## Abstract

We introduce an all-optical, format transparent hash code generator and a hash comparator for data packets verification with low latency at high baudrate. The device is reconfigurable and able to generate hash codes based on arbitrary functions and perform the comparison directly in the optical domain. Hash codes are calculated with custom interferometric circuits implemented with a Fourier domain optical processor. A novel nonlinear scheme featuring multiple four-wave mixing processes in a single waveguide is implemented for simultaneous phase and amplitude comparison of the hash codes before and after transmission. We demonstrate the technique with single polarisation BPSK and QPSK signals up to a data rate of 80 Gb/s.

© 2013 OSA

## 1. Introduction

Detection and correction of mistaken data is a critical function in information systems. Therefore, numerous error management techniques have been developed, including Forward Error Correction (FEC), checksums, cyclic redundancy checks and more generally hash functions [1]. The underlying principle of any hash method is the computation of a number as a signature of a data packet mapping the original data to a value in a smaller mathematical space [2]. Identical blocks of data yield the same hash code, while different ones should have different signatures, heralding an error. In a transmission system, failure can be detected with high probability by comparing the hash before and after propagation. With a higher degree of complexity, FEC algorithms are able to repair corrupted data without re-transmission, and are in use in most current telecommunication networks [3] allowing coding gains of over 10 dB [4–6]. These integrity check methods imply the transmission of some redundant information (i.e. the hash codes) and usually result in increased latency and power consumption due to the required processing.

In the context of high bandwidth optical communications, these algorithms are part of the Digital Signal Processing (DSP) performed at both the transmitter and the receiver [7]. The intense processing operations required introduce constraints in terms of bandwidth, energy efficiency and latency [8,9]. An implementation of a hash function directly in the optical domain could significantly reduce these burdens. A recent report established the feasibility of a Semiconductor Optical Amplifiers (SOA) based hash encoder and decoder. However, the proposed scheme only works for On-Off Keying (OOK) signals of limited bandwidth [10,11] and cannot be generalised to advanced modulation formats which are now used extensively in communication systems [12].

Here we introduce and demonstrate for the first time an all-optical, format transparent, hash code verified transmission link comprising a low latency hash code generator and comparator. In this scheme, the hash code is generated using a Fourier domain optical processing operation on the data signal, while the hash code comparator is implemented via coherent optical subtraction based on multiple Four Wave Mixing (FWM) processes in a nonlinear medium. Data validation consists of comparing hash signals calculated before and after transmission. In contrast to most electronic methods, which incorporate the hash codes into the bitstream or packets, we transmit the codes on a separate wavelength channel thus avoiding the need for sophisticated bit-rate adjustment, check symbol insertion and segmentation schemes. Experiments are reported for a 40 Gb/s single channel Binary Phase Shift Keying (BPSK) signal and a 80 Gb/s single channel Quadrature Phase Shift Keying (QPSK) signal. Our approach can be easily scaled to higher symbol rates and modulation formats without modification. This work represents a key result for ultra-low latency optical networks.

## 2. Principle

Hash based error detection codes require transmission of redundant information along with the data. In most electronic systems it is concatenated to the payload of each data packet. In our method however, the original data channel remains unchanged while the hash code is transmitted on a parallel wavelength channel as depicted on Fig. 1. At the receiver side, integrity of the data is checked by comparing the hash code from before to the one after transmission via all-optical signal subtraction.

The functional diagram in Fig. 2 illustrates the successive transformations of the optical channels. The same data is encoded onto two phase locked WDM channels. One channel is kept as it is, while the other is used as a base for computing the hash signal (Hash 1) in a first hash generator device. Both channels are then propagated through the link. At the receiver, the comparison is performed by calculating the hash (Hash 2) from the received data channel using the same hash function and combining it with Hash 1 and two phase-locked pump waves. The four waves, occupying different wavelengths, are sent through a nonlinear medium to carry out the hash comparison. Upon nonlinear propagation, the two hash channels are translated to the same wavelength channel (Idler) by degenerate FWM with the two pump waves. If the relative phase between the hash channels is set to *π*, the wavelength conversion will result in a coherent subtraction, i.e. if the hash codes are the same, then destructive interference cancels the optical power at the translated wavelength. A transmission error causing the hash codes to differ would unbalance the interference term and trigger a spike at the idler wavelength, producing an error signal which can be extracted by bandpass filtering.

The hash code of an N-symbol packet is calculated by multiplying N successive symbols with custom weight and sign coefficients and coherently adding them. Such an operation can be realized using a multipath interferometric circuit (MIC) with tuneable phase offset and attenuation, represented on the right part of Fig. 5. The sign of the coefficients is controlled by the relative phase of the different interferometric arms, while the weight can be set via attenuation. We use a Fourier Domain Programmable Optical Processor (FD-POP) configured as a custom MIC by implementing the corresponding phase and amplitude transfer functions. Unlike previous methods [10, 13], this is compatible with advanced modulation formats and allows for easily reconfiguring packet length and the hash function without any physical change to the setup. Wavelength selective delay, phase control and attenuation are implemented in the FD-POP [14, 15], as detailed in section 3. The resulting hash signal takes the form of a multilevel phase- and amplitude-coded channel at same rate as the data. Note that, because the hash code is generated from N data symbols, its required bandwidth can be reduced to 1/Nth of this value by sampling, as further explained in section 4.

In contrast to previous systems that only allowed for comparing binary intensity coded signals, our hash comparator enables simultaneous comparison of multi-level phase and amplitude encoding. A more detailed explanation of the scheme is depicted in Fig. 3. The two phase-locked hash channels to be compared (Eqs (1) and (2)) are co-propagated with two pumps separated by half their spectral separation $\frac{\mathrm{\Delta}\nu}{2}$ (Eqs (3) and (4)).

These four waves have phasors *E _{H}*

_{1},

*E*

_{H}_{2},

*E*

_{P}_{1}and

*E*

_{P}_{2}, amplitudes

*A*

_{H}_{1},

*A*

_{H}_{2}and

*A*

_{P}_{1}=

*A*

_{P}_{2}and wave vectors

*k*

_{H}_{1},

*k*

_{H}_{2},

*k*

_{P}_{1}and

*k*

_{P}_{2}. As a consequence of the choice of frequency separations, first order FWM products of the pairs Hash 1 - Pump 1 and Hash 2 - Pump 2 appear at same frequency to add up coherently and have phasors

*E*

_{I}_{1}=

*A*

_{I}_{1}

*e*

^{iϕI1}and

*E*

_{I}_{2}=

*A*

_{I}_{2}

*e*

^{iϕI2}. The phase matching condition of FWM [16] determines the wave vectors of the generated idlers

*k*

_{I}_{1}= −

*k*

_{H}_{1}+ 2

*k*

_{P}_{1}and

*k*

_{I}_{2}= −

*k*

_{H}_{2}+ 2

*k*

_{P}_{2}. By developing the expression of the idler fields, one can deduce the phase relations of these idlers [17]:

Where the two phase locked pumps have been set with equal phases *ϕ _{P}*

_{1}=

*ϕ*

_{P}_{2}=

*ϕ*. In order to operate coherent subtraction, the hash signals are set with opposite phases

_{P}*ϕ*

_{H}_{2}=

*ϕ*

_{H}_{1}+

*π*. Given that the degenerate FWM products amplitudes verify the relations ${A}_{I1}\propto {A}_{H1}{A}_{P1}^{2}$ and ${A}_{I2}\propto {A}_{H2}{A}_{P2}^{2}$, the total idler field generated is

*ϕ*is not relevant for the error signal and can be omitted. The subtraction in the complex space implies that the total intensity at idlers frequency cancels only if

_{P}*A*

_{H}_{1}=

*A*

_{H}_{2}. Any mismatch between the hash signals translates into an idler spike signalling an error. This requires Hash 1 and Hash 2 to be phase locked (which is automatically the case if the two initial copies of the signal come from the same broadband source) and Pump 1 and Pump 2 to be phase locked. Importantly no phase relation is required between the hash channels and the two pumps.

## 3. Experiment and results

The experimental setup is shown in Fig. 4. The signal is
generated from a mode-locked fibre laser that delivers a 40 GHz pulse train (2 ps full width at half
maximum) at 1550 nm. The spectrum is broadened inside a highly nonlinear fibre (HNLF) and filtered
to obtain a quasi-flat comb spectrum over a bandwidth of 6 nm [18]. The pulse train is then encoded using two successive phase
modulators driven by two independent pseudo-random bit sequences (PRBS) of either 64 bits (Figs. 6 and 8) or
2^{31} – 1 bits (Fig. 10) and biased to deliver a *π* and $\frac{\pi}{2}$ phase shift in order to generate an 80 Gb/s QPSK signal [19]. The 40 Gb/s BPSK signal is generated by bypassing the
second modulator.

The hash is calculated by coherent addition of *N* successive symbols with custom
phase and amplitude offsets. This could be performed in an integrated MIC with calibrated phase
shifts and attenuations on each arm illustrated on the right of Fig.
5. Here we use a more flexible solution based on a FD-POP. The effect of the linear MIC is
fully represented by its spectral phase and amplitude transfer function programmed into the FD-POP device.

The pass channel of the wavelength selective MIC is transmitted through a flat top bandpass
filter with constant phase. The hash channel results from equal splitting of the field
*E _{S}* =

*A*

_{S}e^{iϕS}into N arms, each delayed by an integer number of symbol lengths Δ

*L*= (

_{j}*j*− 1)Δ

*L*

_{symbol}(j indexes the arms). Before recombination of the arms, each path is attenuated by

*β*and offset in phase by

_{j}*ϕ*according to the desired hash function equation. The field after propagation in arm

_{j}*j*is ${E}_{j}=\frac{1}{\sqrt{N}}{A}_{S}{e}^{i{\varphi}_{S}}\stackrel{\text{attenuation}}{\overbrace{\sqrt{{\beta}_{j}}}}\stackrel{\text{delay}}{\overbrace{{e}^{ik\mathrm{\Delta}{L}_{j}}}}\stackrel{\text{phase}\hspace{0.17em}\text{offset}}{\overbrace{{e}^{i{\varphi}_{j}}}}$. At the output of the device the delayed complex fields are passively combined resulting in:

*β*≤ 1. Let us define ${\nu}_{j}=\frac{c}{\mathrm{\Delta}{L}_{j}}$ being the frequency offset associated to the delay j such that $k\mathrm{\Delta}{L}_{j}=2\pi \frac{\nu}{{\nu}_{j}}$. The amplitude transfer function is written

_{j}*H*=

_{N}*B*+

_{N}*B*

_{N}_{+1}

*e*, where

^{iπ}*H*and

_{N}*B*are the optical field amplitudes of the hash and data at symbol

_{N}*N*. The green and blue traces correspond to 3-symbols packets with hash definitions respectively ${H}_{N}={B}_{N}+{B}_{N+1}{e}^{i\pi}+\frac{1}{3}{B}_{N+2}{e}^{i\pi}$ and ${H}_{N}={B}_{N}+{B}_{N+1}+\frac{2}{3}{B}_{N+2}{e}^{i\pi}$. Other hash definitions can be obtained by choosing linear combinations of the

*B*with other coefficients and phases.

_{N}The calculated hash keys using the above functions for 40 Gb/s BPSK and 80 Gb/s QPSK signals made of 64 symbols are shown on Fig. 6. Changing the hash parameters leads to different hash sequences for the same initial signal. In this experiment, hash key and data signal are transmitted through a short fibre link made of 50 m of SMF and 20 m of DCF. Note that the time traces and eye diagrams represent only the intensity of the hash channel. Information is also contained in its phase, which is not shown in the traces but is taken into account by the coherent signal comparator. Noise is mostly introduced in the signal generation by the phase modulator delivering the $\frac{\pi}{2}$ phase shift.

In order to compare the hash key calculated from the transmitted signal to the input signal hash
we use a second FD-POP at the end of the link. The FD-POP calculates the receiver hash key from the
transmitted data channel using the same phase and amplitude transfer function as described for the
transmitter, while leaving the transmitted hash channel untouched. The relative phase between the
transmitted hash channel and the hash calculated from the transmitted data signal is adjusted to
*π* by the FD-POP to result in coherent subtraction.

The pump pulse train is coupled to a second input port of the FD-POP and shaped to obtain a dual pump configuration with half the spectral separation of the hash signals. The hash and pump inputs are combined inside the FD-POP to form the input of the comparator. After amplification to a total optical power of 300mW and out-of-band noise filtering, nonlinear mixing occurs in a 30 m span of HNLF. The signals both have powers 10 dB lower than the pumps.

Figure 7 shows the output spectrum measured after the HNLF
for three configurations: *solid green:* the two hash functions are identical,
resulting in idler output power at zero level due to coherent subtraction (*H*1
– *H*2); *dashed black:* the hash functions are programmed
differently at the receiver and the emitter, resulting in unbalanced coherent subtraction and
therefore output pulses indicating errors ; *dotted blue:* the hash functions are
equal, but one bit every 512 bits presents an error that triggers an idler spike at the comparator
output. However, the effect on the spectrum is barely noticeable in the last case, due to the low
duty cycle (1/512) of the error pulses.

Error detection is performed in the time domain, by narrow band (70 GHz) spectral filtering at the frequency of the first order FWM products (detailed in the inset), to extract the idler. After amplification, the hash verification signal is viewed on a sampling scope with 65 GHz bandwidth.

The amplitude of the error signal translates to the degree of mismatch between the hash keys and the degree of packet reliability within the limit of small errors. Indeed a small phase and amplitude offset applied to one symbol causes a proportional change in the hash function. Note however, that stronger perturbations or changes to multiple symbols have very small, but nonzero, probability of cancelling out in the hash calculation.

Figure 8 relates the comparator output to the spectrum of the extracted idler for an 80 Gb/s QPSK data. When both hash functions are generated using the same parameters before and after transmission, the mismatch signal after the comparator is constant zero, reporting no error (bottom left). If the hash signals are generated with different hash functions on both generators, the output is nonzero heralding transmission errors (bottom right) at every symbol.

Figure 9 shows a variation of the setup introduced in
Fig. 4 in order to create localized errors in the data signal
in the case of BPSK encoding with 2^{31} – 1 PRBS data. The two replicate channels
encoded with a first phase modulator (PM) are split onto two arms. One passes through a second phase
modulator driven by a separate pattern generator operating a *π* phase shift
to one bit every 512 symbols. The other arm is delayed and adjusted in phase with a phase shifter
(PS) to exactly match the path lengths of the interferometer. Both paths are recombined inside the
first FD-POP operating the hash calculation by assigning the two wavelength channels to different
ports of the device. This structure keeps the two data channels identical, *except*
for introducing a one symbol error every 512 symbols. The relative phase between the two paths is
set manually via the phase shifter and phase locking is maintained by placing the interferometric
structure inside an enclosure to isolate it from vibrations and thermal drift.

A single bit error yield idlers mismatch in the comparator at the symbols that have different hash keys. For a hash function calculated for data packets made of N symbols, the error signal exhibits N spikes, due to the fact that all of the N hash keys involving the mistaken bit are altered. Figure 10 shows the comparator output for a single bit error when data packets contain 3 bits (N=3). Similarly, a single bit error during transmission in a real system would change the hash code of the data channel, leading to a spike at the comparator output.

## 4. Discussion

#### 4.1. Tolerance to long distance transmission

In order to verify the validity of the technique for propagation through a longer path, we implemented the system on a 40 Gb/s OOK link made of 20.72 km of SMF and a matching spool of DCF (340 ps/nm) as presented on the left diagram of Fig. 11. Residual dispersion was further compensated inside the end-of-link FD-POP by applying an additional quadratic spectral phase. The hash key channel was configured for 3-bit packets according to the equation ${H}_{N}={B}_{N}-{B}_{N+1}+\frac{1}{3}{B}_{N+2}$.

The only concern related to the addition of the mid-haul link was a slow scale timing drift between the transmitted signal and the pump (that follows another path) due to ambient temperature fluctuations. In our setup, the pump and signals were found to be significantly desynchronized within a period of about 10 s. This issue, however, would not show up in a real system where the pump pulse train would be generated based on a clock recovery module from the received signal. Importantly, the coherent comparator is not affected by the phase drift between hash and pump channels as mentioned in the principle section.

Figure 11 features the optical spectrum of the idlers and the corresponding eye diagrams for two cases. The solid green trace shows the destructive interference between idlers when transmitted and received hashes are equal and no error occurs. The dashed black trace marks the increase in total idler power when the comparator is unbalanced by configuring both hashes with different settings, which is equivalent to errors occurring at every bit. The corresponding time trace of the error signal, measured with a sampling oscilloscope, still comprises symbols apparently without error (error signal at zero), which is due to the fact that the data packets are formed of only three bits. Hence there is still a high probability of having equal hash keys for different signals.

#### 4.2. Extension of the method to higher symbol rates

The potential for high baudrate operation enabled by the ultra fast reaction time of Kerr effect exploited in the comparator offers a solution for error management at symbol rates inaccessible to electronics.

Our implementation of the hash generator is particularly well-suited for ultra high baudrate OTDM signals. The delay of our FD-POP is limited to about 50 ps [20], which at 40 Gbaud only allows hash calculation for packets of up to 3 symbol (note that this still corresponds to a bit-length of 6 in case of QPSK). However, increasing the symbol rate to 640 Gbaud, for example, would enable processing of packets of up to 32 symbols. Also hash code based verification of an OTDM channel only requires one instance of the hash generation and comparison infrastructure, while WDM systems would need separate hash comparators for all channels.

#### 4.3. Latency

The latency introduced by our system is primarily determined by the 150 ns propagation time through the 30 m of HNLF. This latency can be almost entirely removed by either unwinding the HNLF so that it is part of the transmission link or by replacing it by an on-chip nonlinearity [21].

We acknowledge the fact that DSP based error correction mechanisms provide much more sophisticated solutions. However, these introduce significant latency that can be removed by using the all-optical method proposed in this work.

#### 4.4. Hash channel sampling for improved bandwidth efficiency

In the experiment described in this paper, the hash channel has the same bandwidth as the data channel because a hash code is generated at every symbol period. However, it can be downsampled to 1/N of the original baudrate to keep only one hash code per data packet made of N symbols, which is enough for error detection. This could be done for example, by sampling the hash with an electro-absorption modulator [22] followed by a narrow-band filter or, for ultra high bandwidth OTDM signals, by nonlinear optical sampling [23, 24]. The resulting lower bandwidth hash channel would be less subject to distortions and have better spectral efficiency.

#### 4.5. Effect of dispersion

Residual chromatic dispersion can cause timing misalignment of the symbols in the data and hash channels transmitted at different wavelengths. To counter this, the FD-POP provides a flexible way to compensate for group velocity dispersion as well as higher orders of dispersion, at the same time as they apply the hash phase masks [20]. This is the method used in our 20.72 km link transmission to remove the residual delay due to imprecise dispersion compensation by the DCF section.

Also, solutions have been demonstrated for automatic compensation of fluctuations of multiple orders of dispersion using a FD-POP as tuneable compensator [25]. In presence of strongly varying dispersion, the FD-POP devices already used for the hash function generation can be feedback-controlled to cancel dispersion in real time.

#### 4.6. Phase relations

The comparator requires the received data and hash signals to be phase locked. This condition is automatically verified provided that the hash is generated from the signal itself and that both channels propagate along the same path of fibres and amplifiers. Although the pumps involved in the comparator must also be phase locked, no phase condition is required between signals and pumps.

However, accidental desynchronization of the two channels or introduction of phase noise in long amplified links may degrade the action of the comparator. A perturbation Δ*ϕ* of the relative phase between hash and data channels would introduce a maximum power inaccuracy in the error signal of the order of
$\frac{{I}_{\text{ADD}}}{2}$ (1 − *cos*(Δ*ϕ*)), where *I*_{ADD} is the maximum total idler power when the phase relation is set in the adder configuration (*ϕ _{H}*

_{1}=

*ϕ*

_{H}_{2}). A dependence of the total idler power of this type has effectively been measured when sweeping the relative phase over a 2

*π*range (Fig. 12). In the case of our demonstration of a 20.72 km link reported in paragraph 4.1, no effect of phase noise could be observed and the extinction ratio of the coherent subtracter was similar to the one measured for the back-to-back transmission.

## 5. Conclusion

We have shown flexible generation of hash keys using a linear optical device for high bandwidth optical signals encoded with complex modulation formats. Comparison of hash keys before and after transmission is implemented by coherent all-optical subtraction via a novel dual FWM scheme. This scheme is to be considered as a compromise between the high latency introduced by DSP FEC operation and a latency free link without error detection. The method is demonstrated with an 80 Gb/s QPSK signal.

## Acknowledgments

The authors acknowledge the Australian Research Council (ARC) Centres of Excellences Program (Project CE110001018), Laureate Fellowship (Project FL120100029), Discovery Early Career Researcher Award (DECRA) (Project DE120101329) and an ARC Linkage grant with Finisar Australia (Project LP120100661).

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