## 1.

## Introduction

An all-optical flip flop (AOFF) is an essential component for latching functions in high-speed all-optical processing applications.^{1, 2} Currently, an AOFF can be realized using the coupled multimode-interference bistable laser diodes scheme^{3, 4} or by a symmetric Mach-Zehnder (SMZ) switch with a single-pulse counter-propagation control-signal feedback loop.^{5} In the former scheme, a number of wavelengths are required; whereas in the latter scheme, only a single wavelength is employed with a feedback loop (FBL) to enhance the AOFF configuration simplicity. Because the real-time signal-propagation delay associated with the FBL is hundreds of picoseconds,^{5} there is a lag in feedback signal (i.e., requiring a sufficient transient time equivalent to the FBL delay to fully set the AOFF in an on state) when switching the AOFF to the on state. In addition, the counterpropagation between a control and input signal in the SMZ will result in an additional delay in the rising and falling edges of AOFF output.^{6} As a result, these proposed AOFFs operate on the order of nanoseconds. Therefore, achieving a fast response time and an on interval that is shorter than the transient time are the issues in FBL-based AOFF employed in high-speed applications. Here, we propose a new AOFF configuration assisted by a FBL SMZ with multiple forward-control signals (set
$S$
and reset
$R$
) to overcome these limitations.

## 2.

## AOFF Operation

An AOFF circuit block diagram and its operation principle are depicted in Fig. 1. The AOFF is composed of a SMZ switch^{5, 7} with a continuous-wave (cw) signal input; set and reset control inputs in the upper and lower control arms, respectively; and a FBL (with a signal propagation delay of
${T}_{\mathrm{FBL}}$
) feeding
$\beta \%$
of power from the AOFF output
$\left(Q\right)$
to the upper control arm of the SMZ. Polarization controllers are used to introduce an orthogonal polarization between the cw and control signals, and consequently, a polarization beamsplitter is used at the output of the SMZ to separate them. In the absence of the optical pulses at control inputs, and providing that both semiconductor optical amplifiers (SOAs) are identical, the SMZ is in a balance state because the signal gain and phase profiles in both arms in the SMZ are the same; thus, the cw signal propagating in both arms will not emerge at the AOFF output (i.e., in the off state). A single set pulse will pass through a number of paths with different delays and attenuators to produce a multiplexed pulse set
$S$
in
${T}_{\mathrm{FBL}}$
, before being applied to the upper control input of the SMZ for toggling the AOFF to the on state. The first pulse of
$S$
will saturate
${\mathrm{SOA}}_{1}$
, thus inducing an imbalance in gain and phase profiles between two arms and hence causing a switching cw signal to
$Q$
. To maintain the AOFF in the on state, i.e., a flat SOA gain saturation level, a portion
$\beta \%$
of
$Q$
output power
${P}_{\mathrm{FBL}}$
is fed back to the upper control input of the SMZ. However, since
${P}_{\mathrm{FBL}}$
takes a
${T}_{\mathrm{FBL}}$
to arrive at
${\mathrm{SOA}}_{1}$
,
$S$
pulses following the first pulse continue to maintain the
${\mathrm{SOA}}_{1}$
saturation, thus precluding gain from recovering to its initial value when the first pulse exits
${\mathrm{SOA}}_{1}$
while
${P}_{\mathrm{FBL}}$
still has yet to arrive. Similar to the set pulse, a reset pulse, after a delay of
${T}_{\mathrm{ON}}$
(the on interval), creates
$R$
, which is applied to the lower control input of the SMZ. The first pulse of
$R$
saturates the
${\mathrm{SOA}}_{2}$
gain dropping it to the same level of
${\mathrm{SOA}}_{1}$
saturating gain (i.e., restoring the gain and phase balance between SMZ arms) and once again toggling the AOFF to its off state because cw is no longer switched to
$Q$
. Note
${P}_{\mathrm{FBL}}$
is still in the upper control port within a subsequent
${T}_{\mathrm{FBL}}$
period although there is no output signal at
$Q$
. To retain the same gain level in both SOAs in this period, the following pulses in
$R$
will ensure a continuous gain saturating of
${\mathrm{SOA}}_{2}$
for the SMZ to be in balance, thus completely turning off the
$Q$
signal during and after
${T}_{\mathrm{FBL}}$
once the reset signal is applied.

## 3.

## AOFF Stability

The temporal gain of the output
$Q$
is expressed by:^{7}

## 1

$$Q\left(t\right)=\mathrm{K}({G}_{1}\left(t\right)+{G}_{2}\left(t\right)-2\sqrt{{G}_{1}\left(t\right){G}_{2}\left(t\right)}\mathrm{cos}\{-\frac{{\alpha}_{LEF}}{2}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\left[\frac{{G}_{1}\left(t\right)}{{G}_{2}\left(t\right)}\right]\}),$$^{7}

## 2

$$G\left(t\right)=\frac{P({L}_{\mathrm{SOA}},t)}{P(0,t)}=\mathrm{exp}\left[\Gamma g{\int}_{0}^{{L}_{\mathrm{SOA}}}N(z,t)\mathrm{\Delta}z\right],$$## 3

$$\frac{\partial N\left(t\right)}{\partial t}=\frac{{I}_{e}}{q{V}_{\mathrm{SOA}}}-\frac{N\left(t\right)}{{\tau}_{e}}-\frac{P\left(t\right)g[N\left(t\right)-{N}_{T}]}{hv{A}_{\mathrm{SOA}}},$$## 4.

## Results and Discussion

The AOFF operation is validated using VPI simulation software. Simulation and SOA device parameters are given in Table 1. Note that the average power of
$S$
is
$3\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$
greater than
$R$
because
$S$
is reduced by
$3\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$
when coupled with
${P}_{\mathrm{FBL}}$
to ensure that the SOAs are excited with the same set/reset powers. The
${T}_{\mathrm{FBL}}$
is approximated as
$0.2\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$
, equivalent to a
$40\text{-}\mathrm{mm}$
optical waveguide FBL.^{5} The SOA model is assumed to be polarization-independent, though in practical systems, polarization-gain dependence (
$\sim 1$
to
$2\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$
) and the imperfect polarization states of the cw and set/reset signals will slightly affect AOFF operation. The flip-flop operation is illustrated in Fig. 2. A series of set and reset single pulses, shown in Fig. 2a, are applied to the AOFF in a range of
${T}_{\mathrm{ON}}$
values of 0.1, 0.2, 0.5, 1, 2, and
$5\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$
. The resultant temporal gain profiles of SOAs corresponding with the set/reset signals are observed in Fig. 2b. During a period of
${T}_{\mathrm{ON}}$
, the
${\mathrm{SOA}}_{1}$
gain is kept at the same saturation level by both
$S$
and
${P}_{\mathrm{FBL}}$
. Figure 2c displays the AOFF-output waveforms. There are ripples at the leading edge of the
$Q$
output signal in the on state during a
${T}_{\mathrm{FBL}}$
owing to the variation in the
${\mathrm{SOA}}_{1}$
gain profile caused by the discrete excitations on
${\mathrm{SOA}}_{1}$
by pulses in
$S$
. When the AOFF is switched off, a small residual signal, lasting in
${T}_{\mathrm{FBL}}$
, still emerges at
$Q$
. This is due to the gain variation of
${\mathrm{SOA}}_{2}$
caused by multiple-pulse excitations of
$R$
in contrast to a flat gain profile of
${\mathrm{SOA}}_{1}$
maintained by a leftover of constant
${P}_{\mathrm{FBL}}$
within that
${T}_{\mathrm{FBL}}$
, hence, causing ripples at the trailing edge of the Q signal. It will, therefore, result in on/off CR deterioration.

## Table 1

Simulation and SOA device parameters.

Parameters | Value |
---|---|

Input power ${P}_{\mathrm{CW}}$ | $0\phantom{\rule{0.3em}{0ex}}\mathrm{dBm}$ |

Gaussian pulse width | $20\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ |

Signal wavelength | $1554\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ |

${P}_{\mathrm{S}}$ (peak power of first pulse) | $13.5\phantom{\rule{0.3em}{0ex}}\mathrm{dBm}$ |

${P}_{\mathrm{S}}$ (peak power of following pulses) | $8.5\phantom{\rule{0.3em}{0ex}}\mathrm{dBm}$ |

${P}_{\mathrm{R}}$ (peak power of first pulse) | $10.5\phantom{\rule{0.3em}{0ex}}\mathrm{dBm}$ |

${P}_{\mathrm{R}}$ (peak power of following pulses) | $5.5\phantom{\rule{0.3em}{0ex}}\mathrm{dBm}$ |

SOA linewidth enhancement factor ${\alpha}_{\mathrm{LEF}}$ | 5 |

SOA length ${L}_{\mathrm{SOA}}$ | $0.5\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ |

SOA confinement factor $\Gamma $ | 0.2 |

SOA carrier density at transparency ${N}_{\mathrm{T}}$ | $1.4\times {10}^{24}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{-3}$ |

SOA spontaneous emission factor ${n}_{\mathrm{sp}}$ | 2 |

DC-bias ${l}_{e}$ | $150\phantom{\rule{0.3em}{0ex}}\mathrm{mA}$ |

FBL delay ${T}_{\mathrm{FBL}}$ | $0.2\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$ |

Splitting factor $\beta $ | 15% |

The graphs in Fig. 3 show that the highest achieved CR is $22\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$ at $\beta =15\%$ [AOFF total output power is $14.5\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$ ; see Fig. 2c] where the conditions in Eqs. 4, 5 are satisfied at ${T}_{\mathrm{ON}}=1\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$ . It is also shown that the AOFF output signal is relatively flat during ${T}_{\mathrm{ON}}$ and the observed IVR is 0.95. Beyond this optimum operation point, both CR and IVR are considerably decreased due to high residual power and improper feedback power, respectively. Note that high $\beta $ results in flat-level performance in CR and IVR; however, since ${\mathrm{SOA}}_{1}$ gain is saturated due to high-power ${P}_{\mathrm{FBL}}$ , their values are noticeably small.

## 5.

## Conclusions

A new AOFF configuration based on a SMZ with FBL and multiple-pulse forward set/reset signals is proposed. A multiple set/reset control-signal scheme fully overcomes the feedback-loop delay, thus making AOFF suitable for high-speed memory or signal processing applications where ${T}_{\mathrm{ON}}$ is required to be as small as a few hundred picoseconds regardless of the FBL delay. In addition, the forward controls enhanced the AOFF toggling response within the pulse width of the set and reset signals. On/off contrast and intensity variation ratios of $22\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$ and 0.95, respectively, are achieved at the optimum operating point.