2 THz) represents the bandwidth of the BPF. For the EDFA, we assumed a Gaussian profile given bywhere B EDFA = 2π × 4 THz was chosen to account for the measured gain variation of about 1dB in the C-band. Figure 10 shows two theoretical curves calculated with or without including the effect of the BPF and the EDFA. As it can be seen, measured pulse widths agree well with the theoretical estimation obtained with the effects of the BPF and the EDFA.In the present experiment, the insufficient bandwidth of the BPF mainly limited the width of the restored pulse to 480 fs. This pulse width is, however, comparable to the width of the pulses used in the demonstration of Tbit/s-OTDM transmissions [3,4] and shows that P-TDC is applicable to Tbit/s OTDM transmissions. If the double pass configuration is applied to 100-km DSF, 400 fs pulse is estimated to be broadened to 500 fs by the residual FOD. Therefore, it is recommended to use optimum configuration in the Tbit/s OTDM transmission over 100 km. On the other hand, P-TDC in the double pass configuration is suitable as an all fiber device to externally control the chirped pulse from a femtosecond laser. In this case, optical fibers with shorter length may be sufficient. We have already confirmed basic performance in a P-TDC that consisted of a 500-m DSF and a 32-m DCF [15]. For the compensation of pulses narrower than 400 fs, FC needs to have sufficiently wide bandwidth to avoid pulse broadening. Recently, filters having a bandwidth larger than 80 nm are commercially available, and high efficiency and broadband FWM can be achieved without using an EDFA if SBS-suppressed HNLF is used [16]. Therefore, it is possible to eliminate the pulse broadening effect observed in the present experiment.
Finally, we note that P-TDC is not wavelength maintaining. However, by cascading another frequency converter, P-TDC can be wavelength tunable and produce same wavelength as the input signal if necessary.
7. Conclusion
We presented a theory for P-TDC and showed that CD compensation up to the 4th order is possible by properly arranging SMF, DSF and DCF. In the experiment, we successfully transmitted 400fs optical pulses through a dispersion managed 6km-DSF with tunning characteristics in good agreement with the theoretical estimation. Due to insufficient bandwidth of FC, restored pulse was broadened to 480 fs, which is still sufficient for 1.28 Tbit-OTDM transmission. The pulse broadening can be eliminated by proper selection of optical components. The results confirm the usefulness of P-TDC in the future ultra-high speed OTDM transmission or in the chirp control of femtosecond pulses.
Acknowledgments
Part of this work was supported by Special Coordination Funds for Promoting Science and Technology of MEXT.
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