分数时间Talbot效应中幅度波动的演变
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Received June 2, 2019, accepted June 24, 2019, date of publication June 27, 2019, date of current version July 16, 2019.
Digital Object Identifier 10.1109/ACCESS.2019.2925367
Evolution of Amplitude Fluctuation in
Fractional Temporal Talbot Effect
HAO CHI
1
, (Senior Member, IEEE), JUNNA XING
2
, SHUNA YANG
1
, AND TAO JIN
2
1
School of Communication Engineering, Hangzhou Dianzi University, Hangzhou 310018, China
2
College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China
This work was supported in part by the National Natural Science Foundation of China under Grant 61575171 and Grant 61675180,
and in part by the Zhejiang Provincial Natural Science Foundation under Grant LQ18F050002.
ABSTRACT Temporal Talbot phenomena occur when a periodic optical pulse train propagates through a
dispersive medium with a proper dispersion amount, which includes integer and fractional orders depending
on the dispersion amount. The fractional temporal Talbot (FTT) effect has attracted great interest because of
its potentials in repetition rate multiplication of optical pulse train and passive amplification of short pulses.
In this paper, we investigate the evolution of amplitude fluctuation in FTT systems from the viewpoint of
the frequency-dependent fading of pulse train envelope. It is found that the envelope frequency response
of FTT is different from that of integer orders since there is waveform-to-waveform phase profile in the
output pulse train in FTT systems. The noise reduction phenomenon in FTT systems is analyzed based on
the derived frequency response. A closed-form expression of the noise reduction ratio is derived for the first
time based on the analysis of the noise power spectral density. With the given model, we are able to predict
the fluctuation suppression effect in FTT systems more precisely.
INDEX TERMS Talbot phenomenon, temporal Talbot effect, pulse repetition rate multiplication.
I. INTRODUCTION
Temporal self-imaging phenomena, also referred to as
temporal Talbot effect, are the time-domain counterpart of
the spatial Talbot effect [1]–[4]. The temporal Talbot effect
occurs when a periodic temporal signal (for instance, a short
pulse train) passes a dispersive medium with a proper disper-
sion value. Depending on the dispersion amount, the temporal
Talbot effect can be categorized into integer-order one and
fractional-order one. In an integer temporal Talbot (ITT)
system, the input periodic pulse train is exactly replicated at
the output. This feature can be applied for the accurate mea-
surement of dispersion value of a dispersion medium [5], [6].
If a time lens (quadratic phase modulation) is configured
preceding the dispersive medium, time-domain compres-
sion or stretching of original optical waveforms while keep-
ing their temporal profiles can be achieved [7]–[9]. A major
merit of the FTT effect is that the repetition rate of the peri-
odic short pulses can be multiplied while without distorting
the pulse waveform. Accordingly, the FTT effect provides a
promising solution to the generation and delivering of optical
The associate editor coordinating the review of this manuscript and
approving it for publication was Sukhdev Roy.
pulse trains with ultra-high repetition rates [10]–[16]. Note
that the generated pulse train exists a waveform-to-waveform
residual temporal phase structure in the FTT effect, which
is different from that in the ITT effect. This residual phase
profile can be employed to realize inverse FTT effect, by
which passive intensity amplification of repetitive pulses has
been demonstrated [17]–[18].
The FTT effect with uniform envelope of input pulse train
has been widely investigated [10]–[19]. It has been found that
compared with the input pulse train, the intensity noise of
the generated pulse train in a passive amplification system
based on the inverse FTT effect is largely reduced [15], [16].
Therefore, it is of great interest to study the evolution of
amplitude fluctuation of the pulse train in a FTT system as
well as the phenomenon of intensity noise mitigation. In [20],
Pudo and Chen derived the upper limit of the peak inten-
sity fluctuations in the FTT effect for pulse repetition rate
multiplication. In [21], they presented an effective approach
to theoretically predict the variation of amplitude noise and
timing jitter in periodic optical pulse train using a simple
probabilistic model, which shows that the temporal Talbot
effect has an inherent property of mitigating both pulse ampli-
tude noise and timing jitter. In [22], [23], we have analyzed
VOLUME 7, 2019
This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/
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