Noiseless intensity amplification of repetitive signals by coherent addition using the temporal Talbot effect

Spectral recovery of broadband waveforms via cross-phase modulation based tunable Talbot amplifier

Physical processes in the Fourier domain play a crucial role in various applications such as spectroscopy, quantum technology, ranging, radio-astronomy, and telecommunications. However, the presence of stochastic noise poses a significant challenge in the detection of broadband spectral waveforms, especially those with limited power. In this study, we propose and experimentally demonstrate a cross-phase modulation (XPM) based spectral Talbot amplifier to recover the broadband spectral waveforms in high fidelity. Through the combination of spectral phase filtering and XPM nonlinear effect in an all-fiber configuration, we demonstrate spectral purification of THz-bandwidth spectral waveforms submerged in strong noise. The proposed spectral Talbot amplifier provides tunable amplification factors from 3 to 10, achieved by flexible control on the temporal waveform of the pump and the net dispersion. We demonstrate up to 10-dB remarkable improvement on optical signal-to-noise ratio (OSNR) while preserving the spectral envelope. Furthermore, our system allows frequency-selective reconstruction of noisy input spectra, introducing a new level of flexibility for spectral recovery and information extraction. We also evaluate numerically the impact of pump intensity deviation on the reconstructed spectral waveforms. Our all-optical approach presents a powerful means for effective recovery of broadband spectral waveforms, enabling information extraction from a noise-buried background.

The dissipative Talbot soliton fiber laser

Talbot effect, characterized by the replication of a periodic optical field in a specific plane, is governed by diffraction and dispersion in the spatial and temporal domains, respectively. In mode-locked lasers, Talbot effect is rarely linked with soliton dynamics since the longitudinal mode spacing and cavity dispersion are far away from the self-imaging condition. We report switchable breathing and stable dissipative Talbot solitons in a multicolor mode-locked fiber laser by manipulating the frequency difference of neighboring spectra. The temporal Talbot effect dominates the laser emission state-in the breathing state when the integer self-imaging distance deviates from the cavity length and in the steady state when it equals the cavity length. A refined Talbot theory including dispersion and nonlinearity is proposed to accurately depict this evolution behavior. These findings pave an effective way to control the operation in dissipative optical systems and open branches in the study of nonlinear physics.

Experimental demonstration of passive microwave pulse amplification via temporal Talbot effect

The temporal Talbot effect is a passive phenomenon that occurs when a periodic signal propagates through a dispersive medium with a quadratic phase response that modulates the output pulse repetition rate based on the input period. As previously proposed, this effect enables innovative applications such as passive amplification. However, its observation in the microwave regime has been impractical due to the requirement for controlled propagation through a highly dispersive waveguide. To overcome this challenge, we employed an ultra-wide band linearly chirped Bragg grating within a standard microwave X-Band waveguide. By utilizing backwards Talbot array illuminators aided by particle swarm optimization, we achieved passive amplification with a gain of 3.45 dB and 4.03 dB for gaussian and raised cosine pulses, respectively. Furthermore, we numerically verified that with higher quality substrates this gain can be theoretically increased to over 8 dB. Our work paves the way for numerous applications of the Talbot effect in the microwave regime, such as temporal cloaking, sub-noise microwave signal detection, microwave pulse shaping, and microwave noise reduction.

Bright and dark Talbot pulse trains on a chip

Temporal Talbot effect, the intriguing phenomenon of the self-imaging of optical pulse trains, is extensively investigated using macroscopic components. However, the ability to manipulate pulse trains, either bright or dark, through the Talbot effect on integrated photonic chips to replace bulky instruments has rarely been reported. Here, we design and experimentally demonstrate a proof-of-principle integrated silicon nitride device capable of imprinting the Talbot phase relation onto in-phase optical combs and generating the two-fold self-images at the output. We show that the GHz-repetition-rate bright and dark pulse trains can be doubled without affecting their spectra as a key feature of the temporal Talbot effect. The designed chip can be electrically tuned to switch between pass-through and repetition-rate-multiplication outputs and is compatible with other related frequencies. The results of this work lay the foundations for the large-scale system-on-chip photonic integration of Talbot-based pulse multipliers, enabling the on-chip flexible up-scaling of pulse trains' repetition rate without altering their amplitude spectra.

Pulse rate multiplier based on the temporal Talbot effect in birefringent optical filters

In this paper, we propose a novel approach to implement a pulse rate multiplier based on the temporal self-imaging effect using, for the first time to our knowledge, a birefringent optical filter. The proposed filter, with periodic quadratic phase-only filtering induced through engineered polarization mode dispersion, contains N-stage hybrid birefringent crystals set between an input polarizer and an analyzer. Each stage is composed of an identical section and a variable section. An optimization algorithm is used to determine the opto-geometrical parameters of the filter. Preliminary results for 10-stage, 12-stage, 16-stage, and 20-stage birefringent filters show very high fidelity for multiplying a 10 GHz input pulse rate by factors of two, four, six, and eight, respectively, without distorting the individual pulse properties.

LRTM effect and electronic crystal imaging on silicon surface

Some interesting phenomena have been observed in the laser reflecting Talbot magnification (LRTM) effect discovered at first, in which the high-order nonlinear imaging and the plasmonic structures imaging occur. The LRTM effect images were obtained on the 1D and 2D photonic crystals fabricated by using nanosecond pulsed laser etching on silicon surface, where the high-order nonlinear imaging on the 1D and 2D photonic crystals was observed interestingly. The theory result is consistent with the experimental one, which exhibits that the suitable wave-front shape of injection beam selected in optical route can effectively enlarge the magnification rate and elevate the resolution of the Talbot image. Especially the periodic plasmonic structures on silicon surface have been observed in the LRTM effect images, which have a good application in the online detection of pulsed laser etching process. The temporary reflecting Talbot images exhibit that the electrons following with photonic frequency float on plasma surface to form electronic crystal observed on silicon at first, which is similar with the Wigner crystal structure.

Temporal optical besselon waves for high-repetition rate picosecond sources

We analyse the temporal properties of the optical pulse wave that is obtained by applying a discrete set of spectral π/2 phase shifts to continuous-wave light that is phase-modulated by a temporal sinusoidal wave. We develop an analytical model to describe this new optical waveform that we name ‘besselon’. We also discuss the reduction of sidelobes in the pulse intensity profiles by means of an additional spectral π phase shift, and show that the resulting pulses can be efficiently time-interleaved. The various predicted properties of the besselon are confirmed by experiments demonstrating the generation of low duty cycle, high-quality pulses at repetition rates up to 28 GHz.

Frequency-domain ultrafast passive logic: NOT and XNOR gates

Electronic Boolean logic gates, the foundation of current computation and digital information processing, are reaching final limits in processing power. The primary obstacle is energy consumption which becomes impractically large, > 0.1 fJ/bit per gate, for signal speeds just over several GHz. Unfortunately, current solutions offer either high-speed operation or low-energy consumption. We propose a design for Boolean logic that can achieve both simultaneously (high speed and low consumption), here demonstrated for NOT and XNOR gates. Our method works by passively modifying the phase relationships among the different frequencies of an input data signal to redistribute its energy into the desired logical output pattern. We experimentally demonstrate a passive NOT gate with an energy dissipation of ~1 fJ/bit at 640 Gb/s and use it as a building block for an XNOR gate. This approach is applicable to any system that can propagate coherent waves, such as electromagnetic, acoustic, plasmonic, mechanical, or quantum.

Typically, Boolean logic gates have to compromise between high speed and low energy consumption which can become limiting at scale. Here, the authors demonstrate architectures for NOT and XNOR gates that enable simultaneous low power and fast operation.

On-chip dispersive phase filters for optical processing of periodic signals

We develop a dispersive phase filter design framework suitable for compact integration using waveguide Bragg gratings (WBGs) in silicon. Our proposal is to utilize an equivalent "discrete" spectral phase filtering process, in which the original continuous quadratic spectral phase function of a group velocity dispersion (GVD) line is discretized and bounded in a modulo 2π basis. Through this strategy, we avoid the phase accumulation of the GVD line, leading to a significant reduction in device footprint (length) as compared to conventional GVD devices (e.g., using a linearly chirped WBG). The proposed design is validated through numerical simulations and proof-of-concept experiments. Specifically, using the proposed methodology, we demonstrate 2× pulse repetition-rate multiplication of a 10 GHz picosecond pulse train by dispersion-induced Talbot effect on a silicon chip.

Real-time discrete Fourier transformer with complex-valued outputs based on the inverse temporal Talbot effect

Discrete Fourier transform (DFT) plays an important role in digital signal processing. In this paper, we present a novel optical real-time discrete Fourier transformer with complex-valued outputs, which is enabled by the inverse temporal Talbot effect. In the system, an input pulse train is first quadratically phase-modulated as in an inverse temporal Talbot system and then split into two channels. In the first channel, the pulse train is further amplitude-modulated pulse-by-pulse by a discrete data sequence to be transformed. In the second channel, a reference signal modulates the pulse train, which is for removing the residual quadratic phase profile in the output pulse train. The pulse trains in the two channels propagate through a shared dispersion medium with a proper dispersion value determined by the inverse temporal Talbot effect. A 90-degree optical hybrid and two balanced photodetectors are employed to retrieve the real and imaginary parts of the DFT results. In this scheme, the pulse repetition rate of the output pulse train is equal to the input one. In addition, we present a full theoretical framework to explain exactly the DFT relationship. We also demonstrate that the input data sequence can be complex-valued with the help of an I/Q modulator.

Generalized Talbot self-healing and noise mitigation of faulty periodic images

Obtaining high-quality images from physical systems, objects, and processes is fundamental for a myriad of areas of science and technology. However, in many situations, the measured images contain defects and/or are accompanied by noise, degrading the quality of the measurement. Recently, a variant of the well-known Talbot self-imaging effect has been shown to redistribute the energy of a spatially periodic collection of images, obtaining output images with increased energy with respect to the input ones. In this work we experimentally demonstrate that such an energy redistribution method has the unique capabilities of increasing the coherent energy level of a periodic set of images over that of the incoherent noise, even allowing images completely buried under noise to be recovered. We further demonstrate that the process can mitigate potential faults of the periodic image structure, including blocked images, spatial jitter, and coherent noise, offering important enhancements (e.g., in regards to the quality of the recovered individual images) in the self-healing capabilities of Talbot self-imaging.

Conformally Mapped Multifunctional Acoustic Metamaterial Lens for Spectral Sound Guiding and Talbot Effect

We demonstrate a conformally mapped multifunctional acoustic metamaterial Mikaelian lens. Mikaelian lens is a gradient medium with a hyperbolic secant refractive index profile that can realize functions like beam self-focusing. Unlike the conventional design approaches, with a conformal transformation method, only isotropic material parameters with gradient refractive index profiles are required for the construction of such lens. To realize desired gradient index distribution, we carefully design a new type of cross-channel-shaped acoustic metamaterial, whose refractive index can be effectively modulated by simply changing the slit opening size. The distinct capabilities of the metamaterial Mikaelian lens in manipulating acoustic waves are experimentally verified with the fabricated sample. Simultaneous sound guiding and Talbot effects, which normally require respective geometrical and wave acoustic approximations, are observed in simulations and experiments. Furthermore, those effects of shaping acoustic wave propagations were validated within a relatively wide frequency range. Our study reveals how the conformal transformation method can help to bridge the ray acoustics with wave acoustics. It offers opportunities to the development of novel multifunctional acoustic devices for various applications, such as sound and particle manipulations.

Investigation of temporal Talbot operation in a conventional optical tapped delay line structure

We propose a novel scheme of temporal Talbot effect achieving optical pulse train repetition-rate multiplication in a conventional tapped delay line structure. While it is generally used for spectral amplitude filtering, we show that such architecture could also be configured for spectral phase-only filtering, as well as for a combination of amplitude and phase filtering regimes. We theoretically derive and numerically simulate the working principle of the concept, followed by a proof-of-principle experimental demonstration using an off-the-shelf Mach-Zehnder delay line interferometer, which corresponds to the simplest version of the proposed structure. We address the efficiency, and potential performance degradation in the presence of power imbalance and delay line length inaccuracy of the architecture, together with applied phase error.

Discrete refraction and reflection in temporal lattice heterostructures

By using a fiber loop with a phase modulator, we simulate the refraction and reflection effects of optical pulses at the heterointerface in the time domain, which is formed by abruptly varying the modulation depth or frequency. When the variation is periodically imposed on the optical pulse, the heterointerface is vertical and may lead to total internal reflection. The temporal refraction can be controlled by setting different Bloch wave vectors at incidence. As the variation occurs at a specific moment during the pulse propagation, a horizontal interface appears, and the negative refraction and pulse splitting in the time domain could be observed. We also show that the combination between the straight and tilted lattice could provide another way to control the temporal refraction. The study may find great applications in signals processing and optical communication.

Dispersion compensation by a liquid lens (DisCoBALL)

We present dispersion compensation by a liquid lens (DisCoBALL), which provides tunable group-delay dispersion (GDD) that is high speed, has a large tuning range, and uses off-the-shelf components. GDD compensation is crucial for experiments with ultrashort pulses. With an electrically tunable lens (ETL) at the Fourier plane of a 4f grating pair pulse shaper, the ETL applies a parabolic phase shift in space and therefore a parabolic phase shift to the laser spectrum, i.e., GDD. The GDD can be tuned with a range greater than 2×105  fs2 at a rate of 100 Hz while maintaining stable coupling into a single-mode fiber.

Frequency diffraction management through arbitrary engineering of photonic band structures

It is of fundamental interest to control light diffraction in discrete optical systems. However, photon hopping in discrete systems is dominated by the nearest-neighbor coupling, limiting the realization of nonlocal diffraction phenomena. Here, we generalize the discrete diffraction from spatial to the frequency domain using optical phase modulators. By inducing long-rang couplings in the frequency lattice through periodic modulation signals, we find the lattice band structure can be artificially engineered, giving rise to the realization of arbitrary frequency diffraction. Particularly, we create linear, bilinear and semicircular band structures using sawtooth, triangular and semicircular modulation waveforms and realize the directional, bidirectional, omnidirectional frequency diffraction as well as the spectral "superlens". We also revisit frequency discrete Talbot effect and generalize the allowed incident period to arbitrary integers through band structure engineering. Moreover, as the frequency transition also carries a wave vector mismatch, an effective electric field will emerge, through which we can realize frequency Bloch oscillations that manifest the effects of arbitrary spectral routing and self-imaging. The study paves a promising way towards versatile spectrum management for both optical communications and signal processing.

Arbitrary energy-preserving control of the line spacing of an optical frequency comb over six orders of magnitude through self-imaging

Spectral self-imaging (SI) is an efficient technique for controlling the line spacing (LS) of optical frequency combs (OFC). However, the degree of control is relatively limited, since the LS of the output comb must be set to be an integer sub-multiple of the input one. This technique can be extended to achieve arbitrary control of the comb LS by pre-conditioning the input comb with a properly designed spectral phase mask. This way, the output LS can be set to be any desired integer or fractional multiple of the input one. This generalized spectral SI process is intrinsically energy-preserving, which enables passive amplification of individual spectral lines of the comb when the scheme is designed for LS increase. Here we demonstrate the unique capabilities of generalized spectral SI in a simple dedicated fiber-optics platform, based on a frequency-shifting recirculating loop. When seeded with an external CW laser, the loop delivers a frequency comb with an arbitrary and reconfigurable quadratic spectral phase. We report lossless arbitrary control of the LS of the generated OFCs over six orders of magnitude, from the kHz to the GHz range, including passive amplification of individual comb lines by factors as high as 17 dB. The LS control is produced without modifying the features of the frequency comb. Practical applications of this LS control method are discussed.

Discrete temporal Talbot effect in synthetic mesh lattices

We investigate the discrete temporal Talbot effect in a synthetic mesh lattice by employing two coupled fiber loops with different lengths. The lattice consists of the round-trip number and time delay of pulse trains propagating in the fiber loops. The Talbot effect occurs only as the incident pulse train in one loop has a temporal period that is 1, 2, or 4 folds of time interval corresponding to the length difference of the two loops. By varying the splitting ratio of coupler connecting the two loops, the lattice band structure can be engineered and so do the Talbot distance, which can be further tuned by imposing an initial linear phase distribution on the incident pulse train. In addition, the incident periods for Talbot effect can also be fractional fold by using time multiplexing. The study may find applications in temporal cloaking, passive amplifying, and pulse repetition rate multiplication.

Programmable passive Talbot optical waveform amplifier

We introduce and experimentally demonstrate a new design for passive Talbot amplification of repetitive optical waveforms, in which the gain factor can be electrically reconfigurable. The amplifier setup is composed of an electro-optic phase modulator followed by an optical dispersive medium. In contrast to conventional Talbot amplification, here we achieve different amplification factors by using combinations of fixed dispersion and programmable temporal phase modulation. To validate the new design, we experimentally show tunable, passive amplification of picosecond optical pulses with gain factors from m = 2 to 30 using a fixed dispersive line (a linearly chirped fiber Bragg grating).

CW-to-pulse conversion using temporal Talbot array illuminators

We report on the linear conversion of continuous-wave (CW) laser light to optical pulses using temporal Talbot array illuminators (TAIs) with fractional orders 1/q(q≤10), implemented by use of multilevel PM and dispersive propagation in a chirped fiber Bragg grating. The generated, sub-nanosecond optical pulse trains have repetition rates in the gigahertz range and show the presence of satellite pulses originated by the finite electrical modulation bandwidth (7.5 GHz). Though this fact impacts the resulting extinction ratio, an experimental comparison with time and Fresnel lenses indicates that temporal TAIs represent compact systems with high light gathering efficiency (>87%) at moderate values of compression (q≤8), which can be tailored in repetition rate, gain, or width, through the fractional Talbot order for its use in pulse compression systems fed by CW light.

On the structure of quadratic Gauss sums in the Talbot effect

We report on the detailed derivation of the Gauss sums leading to the weighting phase factors in the fractional Talbot effect. In contrast to previous approaches, the derivation is directly based on the two coprime integers p and q that define the fractional Talbot effect so that, using standard techniques from the number theory, the computation is reduced, up to a global phase, to the trivial completion of the exponential of the square of a sum. In addition, it is shown that the Gauss sums can be reduced to only two cases, depending on the parity of integer q. Explicit and simpler expressions for the two forms of the Talbot weighting phases are also provided. The Gauss sums are presented as a discrete Fourier transform pair between quadratic phase sequences showing perfect periodic autocorrelation and a connection with the theory of biunimodular sequences is presented. In addition, the Talbot weighting factors of orders 1/q and 2/q are reduced to a closed form, and the equivalence to existing characterizations of Talbot weighting phases is also discussed. The relationship with one-dimensional multilevel phase structures is exemplified by the study of Talbot array illuminators. These results simplify and extend the description of the role played by Gauss sums in the fractional Talbot effect, providing a compact synthesis of previous results.

Diffraction-Induced Bidimensional Talbot Self-Imaging with Full Independent Period Control

We predict, formulate, and observe experimentally a generalized version of the Talbot effect that allows one to create diffraction-induced self-images of a periodic two-dimensional (2D) waveform with arbitrary control of the image spatial periods. Through the proposed scheme, the periods of the output self-image are multiples of the input ones by any desired integer or fractional factor, and they can be controlled independently across each of the two wave dimensions. The concept involves conditioning the phase profile of the input periodic wave before free-space diffraction. The wave energy is fundamentally preserved through the self-imaging process, enabling, for instance, the possibility of the passive amplification of the periodic patterns in the wave by a purely diffractive effect, without the use of any active gain.

Mitigating nonlinear propagation impairments of ultrashort pulses by fractional temporal self-imaging

We present a new approach to mitigate nonlinear impairments-mainly induced by self-phase modulation (SPM)-of high-repetition-rate optical pulses propagating through fiber-optic devices (amplifiers, propagation lines, etc.). The proposed approach is based on pulse division before nonlinear propagation, followed by pulse recombination using fractional temporal self-imaging (also known as the Talbot effect) in a dispersive medium. This approach directly addresses practical limitations of previous mitigation methods when applied to a train of pulses with a high repetition rate, in the gigahertz range and above. Effective reduction of SPM by a factor of ≃5 is experimentally demonstrated on picosecond optical pulses at a repetition rate of 6 GHz. The proposed method can be scaled to achieve higher SPM-reduction factors using a compact and robust fiber-optics scheme.

Extended temporal cloak based on the inverse temporal Talbot effect

A temporal cloak with a significantly extended cloaking window and spatial distribution is created using the inverse temporal Talbot effect. The continuously cloaking window and the total cloaking ratio are 196 ps and 74%, respectively, which are 5.4 and 1.6 times larger than the previous record. Moreover, the cloak is maintained over 5-km of dispersion-compensating fiber (DCF), which enables cloaking temporal events at multiple positions simultaneously. To demonstrate the cloaking performance, both message-encoded and pseudo-random temporal events are successfully concealed. Last, but not least, since our configuration does not require opposite sign of dispersion, the idea can be applied analogously to the spatial domain according to the space-time duality, thus also enriching the spatial cloaking technique.

All-optical sampling and magnification based on XPM-induced focusing

We theoretically and experimentally investigate the design of an all-optical magnification and sampling function free from any active gain medium or additional amplified spontaneous noise emission. The proposed technique is based on the co-propagation of an arbitrary shaped signal together with an orthogonally polarized intense fast sinusoidal beating within a normally dispersive optical fiber. This process allows us to experimentally demonstrate a 40-GHz sampling operation as well as an 8-dB magnification of an arbitrary shaped nanosecond signal around 1550 nm in a 5-km long optical fiber. The experimental observations are in good agreement with numerical and theoretical analysis.

Talbot Effect for Exciton Polaritons

We demonstrate, experimentally and theoretically, a Talbot effect for hybrid light-matter waves-an exciton-polariton condensate formed in a semiconductor microcavity with embedded quantum wells. The characteristic "Talbot carpet" is produced by loading the exciton-polariton condensate into a microstructured one-dimensional periodic array of mesa traps, which creates an array of phase-locked sources for coherent polariton flow in the plane of the quantum wells. The spatial distribution of the Talbot fringes outside the mesas mimics the near-field diffraction of a monochromatic wave on a periodic amplitude and phase grating with the grating period comparable to the wavelength. Despite the lossy nature of the polariton system, the Talbot pattern persists for distances exceeding the size of the mesas by an order of magnitude. Thus, our experiment demonstrates efficient shaping of the two-dimensional flow of coherent exciton polaritons by a one-dimensional "flat lens."

Reconfigurable Optical Signal Processing Based on a Distributed Feedback Semiconductor Optical Amplifier

All-optical signal processing has been considered a solution to overcome the bandwidth and speed limitations imposed by conventional electronic-based systems. Over the last few years, an impressive range of all-optical signal processors have been proposed, but few of them come with reconfigurability, a feature highly needed for practical signal processing applications. Here we propose and experimentally demonstrate an analog optical signal processor based on a phase-shifted distributed feedback semiconductor optical amplifier (DFB-SOA) and an optical filter. The proposed analog optical signal processor can be reconfigured to perform signal processing functions including ordinary differential equation solving and temporal intensity differentiation. The reconfigurability is achieved by controlling the injection currents. Our demonstration provitdes a simple and effective solution for all-optical signal processing and computing.

On the generality of the Talbot condition for inducing self-imaging effects on periodic objects

Integer and fractional self-imaging effects can be induced on periodic waveforms across the time, frequency, space, or angular frequency domains by imposing a quadratic phase profile along the corresponding Fourier dual domain. This phase must satisfy the well-known "Talbot condition." The resulting period-divided fractional self-images exhibit deterministic pulse-to-pulse phase variations that arise from the solution of a Gauss sum. In turn, these self-images can be regarded as inducing a Talbot effect in the Fourier dual domain. This suggests the possibility of observing self-imaging effects by imposing phase profiles that are not defined by the Talbot condition. In this Letter, we show otherwise that the phase profiles retrieved from a Gauss sum also satisfy the Talbot condition, which implies that this condition may encompass all possible quadratic phase patterns for inducing self-imaging effects. We establish here the precise relationships between the solutions of Gauss sums and the corresponding Talbot phases, and derive additional properties of Talbot phase patterns of fundamental and practical interest.

Sub-harmonic periodic pulse train recovery from aperiodic optical pulse sequences through dispersion-induced temporal self-imaging

Temporal self-imaging effects (TSIs) are observed when a periodic pulse train propagates through a first-order dispersive medium. Under specific dispersion conditions, either an exact, rate multiplied or rate divided image of the input signal is reproduced at the output. TSI possesses an interesting self-restoration capability even when acting over an aperiodic train of pulses. In this work, we investigate and demonstrate, for the first time to our knowledge, the capability of TSI to produce periodic sub-harmonic (rate-divided) pulse trains from aperiodic sequences. We use this inherent property of the TSI to implement a novel, simple and reconfigurable sub-harmonic optical clock recovery technique from RZ-OOK data signals. The proposed technique features a very simple realization, involving only temporal phase modulation and first-order dispersion and it allows one to set the repetition rate of the reconstructed clock signal in integer fractions (sub-harmonics) of the input bit rate. Proof-of-concept experiments are reported to validate the proposed technique and guidelines for optimization of the clock-recovery process are also outlined.

Lossless fractional repetition-rate multiplication of optical pulse trains

We propose and experimentally demonstrate repetition-rate multiplication of picosecond optical pulse trains by a fractional factor based on temporal self-imaging, involving temporal phase modulation and first-order dispersion. Multiplication factors of 1.25, 1.33, 1.5, 1.6, 1.75, 2.25, 2.33, and 2.5 are achieved with high fidelity from a mode-locked laser with an input repetition-rate between 10 and 20 GHz.