arXiv subjects

Kevin Zelaya

Publications and source records attributed to Kevin Zelaya.

At least 19 recordsLinked to original sources

arXiv2026

Black-Box Coherence Matrix Eigen-Spectroscopy with Programmable Photonics

The precise characterization of spatial optical coherence is fundamental to emerging applications in optical communications and computational imaging. However, extracting the full coherence matrix traditionally requires phase-sensitive interferometry, which is highly vulnerable to environmental noise and poses severe scalability challenges for integrated photonics. Here, we introduce an architecture-agnostic framework for analyzing and controlling partially coherent light on programmable photonic circuits. By leveraging the Schur-Horn theorem, our approach systematically diagonalizes the incident coherence matrix, relying solely on output intensity measurements and entirely circumventing the need for complex phase retrieval. We experimentally validate this black-box protocol on a low-depth, non-universal photonic integrated circuit, successfully reconstructing the hidden eigenvalues of mixed states generated from up to four mutually incoherent sources. Furthermore, we demonstrate active, in-situ statistical light control by introducing non-unitary amplitude modulation to significantly enhance interference visibility, exposing a fundamental physical trade-off between coherence enhancement and optical loss. Inherently resilient to hardware constraints and experimental noise, this scalable paradigm establishes a robust pathway for realizing ultra-compact, on-chip spatial coherence analyzers.

physics.optics↗

arXiv2026

Architecture-agnostic analysis of partially coherent light with programmable photonics

The precise characterization of the spatial degree of coherence of a radiation field is important for assessing its suitability for specific applications in optical communications, advanced imaging, and quantum information processing. However, measuring the full coherence matrix traditionally requires complex, phase-sensitive interferometric setups that are highly susceptible to noise and difficult to scale on integrated platforms. To address this, we propose an architecture-agnostic approach for analyzing partially coherent light that is compatible with any universal programmable photonic unitary circuit, regardless of its internal topology. Leveraging the Schur-Horn theorem, our method diagonalizes the output coherence matrix, enabling direct extraction of its eigenvalues from output power measurements alone. We numerically validate this framework across various universal topologies and demonstrate its efficacy even in under-parameterized, non-universal architectures with only minor loss in precision. Finally, our black-box optimization approach proves inherently resilient to arbitrary optical losses and component deviations, paving the way for robust, lower-depth, and programmable spatial coherence analyzers.

physics.optics↗

arXiv2026

Non-Hermitian Synthetic Phase Shifter: Topologically-Protected Phase Control via Tunable Losses

Phase shifters are fundamental reconfigurable components in photonic circuits. In conjunction with passive elements, they control light flow and serve as foundational building blocks for diverse applications, including communication, sensing, analog signal processing, and quantum control. Conventional phase shifters achieve phase control by modulating the refractive index through various physical mechanisms such as thermo-optic or electro-optic effects. However, despite expectations that such index-based approaches would integrate seamlessly, they, in practice, restrict circuit size, bandwidth, and scalability and thus become bottlenecks to large-scale photonic integration. Here, we introduce an alternative phase-control approach based on optical loss modulation. We demonstrate a synthetic phase shifter that uses two independently controlled loss-modulation stages combined with multipath interference to achieve full-cycle phase tunability while maintaining constant amplitude. We develop a theoretical framework based on conserved topological charges to demonstrate how synthetic phase control can be achieved via non-Hermitian effects, enabling robust topologically-protected phase control. By shifting the paradigm from index control to loss modulation, the proposed synthetic phase shifter could pave the way for scalable integrated photonic systems that support applications from communications and sensing to photonic classical and quantum information processing.

physics.optics↗

arXiv2025

Programmable Photonic Circuits with Embedded Feedback for Parallel Multi-Wavelength Operations

Linear transformations are cornerstone operations utilized in modern computing, but are computationally expensive on current electronic platforms. Optical computing has been positioned as a new computing solution, promising high speed and energy efficiency by exploiting the available degrees of freedom of light. Although solutions exist in the optical domain, there is a continuous search for compact solutions that properly utilize the limited chip space and exploit various degrees of freedom of light. Here, we introduce and experimentally demonstrate a compact, programmable photonic integrated circuit (PIC) architecture that operates on both spatial and frequency degrees of freedom by leveraging embedded optical feedback loops. This architecture enables universal linear unitary transforms by combining resonators with passive linear mixing layers and tunable active phase layers. The strong dispersion achieved from the resonant loops enables multi-frequency operation and reduces the number of required active layers to achieve universality. This solution reduces the optical port requirements, minimizes power losses, and leverages resonances to enable massive parallel computing in the frequency domain. The fabricated samples are compatible with silicon-on-insulator platforms and operate at single- and dual-frequency modes. The experimental setup demonstrates the ability to perform in situ training in both cases, validating the parallel-computing capabilities of the PICs. This work highlights the potential of feedback-loop PICs for scalable, compact, and energy-efficient linear optical computing.

physics.optics↗

arXiv2025

Programmable Space-Frequency Linear Transformations in Photonic Interlacing Architectures

Programmable photonic circuits are versatile platforms that route light through multiple interference paths using reconfigurable optoelectronic elements to perform complex discrete linear operations. These circuits offer the potential for high-speed and low-power photonic information processing in various applications. The mainstream research on programmable photonics has focused on implementing linear operations on discrete signals encoded in the modal amplitudes of an array of spatially separated single-mode waveguides. However, many photonic device applications require simultaneous transformations in the space-frequency domain, where information is encoded in both the spatial modes of waveguides and their spectral content. Here, we experimentally demonstrate linear space-frequency transformations using a $4 \times 4$-port programmable silicon photonic circuit with an alternating architecture. This design leverages the limited dispersion of coupled waveguide arrays to enable linear operations with reconfigurable frequency-dependent matrix elements. We utilize this device to perform wavelength demultiplexing and filtering. This architecture platform can pave the way for versatile devices with applications ranging from wavelength routing to programmable dispersion control.

physics.optics↗

arXiv2025

Universality of Photonic Interlacing Architectures for Learning Discrete Linear Unitaries

Recent investigations suggest that the discrete linear unitary group $U(N)$ can be represented by interlacing a finite sequence of diagonal phase operations with an intervening unitary operator. However, despite rigorous numerical justifications, no formal proof has been provided. Here, we show that elements of $U(N)$ can be decomposed into a sequence of $N$-parameter phases alternating with $1$-parameter propagators of a lattice Hamiltonian. The proof is based on building a Lie group by alternating these two operators and showing its completeness to represent $U(N)$ for a finite number of layers, which is numerically found to be exactly $N$. This architecture can be implemented using elementary optical components and can successfully reconstruct arbitrary unitary matrices. We propose example devices such as optical logic gates, which perform logic gate operations using a single-layer lossless and passive optical circuit design.

quant-ph↗

arXiv2025

Embedding Matrices in Programmable Photonic Networks with Flexible Depth and Width

We show that programmable photonic circuit architectures composed of alternating mixing layers and active layers offer a high degree of flexibility. This alternating configuration enables the systematic tailoring of both the network's depth (number of layers) and width (size of each layer) without compromising computational capabilities. From a mathematical perspective, our approach can be viewed as embedding an arbitrary target matrix into a higher-dimensional matrix, which can then be represented with fewer layers and larger active elements. We derive a general relation for the width and depth of a network that guarantees representing all $N \times N$ complex matrix operations. Remarkably, we show that just two such active layers, interleaved with passive mixing layers, are sufficient to universally implement arbitrary matrix transformations. This result promises a more adaptable and scalable route to photonic matrix processors.

physics.optics↗

arXiv2025

Integrated Photonic Programmable Random Matrix Generator with Minimal Active Components

Random matrices are fundamental in photonic computing because of their ability to model and enhance complex light interactions and signal processing capabilities. In manipulating classical light, random operations are utilized for random projections and dimensionality reduction, which are important for analog signal processing, computing, and imaging. In quantum information processing, random unitary operations are essential to boson sampling algorithms for multiphoton states in linear photonic circuits. In photonic circuits, random operations are realized through disordered structures resulting in fixed unitary operations or through large meshes of interferometers and reconfigurable phase shifters, which require a large number of phase shifters. In this article, we introduce a compact photonic circuit for generating random matrices by utilizing programmable phase modulation layers interlaced with a fixed mixing operator. We show that using only two random phase layers is sufficient for producing output optical signals with a white-noise profile, even for highly sparse input optical signals. We experimentally demonstrate these results using a silicon photonics circuit with tunable thermal phase shifters and utilize waveguide lattices as mixing layers. The proposed circuit offers a practical method for generating random matrices for photonic information processing and for applications in data encryption.

physics.optics↗

arXiv2024

Photonic Matrix Multiplier Makes a Direction-Finding Sensor

We introduce a photonic integrated circuit solution for the direction-of-arrival estimation in the optical frequency band. The proposed circuit is built on discrete sampling of the phasefront of an incident optical beam and its analog processing in a photonic matrix-vector multiplier that maps the angle of arrival into the intensity profile at the output ports. We derive conditions for perfect direction-of-arrival sensing for a discrete set of incident angles and its continuous interpolation and discuss the angular resolution and field-of-view of the proposed device in terms of the number of input and output ports of the matrix multiplier. We show that while, in general, a non-unitary matrix operation is required for perfect direction finding, under certain conditions, it can be approximated with a unitary operation that simplifies the device complexity while coming at the cost of reducing the field of view. The proposed device will enable real-time direction-finding sensing through its ultra-compact design and minimal digital signal processing requirements.

physics.optics↗

arXiv2024

Flat-band engineering of quasi-one-dimensional systems via supersymmetric transformations

We introduce a systematic method to spectrally design quasi-one-dimensional crystal models described by the Dirac equation in the low-energy regime. The method is based on the supersymmetric transformation applied to an initially known pseudo-spin-1/2 model. This allows extending the corresponding susy partner so that the new model describes a pseudo-spin-1 system. The spectral design allows the introduction of a flat-band and discrete energies at will into the new model. The results are illustrated in two examples where the Su-Schriefer-Heeger chain is locally converted into a stub lattice.

cond-mat.mes-hall↗

arXiv2024

The Goldilocks Principle of Learning Unitaries by Interlacing Fixed Operators with Programmable Phase Shifters on a Photonic Chip

Programmable photonic integrated circuits represent an emerging technology that amalgamates photonics and electronics, paving the way for light-based information processing at high speeds and low power consumption. Programmable photonics provides a flexible platform that can be reconfigured to perform multiple tasks, thereby holding great promise for revolutionizing future optical networks and quantum computing systems. Over the past decade, there has been constant progress in developing several different architectures for realizing programmable photonic circuits that allow for realizing arbitrary discrete unitary operations with light. Here, we systematically investigate a general family of photonic circuits for realizing arbitrary unitaries based on a simple architecture that interlaces a fixed intervening layer with programmable phase shifter layers. We introduce a criterion for the intervening operator that guarantees the universality of this architecture for representing arbitrary $N \times N$ unitary operators with $N+1$ phase layers. We explore this criterion for different photonic components, including photonic waveguide lattices and meshes of directional couplers, which allows the identification of several families of photonic components that can serve as the intervening layers in the interlacing architecture. Our findings pave the way for efficiently designing and realizing novel families of programmable photonic integrated circuits for multipurpose analog information processing.

physics.optics↗

arXiv2024

Integrated Photonic Fractional Convolution Accelerator

An integrated photonic circuit architecture to perform a modified-convolution operation based on the Discrete Fractional Fourier Transform (DFrFT) is introduced. This is accomplished by utilizing two nonuniformly-coupled waveguide lattices with equally-spaced eigenmode spectra and with different lengths that perform DFrDT operations of complementary orders sandwiching a modulator array. Numerical simulations show that smoothing and edge detection tasks are indeed performed even for noisy input signals.

physics.optics↗

arXiv2023

Learning Arbitrary Complex Matrices by Interlacing Amplitude and Phase Masks with Fixed Unitary Operations

Programmable photonic integrated circuits represent an emerging technology that amalgamates photonics and electronics, paving the way for light-based information processing at high speeds and low power consumption. Considering their wide range of applications as one of the most fundamental mathematical operations there has been a particular interest in programmable photonic circuits that perform matrix-vector multiplication. In this regard, there has been great interest in developing novel circuit architectures for performing matrix operations that are compatible with the existing photonic integrated circuit technology which can thus be reliably implemented. Recently, it has been shown that discrete linear unitary operations can be parameterized through diagonal phase parameters interlaced with a fixed operator that enables efficient photonic realization of unitary operations by cascading phase shifter arrays interlaced with a multiport component. Here, we show that such a decomposition is only a special case of a much broader class of factorizations that allow for parametrizing arbitrary complex matrices in terms of diagonal matrices alternating with a fixed unitary matrix. Thus, we introduce a novel architecture for physically implementing discrete linear operations. The proposed architecture is built on representing an $N \times N$ matrix operator in terms of $N+1$ amplitude-and-phase modulation layers interlaced with a fixed unitary layer that could be implemented via a coupled waveguide array. The proposed architecture enables the development of novel families of programmable photonic circuits for on-chip analog information processing.

physics.optics↗

arXiv2023

Auto-calibrating Universal Programmable Photonic Circuits: Hardware Error-Correction and Defect Resilience

It is recently shown that discrete $N\times N$ linear unitary operators can be represented by interlacing $N+1$ phase shift layers with a fixed intervening operator such as Discrete Fractional Fourier Transform (DFrFT). Here, we show that introducing perturbations to the intervening operations does not compromise the universality of this architecture. Furthermore, we show that this architecture is resilient to defects in the phase shifters as long as no more than one faulty phase shifter is present in each layer. These properties enable post-fabrication auto-calibration of such universal photonic circuits, effectively compensating for fabrication errors and defects in phase components.

cs.ET↗

arXiv2023

Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions

This manuscript explores the Darboux transformation employed in the construction of exactly solvable models for pseudospin-one particles described by the Dirac-type equation. We focus on the settings where a flat band of zero energy is present in the spectrum of the initial system. Using the flat band state as one of the seed solutions substantially improves the applicability of the Darboux transformation, for it becomes necessary to ensure the Hermiticy of the new Hamiltonians. This is illustrated explicitly in four examples, where we show that the new Hamiltonians can describe quasi-particles in Lieb lattice with inhomogeneous hopping amplitudes.

quant-ph↗

arXiv2023

Lieb lattices and pseudospin-1 dynamics under barrier- and well-like electrostatic interactions

This work considers the confining and scattering phenomena of electrons in a Lieb lattice subjected to the influence of a rectangular electrostatic barrier. In this setup, hopping amplitudes between nearest neighbors in orthogonal directions are considered different, and the next-nearest neighbor interaction describes spin-orbit coupling. This makes it possible to confine electrons and generate bound states, the exact number of which is exactly determined for null parallel momentum to the barrier. In such a case, it is proved that one even and one odd bound state is always generated, and the number of bound states increases for non-null and increasing values of the parallel momentum. That is, bound states carry current. In the scattering regime, the exact values of energy are determined where the resonant tunneling occurs. The existence of perfect tunneling energy in the form of super-Klein tunneling is proved to exist regardless of the bang gap opening. Finally, it is shown that perfect reflection appears when solutions are coupled to the intermediate flat-band solution.

cond-mat.mes-hall↗

arXiv2022

Landau levels and snake states of pseudo-spin-1 Dirac-like electrons in gapped Lieb lattices

This work reports the three-band structure associated with a Lieb lattice with arbitrary nearest and next-nearest neighbors hopping interactions. For specific configurations, the system admits a flat band located between two dispersion bands. Three inequivalent Dirac valleys are identified so that the quasi-particles are effectively described by the spin-1 Dirac-type equation. Under external homogeneous magnetic fields, the Landau levels are exactly determined as the third-order polynomial equation for the energy can be solved using Cardano's formula. It is also shown that an external anti-symmetric field promotes the existence of current-carrying states, so-called snake states, confined at the interface where the external field changes its sign.

cond-mat.mes-hall↗

arXiv2022

On the general family of third-order shape-invariant Hamiltonians related to generalized Hermite polynomials

This work reports and classifies the most general construction of rational quantum potentials in terms of the generalized Hermite polynomials. This is achieved by exploiting the intrinsic relation between third-order shape-invariant Hamiltonians and the fourth Painlevé equation, such that the generalized Hermite polynomials emerge from the $-1/x$ and $-2x$ hierarchies of rational solutions. Such a relation unequivocally establishes the discrete spectrum structure, which, in general, is composed as the union of a finite- and infinite-dimensional sequence of equidistant eigenvalues separated by a gap. The two indices of the generalized Hermite polynomials determine the dimension of the finite sequence and the gap. Likewise, the complete set of eigensolutions can be decomposed into two disjoint subsets. In this form, the eigensolutions within each set are written as the product of a weight function defined on the real line times a polynomial. These polynomials fulfill a second-order differential equation and are alternatively determined from a three-term recurrence relation (second-order difference equation), the initial conditions of which are also fixed in terms of generalized Hermite polynomials.

math-ph↗