Research

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.

Figure: (a) Schematic of the on-chip layout utilized for coupling light in and out of the WBG-based phase filter. The zoomed-in view shows the SEM image of one of the fabricated WBGs. The cross-sectional schematic of the fully-etched silicon waveguide on top of the buried oxide is also shown; H and W are the waveguide height and width, respectively. ?W is the corrugation width. ? is the nominal grating period. Subwavelength grating-based grating couplers (GCs) couple the fundamental transverse-electric (TE)-like mode into the SOI chip with a device layer thickness of 220 nm. A Y-splitter collects the reflected signal from the WBG. A 20 ?m linear adiabatic taper connects the input single-mode waveguide (W = 0.5 ?m) with the 2 ?m wide multimode waveguide, thus ensuring fundamental-mode operation inside the WBG. The transmitted signal from the WBG is terminated using a taper. (b) Target reflectivity (left) and the spectral phase profile (right) of the discrete phase filter with ?_r = 10 GHz, superimposed with the spectrum of the input 24 Gb/s NRZ-OOK 2¹⁵?1 PRBS signal (red). (c) Coupling coefficient (?) profile: magnitude |?(z)| on the left and phase ?_?(z) on the right. (d) Variation of ?_AP along the WBG’s length. Inset shows a zoom of the sinusoidal variation. (e) Measured reflectivity of the WBG (top) and spectral phase response along the filter’s passband (bottom), centred at ? 1552 nm. The dashed trace shows the simulated response.

[1] S. Kaushal, A. Roberge, R. Kashyap, J. Azaña, “Ultra-compact silicon photonics highly dispersive elements for low-latency signal processing,” Optics Express, 31(3), pp.3467-3478 (2023).

The implementation of all-optical circuits for computing, information processing, and networking could overcome the severe speed limitations currently imposed by electronic-based systems. A promising approach toward the implementation of ultrafast all-optical circuits is to emulate the developments in the electronic domain, i.e., to follow similar component and design strategies, using photonic technologies. For this purpose, basic building blocks for high-speed analog optical signal processing need to be developed, including optical differentiators, integrators, Fourier transformers and Hilbert transformers. Such developments have recently attracted an increasing interest for optical communications, pulse shaping or sensing applications that use optical signals.
An all-optical temporal differentiator is a fundamental function for ultrafast signal processing, which provides the derivative of the time-domain complex envelope of an arbitrary input optical signal. In general, an all-optical temporal differentiator can be realized using a linear optical device that has a spectral transfer function proportional to the term (?-?₀)^N, where N is the differentiation order, ? is the optical frequency variable and ?₀ is the optical carrier frequency of the optical signal to be processed. This functionality can be implemented using a linear optical filter providing a linear amplitude (V-shaped) spectral response over its operation bandwidth with a complex zero at the carrier frequency of the signal under test. All-optical differentiators have been designed and demonstrated with operation bandwidths up to a few THz by use of an integrated-optic transversal filter approach, fiber gratings, silicon ring resonator and Mach-Zehnder interferometers.
We have recently proposed and experimentally realized a novel ultra-broadband all-optical differentiator scheme based on a simple and widely available technology, namely a wavelength-selective directional coupler made of non-identical waveguides in an integrated-waveguide or optical fiber structure. The distinctive feature of the differentiator based on a directional coupler is that it can offer an extremely broad bandwidth, ~25 THz in our experimental demonstrations, a world record operation bandwidth.

Figure: (a) Schematic diagram of the wavelength-selective directional coupler used for ultrafast optical differentiation; (b) Measured and simulated spectral magnitude and phase response; (c) Experimental setup for characterization. (d) Experimental results of optical temporal differentiation and flat-top pulse shaping by shifting the wavelength of an input Gaussian-like optical pulse with respect to the resonance of the differentiator.

[1] M. Li, H.-S. Jeong,J. Azaña, and T.-J. Ahn, “25-terahertz-bandwidth all-optical temporal differentiator,” Optics Express 20, 28273–28280 (2012).

All-optical analog circuits for computing, information processing and networking could overcome the severe speed (i.e., bandwidth) limitations presently imposed by the use of electronics. However, in photonics, there are very few fundamental ‘building blocks’ equivalent to those used in electronics (e.g. differentiators, integrators, memory elements etc.) to build up complex circuits for advanced analysis, processing and computation. Realizing these photonic building blocks in a monolithic platform – ideally compatible with CMOS technology – represents a crucial step for the future development of ultrafast computing and information processing circuits on a chip. Our group has pioneered worldwide the design and experimental realization of several key basic ‘building blocks’ for ultrafast analog optical signal processing, most prominently, optical temporal differentiators and integrators, real-time optical Fourier and Hilbert transformers etc. As a very relevant example, we reported the first monolithic photonic integrator based on a passive micro-ring resonator in a CMOS compatible platform, performing an unprecedented time-bandwidth product of ~100 (~200 GHz processing bandwidth and ~800 ps integration time window), shown in [1]:

Plot (a) shows a schematic of the used integrated micro-ring resonator device, illustrating its working principle as a photonic temporal integrator. In the plots (b), (c), and (d), the input/output system time-domain response is represented. More specifically, the cumulative time integral has been performed on different waveforms: i) the optical pulse directly generated by the laser source (b, inset-2); ii) a sequence of two pi-shifted pulses with a temporal delay of 275 ps (c, inset); and iii) a strongly chirped optical pulse with a field-amplitude time duration around 1,340 ps, corresponding to an intensity time-width of ~800 ps (d, inset). This latter pulse was generated by propagation of the original laser pulse through a highly dispersive chirped fiber Bragg grating (FBG). The corresponding experimental (black curve) and theoretical (red curve) time integrals are represented in the main plots. Inset b-2) depicts the experimental impulse response obtained by using a fast (~8 ps) amplified photo-detector.

[1] M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, J. Azaña, “On-chip CMOS compatible all-optical integrator,” Nature Commun. 1:29 doi: 10.1038/ncomms1028 (2010).

Real-time Fourier transformation (RTFT) enables Fourier analysis at speeds beyond conventional digital signal processing. Optical RTFT commonly relies on mapping the spectrum of the waveform under test to the time domain by inducing large amounts of group velocity dispersion, see for instance pioneering work in IEEE J. Quantum Electron. 36, 517-526 (2000). However, the relatively limited dispersion of commonly-available transparent media limits the typical optical frequency resolution of RTFT to above the GHz range. This represents a critical limitation for applications in real-time spectroscopy, ultrafast detection, imaging and sensing, as well as photonic-assisted generation and processing of radio-frequency (RF) signals.
We have recently proposed an RTFT concept that extends the resolution of RTFT analysis to the kHz regime, by avoiding the use of dispersion altogether. The concept is based on the superposition of multiple input signal replicas, which shift simultaneously along the time and frequency domains in a frequency-shifted feedback (FSF) loop.

Under the scheme depicted in Fig. (a), an input signal photon circulates in the FSF loop with a round-trip time ?_c; on each round trip, an acousto-optical frequency shifter (AOFS) shifts the photon’s frequency by f_s. An intra-cavity bandpass filter and amplifier controls the number of round trips in the loop. Assuming that the product of the round-trip time and frequency shift equals an integer (p = 1, 2, 3, …), the shape of the output time trace reproduces the optical spectrum profile of the input. The inverse of a photon’s total lifetime in the loop gives the technique’s frequency resolution. Fig. (b) shows the obtained RTFT time traces of a continuous-wave laser modulated with a single radio-frequency tone of frequency f_m. Fig. (c) compares the input spectrum under analysis with the obtained time trace (f_m = 200 kHz).

We have demonstrated successful RTFT of optical signals with a frequency resolution as high as about 30 kHz, and a time-bandwidth product higher than 400 –results that exceed dispersion-based schemes by orders of magnitude. The processing architecture features minimal latency (equal to the inverse of the frequency resolution) and, contrary to other schemes, the method requires neither truncated nor coherent input light. This concept opens new perspectives in optical real-time Fourier analysis, with applications beyond our optical-domain implementation.

[1] H. Guillet de Chatellus, L. Romero Cortés, and J. Azaña, “Optical real-time Fourier transformation with kilohertz resolutions,” Optica 3, 1-8 (2016).

A time lens is the temporal equivalent of a spatial thin lens, typically implemented through quadratic temporal phase modulation of the waveform under analysis. Related with this concept, a temporal zone plate enables the compression of CW light into short optical pulses through a two-step process, involving temporal modulation (e.g., through an electro-optic modulator driven by an electronic waveform generator) followed by chromatic dispersion. Temporal zone plates do not exhibit the limiting trade-off between temporal aperture and frequency bandwidth (temporal resolution) of conventional linear (electro-optic) time lenses, enabling compression of CW light over a much longer temporal period (time aperture). The latest is of critical importance to achieve higher energy pulses. There are two kinds of temporal zone plates – temporal intensity and phase zone plates, which can be realized by temporal intensity and phase modulation, respectively. As an example, temporal phase zone plates, which are the time-domain analog of spatial phase zone plates, are illustrated in Fig.1.

To demonstrate the introduced temporal zone plate concept, we set up a linear optical pulse compression experiment, in which 1st-order, 2nd-order, and 3rd-order temporal phase zone plates are used. The electronic waveforms, which are used to drive the electro-optic phase modulator, are shown in Fig. 2. The temporal apertures for order 1, 2, and 3, which equal to the temporal duration of the electronic waveforms, are 1.88 ns, 3.85 ns, and 5.77 ns, respectively. The corresponding compressed pulse waveforms are shown in Fig. 3. There is a good agreement between numerical simulation (in which the experimental limitation is considered so that it is slightly deviated from the ideal profile) and experiment. For the cases of order n=1, 2, 3, the FWHM of the compressed temporal pulses in the experiments are 38.6 ps, 23.9 ps, and 25.5 ps, respectively. Thus the time-bandwidth products (ratio of temporal aperture to resolution) for these three experiments are 50, 161, and 226, respectively, significantly surpassing the capabilities of conventional time lenses. For further advancements in optimized temporal zone plate designs, see [2] and [3] below.

Fig. 1. Space-time duality. (a) Light focusing by a spatial phase zone plate. (b) Pulse generation and compression from CW light by a temporal phase zone plate. Fig. 2. Ideal and experimentally measured electronic waveforms for temporal phase modulation in the implemented temporal phase zone plates for orders (a) n=1, (b) n=2, and (c) n=3. Fig. 3 Temporally compressed intensity waveforms in the ideal case, simulation, and experiment using temporal phase zone plates of orders (a) n=1, (b) n=2, and (c) n=3. (d)-(f) show a closer view of the compressed optical pulses in (a)-(c). All waveforms are represented in normalized units.

[1] B. Li, M. Li, S. Lou, and J. Azana, “Linear optical pulse compression based on temporal zone plates,” Optics Express, vol. 21, pp. 16814-16830 (2013).

[2] B. Li, M. R. Fernández-Ruiz, S. Lou, J. Azaña, “High-contrast linear optical pulse compression using a temporal hologram,” Opt. Express, vol. 23, pp. 6833-6845 (2015).

C. R. Fernández-Pousa*, R. Maram*, J. Azaña. (2017). CW-to-pulse conversion using temporal Talbot array illuminators. Optics Letters. 42(13): 2427-2430

In this paper, we have provided a comprehensive study of a powerful signal analysis tool, a RTOM scheme, for real-time monitoring of the evolving optical spectrum of WDM data signals in fiber-optics telecommunication links. Our research demonstrates the RTOM system’s versatility to achieve the desired performance for diverse operational conditions, including different modulation formats (amplitude and coherent data signals), modulation strategies (MZM and DML), transmission rates (ranging from 1 Gb/s to 420 Gb/s), and channel spacings (50 GHz to 100 GHz). Through detailed numerical simulations, we have examined the influence of multiple parameters on the spectral monitoring system performance, enabling the optimization of the different design variables. Through numerical and experimental work, we have demonstrated that a realistic RTOM design offers the necessary frequency resolution (~30 GHz) to discern WDM channels separated by a few tens of GHz with a sensitivity level down to ~1 dB. Our investigation extended to analyzing the impact of the different design specifications on the measurement dynamic range offered by the proposed method. A key finding is that the achievable dynamic range is mainly constrained by the noise performance of the photodetection device. Additionally, the RTOM system shows effective operation under relaxed Fraunhofer conditions and in realistic telecommunications environments, such as data signals affected by GVD. Our findings also indicate an enhanced performance of the RTOM system at higher bit rates, confirming its potential interest for wide-ranging applications in advanced optical communication systems.

The RTOM system offers a straightforward method to obtain information regarding the on/off state and relative intensity of WDM channels directly in the time domain, with unprecedented measurement update rates in the MHz range. The distinctive features and advantages of the RTOM system, combined with its straightforward implementation using commonly accessible linear-optics elements, make it a compelling solution for real-time spectral monitoring of telecommunication signals. While the proposed scheme is implemented using fiber-optics technology, this approach has potential to be realized in an integrated-waveguide platform, towards practical deployment in real-world optical telecommunication systems. A main challenge lies in integrating the highly dispersive lines that meet the required specifications. Possible solutions for compact on-chip dispersive lines are under investigation [53]. Another challenge the RTOM system faces is managing the polarization diversity of the input signals, which originate from various sources and can affect measurement accuracy. Introducing a secondary path for alternate polarization offers a potential solution to this issue. Furthermore, the inherent noise of the detection system substantially impacts the dynamic range of the output waveform, potentially reducing the system’s sensitivity. In addition to these challenges, to achieve a finer frequency resolution, comparable to the 0.1 nm precision of an OSA, it is necessary to employ higher dispersion. However, this approach introduces a trade-off, as increased dispersion results in a decreased measurement update rate. Therefore, balancing precision and speed, particularly in applications where both parameters are crucial, will require careful consideration and optimization. Looking ahead, the RTOM technique holds significant promise for enabling effective spectrum monitoring and management in next-generation, high-capacity, and dynamic optical networks, for more efficient, reliable, and agile communication infrastructures. Moreover, the demonstrated system should prove of interest for many other scientific and engineering applications, including next-generation optical sensor monitoring, autonomous vehicles, and medical imaging.

Fig. 1: Experimental setup. The insets show the signal generation, transmission module to disperse the SUT, and RTOM system.

Fig. 2: Influence of various system parameters, including (a) detection noise, (b) MZM-ER, (c) PD-BW, and (d) dispersion on the dynamic range of the retrieved spectrum.

Fig. 3: Numerical simulation demonstrating the RTOM system’s performance in analyzing a dynamically changing input SUT, with variations occurring every five analysis periods, each lasting TR = 200 ns (specifications summarized in Table I). The SUT is the WDM stream of NRZ-OOK data signals operating at a bit rate of 25 Gb/s, spanning the entire C-band with 88 channels and a channel spacing of ~50 GHz. (a) System overall output for the varying SUT, (b) a zoom-in view of the system averaged output every five consecutive samples compared to the averaged reference waveform, and (c) the reference waveform corresponding to an emulated OSA measurement with a 12.5 GHz resolution bandwidth.

[1] A. Shoeib, M. P. Fernández, C. Rowe, R. Maram, P. Ricciardi and J. Azaña, “Real-Time Spectrum Monitoring System for Next-Generation High-Capacity Optical Networks,” Journal of Lightwave Technology, vol. 43, no. 14, pp. 6469-6483, (2025).

[2] A. Shoeib, M. P. Fernández, C. Rowe, R. Maram, P. Ricciardi and J. Azaña, “Fiber-optic spectrum monitoring of wavelength-division-multiplexed telecommunication signals with MHz update rates,” Opt. Lett., vol. 49, no. 5, pp. 1245-1248 (2024).

The last decade has seen the emergence of numerous methods to conceal objects by preventing light from interacting with them. This is known as invisibility cloaking, and solutions have been demonstrated over different regions of the electromagnetic spectrum, and even for waves of very different nature, including acoustic and thermal waves. While effective invisibility solutions have been demonstrated for single- frequency illumination waves, realistic operation conditions require cloaks capable of concealing objects from broadband illumination.
An ideal cloak must restore the exact amplitude and phase distributions of the illumination wave–the full field–at its output. However, current invisibility strategies rely on altering the propagation path of the wave around the object to be concealed. By fundamental operation principle, this approach introduces undesired phase variations among the different frequency components of a broadband illumination wave, thus necessarily distorting the wave’s temporal profile. This way, phase-sensitive or temporal detection renders current invisibility cloaking solutions vulnerable to phase-coherent broadband illumination.
We demonstrated that it is possible to conceal the presence of an object to an observer under broadband illumination by altering the spectrum of the probe wave through reversible transformations of its temporal and spectral phase profiles. This novel approach has been referred to as spectral invisibility cloaking. In particular, the energy spectrum of the illumination wave is first redistributed towards frequency regions where the object to be concealed is transparent, and the wave is subsequently restored to its exact original shape once it has cleared the object. This way, the illumination wave can propagate through the object, entirely unaltered, while avoiding any interaction between object and wave. Our particular demonstration of this general concept made use of a set of phase transformations derived from the theory of the Talbot effect. First, the spectrum of a coherent broadband wave was redistributed into a periodic set of frequency gaps (regions of the wave’s spectrum stripped of energy) through a combination of group velocity dispersion and electro-optical phase modulation. The frequencies of such gaps were chosen to match the interaction spectrum of the object to be concealed, namely, an optical filter consisting of a periodic set of phase-shifted wide absorption bands, in the reported experiments. The spectrally-redistributed wave propagated then through the filter without interacting with it, and the applied transformations were reversed at the output of the filter, recovering both the spectral and temporal profiles of the original wave. When the cloak transformations were not applied, the action of the filter (its signature) was clearly observed in both the frequency and time domains.
We believe that the spectral invisibility concept, by virtue of preserving the full-field profile of the illumination wave, paves the way towards development of practical broadband invisibility cloaks.

Figure: Spectral invisibility cloaking. (a) Process of concealing the signature of an object from detection by a broadband illumination wave through reversible redistribution of the wave’s frequency spectrum. (b) and (c) show experimental results (frequency spectra and temporal autocorrelation traces, respectively) of a proof-of-concept demonstration of spectral invisibility cloaking of an object (optical filter) illuminated by a short pulse of light: (1) Broadband illumination wave, (2) object’s signature when the cloak is inactive, and (3) output of the cloak, showing concealment of the object’s presence. The idea is explained with this concept video, further described by this short experiment video.

This work has attracted much attention worldwide, from news platforms such as Global news (Canada), both online and on the radio (July 5 2018, time mark 01h:02min), Lapresse (Québec), The Times (UK), El País (Spain), Radio Televisión Española (Spain), ANSA (Italy), Optics and Photonics news (USA), to name a few.

Temporal imaging and related concepts provide new, unique opportunities for generation, measurement and processing of time-domain waveforms across a wide range of frequency regimes, from electronic and radio-frequency (RF) signals to ultrafast optical information. Temporal imaging systems developed to date are based on suitable combinations of dispersive processes and time lenses, and they generally rely on coherent optics. For high performance (high time resolution over a long temporal aperture), these systems require the use of short-pulse light sources (e.g. mode-locked lasers) and precise coherent phase control of the involved waveforms. These requirements represent a fundamental hurdle to the practical use of these methods. Temporally incoherent light sources are inherently broadband and they are significantly simpler and more affordable than their coherent counterparts. We have recently proposed and experimentally demonstrated the first scheme for temporal imaging, including time-to-frequency mapping and temporal magnification or compression, of incoherent-light intensity waveforms. The scheme is based on a time-domain equivalent of a classical pinhole camera illuminated by incoherent light, and it employs only temporal intensity modulation (time-domain pinhole) combined with two dispersive lines. We have reported demonstration of incoherent-light temporal imaging of RF waveforms with a resolution of ~50 ps over a temporal aperture exceeding 8 ns, using a ~146-ps temporal pinhole. Our proposal opens up entirely new possibilities for realization of a wide variety of critical high-speed signal processing modules using simple and practical incoherent light-wave schemes.

Fig. 1 Incoherent-light temporal imaging concept (a, b) and experimental results (c, d). (a) Illustration of an incoherent-light spatial imaging system (pinhole camera) based on free-space diffraction and a pinhole. (b) Proposed scheme for incoherent-light temporal imaging, which is constructed as the temporal equivalent of the incoherent-light pinhole camera, involving temporal group-velocity dispersion and intensity modulation with a fast temporal shutter (temporal pinhole). (c) Temporal intensity profile (solid black) of the output image compared with the scaled input temporal waveform (dashed blue), where the scaling between input time and output time is the predicted magnification factor M = (±1981 ps/nm) / (±692 ps/nm)=2.86. (f) Spectrum (solid red) of the output image compared with the input temporal waveform (dashed blue), where the scaling between input time and normalized output wavelength (with respect to the signal’s central optical wavelength) is the predicted time-to-frequency mapping factor, 692 ps/nm. All profiles in (b)-(d) are averaged for 256 times.

[1] B. Li and J. Azaña, Opt. Lett. 39, 4243 (2014).

[2] B. Li, J. Azaña, “Theory of incoherent-light temporal imaging systems based on a temporal pinhole,” IEEE/OSA J. Lightwave Technol., vol. 34, pp. 2758 – 2773 (2016).

We proposed a very general concept for user-defined, arbitrary linear processing of incoming high-speed RF (microwave, millimeter-wave) signals through temporal modulation of the signal under analysis by a spectrally-shaped broadband incoherent lightwave followed by optical chromatic dispersion [1].
Such a concept is referred to as “time-spectrum convolution” and it has enabled implementation of many important functionalities on high-speed RF signals. As an example, a wide range of time-domain signal processing operations are based on the use of large amounts of group-velocity dispersion (GVD) over time-limited waveforms. Dispersion-engineering has been extensively used in the optical domain for applications such as real-time Fourier transformation (RTFT), real-time reflectometry and interferometry, pulse repetition rate multiplication, temporal imaging etc. Similar concepts have also proved extremely useful in other frequency regions, including the microwave domain. However, in the microwave domain, there is a lack of devices capable of inducing a large amount of GVD, namely above  a few ns², over a wide frequency range (0 ~ 100 GHz). Plot (A) shows an schematic of a fiber-optics incoherent-light configuration based on the time-spectrum convolution concept aimed at inducing extraordinary GVD amounts on electrical (RF) waveforms (double-pulse in the illustration) [2].
This system is capable of fulfilling the above defined stringent GVD-bandwidth requirements. In the illustrated example, a GVD equivalent to that of 185,000 km of standard single-mode fiber (SMF) is induced on the input microwave signal by propagation through a section of only 120 km of SMF. (B) Results corresponding to an example of real-time Fourier transformation (linear frequency-to-time mapping) of a nanosecond-long input microwave signal with a full bandwidth approaching 20 GHz (input signal shown in the top plot). The bottom plot shows the measured output temporal waveform (blue curve, bottom axis) as compared with the signal input spectrum (green curve, top axis). Temporal differentiation and integration of high-speed microwave signals have been also demonstrated by our group based on the same time-spectrum convolution concept (see for instance Ref. [3] below)

[1] Y. Park, J. Azaña, “Optical signal processors based on time-spectrum convolution process,” Opt. Lett., vol. 35, pp. 796-798 (2010).

[2] Y. Park, J. Azaña, “Ultrahigh dispersion of broadband microwave signals by incoherent photonic processing,” Opt. Express, vol. 18, pp. 14752-14761 (2010).

[3] A. Malacarne, R. Ashrafi, M. Li, S. LaRochelle, J. Yao, J. Azaña, “Single-shot photonic time-intensity integration based on a time-spectrum convolution system,” Opt. Lett., vol. 37, pp. 1355-1357 (2012).

Our group conducts active research in quantum optics, particularly on phase-only transformations for the generation and processing of quantum states [1]. Temporal phase modulation and spectral phase filtering are especially important for quantum processing because they provide a versatile framework that is inherently low-loss, a critical requirement in quantum information where signals cannot be amplified. These manipulations can be interpreted as approximations to unitary transformations on a quantum state (up to device insertion loss), enabling wavefunction shaping, quantum-state generation and processing, as well as quantum-state characterization and detection.

Building on this work, we showed the generation of high-dimensional frequency-domain quantum states using telecommunications and integrated-photonics components [2], depicted in (a). In (a1), we show the experimental setup for high-dimensional state generation and control. A passively mode-locked laser was spectrally filtered to excite a single resonance of an integrated microring resonator. Spontaneous four-wave mixing (SFWM) (left inset) generated photon pairs (signal and idler) symmetrically about the pump and in a quantum superposition of frequency modes defined by the resonances. Programmable filters and a modulator were used to manipulate the state (right inset: frequency sideband generation versus frequency ?), before detection by two single-photon counters. (a2) Quantum-interference characterization of qudits with D=4, by projecting the states onto superpositions of 4 frequency modes with different phases. By varying these phases, we observed corresponding changes in coincidence counts (the flat black curve is the recorded background). A Raw visibility of 86.4% (without background subtraction) was obtained, exceeding the threshold of 81.7% required to violate a Bell inequality for this 4-dimensional state. (a3) Exploiting arbitrary, independent projection measurements on signal and idler, we performed full quantum-state tomography to reconstruct the density matrix of the entangled qudit states, achieving a fidelity of 76.6% for D=4, in very good agreement with the expected maximally entangled states.

To better understand the effect of dispersion on entangled photon pairs, we developed a generalized framework for nonlocal dispersion cancellation leveraging the correlations observed in the sum of arrival times, rather than the usual analysis method based on the difference of arrival times, which we demonstrate as a means for dispersion-resilient quantum communications [3]. In (b), we show experimental results for quantum interference of dispersed entangled photon pairs. (b1) Biphoton time-of-arrival maps of destructive quantum interference without added dispersion. Histograms of the sum t_s + t_i (green) and difference t_s – t_i (orange) correlations are shown, with their respective biphoton post-selection regions outlined by green and orange dashed lines. Intersections of these regions with the blue dashed box correspond to applying both single- and biphoton post-selection. (b2) Quantum-interference patterns obtained by retrieving the post-selected sum (green circles) and difference (orange crosses) correlations within the blue dashed box, with corresponding fits (dashed curves). (b3) Biphoton time-of-arrival maps of destructive interference after propagation through a total of 200 km of SMF-equivalent dispersion, with sum and difference histograms. (b4) Resulting interference patterns for the post-selected region in both cases. Notice that a violation of Bell’s inequality, with a visibility above 71%, is achieved using the sum correlation approach but not with the conventional difference correlation approach.

We also implemented temporal imaging on entangled photon pairs to mitigate quantum-system noise [4]. Through coherent energy redistribution, the correlated joint distribution is reshaped into peaks, enabling discrimination from a noise background that remains diffuse. In (c), we show experimental results on this redistribution. (c1) Histogram of single counts for the input signal photon (the idler is similar). (c2) Associated biphoton temporal distribution with the post-selection window outlined in yellow. (c3–c4) Same as (c1–c2) at the output of the denoising module, showing the expected focused peaks. This yields significant improvements in key quantum metrics, including the coincidence-to-accidental ratio, quantum-interference visibility, and fidelity.

[1] C. Rowe et al., “Linear optical wave energy redistribution methods for photonic signal processing,” npj Nanophoton., vol. 2, no. 1, Apr. 2025, doi: 10.1038/s44310-025-00060-x.

[2] M. Kues et al., “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature, vol. 546, no. 7660, pp. 622–626, June 2017, doi: 10.1038/nature22986.

[3] H. Yu et al., “Exploiting Nonlocal Correlations for Dispersion-Resilient Quantum Communications,” Phys. Rev. Lett., vol. 134, no. 22, p. 220801, June 2025, doi: 10.1103/PhysRevLett.134.220801.

[4] B. Crockett et al., “Enhancing the Quantum Correlation of Biphotons via Coherent Energy Redistribution,” in Optical Fiber Communication Conference (OFC), San Diego (CA), USA, 2023, p. Th3J.6.

Traditional amplifiers employ an external power source to multiply the incoming signal carrier through an active gain process. In addition to amplifying the signal, this process introduces various forms of noise and distortion, such as amplified spontaneous emission noise (ASE), pulse-to-pulse intensity fluctuations, and timing-jitter. In this work, we developed a noiseless passive amplification technique for repetitive waveforms without using active gain [1, 2]. Our technique employs lossless repetition-rate division of the input periodic waveform train through a dispersion-induced self-imaging (Talbot) effect, inherently leading to energy amplification of the input individual waveforms. When inputting a noisy train, this technique can reduce pulse-to-pulse intensity fluctuations and timing-jitter, enhance the pulse extinction ratio, and reduce ASE fluctuations by a desired factor to improve signal quality. In particular, Talbot amplification can reduce ASE noise similar to a real-time averaging process.

Fig. 1(a) illustrates the concept of our passive amplification technique. Application of a prescribed temporal phase-modulation profile [1] to the input periodic pulse train produces new frequency components, and the subsequent dispersion-induced temporal self-imaging effect temporally re-distributes the new spectrum to coherently add the energy of the original repetitive waveforms into fewer identical but amplified waveforms. Fig. 1 (b) shows an experimental sampling oscilloscope time trace for passive amplification of picosecond pulses by a factor m=15.

Figs. 1(c)-(e) show how Talbot amplification behaves as a conventional averaging process, e.g., scope averaging, on ASE-like intensity noise fluctuations. Fig 1(c) shows experimental data for the coefficient of variance (CV), the ratio of the standard deviation to the mean for the top level, of a noisy pulse (OSNR=10) vs. the inverse of the square root of the amplification factor m=N (red squares). Also shown is the CV vs. the inverse of the square root of number of scope averages N (blue circles), demonstrating the equivalence of Talbot amplification to averaging. The theoretical trend line for scope averaging, which scales as ?N, is overlaid (dashed green). Experimental sampling oscilloscope traces in Fig. 1(d) and 1(e) show how the point-to-point fluctuation is nearly the same for scope averaging and Talbot amplification. Fig 1(d) shows results for a pulse without passive amplification and a regular scope average of N=15, and Fig. 1(e) shows results for a Talbot-amplified pulse by m=15 with no scope averaging. Passive amplification is therefore equivalent to a real-time optical average. Said another way, Fig 1(e) is the equivalent of Fig 1(d) without the need for detection and post-processing. Such a real-time average could be particularly important where a clean pulse is needed directly in the optical domain. Repetitive waveforms buried under a noise floor have been successfully extracted from the noise using the Talbot passive amplification method [1, 2]. Through a suitable exchange of the temporal phase modulation and dispersive phase filtering stages, the method has been successfully applied to passive noiseless amplification of repetitive waveforms along the frequency domain, i.e., optical frequency combs [3, 4] .

Fig. 1 (a) Passive waveform amplification concept, assuming m = 3. (b) Sampling oscilloscope time traces (input: dashed blue; output: solid red) for amplification factor m=15. (c) Ratio of pulse variance to mean vs. 1/?N, where N = m. (d) and (e) Electrical sampling oscilloscope traces (d) without passive amplification, scope average N=15, (e) m=15 and no scope averaging, for OSNR=10.

[1] R. Maram, J. van Howe, M. Li, and J. Azaña, “Noiseless intensity amplification of repetitive signals by coherent addition using the temporal Talbot effect,” Nat. Commun. 5:5163 doi: 10.1038/ncomms6163 (2014).

[2] R. Maram*, M. Seghilani*, J. Jeon*, X.-Z. Li*, L. Romero Cortés*, J. van Howe, J. Azaña. (2018). Demonstration of input-to-output gain and temporal noise mitigation in a Talbot amplifier. IEEE Photonics Technology Letters. 30(8): 665-668.

[3] L. Romero Cortés, R. Maram, H. Guillet de Chatellus, J. Azaña. (2018). Subnoise detection and passive amplification of frequency combs through customized coherent spectral energy redistribution. Physical Review Applied. 9: 064017-(1-7)

[4] L. Romero Cortés, R. Maram, H. Guillet de Chatellus, J. Azaña. (2019). Arbitrary energy-preserving control of optical pulse trains and frequency combs through generalized Talbot effects. Laser and Photonics Review. 13: article #1900176.

We present a passive amplification method based on the Talbot effect that allows for single-shot recovery of arbitrary signals buried under noise. The scheme can be reconfigured to operate on either narrowband or broadband signals, representing a comprehensive approach to weak, noise-dominated signal recovery.

[1] B. Crockett, L. Romero Cortés, S. R. Konatham, and J. Azaña. (2021). Full recovery of ultrafast waveforms lost under noise. Nature Communications. 12, 2402.

User-defined manipulation of the temporal evolution of an electromagnetic (EM) wave’s frequency components, the so-called time-frequency (TF) distribution, in a versatile and real-time fashion remains very challenging in many modern and emerging applications, including next-generation telecommunication systems and intelligent remote sensing platforms (Radar and Lidar). The key feature is that these dedicated filtering operations in the applications need to be reconfigured at a very high speed, in a nanosecond scale or even faster, while offering a set of specifications commensurate with the target performance, including operation over broad frequency bandwidths, e.g., over tens of GHz, and low latency (ns-scale).

We have recently proposed a concept for user-defined real-time manipulation of the joint TF distribution of EM waves directly in the analogue domain, ideally suited for operation on high-speed waves. The proposed approach combines the versatility of the DSP approach with the performance (e.g., processing speed and bandwidth) of a photonic solution. As illustrated in Fig. 1(d), our strategy involves mapping the TF distribution (the STFT) of the incoming wave along the time domain, which in turns enables a user-defined manipulation of the wave’s TF distribution through temporal modulation techniques. Since the time-mapped STFT is achieved using two consecutive phase transformations (along the temporal and spectral domains, respectively), the processed wave can be recovered by simply applying the opposite phase manipulations.

We experimentally demonstrated the use of this concept for realization of important functionalities beyond the potential of present technologies, an arbitrary manipulation of the joint TF distribution of the input microwave signal over a full bandwidth up to 92 GHz, with rapid tuning speeds, in the nanosecond range, and with a fine frequency resolution, down to a few hundreds of MHz, and the direct synthesis of high-speed waves with user-defined sophisticated TF distributions.

Fig. (a) Schematic diagram of the proposed joint time-frequency filtering concept. (b) Demonstration of broadband joint time-frequency (TF) filtering with nanosecond resolution.

[1] X. Zhu , B. Crockett, C. ML Rowe, H. Sun, and J. Azaña, “Agile manipulation of the time-frequency distribution of high-speed electromagnetic waves.” Nature Communications, vol. 15, no. 1, pp. 8942, (2024).

Dynamic identification of instantaneous microwave or mm-wave frequencies is a critical functionality in widespread applications such as broadband communications, biomedical instrumentation, electronic countermeasures, radar and more. Photonics solutions have demonstrated the potential to overcome the lack of flexibility and severe bandwidth limitations of current electronic instantaneous frequency measurement (IFM) systems. However, they suffer from at least one of the following critical problems: they are either implemented using costly, bulky discrete components, and/or they are based on nonlinear-optics processes, requiring high optical powers for operation. These limitations represent a fundamental hurdle towards the use of photonic-based IFM systems in practical, real-world applications.

In a recent demonstration, we used a simple integrated optical waveguide Bragg grating (WBG) filter on silicon, approximately 65 µm long (Fig. 1, left), to implement an ultra-compact, fully linear IFM system. The operating principle uses the WBG transmission (TX) and reflection (RX) responses that, over a certain frequency region, display opposite slope versus frequency (Fig. 1, right). Those opposite slopes are used to create an RF-frequency discriminator as shown in Fig. 2. The RF signal whose frequency is to be identified modulates an optical carrier; the single-sideband modulated signal enters the WBG; the transmission (TX) and reflection (RX) outputs of the WBG enter two equal photodetectors (PDs); the PDs output power ratio defines the amplitude comparison function (ACF), which shows an increasing value versus frequency and can be used as a frequency discriminator.

The device in Fig. 1 provides 3 orders of magnitude more compactness (tens of microns vs. millimeters or even centimeters) and the system requires 10 times less optical power (down to ~10 mW) than previously reported on-chip photonic-based IFM systems, and is capable of operation over a bandwidth beyond 30 GHz. The measurement accuracy offered by this platform reaches 0.026%, comparable to systems employing km-long optical fibers, but with the potential of 5 orders of magnitude less latency (tens of picoseconds).

We also demonstrated that the system can successfully identify a frequency-varying microwave signal in a dynamic fashion, i.e. identifying not only the frequency components of an incoming unknown microwave signal but also their instantaneous location in time, without any need for a fast oscilloscope or a high-frequency spectrum analyzer. In particular, we showed how the reported photonic IFM platform enables dynamic identification of instantaneous frequencies well above 10 GHz using simple, widely accessible electronic circuits with detection/measurement bandwidths in the sub-GHz range and below (Fig. 3).

Figure 1 | Silicon WBG and optical responses. Left: (a) Schematic of the silicon WBG (PS-WBG) employed as a linear-optics frequency discriminator. TX port, transmission port; RX port, reflection port. (b) Scanning electron microscope (SEM) image of the strip waveguide with sidewall corrugations (scale bar, 500 nm). (c) Y-branch used to access the reflection port of the PS-WBG. Right: simulated (dashed line) and measured (solid line; a) linear optical transmission and (b) reflection spectral responses of the PS-WBG; (c,d) zoom with overlapped OSSB+C spectrum. The optical responses are normalized to the maximum.

Figure 2 | IFM system set-up and RF responses. Left: schematic of the experimental set-up of the IFM system, including continuous-wave laser (CW), polarization maintaining fibre (PM), polarization controller (PC), dual-parallel Mach-Zehnder modulator (DP-MZM), erbium-oped fibre amplifier (EDFA), phase-shifted waveguide Bragg grating (PS-WBG) and photodetector (PD). RX, reflection port; TX, transmission port. Right: RF response of TX and RX ports; Amplitude comparison function (ACF).

Figure 3 | Experiment of dynamic frequency identification. (a) An RF signal with unknown frequency content enters the photonic IFM system in Fig. 3. (b) The time-domain signal at the IFM output is amplitude-coded according to the time-varying frequency content of the input signal. (c) The instantaneous power is extracted by self-mixing and low-pass filtering. (d) Using the inverse ACF, the RF frequency content is estimated in a dynamic manner. (e) The spectrogram of the frequency-hopping input sequence is shown for comparison. (f–j) Input sequence with frequency components at 2.4–6–12–4.8 GHz: (f) input waveform; (g) waveform processed by the IFM system, (h) average power extracted by mixing and low pass filtering, (i) estimated instantaneous frequency, (j) calculated spectrogram of the input sequence, shown for comparison to the estimated frequency in (i).

[1] Burla, M., Wang, X., Li, M., Chrostowski, L. & Azaña, J. Wideband dynamic microwave frequency identification system using a low-power ultracompact silicon photonic chip. Nat. Commun. 7, 13004 doi: 10.1038/ncomms13004 (2016).

[2] L. Romero Cortés*, D. Onori*, H. Guillet de Chatellus, M. Burla, J. Azaña. (2020). Towards on-chip photonic-assisted radio-frequency spectrum measurement and monitoring (INVITED). Optica. 7(5): 434-447.