Fiber-optic spectrum monitoring of wavelength-division-multiplexed telecommunication signals with MHz update rates

We propose a novel (to our knowledge) and simple real-time optical monitoring (RTOM) system for dynamic spectral analysis of telecommunication signals, involving electro-optic (EO) temporal sampling followed by dispersion-induced frequency-to-time mapping and high-speed photodetection. This system enables tracking of the presence and relative intensity of multiple wavelength-division-multiplexed (WDM) data streams that span over a broad frequency band with high resolution, accuracy, and fast measurement update rates. We derive the design conditions and trade-offs of the proposed scheme and report proof-of-concept experiments and a numerical result that demonstrate successful spectral monitoring of dense-WDM signals with different modulation formats and bit rates, over the full C-band, with the needed resolution to discern channels separated by a few tens of GHz, and with an unprecedented fast measurement update rate in the MHz range.

Compact optical convolution processing unit based on multimode interference

Convolutional neural networks are an important category of deep learning, currently facing the limitations of electrical frequency and memory access time in massive data processing. Optical computing has been demonstrated to enable significant improvements in terms of processing speeds and energy efficiency. However, most present optical computing schemes are hardly scalable since the number of optical elements typically increases quadratically with the computational matrix size. Here, a compact on-chip optical convolutional processing unit is fabricated on a low-loss silicon nitride platform to demonstrate its capability for large-scale integration. Three 2 × 2 correlated real-valued kernels are made of two multimode interference cells and four phase shifters to perform parallel convolution operations. Although the convolution kernels are interrelated, ten-class classification of handwritten digits from the MNIST database is experimentally demonstrated. The linear scalability of the proposed design with respect to computational size translates into a solid potential for large-scale integration.

All-fibre phase filters with 1-GHz resolution for high-speed passive optical logic processing

Photonic-based implementation of advanced computing tasks is a potential alternative to mitigate the bandwidth limitations of electronics. Despite the inherent advantage of a large bandwidth, photonic systems are generally bulky and power-hungry. In this respect, all-pass spectral phase filters enable simultaneous ultrahigh speed operation and minimal power consumption for a wide range of signal processing functionalities. Yet, phase filters offering GHz to sub-GHz frequency resolution in practical, integrated platforms have remained elusive. We report a fibre Bragg grating-based phase filter with a record frequency resolution of 1 GHz, at least 10× improvement compared to a conventional optical waveshaper. The all-fibre phase filter is employed to experimentally realize high-speed fully passive NOT and XNOR logic operations. We demonstrate inversion of a 45-Gbps 127-bit random sequence with an energy consumption of ~34 fJ/bit, and XNOR logic at a bit rate of 10.25 Gbps consuming ~425 fJ/bit. The scalable implementation of phase filters provides a promising path towards widespread deployment of compact, low-energy-consuming signal processors.

Ultra-compact silicon photonics highly dispersive elements for low-latency signal processing

On-chip optical group-velocity dispersion (GVD) is highly desired for a wide range of signal processing applications, including low-latency and low-power-consumption dispersion compensation of telecommunication data signals. However, present technologies, such as linearly chirped waveguide Bragg gratings (LCWBGs), employ spectral phase accumulation along the frequency spectrum. To achieve the needed specifications in most applications, this strategy requires device lengths that are not compatible with on-chip integration while incurring in relatively long processing latencies. Here, we demonstrate a novel design strategy that utilizes a discretized and bounded spectral phase filtering process to emulate the continuous spectral phase variation of a target GVD line. This leads to a significant reduction of the resulting device length, enabling on-chip integration and ultra-low latencies. In experiments, we show GVD compensation of both NRZ and PAM4 data signals with baud rates up to 24 GBd over a 31.12-km fibre-optic link using a 4.1-mm WBG-based on-chip phase filter in a silicon-on-insulator (SOI) platform, at least 5× shorter compared to an equivalent LCWBG, reducing the processing latency down to ∼ 100 ps. The bandwidth of the mm-long device can be further extended to the THz range by employing a simple and highly efficient phase-only sampling of the grating profile. The proposed solution provides a promising route toward a true on-chip realization of a host of GVD-based all-optical analog signal processing functionalities.

Broadly tunable and ultra-highly selective detection of radio frequency signals enabled by a silicon photonic chip

Precise and agile detection of radio frequency (RF) signals over an ultra-wide frequency range is a key functionality in modern communication, radar, and surveillance systems, as well as for radio astronomy and laboratory testing. However, current microwave solutions are inadequate for achieving the needed high performance in a chip-scale format, with the desired reduced cost, size, weight, and power. Photonics-based technologies have been identified as a potential solution but the need to compensate for the inherent noise of the involved laser sources have prevented on-chip realization of wideband RF signal detection systems. Here, we report an approach for ultra-wide range, highly-accurate detection of RF signals using a conceptually novel feed-forward laser's noise cancelling architecture integrated on chip. The technique is applied to realization of an RF scanning receiver as well as a complete radar transceiver integrated on a CMOS-compatible silicon-photonics chip, offering an unprecedented selectivity > 80 dB, spectral resolution < 1 kHz, and tunability in the full 0.5-35 GHz range. The reported work represents a significant step towards the development of integrated system-on-chip platforms for signal detection, analysis and processing in cognitive communication and radar network applications.

Versatile metal-wire waveguides for broadband terahertz signal processing and multiplexing

Waveguides play a pivotal role in the full deployment of terahertz communication systems. Besides signal transporting, innovative terahertz waveguides are required to provide versatile signal-processing functionalities. Despite fundamental components, such as Bragg gratings, have been recently realized, they typically rely on complex hybridization, in turn making it extremely challenging to go beyond the most elementary functions. Here, we propose a universal approach, in which multiscale-structured Bragg gratings can be directly etched on metal-wires. Such an approach, in combination with diverse waveguide designs, allows for the realization of a unique platform with remarkable structural simplicity, yet featuring unprecedented signal-processing capabilities. As an example, we introduce a four-wire waveguide geometry, amenable to support the low-loss and low-dispersion propagation of polarization-division multiplexed terahertz signals. Furthermore, by engraving on the wires judiciously designed Bragg gratings based on multiscale structures, it is possible to independently manipulate two polarization-division multiplexed terahertz signals. This platform opens up new exciting perspectives for exploiting the polarization degree of freedom and ultimately boosting the capacity and spectral efficiency of future terahertz networks.

Waveguides that can provide complex signal-processing functionalities while guiding terahertz signals are desired. Here, the authors report the independent processing of multiplexed signals by engineering the metal surface of a four-wire waveguide.

Group-velocity dispersion emulator using a time lens

We report a novel method to continuously track the temporal evolution of an arbitrary complex waveform as it propagates through a group-velocity dispersion medium by using a single-frequency-driven phase modulator. The proposed method exploits the fact that the frequency spectrum of a given (input) waveform, following a suitable sinusoidal temporal phase modulation, exhibits the same shape as that of a dispersed version of the same temporal waveform after propagation through a prescribed amount of dispersion. In experiments, we track the dispersion-induced temporal evolution of different optical picosecond pulsed waveforms by tuning the frequency and/or amplitude of the phase modulation signal and observing the resulting shapes in the optical frequency domain. A good agreement is obtained between the measured spectra and predicted temporal shapes of the propagating waveform for different amounts of dispersion. Moreover, the method is successfully applied on a chirped optical pulse to find the optimal pulse compression conditions.

High-speed serial deep learning through temporal optical neurons

Deep learning is able to functionally mimic the human brain and thus, it has attracted considerable recent interest. Optics-assisted deep learning is a promising approach to improve forward-propagation speed and reduce the power consumption of electronic-assisted techniques. However, present methods are based on a parallel processing approach that is inherently ineffective in dealing with the serial data signals at the core of information and communication technologies. Here, we propose and demonstrate a sequential optical deep learning concept that is specifically designed to directly process high-speed serial data. By utilizing ultra-short optical pulses as the information carriers, the neurons are distributed at different time slots in a serial pattern, and interconnected to each other through group delay dispersion. A 4-layer serial optical neural network (SONN) was constructed and trained for classification of both analog and digital signals with simulated accuracy rates of over 79.2% with proper individuality variance rates. Furthermore, we performed a proof-of-concept experiment of a pseudo-3-layer SONN to successfully recognize the ASCII codes of English letters at a data rate of 12 gigabits per second. This concept represents a novel one-dimensional realization of artificial neural networks, enabling a direct application of optical deep learning methods to the analysis and processing of serial data signals, while offering a new overall perspective for temporal signal processing.

Full recovery of ultrafast waveforms lost under noise

The ability to detect ultrafast waveforms arising from randomly occurring events is essential to such diverse fields as bioimaging, spectroscopy, radio-astronomy, sensing and telecommunications. However, noise remains a significant challenge to recover the information carried by such waveforms, which are often too weak for detection. The key issue is that most of the undesired noise is contained within the broad frequency band of the ultrafast waveform, such that it cannot be alleviated through conventional methods. In spite of intensive research efforts, no technique can retrieve the complete description of a noise-dominated ultrafast waveform of unknown parameters. Here, we propose a signal denoising concept involving passive enhancement of the coherent content of the signal frequency spectrum, which enables the full recovery of arbitrary ultrafast waveforms buried under noise, in a real-time and single-shot fashion. We experimentally demonstrate the retrieval of picosecond-resolution waveforms that are over an order of magnitude weaker than the in-band noise. By granting access to previously undetectable information, this concept shows promise for advancing various fields dealing with weak or noise-dominated broadband waveforms.

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.

Nonlinear time-lens with improved power efficiency through a discrete multilevel pump: publisher's note

This publisher's note contains corrections to Opt. Lett.45, 3557 (2020).OPLEDP0146-959210.1364/OL.396342.

Nonlinear time-lens with improved power efficiency through a discrete multilevel pump

We report a novel, to the best of our knowledge, all-optical discrete multilevel time-lens (DM-TL) design based on cross-phase modulation (XPM). In this approach, the pump is synthesized such as the quadratic phase modulation is applied to the probe in constant-level time-bins with a maximum phase excursion of 2π. As a result, a considerable reduction in the required pump power is achieved in comparison to the conventional approach based on a parabolic pump. To illustrate the concept, the proposed DM-TL is here applied to the energy-preserving conversion of a continuous-wave (CW) signal into a train of pulses according to the theory of temporal Talbot array illuminators. We demonstrate CW-to-pulse conversion gains up to 12 at repetition rates exceeding 16 GHz, with a power saving with respect to the conventional parabolic TL that is more significant for increasing conversion gains.

Real-time measurement of complex fast signals by bandwidth compression in frequency shifting loops

We report coherent time-to-frequency mapping in frequency shifting loops (FSLs). We show that when seeded by a temporal signal shorter than the inverse of the frequency shift per roundtrip, the optical spectrum at the FSL output consists of a periodic replica of the input waveform, whose temporal amplitude and phase profiles are mapped into the frequency domain. We provide an experimental demonstration of this phenomenon and show how this simple setup enables real-time measurement of fast non-repetitive input RF signals with a detection chain two orders of magnitude slower than the input signal.

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.

Discretely programmable microwave photonic filter based on temporal Talbot effects

We propose and experimentally demonstrate a reconfigurable microwave photonic filter based on temporal Talbot effects. The microwave signal is first uniformly sampled by a train of optical pulses through electro-optic intensity modulation. The sampled optical pulses are then directed to a Talbot-based optical signal processor, consisting of an electro-optic temporal phase modulator and a chromatic dispersion line. The Talbot-based microwave photonic filter (TMPF) exploits the inherent properties of the Talbot self-imaging effect for mitigating pulse-to-pulse intensity fluctuations of optical pulses to transmit some fluctuation frequencies and mitigate or entirely block other microwave spectral components. The output microwave signal is finally reconstructed from the processed optical pulses and the resultant RF response is measured by a network analyzer. The TMPF exhibits an RF response with periodic, symmetric-profile passbands whose center frequency and free spectral range (FSR) are defined by the sampling rate and the dispersion value. The filter passbands can be reconfigured electrically, in discrete steps, by adjusting the modulation function of the phase modulator, i.e., without the need for manual adjustment of the optical components. This enables the capability of selection of specific passbands among the primary passbands. The phase modulation function is provided using an arbitrary waveform generator, with the potential for fast tuning of the filter's spectral response. The bandwidth of the filter passband can also be easily customized by adjusting the sampling pulse's temporal width using an optical bandpass filter. Examples of filter performance in various passband configurations are also presented in the time domain to further validate the operation of the filter.

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.

Reconfigurable photonic generation of broadband chirped waveforms using a single CW laser and low-frequency electronics

Broadband radio-frequency chirped waveforms (RFCWs) with dynamically tunable parameters are of fundamental interest to many practical applications. Recently, photonic-assisted solutions have been demonstrated to overcome the bandwidth and flexibility constraints of electronic RFCW generation techniques. However, state-of-the-art photonic techniques involve broadband mode-locked lasers, complex dual laser systems, or fast electronics, increasing significantly the complexity and cost of the resulting platforms. Here we demonstrate a novel concept for photonic generation of broadband RFCWs using a simple architecture, involving a single CW laser, a recirculating frequency-shifting loop, and standard low-frequency electronics. All the chirp waveform parameters, namely sign and value of the chirp rate, central frequency and bandwidth, duration and repetition rate, are easily reconfigurable. We report the generation of mutually coherent RF chirps, with bandwidth above 28 GHz, and time-bandwidth product exceeding 1000, limited by the available detection bandwidth. The capabilities of this simple platform fulfill the stringent requirements for real-world applications.

Producing versatile radio-frequency chirped waveforms often requires complicated techniques. The authors use a fiber-optic frequency-shifting loop to create a low-complexity photonic chirp generator with high bandwidth and fully flexible properties for application in radar, spectroscopy, and imaging.

Generation and Coherent Control of Pulsed Quantum Frequency Combs

We present a method for the generation and coherent manipulation of pulsed quantum frequency combs. Until now, methods of preparing high-dimensional states on-chip in a practical way have remained elusive due to the increasing complexity of the quantum circuitry needed to prepare and process such states. Here, we outline how high-dimensional, frequency-bin entangled, two-photon states can be generated at a stable, high generation rate by using a nested-cavity, actively mode-locked excitation of a nonlinear micro-cavity. This technique is used to produce pulsed quantum frequency combs. Moreover, we present how the quantum states can be coherently manipulated using standard telecommunications components such as programmable filters and electro-optic modulators. In particular, we show in detail how to accomplish state characterization measurements such as density matrix reconstruction, coincidence detection, and single photon spectrum determination. The presented methods form an accessible, reconfigurable, and scalable foundation for complex high-dimensional state preparation and manipulation protocols in the frequency domain.

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).

Fully digital programmable optical frequency comb generation and application

We propose a fully digital programmable optical frequency comb (OFC) generation scheme based on binary phase-sampling modulation, wherein an optimized bit sequence is applied to phase modulate a narrow-linewidth light wave. Programming the bit sequence enables us to tune both the comb spacing and comb-line number (i.e., number of comb lines). The programmable OFCs are also characterized by ultra-flat spectral envelope, uniform temporal envelope, and stable bias-free setup. Target OFCs are digitally programmed to have 19, 39, 61, 81, 101, or 201 comb lines and to have a 100, 50, 20, 10, 5, or 1 MHz comb spacing. As a demonstration, a scanning-free temperature sensing system using a proposed OFC with 1001 comb lines was also implemented with a sensitivity of 0.89°C/MHz.

In-fiber high-speed recognition of incoherent-light broadband energy spectrum patterns

A fiber-optic system is proposed and experimentally demonstrated for real-time, on-the-fly identification of an incoherent-light energy spectrum pattern based on dispersion-induced time-spectrum convolution. In the proposed system, the incoming frequency-spectrum patterns to be identified are modulated by a time-mapped version of the target intensity profile. Following propagation through a suitable fiber-optic dispersive medium, the measured output temporal waveform provides a correlation of the incoming spectra with the programmed target pattern. This enables direct, real-time detection of the matching energy spectra, without any further numerical post-processing. We experimentally demonstrate successful recognition of a target infrared spectral pattern, extending over a bandwidth of 1.5 THz with a resolution of ∼12  GHz, with sub-megahertz update rates. A path for further performance improvements is also suggested.

Bit-rate-transparent optical return-to-zero-to-nonreturn-to-zero format conversion based on linear spectral phase filtering of the RZ signal

We propose a novel and simple design for all-optical bit-rate-transparent return-to-zero (RZ)-to-nonreturn-to-zero (NRZ) telecommunication data format conversion based on linear spectral phase filtering of the RZ signal. The proposed concept is numerically analyzed and experimentally validated through successful format conversion of a 640 Gbit/s coherent RZ signal into the equivalent NRZ time-domain data using a simple phase filter realized by a commercial optical waveshaper.

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.

SNR enhancement in high-resolution phase-sensitive OTDR systems using chirped pulse amplification concepts

Phase-sensitive optical time-domain reflectometry (φOTDR) is widely used for the distributed detection of mechanical or environmental variations with resolutions of typically a few meters. The spatial resolution of these distributed sensors is related to the temporal width of the input probe pulses. However, the input pulse width cannot be arbitrarily reduced (to improve the resolution), since a minimum pulse energy is required to achieve a good level of signal-to-noise ratio (SNR), and the pulse peak power is limited by the advent of nonlinear effects. In this Letter, inspired by chirped pulse amplification concepts, we present a novel technique that allows us to increase the SNR by several orders of magnitude in φOTDR-based sensors while reaching spatial resolutions in the centimeter range. In particular, we report an SNR increase of 20 dB over the traditional architecture, which is able to detect strain events with a spatial resolution of 1.8 cm.

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.

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

Corrections to Eqs. (12) and (15) in our recent publication [Opt. Lett.41, 340 (2016)OPLEDP0146-959210.1364/OL.41.000340] are presented in this erratum.

Photonic Hilbert transformers based on laterally apodized integrated waveguide Bragg gratings on a SOI wafer

We experimentally demonstrate high-performance integer and fractional-order photonic Hilbert transformers based on laterally apodized Bragg gratings in a silicon-on-insulator technology platform. The sub-millimeter-long gratings have been fabricated using single-etch electron beam lithography, and the resulting HT devices offer operation bandwidths approaching the THz range, with time-bandwidth products between 10 and 20.

Time-domain Vander-Lugt filters for in-fiber complex (amplitude and phase) optical pulse shaping

The time-domain counterpart of spatial Vander-Lugt filters is proposed for the first time, to the best of our knowledge. The concept enables reshaping an ultrashort optical pulse into a desired complex (amplitude and phase) arbitrary temporal pulse waveform using a setup configuration similar to that of previously demonstrated fiber-optic time-domain pulse-intensity shapers, i.e., using a single temporal amplitude modulator between two opposite-dispersive all-fiber media. The proposal is experimentally validated through reconfigurable generation of two complex-valued pulse shapes, namely, a 60 ps asymmetrical triangular pulse with controlled parabolic phase and a 4-symbol 16-QAM picosecond pulse code sequence.

Femtosecond pulse shaping using wavelength-selective directional couplers: proposal and simulation

The femtosecond pulse-shaping capabilities of wavelength-selective directional couplers are investigated. Numerical results show that, depending on the coupling length and coupling coefficient, one can achieve very different temporal shapes at the output of the directional couplers. For instance, temporal re-shaping of Gaussian-like pulses into Hermite-Gaussian pulses, parabolic pulses, square temporal waveforms and sequences of equalized multiple pulses with time widths down to the femtosecond range can be achieved using readily feasible fiber/waveguide designs. The detrimental influence of the second-order variation of the detuning factor in these pulse shapers is also numerically investigated.

In-fiber reconfigurable generation of arbitrary (asymmetric) picosecond temporal intensity waveforms by time-domain optical pulse shaping

A fiber-optic programmable optical pulse shaper is experimentally demonstrated using multi-level phase-only linear filtering, capable of synthesizing arbitrary (including asymmetric) temporal intensity waveforms. The reconfigurable filtering operation is implemented in the time domain with a single electro-optic phase modulator (EO-PM) driven by a high-speed electronic arbitrary waveform generator (AWG). The required multi-level modulation signal is calculated from a combination of optimization algorithms, namely the Gerchberg-Saxton algorithm (GSA) and a genetic algorithm (GA). We report the synthesis of high-quality, arbitrary temporal intensity profiles, including asymmetric triangular waveforms and ∼150  Gbaud random on-off keying (OOK) pulse and pulse amplitude-modulation (PAM) code sequences, with a temporal resolution of ∼2  ps over a maximum time window of ∼60  ps.

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.

640 Gbit/s return-to-zero to non-return-to-zero format conversion based on optical linear spectral phase filtering

We propose a novel approach for all-optical return-to-zero (RZ) to non-return-to-zero (NRZ) telecommunication data format conversion based on linear spectral phase manipulation of an RZ data signal. The operation principle is numerically analyzed and experimentally validated through successful format conversion of a 640 Gbit/s coherent RZ signal into the equivalent NRZ time-domain data using a simple phase filter implemented by a commercial optical waveshaper.

Real-time Fourier transformation of lightwave spectra and application in optical reflectometry

We propose and experimentally demonstrate a fiber-optics scheme for real-time analog Fourier transform (FT) of a lightwave energy spectrum, such that the output signal maps the FT of the spectrum of interest along the time axis. This scheme avoids the need for analog-to-digital conversion and subsequent digital signal post-processing of the photo-detected spectrum, thus being capable of providing the desired FT processing directly in the optical domain at megahertz update rates. The proposed concept is particularly attractive for applications requiring FT analysis of optical spectra, such as in many optical Fourier-domain reflectrometry (OFDR), interferometry, spectroscopy and sensing systems. Examples are reported to illustrate the use of the method for real-time OFDR, where the target axial-line profile is directly observed in a single-shot oscilloscope trace, similarly to a time-of-flight measurement, but with a resolution and depth of range dictated by the underlying interferometry scheme.

Experimental demonstration of sub-picosecond optical pulse shaping in silicon based on discrete space-to-time mapping

We experimentally demonstrate on-chip optical pulse shaping based on discrete space-to-time mapping in cascaded co-directional couplers. The demonstrated shapers validate a recent design methodology that exploits the direct relationship between the discrete complex spatial apodization profile of a structure of cascaded couplers and the time-domain impulse response of the device. In this design, the amplitude and phase of the apodization profile can be controlled through the coupling strength of each coupler and the relative time delay between the waveguides connecting consecutive couplers, respectively. This design methodology has been successfully used to demonstrate direct synthesis of high-quality flat-top and phase-coded pulse trains with resolutions down to the sub-picosecond range using passive devices in a silicon-on-insulator platform.

Observation of spectral self-imaging by nonlinear parabolic cross-phase modulation

We report an experimental demonstration of spectral self-imaging on a periodic frequency comb induced by a nonlinear all-optical process, i.e., parabolic cross-phase modulation in a highly nonlinear fiber. The comb free spectral range is reconfigured by simply tuning the temporal period of the pump parabolic pulse train. In particular, undistorted FSR divisions by factors of 2 and 3 are successfully performed on a 10 GHz frequency comb, realizing new frequency combs with an FSR of 5 and 3.3 GHz, respectively. The pump power requirement associated to the SSI phenomena is also shown to be significantly relaxed by the use of dark parabolic pulses.

Generation of high-quality parabolic pulses with optimized duration and energy by use of dispersive frequency-to-time mapping

We propose and demonstrate a novel linear-optics method for high-fidelity parabolic pulse generation with durations ranging from the picosecond to the sub-nanosecond range. This method is based on dispersion-induced frequency-to-time mapping combined with spectral shaping in order to overcome constraints of previous linear shaping approaches. Temporal waveform distortions associated with the need to satisfy a far-field condition are eliminated by use of a virtual time-lens process, which is directly implemented in the linear spectral shaping stage. Using this approach, the generated parabolic pulses are able to maintain most energy spectrum available from the input pulse frequency bandwidth, regardless of the target pulse duration, which is not anymore limited by the finest spectral resolution of the optical pulse spectrum shaper. High-quality parabolic pulses, with durations from 25ps to 400ps and output powers exceeding 4dBm before amplification, have been experimentally synthesized from a picosecond mode-locked optical source using a commercial optical pulse shaper with a frequency resolution >10GHz. In particular, we report the synthesis of full-duty cycle parabolic pulses that match up almost exactly with an ideal fitting over the entire pulse period.

All-optical wavelength conversion based on time-domain holography: erratum

Eq. (5.1) in our recently published manuscript is incorrect. We provide the correct equation for the effective phase mismatch of the wavelength converted signal under the conditions detailed in the manuscript.

PROUD-based method for simple real-time in-line characterization of propagation-induced distortions in NRZ data signals

A simple, in-line method for real-time full characterization (amplitude and phase) of propagation distortions arising because of group velocity dispersion and self-phase modulation on 10-20 Gbps transmitted NRZ optical signals is reported. It is based on phase reconstruction using optical ultrafast differentiation (PROUD), a linear and self-referenced technique. The flexibility of the technique is demonstrated by characterizing different data stream scenarios. Experimental results were modeled using conventional propagation equations, showing good agreement with the measured data. It is envisaged that the proposed method could be used in combination with DSP techniques for the estimation and compensation of propagation distortions in fiber links, not only in conventional IM/DD systems, but also in coherent systems with advanced modulation formats.

Optical pulse shaping based on discrete space-to-time mapping in cascaded co-directional couplers

We propose and numerically validate a new design concept for on-chip optical pulse shaping based on discrete space-to-time mapping in cascaded co-directional couplers. We show that under weak-coupling conditions, the amplitude and phase of the discrete complex apodization profile of the device can be directly mapped into its temporal impulse response. In this scheme, the amplitude and phase of the apodization profile can be controlled by tuning the coupling strength and relative time delay between the couplers, respectively. The proposed concept enables direct synthesis of the target temporal waveforms over a very broad range of time-resolution, from the femtosecond to the sub-nanosecond regime, using readily feasible integrated waveguide technologies. Moreover, the device offers compactness and the potential for reconfigurability.

All-optical wavelength conversion based on time-domain holography

All-optical wavelength conversion of a complex (amplitude and phase) optical signal is proposed based on an all-optical implementation of time-domain holography. The temporal holograms are generated through a cross-phase modulation (XPM) process in a highly-nonlinear optical fiber, avoiding the necessity of accomplish the phase matching condition between the involved pump and probe signals, and reducing the power requirements compared to those of the traditional wavelength conversion implementations using four wave mixing (FWM). The proposed scheme also achieves symmetric conversion efficiency for up- and down-conversion. As a proof-of-concept, wavelength conversion of a train of 10 GHz chirped Gaussian-like pulses and their conjugated is experimentally demonstrated.

Time-delay to intensity mapping based on a second-order optical integrator: application to optical arbitrary waveform generation

We propose and validate experimentally a time-delay to intensity mapping process based on second-order optical integrators. This mapping provides dynamic control of the intensity modulation profile of a waveform based on a purely passive and linear process. In particular, we can realize linear intensity control by tuning the time-delay between two optical pulses launched into a second-order optical integrator. We suggest and experimentally prove the use of this mapping process for reconfigurable optical arbitrary waveform generation.

Phases of Talbot patterns in angular self-imaging

The original Talbot (self-imaging) effect is observed in the vicinity of a grating of slits shined with a plane wave, and results in periodic images of the initial diffraction pattern (integer Talbot effect) and the appearance of images with a periodicity reduced by an integer factor (fractional Talbot effect). Most of the studies on Talbot effect so far have focused on the distribution of the intensity of the diffracted light. However, the phases of the Talbot images, obtained in both the integer and fractional self-imaging cases, can be calculated in a closed form and display interesting auto-correlation properties. This paper reports what is, to the best of our knowledge, the first experimental investigation of the phases of Talbot images beyond the integer self-imaging case. We address the problem of experimental measurement of the phases of the Talbot images in the equivalent frame of the angular Talbot effect, a recently reported manifestation of the Talbot effect in the far field. The phases of the Talbot images are measured by far-field holography, and the obtained results are in excellent agreement with theoretical calculations. They also suggest the possibility of using the scheme for a precise "fractional ruler" aimed at distances' measurements.

Implementation of the photonic time-stretch concept using an incoherent pulsed light source

We propose a new technique to realize photonic time stretching of radio-frequency (RF) signals by using a time-gated (pulsed) incoherent-light source. The proposed system provides similar performance specifications (stretch factor, temporal aperture, and resolution) to those of a conventional coherent system but using a temporal gating process that is significantly longer than the transform-limited pulse duration of the equivalent coherent configuration. We experimentally demonstrate temporal magnification and compression of high-speed RF signals, with time-stretch factors ranging from 0.65 to 8.66, using a broadband (11.6 nm) incoherent-light source temporally gated over ∼163  ps. In one of the reported experiments, we achieve a resolution of ∼67.5  ps over a temporal aperture of ∼23  ns, representing a time-bandwidth product of >340.

Incoherent-light temporal stretching of high-speed intensity waveforms: reply to comment

This is a reply to the recent comment [Opt. Lett.40, 1438 (2015)10.1364/OL.40.001438OPLEDP0146-9592] by Brian H. Kolner. We offer some additional explanations for his clarifications.

High-contrast linear optical pulse compression using a temporal hologram

Temporal holograms can be realized by temporal amplitude-only modulation devices and used for generation and processing of complex (amplitude and phase) time-domain signals. Based on the temporal hologram concept, we numerically and experimentally demonstrate a novel design for linear optical pulse compression using temporal modulation of continuous-wave light combined with dispersion. The newly introduced scheme overcomes the undesired background problem that is intrinsic to designs based on temporal zone plates, while also offering an energy efficiency of ~25%. This pulse compression scheme can ideally provide an arbitrarily high time-bandwidth product using a low peak-power modulation driving signal, though in practice it is limited by the achievable modulation bandwidth and dispersion amount.

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.