1. Introduction

Continuously tunable delays are key components in a number of applications of high practical interest: all-optical routing [1], optical correlation [2], high-speed gating [3], arbitrary waveform generation [4], beam steering sensing [5], and detection. Optical tunable delay lines can be divided into two main classes based on the operating principle. The first class (commonly called “slow light”) utilizes the rapid refractive index change associated with nearby optical resonances. Although delay values of several pulse durations have been demonstrated with this approach, a fundamental delay-bandwidth issue [6] limits the maximally achievable delay for a given signal bandwidth. In the second class of delay engineering, the common approach is based on signal wavelength translation to a different carrier (or idler) and propagation in a dispersive waveguide. Delay tuning is achieved by changing the wavelength of the created idler resulting in the desired delay in the dispersive waveguide. Highly nonlinear fibers (HNLFs) [7–9], periodically polled lithium niobate structures (PPLN) [10] and Si waveguides [11] have all been used as wavelength converting elements. Conversion in HNLF was used for existing record results as its conversion efficiency and wide operating bandwidth are significantly superior to those of alternative platforms. More importantly, HNLFs can be easily incorporated into fiber-based setups with negligibly small coupling loss, and can be packaged on spools with diameters smaller than 20 mm.

In this paper we demonstrate a two-pump parametric tunable optical delay line based on three cascaded conversions in highly nonlinear fibers. Furthermore, we provide detailed characterization of the demonstrated delay [12]. The performance of this buffering element was measured for a 40-Gbps channel using long (2³¹-1) pseudo-random pattern bit-error testing. The delay configuration provided full compensation for the dispersion and the timing jitter. The measured tuning delay range is the longest achieved value for 40-Gb/s signals reported to date.

2. Principle of operation

The operating principle for delay lines based on wavelength converters and dispersive elements is easily understood [7]: the input signal is mapped to a new carrier wavelength that will propagate with a different group velocity in the dispersive medium, and correspondingly, accumulate a different delay than that of the original signal. It is critically important to note that almost all practical applications [1–5] require that the delayed output signal wavelength be identical to the input wavelength. More importantly, the delay value also must be independent of the operational wavelength. Consequently, an additional wavelength conversion is necessary after the dispersive element.

Owing to the finite bandwidth of the delayed signals, the process of delay accumulation by means of propagation in a dispersive medium inherently imposes a significant amount of group-velocity-dispersion-induced inter-symbol interference on the signal. Therefore, dispersion compensation is necessary. The compensation of dispersion can be facilitated by phase conjugation which, for a properly chosen wavelength conversion process, allows reuse of the dispersive block, in analogy with mid-span phase conjugation [13]. The accumulated delay in the above approach can be calculated by integrating the dispersion profile over the wavelength range between the original and idler [7]. Unfortunately, this technique does not provide for exact compensation of the dispersion across the full tuning interval due to non-vanishing third (and/or higher) order dispersion, since the dispersion compensation and group-velocity-dispersion accumulation do not occur at the same wavelength. Consequently, a non-negligible uncompensated distortion can be a source of impairment at high modulation rates [7].

 

Fig. 1. Principle of transparent operation with dispersion compensation using three conversions. Acronyms and symbols are transmitter Tx, receiver Rx, dispersions D and D _Pre; C-band (or blue) pump wavelength λ_C; L-band (or red) parametric pump wavelength λ_L; input and output signal wavelength λ_S; idler or intermediate wavelengths λ_I ⁽¹⁾ and λ_I ⁽²⁾.

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In order to address this basic limitation, Namiki [14,15] proposed a new, triple-conversion architecture. The main idea in [14,15] is to accumulate delay, not between the original wavelength λ_S and the newly created idler, but between the original signal and two closely spaced phase conjugated idlers at λ_I ⁽¹⁾ and λ_I ⁽²⁾. Naturally, the approach requires an additional wavelength conversion as the intermediate λ_I ⁽²⁾ idler must now be created from (λ_I ⁽¹⁾). The triple-conversion delay principle is illustrated in Fig. 1. In the presence of a non-vanishing wavelength difference between the idlers, a non-zero dispersion slope will result in a net total dispersion because the signal propagates twice through the same dispersive block, once at wavelength λ_I ⁽¹⁾ and once at wavelength λ_I ⁽²⁾. However, full second-order dispersion compensation can be achieved by introducing a dispersion pre-emphasis, D _Pre, for the input signal, together with proper choice of wavelengths λ_I ⁽¹⁾ and λ_I ⁽²⁾ [9] (see Fig. 1), satisfying the relationship:

Here, D(λ _I ⁽¹⁾) and D(λ _I ⁽²⁾) are the dispersions of the dispersive block at the idler wavelengths. An additional advantage of the approach [14,15] is that the required dispersion is nearly halved relative to the standard scheme. From practical considerations, the value of DPre should be high enough to provide adequate frequency separation between the idlers to facilitate proper filtering.

3. Experimental setup

The setup used in the experiment is shown in Fig. 2. Highly nonlinear fibers (HNLFs) with flattened dispersion profiles were used as nonlinear media for wavelength conversions. The wavelengths of the pumps were selected to generate idler wavelengths that simultaneously provided (i) the desired delay and (ii) full dispersion compensation. A combination of a phase modulator and an intensity carver was used to generate a 0.8 nm-wide (100 GHz) 40-Gb/s, return-to-zero-differential-phase-shift-keyed (RZ-DPSK) signal at 1562 nm (Tx). The pattern was a pseudo-random bit sequence of length 2³¹-1. A long pattern length, used as a standard in OC-768 tests, is necessary to identify any pattern-dependent penalties in the system. The modulated signal mixed with the filtered external noise (ASE) prior to the delay element. The adopted layout enables rigorous performance quantification, allowing assessment of the penalties due to both the signal distortion in the delay element, and the optical noise originating in the delay element.

A 75-km non-zero dispersion shifted fiber was used as dispersion pre-emphasis (D _Pre), providing a partial third-order dispersion compensation of the dispersive block, and allowing a 5- to 8-nm separation between idler wavelengths over the entire tuning range. After amplification (A ₂), the signal was shifted to λ _I ⁽¹⁾ in a two-pump parametric converter (HNLF₁), filtered (F ₁), and passed through a delay block consisting of a set of dispersion- compensating fibers (DCFs) with an aggregate dispersion (D) of -19 ns/nm at 1565 nm, as shown by the lower (red) curve in Fig. 1. In order to compensate more than 100 dB of loss in the dispersive block, the DCFs were counter-directionally Raman pumped, resulting in 3.2-dB equalized gain for the entire tuning range. After the dispersive block, the idler at λ _I ⁽¹⁾ was amplified (A ₅), then converted (and phase-conjugated) to λ _I ⁽²⁾ in a single-pumped parametric converter containing a 175-m HNLF (HNLF₂) characterized by a nonlinearity coefficient, γ, of 15 W^-1 km^-1, and a zero-dispersion wavelength, λ ₀, of 1562 nm. The signal subsequently passed through the previously used dispersive line, was amplified (A6) and converted back to the original wavelength λ _S in a third 100-m dispersion flattened HNLF (HNLF₃) with γ=12 W^-1 km^-1. The output optical signal-to-noise ratio (OSNR) after each of the two passes through the dispersive block exceeded 30 dB (within a 0.1-nm bandwidth). The two-stage thin film tunable filters (F _1-3) were used after every converter stage to separate the created signals from the parametric pumps. One-stage tunable filters, not shown in Fig. 2, were placed after every amplifier to suppress the spontaneous noise. The variable optical attenuators (VOA _1-2) were used to limit power launched into DCF blocks to eliminate distortions induced by fiber nonlinear effects. The polarization states of the signals were optimized by polarization controllers PC _2-6 to provide maximum conversion efficiency.

 

Fig. 2. The experimental setup. Acronyms: ASE – amplified spontaneous emission (noise); PC – polarization controller; A – amplifier; F – filter; Tx – transmitter; Rx – receiver; HNLF – highly nonlinear fiber; VOA – variable optical attenuator; DCF – dispersion compensating fiber.

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At the output, the pre-amplified (A ₇) 40-Gb/s delayed signal was detected in a balanced DPSK receiver (Rx), electronically de-multiplexed into four 10-Gb/s streams and the bit-error-ratio (BER) was measured in order to quantify the performance of the constructed delay element. The performance penalty was quantified by varying the OSNR at the transmitter side (see Fig. 2).

Two of the HNLFs were sufficiently short so the pump phase dithering suppressing the stimulated Brillouin scattering (SBS) was required only in the second one-pump converter. It is important to note that only two pumps (P_λC=2 W, P_λL=3 W) distributed among the converting stages were used. This configuration guaranteed identical input and output signal wavelengths [9], thus fulfilling a fundamental requirement for an optical delay block. In particular, the red pump λL was utilized at every conversion stage, while the blue pump λ_C was used for the first and the last wide-band conversions. In the experiment, only the red pump (L-band) was phase modulated using a single 50-MHz harmonic, while the blue (C-band) pump was left unmodulated. The pump carrier modulation is transferred to a carrier modulation of the created idlers causing significant phase modulation to amplitude modulation (PM-AM) transfer, as well as deterministic jitter after propagation through the highly dispersive line. The particular combination of four wave mixing processes used presented an opportunity for a previously proposed [9] phase dithering cancellation approach.

By properly matching the phases of the modulated pumps and the generated idlers, the carrier modulation can be perfectly compensated after passing all three converters, as illustrated in Fig. 3. The dotted horizontal arrows indicate the direction of the pump carrier shift, whereas the shaded areas schematically depict the corresponding broadened carrier bandwidth, which is a consequence of the pump phase modulation.

 

Fig. 3. A principle of the carrier modulation compensation.

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3. Results and discussions

As explained in the previous two sections, the signal delay is varied by tuning the wavelengths of both pump lasers. Specifically, the wavelength of the L-band pump, λ _L, defines the delay value (blue curve in Fig. 4a) while that of the C-band pump, λC, provides the precise dispersion compensation (green curve in Fig. 4b). The pump positions were determined using the measured DCF dispersion profiles (Fig. 1). In the experiment, the L-band laser was tuned from 1568.5 nm to 1608 nm, addressing the full tunable delay range of 1.56 µs (see Fig. 1). Full dispersion compensation of the 40-Gb/s signal requires precise pump positioning (<0.1nm) owing to its spectral width.

 

Fig. 4. a) Measured delay and the blue pump wavelength as a function of the red pump wavelength. b) The waveforms corresponding to extreme red pump positions.

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The performance is shown in Fig. 5. The measured performance penalty at a 10^-9 BER varied between 6 and 7 dB across the full tuning range, (see Fig. 5). The sizeable penalty is attributed to concatenated filtering and the delay-element noise figure. The signal is filtered fourteen times before exiting the setup, resulting in significant equivalent bandwidth limiting. In order to verify the effect of filtering, an additional measurement was performed on the 40-Gb/s RZ-DPSK back-to-back signal by adding a 0.4-nm filter, corresponding approximately to the equivalent bandwidth of the concatenated filtering inside the delay element. The performance curve is shown in the blue dashed line in Fig. 5. As can be seen, the penalty from bandwidth restriction alone is 3 dB, implying an additional 3- to 4-dB penalty due to the delay-element noise figure of the Raman-amplified dispersive block and the three wavelength conversions. The result is in perfect accord with the previously measured performance of a 10-Gb/s signal [9] which was unaffected by filtering and exhibited only a 3-dB penalty due to the excess noise build-up in the dispersive block.

 

Fig. 5. Measured delay line performance of the 40-Gb/s RZ-DPSK (return-to-zero differential-phase-shift-keyed) channel.

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Thus, it can be concluded that ultimate limit to the all-optical delay generation based on the adopted approach is ultimately limited by noise accumulation in the dispersive block, and can be extended by adopting dispersive elements with significantly lower loss per unit dispersion. Although, the method used significantly relaxes the delay limitations due to the finite third (and higher) order dispersion, the effect of the third order dispersion becomes more pronounced for signal bandwidths wider than 40 GHz. However, the last obstacle can be significantly diminished by proper dispersion engineering of the dispersion pre-emphasis element(s) [15].

4. Conclusion

A record delay-bitrate product of 62,400 is demonstrated for 40-Gb/s RZ-DPSK signal using a parametric delay element employing parametric dispersion compensation in a self-conjugating architecture based on a cascade of one degenerate and two non-degenerate four-wave mixing processes. The result is the first reported all-optical delay of a binary 40-Gb/s signal surpassing 1 µs, and is the record delay-bandwidth product demonstrated to date. The 40-Gb/s RZ-DPSK performance characterization validates the delay implementation in high-speed amplitude and phase modulated formats.