arXiv subjects

Peter Horak

Publications and source records attributed to Peter Horak.

At least 19 recordsLinked to original sources

arXiv2025

Advanced mirror shapes for mode enhancement in plano-concave cavities

Optical cavities are frequently used in quantum technologies to enhance light matter interactions, with applications including single photon generation and entanglement of distant emitters. The Fabry-P\'{e}rot resonator is a popular choice for its high optical access and large emitter-mirror separation. A typical configuration, particularly for emitters that should not be placed close to the mirror surface like trapped ions and Rydberg atoms, features two spherical mirrors placed around a central emitter, but this arrangement can put demanding requirements on the mirror alignment. In contrast, plano-concave cavities are tolerant to mirror misalignment and only require the manufacture of one curved mirror, but have limited ability to focus light in the centre of the cavity. Here we show how mirror shaping can overcome this limitation of plano-concave cavities while preserving the key advantages. We demonstrate through numerical simulations that simple mirror shaping can increase coupling between a plano-concave cavity and a central emitter by an order of magnitude, even rivalling misalignment-sensitive concave-concave counterparts for achievable interaction strength. We use these observations to establish the conditions under which plano-concave cavities with shaped mirrors could improve the performance and practicality of emitter-cavity systems.

physics.optics↗

arXiv2025

Retroreflective surface optimisation for optical cavities with custom mirror profiles

Coupling an emitter to a Fabry-P\'{e}rot optical cavity can provide a coherent and strong light-matter interface whose performance in a variety of applications depends critically on the emitter-photon coupling strength. Altering the typically spherical profiles of the cavity mirrors can improve this coupling strength, but directly optimising the mirror shape is numerically challenging as the multidimensional parameter space features many local optima. Here, we develop a two-step method to optimise mirror surface profiles while avoiding these issues. First, we optimise the target cavity eigenmode for the chosen application directly, and second, we construct the mirror surfaces to retroreflect this optimised target mode at both ends of the cavity. We apply our procedure to different emitter-cavity coupling scenarios. We show that mirror shaping can increase the cooperativity of coupling to a central emitter by a factor of approximately 3 across a wide range of geometries, and that, for coupling two or more emitters to a single cavity mode, the improvement factors can far exceed an order of magnitude.

physics.optics↗

arXiv2025

Profile control of fibre-based micro-mirrors using adaptive laser shooting with $\textit{in situ}$ imaging

Fibre Fabry-Perot cavities (FFPCs) are used in various studies in cavity quantum electrodynamics (CQED) and quantum technologies due to the cavity's small mode volume and compact integration with optical fibres. We develop a novel $\text{CO}_2$ laser machining method that produces well-controlled surface profiles on the end facets of cleaved optical fibres. Using multiple shots in distinct spatial distribution patterns, our method employs a shooting algorithm that adaptively changes laser ablation parameters during the shooting to suppress deviations from the desired profile. This is made possible by $\textit{in situ}$ imaging of the machined profile, its inspection and the usage of the information in the subsequent steps. Underlying this algorithm is a newly found laser ablation parameter, the pause between shots, which controls the accumulation of heat in between successive laser shots and as a result determines the area of impact made by an individual ablation sequence. We fabricate fibre-based micro-mirrors with radii of curvature ranging from 250 $\mu$m to 700 $\mu$m with an effective mirror diameter of 60 $\mu$m in either Gaussian or spherical profiles. Due to the self-correcting nature of our adaptive algorithm, we achieve a near 100\% success rate in the production of desired profiles with low ellipticity. After furnishing the laser machined fibre end facets with high reflectivity coating, FFPCs are formed to demonstrate a high finesse up to 150,000 at an optical wavelength of 854 nm.

physics.optics↗

arXiv2024

Optimising finite-time photon extraction from emitter-cavity systems

We develop methods to find the limits to finite-time single photon extraction from emitter-cavity systems. We first establish analytic upper and lower bounds on the maximum extraction probability from a canonical $\Lambda$-system before developing a numeric method to optimise generic output probabilities from $\Lambda$-systems generalised to multiple ground states. We use these methods to study the limits to finite-time photon extraction and the wavepackets that satisfy them, finding that using an optimised wavepacket ranging between a sinusoidal and exponentially decaying profile can considerably reduce photon duration for a given extraction efficiency. We further optimise the rates of quantum protocols requiring emitter-photon correlation to obtain driving-independent conclusions about the effect of system parameters on success probability. We believe that these results and methods will provide valuable tools and insights for the development of cavity-based single photon sources combining high efficiency and high rate.

quant-ph↗

arXiv2023

Efficient operator method for modelling mode mixing in misaligned optical cavities

The transverse field structure and diffraction loss of the resonant modes of Fabry-Pérot optical cavities are acutely sensitive to the alignment and shape of the mirror substrates. We develop extensions to the `mode mixing' method applicable to arbitrary mirror shapes, which both facilitate fast calculation of the modes of cavities with transversely misaligned mirrors and enable the determination and transformation of the geometric properties of these modes. We show how these methods extend previous capabilities by including the practically-motivated case of transverse mirror misalignment, unveiling rich and complex structure of the resonant modes.

physics.optics↗

arXiv2023

Mode mixing and losses in misaligned microcavities

We present a study on the optical losses of Fabry-P\'erot cavities subject to realistic transverse mirror misalignment. We consider mirrors of the two most prevalent surface forms: idealised spherical depressions, and Gaussian profiles generated by laser ablation. We first describe the mode mixing phenomena seen in the spherical mirror case and compare to the frequently-used clipping model, observing close agreement in the predicted diffraction loss, but with the addition of protective mode mixing at transverse degeneracies. We then discuss the Gaussian mirror case, detailing how the varying surface curvature across the mirror leads to complex variations in round trip loss and mode profile. In light of the severe mode distortion and strongly elevated loss predicted for many cavity lengths and transverse alignments when using Gaussian mirrors, we suggest that the consequences of mirror surface profile are carefully considered when designing cavity experiments.

physics.optics↗

arXiv2022

Convolutional Neural Networks for Mode On-Demand High Finesse Optical Resonator Design

We demonstrate the use of machine learning through convolutional neural networks to solve inverse design problems of optical resonator engineering. The neural network finds a harmonic modulation of a spherical mirror to generate a resonator mode with a given target topology ("mode on-demand"). The procedure allows us to optimize the shape of mirrors to achieve a significantly enhanced coupling strength and cooperativity between a resonator photon and a quantum emitter located at the center of the resonator. In a second example, a double-peak mode is designed which would enhance the interaction between two quantum emitters, e.g., for quantum information processing.

physics.optics↗

arXiv2021

Cavities with Non-Spherical Mirrors for Enhanced Quantum Emitter-Cavity Photon Interaction

We propose a procedure for the significant enhancement of the strong coupling rate between photons in an optical cavity and a single quantum emitter, such as an atom, quantum dot or trapped ion. We show that specially designed, non-spherical mirrors can lead to cavity eigenmodes that exhibit a large field enhancement at the center of the cavity while inducing significantly less beam divergence, and therefore smaller round trip losses and higher cooperativity, than can be achieved by operating a spherical-mirror cavity in the near-concentric regime. We verify our designs using mode matching theory and discuss their robustness relative to different kinds of manufacturing deviations.

physics.optics↗

arXiv2021

Grating-Induced Slow-Light Enhancement of Second Harmonic Generation in Periodically Poled Crystals

The effect of slow light on second harmonic generation in a periodically poled $χ^{(2)}$ nonlinear medium is investigated theoretically. A linear $π$ phase shifted grating is used to slow the group velocity of the fundamental frequency and the resulting field enhancement greatly increases the second harmonic conversion efficiency. A second linear grating at the input end ensures that all output is in the forward direction. We show that almost 100\% conversion efficiency can be achieved for continuous wave pumping at low intensities that generate negligible conversion in the absence of the slow-light grating.

physics.optics↗

arXiv2021

Slow and Stopped Light in Dynamic Moiré Gratings

We investigate a theoretical model for a dynamic Moiré grating which is capable of producing slow and stopped light with improved performance when compared with a static Moiré grating. A Moiré grating superimposes two grating periods which creates a narrow slow light resonance between two band gaps. A Moiré grating can be made dynamic by varying its coupling strength in time. By increasing the coupling strength the reduction in group velocity in the slow light resonance can be improved by many orders of magnitude while still maintaining the wide bandwidth of the initial, weak grating. We show that for a pulse propagating through the grating this is a consequence of altering the pulse spectrum and therefore the grating can also perform bandwidth modulation. Finally we present a possible realization of the system via an electro-optic grating by applying a quasi-static electric field to a poled $χ^{(2)}$ nonlinear medium.

physics.optics↗

arXiv2020

Connected cubic graphs with the maximum number of perfect matchings

It is proved that for $n \geq 6$, the number of perfect matchings in a simple connected cubic graph on $2n$ vertices is at most $4 f_{n-1}$, with $f_n$ being the $n$-th Fibonacci number. The unique extremal graph is characterized as well. In addition, it is shown that the number of perfect matchings in any cubic graph $G$ equals the expected value of a random variable defined on all $2$-colorings of edges of $G$. Finally, an improved lower bound on the maximum number of cycles in a cubic graph is provided.

math.CO↗

arXiv2018

50 Years of the Golomb--Welch Conjecture

Since 1968, when the Golomb--Welch conjecture was raised, it has become the main motive power behind the progress in the area of the perfect Lee codes. Although there is a vast literature on the topic and it is widely believed to be true, this conjecture is far from being solved. In this paper, we provide a survey of papers on the Golomb--Welch conjecture. Further, new results on Golomb--Welch conjecture dealing with perfect Lee codes of large radii are presented. Algebraic ways of tackling the conjecture in the future are discussed as well. Finally, a brief survey of research inspired by the conjecture is given.

cs.IT↗

arXiv2017

Intermodal Four-Wave-Mixing and Parametric Amplification in km-long Fibers

We theoretically and numerically investigate intermodal four-wave-mixing in km-long fibers, where random birefringence fluctuations are present along the fiber length. We identify several distinct regimes that depend on the relative magnitude between the length scale of the random fluctuations and the beat-lengths of the interacting quasi-degenerate modes. In addition, we analyze the impact of polarization mode-dispersion and we demonstrate that random variations of the core radius, which are typically encountered during the drawing stage of the fiber, can represent the major source of bandwidth impairment. These results set a boundary on the limits of validity of the classical Manakov model and may be useful for the design of multimode parametric amplifiers and wavelength converters, as well as for the analysis of nonlinear impairments in long-haul spatial division multiplexed transmission.

physics.optics↗

arXiv2017

Fiber cavities with integrated mode matching optics

In fiber based Fabry-Pérot Cavities (FFPCs), limited spatial mode matching between the cavity mode and input/output modes has been the main hindrance for many applications. We have demonstrated a versatile mode matching method for FFPCs. Our novel design employs an assembly of a graded-index and large core multimode fiber directly spliced to a single mode fiber. This all-fiber assembly transforms the propagating mode of the single mode fiber to match with the mode of a FFPC. As a result, we have measured a mode matching of 90\% for a cavity length of $\sim$400 $μm$. This is a significant improvement compared to conventional FFPCs coupled with just a single mode fiber, especially at long cavity lengths. Adjusting the parameters of the assembly, the fundamental cavity mode can be matched with the mode of almost any single mode fiber, making this approach highly versatile and integrable.

quant-ph↗

arXiv2016

Comparative numerical studies of ion traps with integrated optical cavities

We study a range of radio-frequency ion trap geometries and investigate the effect of integrating dielectric cavity mirrors on their trapping potential. We aim to identify ion trap and cavity configurations that are best suited for achieving small cavity volumes and thus large ion-photon coupling as required for scalable quantum information networks. In particular, we investigate the trapping potential distortions caused by the dielectric material of the cavity mirrors for different mirror orientations with respect to the trapping electrodes, as well as for mirror misalignment. We also analyze the effect of the mirror material properties such as dielectric constants and surface conductivity, and study the effect of surface charges on the mirrors. The smallest trapping potential distortions are found if the cavities are aligned along the major symmetry axis of the electrode geometries. These cavity configurations also appear to be the most stable with respect to any mirror misalignment.

quant-ph↗

arXiv2016

Algebraic Method in Tilings

In this paper we introduce a new algebraic method in tilings. Combining this method with Hilbert's Nullstellensatz we obtain a necessary condition for tiling $n$-space by translates of a cluster of cubes. Further, the polynomial method will enable us to show that if there exists a tiling of $n$-space by translates of a cluster $V$ of prime size then there is a lattice tiling by $V$ as well. Finally, we provide supporting evidence for a conjecture that each tiling by translates of a prime size cluster $V$ is lattice if $V$ generates $n$-space.

math.CO↗

arXiv2015

A Combinatorial Problem Related to Sparse Systems of Equations

Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, one converts it into a system of sparse equations, and then the system is solved to retrieve either a key or a plaintext. Raddum and Semaev proposed new methods for solving such sparse systems. It turns out that a combinatorial MaxMinMax problem provides bounds on the average computational complexity of sparse systems. In this paper we initiate a study of a linear algebra variation of this MaxMinMax problem.

math.CO↗

arXiv2015

Subwavelength line imaging using plasmonic waveguides

We investigate the subwavelength imaging capacity of a two-dimensional fanned-out plasmonic waveguide array, formed by air channels surrounded by gold metal layers for operation at near-infrared wavelengths, via finite element simulations. High resolution is achieved on one side of the device by tapering down the channel width while simultaneously maintaining propagation losses of a few dB. On the other, low-resolution side, output couplers are designed to optimize coupling to free space and to minimize channel cross talk via surface plasmons. Point sources separated by λ/15 can still be clearly distinguished. Moreover, up two 90% of the power of a point dipole is coupled to the device. Applications are high-resolution linear detector arrays and, by operating the device in reverse, high-resolution optical writing.

physics.optics↗