Devices that allow for tunable optical pulse delays are of central importance to numerous fields including optical coherence tomography [1], optical control of phased array antennas for radio frequency communication [2], and optical communications [3]. Given the variety of applications and settings where optical pulse delays are used, it is critical to have a variety of approaches for generating them, and currently there exist several options. The most straightforward approach uses bulk beam splitters and mechanical translation, in which pulses traverse a physical length that can be varied in a continuous fashion. The technique can be made more compact by using a cavity structure, such as a Bragg grating or a microresonator such that the pulses traverse the same length many times. Recent advances in fiber Bragg grating design and device packaging have resulted in the demonstration of tunable devices where one varies the group delay by either varying the wavelength of light or by physically changing the period of the grating [4]. Using a fast device to switch pulses out of a recirculating loop is an ideal way to generate relatively long, discretely variable delays [5]. A technique for generation of continuous delays involves shifting the central wavelength of the pulse and then passing it through a medium with a large amount of group-velocity dispersion (GVD) [6–8]. Each of the approaches described above has benefits and drawbacks in terms of maximum delay, accuracy of delay, wavelength of operation, speed of operation, pulse distortion, and conceptual complexity.

In this paper we present a technique for generating variable pulse delays which uses a combination of fiber dispersion and wavelength conversion and which has the combined advantages of: (i) the ability to generate ps to 10-ns long delays where the delay-to-pulse-width ratio approaches 1000, (ii) continuously variable delay, (iii) compatibility with short (~10 ps) or long (~ns) pulses, (iv) the output signal wavelength and bandwidth are the same as the input, and (v) the output signal phase is related to the input via phase-matching constraints. Note that a few pulse time-shifting schemes based on wavelength conversion followed by dispersion have been demonstrated previously [7,8], however these schemes do not include wavelength reconversion because they are primarily designed to manage small temporal fluctuations such as timing jitter in data streams. By including wavelength reconversion, our system dramatically extends the range of obtainable delays while preserving the spectral properties and phase information of the input signal.

Conceptually the delay generator works by introducing a controllable shift to a signal pulse’s wavelength, passing the pulse through a dispersive fiber, and then shifting the wavelength back to that of the input signal. The change in delay experienced by a pulse is proportional to the wavelength shift multiplied by the GVD of the dispersive fiber. Wavelength conversion is accomplished by using a fiber-optic parametric amplifier (FOPA). Laboratory use of FOPA technology is becoming commonplace, and there are many potentially useful FOPA devices that have been proposed for use in communication systems. Examples include broadband amplifiers [9], signal regenerators [10], and wavelength converters [11, 12]. We use a FOPA for wavelength conversion in this scheme rather than detection and regeneration of the signal at a different wavelength since the nonlinear optical process preserves the signal pulse’s wavelength, amplitude, and phase and avoids optical-to-electronic conversions of the signal pulse stream.

 

Fig. 1. Schematic of the continuously tunable optical delay generator. FPC, fiber polarization controller; det, detector.

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A schematic of the controllable delay generator is shown in Fig. 1. Signal pulses of 10-ps duration and a repetition rate of 75MHz are generated from a tunable, Ti:Sapphire-pumped, optical-parametric oscillator system. A small portion of the signal is detected at point “A” (Fig. 1), and the detected signal is used to modulate a tunable CW laser which serves as the primary pump laser. As such, the input data is used as a clock to trigger the generation of pump laser pulses. The transfer characteristics of the detector and modulator result in pump pulses of roughly 500 ps in duration, which results in the suppression of Brillouin scattering of the pump within the FOPA and ensures that pump pulses are always temporally much longer than the signal pulses. The pump pulses are optically amplified and combined synchronously with the signal pulses via a wavelength division multiplexer (WDM). Parametric amplification of the signal pulses within the 1-km-long highly-nonlinear dispersion-shifted fiber (HNL-DSF) results in the generation of idler pulses that are spectrally shifted according to 2ω_p = ω_s + ω_i, where ω_p, ω_s, and ω_i are the frequencies of the pump, signal, and idler pulses, respectively. After emerging from the HNL-DSF, the pump and signal pulses are filtered away (using a 1-nm band pass filter), and the idler pulses propagate through a Sagnac loop which includes a span of dispersion-compensating fiber (DCF) having a group-velocity dispersion of -74 ps/nm. The temporal delay that the idler pulses acquire is proportional to the original wavelength shift multiplied by the GVD coefficient of the DCF. In a manner similar to that used at the input of the system, a secondary pump is modulated by recovering the clock at point “B” in Fig. 1. The idler pulses are then spectrally shifted back to the original signal wavelength using parametric amplification in the reverse direction through the HNL-DSF. Finally, after passing through a circulator, the pump and idler are filtered from the delayed output signal using a 1-nm band pass filter. Also note that a 5.3 km-long span of standard telecommunication fiber has been included at the input to the system to pre-compensate for pulse broadening in the DCF. The forward- and reverse-amplifier configuration was chosen because we had access to only one spool of HNL-DSF. The effect of counter-propagating pump and signal pulses should have little effect for the pump duty factors greater than 20 used here, and we observed no spurious signals at the output as a result of this choice.

For the measurements presented in this paper the input signal wavelength is fixed at 1565 nm, and the pump wavelength is varied between 1553.5nm and 1558.5 nm. The system is also operated, albeit with slightly smaller variable delays, for signal wavelengths as short as 1562 nm. The system can be altered to operate over a broader range of signal wavelengths by selecting a WDM with different properties; here we use a WDM with an 8-nm bandwidth centered at 1557 nm. Further flexibility in the terms of wavelength can be achieved for different choices of HNL-DSF. The zero-dispersion wavelength for the HNL-DSF used in these experiments is measured to be 1551 ± 2nm, with a slope of 0.04ps/(nm²km). The nonlinear coefficient, γ, is 11 (W·km)^-1.

 

Fig. 2. Experimental results for the all-optical delay. (a) Plotted on the left axis are the measured (points) along with a linear fit (line). Plotted on the right axis is the expected parametric gain as a function of pump wavelength. (b) Corresponding measured temporal traces, as recorded with a 10-GHz detector, of signal pulses for the data points shown in (a).

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Figure 2(a) shows a plot of the expected parametric gain in a single pass through the HNL-DSF as a function of pump wavelength for a signal wavelength of 1565 nm. The peak pump power used in this calculation was 300 mW, which is consistent with the experimental conditions. The plot indicates that there is appreciable gain for pump detunings as large as 12 nm, corresponding to signal-to-idler wavelength conversions of 24 nm. Also shown in Fig. 2(a) is the experimentally measured delay of the signal pulses at the output of the system. Temporal traces of the delayed signal output pulse for different pump wavelengths are shown in Fig. 2(b). The pulses are still well shaped at the output of the system, and delays in excess of 800ps have been demonstrated. In principle, by using a DCF with larger GVD, and including the corresponding amount of pulse GVD precompensation compression at the input, delays of tens of ns can be produced.

 

Fig. 3. Measured optical spectra for the signal pulses at the input (solid line) and output (dot-dash line) of the delay generator.

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Depicted in Fig. 3 are the optical spectra of the input and the delayed pulses. The central wavelength of the output is exactly the same as the input, which is a consequence of generating the pump pulses for both wavelength conversion stages from the same CW laser. The spectral shape is nearly identical down to 8 dB from the peak, at which point we observe considerable noise in the sidebands. This noise is comprised of a combination of amplified spontaneous emission from the erbium-doped fiber and from the parametric amplifiers [13]. The sidebands can be suppressed to some extent by enhanced filtering of the pump at the input to the system [14] as well as by using a narrower spectral filter at the output. It is also worth noting that the sideband noise observed in Fig. 3 can be reduced by using parametric amplifiers pumped with two phase-modulated CW pump lasers compared with those pumped by a single pulsed laser [15, 16].

The experimental results reported here use a 75-MHz optical parametric oscillator as a source for the signal pulses and amplitude modulation of the pump to suppress Brillouin scattering. Implementation as a communication device will require wavelength conversion based on continuous-wave (CW) pumps which include phase (rather than amplitude) modulation to reduce stimulated Brillouin scattering. In a CW-pumped system, it will also be desirable to use two separate FOPAs rather than a single one operated in forward and reverse directions. Fiber-parametric wavelength converters pumped with CW lasers have been demonstrated with +40 dB conversion efficiency and with noise-figures of less than 4 dB [9]. Several research groups have demonstrated efficient wavelength-conversion devices based on fiber-parametric amplifiers operating at communication rates from 10 to 40 Gb/s [17–20]. Typically, the power penalty is reported to be 1dB.

In order to evaluate the feasibility of this scheme at higher data rates, we simulated a similar system where the above-mentioned improvements have been implemented. The signal is 10 Gb/s data and the CW pump is phase modulated with a pseudo-random 2.5 Gb/s pattern. A linear spool of DCF is simulated rather than a Sagnac loop. Use of a CW pump requires the use of two spans of HNL-DSF in the simulation rather than using a single span in both directions. The other system parameters, such as the pump power and the fiber properties are the same as in our experiment. The results (Fig. 4) show that error-free performance is possible with a 3-dB received power penalty. It is possible by optimizing the other system parameters that one could achieve slightly better performance than that shown here. Based on our experimental and numerical observations and on recent advances reported by other research groups, we believe that implementation of a system that can operate at data rates >40 Gb/s is possible.

 

Fig. 4. Plots of bit-error rate (BER) as a function of received power for the simulated system. Results indicate that a system operating at 10 Gb/s will experience a power penalty of 3 dB. Shown also are simulated eye diagrams for the back-to-back signal as well as the converted signal for two different pump wavelength settings.

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A key feature of this system is its ability to maintain relative phase information among the pulses in a pulse train. Phase information integrity is ensured through the phase-matching condition κ = 2k_p - k_s - k_i + γP_pL, where k_p,s,i are the mode propagation constants of the pump, signal, and idler fields, respectively, γ is the nonlinear coefficient, P_p is the pump power, and L is the fiber length. The phase-matching requirement allows this scheme to be used for delaying phase-shift keyed data or for other applications where phase information is important. The scheme is viable even in the case where significant phase modulation of the pump is required to meet high data rate requirements. However, extra care must be taken to apply the phase modulation such that relative phase information between bits is maintained.

There are several system parameters that have not yet been systematically studied as part of this work but will be the subject of future investigations. For example, due to the ultra-fast Kerr nonlinear response of the FOPA, the bandwidth of such a scheme is sufficient to operate with pulses less than 1-ps in duration. Nevertheless, in such a system the impact of dispersive pulse broadening, flatness and width of the FOPA gain profile, and non-uniformity of the GVD profile of the dispersive component need careful attention. In principle, it should also be possible to increase the amount of wavelength shift and/or the amount of GVD in order to increase the magnitude of the delay. The FOPA bandwidth can be made larger than 200 nm, but noise contributions such as stimulated Raman scattering become important for wavelength shifts much greater than 40 nm.

In conclusion, we have demonstrated a continuously variable, all-optical pulse delay that operates in the 1.5 μm telecommunication window and that can be varied by as much as 800 ps. The scheme can be implemented to generate either narrower or broader spans of delay, depending on the needs of a particular user. Delay-to-pulse-width ratios of more than 80 have been demonstrated, and we believe that ratios of 1000 can be achieved. We expect that a continuously tunable optical delay generator will be useful for a variety of applications.

The authors would like to thank Pablo Londero, Dan Gauthier, Eric Corndorf, Bob Boyd, Stojan Radic, and Justin Blows for useful discussions. The authors would also like to acknowledge financial support from the DARPA DSO Slow-Light Program and from the Center for Nanoscale Systems, supported by the NSF under grant No. EEC-0117770.