Laser beams and resonators

Non-Euclidean symmetries of first-order optical systems

We revisit the basic aspects of first-order optical systems from a geometrical viewpoint. In the paraxial regime, there is a wide family of beams for which the action of these systems can be represented as a Möbius transformation. We examine this action from the perspective of non-Euclidean hyperbolic geometry and resort to the isometric-circle method to decompose it as a reflection followed by an inversion in a circle. We elucidate the physical meaning of these geometrical operations for basic elements, such as free propagation and thin lenses, and link them with physical parameters of the system.

Laser-Plasma Spatiotemporal Cyanide Spectroscopy and Applications

This article reports new measurements of laser-induced plasma hypersonic expansion measurements of diatomic molecular cyanide (CN). Focused, high-peak-power 1064 nm Q-switched radiation of the order of 1 TW/cm 2 generated optical breakdown plasma in a cell containing a 1:1 molar gas mixture of N 2 and CO 2 at a fixed pressure of 1.1 × 10 5 Pascal and in a 100 mL/min flow of the mixture. Line-of-sight (LOS) analysis of recorded molecular spectra indicated the outgoing shockwave at expansion speeds well in excess of Mach 5. Spectra of atomic carbon confirmed increased electron density near the shockwave, and, equally, molecular CN spectra revealed higher excitation temperature near the shockwave. Results were consistent with corresponding high-speed shadowgraphs obtained by visualization with an effective shutter speed of 5 nanoseconds. In addition, LOS analysis and the application of integral inversion techniques allow inferences about the spatiotemporal plasma distribution.

Modal instability suppression in a high-average-power and high-finesse Fabry-Perot cavity

An experimental method to remove modal instabilities induced by thermoelastic deformation in optical high-finesse resonators is presented and experimentally investigated in this paper. The method is found suitable for multi-mirror folded monolithic and compact cavities, such as those used in the particle accelerator environment. It is also suitable for very high stacked average power. Here we demonstrate stable operation at the 200 kW intracavity average power.

Efficient nonlinear beam shaping in three-dimensional lithium niobate nonlinear photonic crystals

Nonlinear beam shaping refers to spatial reconfiguration of a light beam at a new frequency, which can be achieved by using nonlinear photonic crystals (NPCs). Direct nonlinear beam shaping has been achieved to convert second-harmonic waves into focusing spots, vortex beams, and diffraction-free beams. However, previous nonlinear beam shaping configurations in one-dimensional and two-dimensional (2D) NPCs generally suffer from low efficiency because of unfulfilled phase-matching condition. Here, we present efficient generations of second-harmonic vortex and Hermite-Gaussian beams in the recently-developed three-dimensional (3D) lithium niobate NPCs fabricated by using a femtosecond-laser-engineering technique. Since 3D χ⁽²⁾ modulations can be designed to simultaneously fulfill the requirements of nonlinear wave-front shaping and quasi-phase-matching, the conversion efficiency is enhanced up to two orders of magnitude in a tens-of-microns-long 3D NPC in comparison to the 2D case. Efficient nonlinear beam shaping paves a way for its applications in optical communication, super-resolution imaging, high-dimensional entangled source, etc.

Generation of light with desirable amplitude and phase profiles with nonlinear wavefront shaping is of great interest for optical technologies. Here, the authors demonstrate efficient nonlinear beam shaping using three-dimensional lithium niobate photonic crystals fabricated using a femtosecond-laser-engineering technique.

Single-longitudinal-mode 1521 nm passively q-switched Er:Yb:YAl3(BO3)4 pulse microchip laser

A single-longitudinal-mode 1521 nm pulse microchip laser Q-switched by a Co²⁺:MgAl₂O₄ saturable absorber was demonstrated in an Er:Yb:YAl₃(BO₃)₄ crystal. The influence of the waist radius of pump beam at 976 nm on the laser performance was investigated. At an incident pump power of 6.54 W and pump beam waist radius of 60 μm, a 1521.4 nm single-longitudinal-mode pulse laser with average output power of 434 mW, energy of 16.5 μJ, repetition frequency of 26.3 kHz and width of 2.9 ns was obtained. The result shows that caused by the mode selection of the saturable absorber and large cavity losses, a single-longitudinal-mode 1.55 μm pulse microchip laser can also be realized in the Er:Yb:YAl₃(BO₃)₄ crystal.

A single shot coherent Ising machine based on a network of injection-locked multicore fiber lasers

Combinatorial optimization problems over large and complex systems have many applications in social networks, image processing, artificial intelligence, computational biology and a variety of other areas. Finding the optimized solution for such problems in general are usually in non-deterministic polynomial time (NP)-hard complexity class. Some NP-hard problems can be easily mapped to minimizing an Ising energy function. Here, we present an analog all-optical implementation of a coherent Ising machine (CIM) based on a network of injection-locked multicore fiber (MCF) lasers. The Zeeman terms and the mutual couplings appearing in the Ising Hamiltonians are implemented using spatial light modulators (SLMs). As a proof-of-principle, we demonstrate the use of optics to solve several Ising Hamiltonians for up to thirteen nodes. Overall, the average accuracy of the CIM to find the ground state energy was ~90% for 120 trials. The fundamental bottlenecks for the scalability and programmability of the presented CIM are discussed as well.

For specific computation problems where electronic digital processors have shortcomings in simulating, an analog optical system may be a solution, Here, the authors present an analog all-optical implementation of a coherent Ising machine based on a network of injection-locked multicore fiber lasers.

Sub-Micron Spatial Resolution in Far-Field Raman Imaging Using Positivity-Constrained Super-Resolution

Raman microscopy is a valuable tool for detecting physical and chemical properties of a sample material. When probing nanomaterials or nanocomposites the spatial resolution of Raman microscopy is not always adequate as it is limited by the optical diffraction limit. Numerical post-processing with super-resolution algorithms provides a means to enhance resolution and can be straightforwardly applied. The aim of this work is to present interior point least squares (IPLS) as a powerful tool for super-resolution in Raman imaging through constrained optimization. IPLS's potential for super-resolution is illustrated on numerically generated test images. Its resolving power is demonstrated on Raman spectroscopic data of a polymer nanowire sample. Comparison to atomic force microscopy data of the same sample substantiates that the presented method is a promising technique for analyzing nanomaterial samples.

Direct measurement of the spectral dependence of Lamb coupling constant in a dual frequency quantum well-based VECSEL

Spectral dependence of Lamb coupling constant C is experimentally investigated in an InGaAlAs Quantum Wells active medium. An Optically-Pumped Vertical-External-Cavity Surface-Emitting Laser is designed to sustain the oscillation of two orthogonally polarized modes sharing the same active region while separated in the rest of the cavity. This laser design enables to tune independently the two wavelengths and, at the same time, to apply differential losses in order to extract without any extrapolation the actual coupling constant. C is found to be almost constant and equal to 0.84 ± 0.02 for frequency differences between the two eigenmodes ranging from 45 GHz up to 1.35 THz.

Open-path cavity ring-down methane sensor for mobile monitoring of natural gas emissions

We present the design, development, and testing results of a novel laser-based cavity ring-down spectroscopy (CRDS) sensor for methane detection. The sensor is specifically oriented for mobile (i.e. vehicle deployed) monitoring of natural gas emissions from oil and infrastructure. In contrast to most commercial CRDS sensors, we employ an open-path design which allows higher temporal response and a lower power and mass package more suited to vehicle integration. The system operates in the near-infrared (NIR) at 1651 nm with primarily telecom components and includes cellular communication for wireless data transfer. Along with basic sensor design and lab testing, we present results of field measurements showing performance over a range of ambient conditions and examples of methane plume detection.

Generalised theory of polarisation modes for resonators containing birefringence and anisotropic gain

Polarisation eigenmode theory is well established for laser cavities in which the principal axes for gain and polarisation elements are parallel. Here we generalise the theory to include the case for gain axes at arbitrary angle to the birefringence, which is the case for Raman lasers based on cubic-class gain crystals that contain stress-induced birefringence. The theory describes regimes dominated by gain, linear or circular birefringence, and the intermediate regime in which elliptically polarised output modes are obtained. Previously reported behaviour for diamond Raman lasers are found to be in accord with the findings. Design criteria are obtained to enable prediction of polarisation behaviour as functions of birefringence and resonator design.

Broadband enhancement of thermal radiation

Broadband thermal radiation sources are critical for various applications including spectroscopy and electricity generation. However, due to the difficulty in simultaneously achieving high absorptivity and low thermal mass these sources are inefficient. We show a platform that enables one to obtain enhanced emission by coupling a thermal emitter to an optical cavity. We experimentally demonstrate broadband enhancement of thermal emission between λ ~2 ̶ 4.2 μm using an inherently poor thermal emitter consisting of tens of nanometers thick SiC film with 10% emissivity (ε_SiC ~0.1). We measure over twofold enhancement of total emission power over the entire spectral band and threefold enhancement of thermal emission over 3 to 3.4 μm. Our platform has the potential to enable development of ideal blackbody sources operating at substantially lower heating powers.

Hermite-Gaussian mode detection via convolution neural networks

Hermite-Gaussian (HG) laser modes are a complete set of solutions to the free-space paraxial wave equation in Cartesian coordinates and represent a close approximation to physically realizable laser cavity modes. Additionally, HG modes can be mode-multiplexed to significantly increase the information capacity of optical communication systems due to their orthogonality. Because cavity tuning and optical communication applications benefit from a machine vision determination of HG modes, convolution neural networks were implemented to detect the lowest 21 unique HG modes with an accuracy greater than 99%. As the effectiveness of a CNN is dependent on the diversity of its training data, extensive simulated and experimental data sets were created for training, validation, and testing.

Laser varifocal system synthesis for longitudinal Gaussian beam shifting

This paper presents a modeling approach of a laser varifocal system for longitudinal Gaussian beam waist shifting. The developed approach is based on laser optics theory, which is considered to be classical optics generalized for coherent radiation. A basic optical system, consisting of two components, was developed using this theory. Components have fixed focal lengths and specific movements. An automated modeling algorithm was proposed, and an example was provided in text. Various systems shown in this paper form a Gaussian beam with required waist parameters and provide its longitudinal shifts, which exceed the length of the near-zone of a focused Gaussian beam. Such systems can be used in laser technologies, including micro- and nano-sized objects manipulation.

Determining topological charge based on an improved Fizeau interferometer

We propose a new method to determine topological charge by using an improved Fizeau interferometer. This interferometer is very easy to realize, as well as interference fringes are very distinct. Phases of vortex, Hermite-Gaussian, and elliptical vortex beams are experimentally verified using this method. It provides a convenient way to determine the sign and magnitude of topological charge. This method may have some potential applications in space optical communication.

Controllable conversion between Hermite Gaussian and Laguerre Gaussian modes due to cross phase

The inter-conversion between the Hermite-Gaussian (HG) modes and the Laguerre-Gaussian (LG) modes is discussed. The HG beams carrying a cross phase can evolve into the LG modes, and vice versa, a LG mode with the cross phase can also transform to the HG mode. This conversion process is accompanied by the intensity rotations of optical beams, and their angular velocities and acceleration are both radially dependent. Initially, the outer intensity peak and the inner intensity hollow rotate in the opposite directions. After that they tend to rotate in the same direction with different velocities. Different patterns can be generated in a controllable way by adjusting the cross phase coefficients. The theoretical results provide a controllable approach for modes generation by engineering the phase structure.

Gas-phase Raman spectroscopy of non-reacting flows: comparison between free-space and cavity-based spontaneous Raman emission

We report on a comparison of free-space and cavity-enhanced Raman spectroscopy for gas-phase measurements of nitrogen and oxygen in ambient air. Real-time analysis capabilities and continuous Raman signals with low power diodes make the technique non-invasive, affordable, compact, and applicable for usage in non-reacting flows. We derive a comprehensive model for estimation of photon emission for both free-space and cavity-based signals and discuss trade-offs in how to organize the cavity geometry for maximum gain relative to free space. Measurements in both free and cavity configurations are compared to the expected signals, demonstrating the usefulness of the model in predicting amplification. The present results can serve as a quick guide on how to use low-power continuous wave lasers in a cavity setup to obtain enhanced laser-induced spontaneous Raman scattering.

Optics-less focusing of XUV high-order harmonics

By experimentally studying high-order harmonic beams generated in gases, we show how the spatial characteristics of these ultrashort extreme-ultraviolet (XUV) beams can be finely controlled when a single fundamental beam generates harmonics in a thin gas medium. We demonstrate that these XUV beams can be emitted as converging beams and thereby get focused after generation. We study this optics-less focusing using a spatially chirped beam that acts as a probe located inside the harmonic generation medium. We analyze the XUV beam evolution with an analytical model and obtain very good agreement with experimental measurements. The XUV foci sizes and positions vary strongly with the harmonic order, and the XUV waist can be located at arbitrarily large distances from the generating medium. We discuss how intense XUV fields can be obtained with optics-less focusing and how the order-dependent XUV beam characteristics are compatible with broadband XUV irradiation and attosecond science.

Versatile total angular momentum generation using cascaded J-plates

Optical elements coupling the spin and orbital angular momentum (SAM/OAM) of light have found a range of applications in classical and quantum optics. The J-plate, with J referring to the photon's total angular momentum (TAM), is a metasurface device that imparts two arbitrary OAM states on an arbitrary orthogonal basis of spin states. We demonstrate that when these J-plates are cascaded in series, they can generate several single quantum number beams and versatile superpositions thereof. Moreover, in contrast to previous spin-orbit-converters, the output polarization states of cascaded J-plates are not constrained to be the conjugate of the input states. Cascaded J-plates are also demonstrated to produce vector vortex beams and complex structured light, providing new ways to control TAM states of light.

Precision analysis and optimization in phase decorrelation OCT velocimetry

Quantitative flow velocimetry in Optical Coherence Tomography is used to determine both the axial and lateral flow component at the level of individual voxels. The lateral flow is determined by analyzing the statistical properties of reflected electro-magnetic fields for repeated measurements at (nearly) the same location. The precision or statistical fluctuation of the quantitative velocity estimation depends on the number of repeated measurements and the method to determine quantitative flow velocity. In this paper, both a method to determine quantitative flow velocity and a model for the prediction of the statistical fluctuations of velocity estimations are developed to analyze and optimize the estimation precision for phase-based velocimetry methods. The method and model are validated by phantom measurements in a bulk scattering medium as well as in intralipid solution in a capillary. Based on the model, the number of repeated measurements to achieve a certain velocimetry precision is predicted.

Theory of Bose condensation of light via laser cooling of atoms

A Bose-Einstein condensate (BEC) is a quantum phase of matter achieved at low temperatures. Photons, one of the most prominent species of bosons, do not typically condense due to the lack of a particle number conservation. We recently described a photon thermalization mechanism which gives rise to a grand canonical ensemble of light with effective photon number conservation between a subsystem and a particle reservoir. This mechanism occurs during Doppler laser cooling of atoms where the atoms serve as a temperature reservoir while the cooling laser photons serve as a particle reservoir. In contrast to typical discussions of BEC, our system is better treated with a controlled chemical potential rather than a controlled particle number, and is subject to energy-dependent loss. Here, we address the question of the possibility of a BEC of photons in this laser cooling photon thermalization scenario and theoretically demonstrate that a Bose condensation of photons can be realized by cooling an ensemble of two-level atoms (realizable with alkaline-earth atoms) inside a Fabry-Pérot cavity.

GaN-based Vertical-Cavity Surface-Emitting Lasers Incorporating Dielectric Distributed Bragg Reflectors

This paper reviews past research and the current state-of-the-art concerning gallium nitride-based vertical-cavity surface-emitting lasers (GaN-VCSELs) incorporating distributed Bragg reflectors (DBRs). This paper reviews structures developed during the early stages of research into these devices, covering both major categories of GaN-based VCSELs: hybrid-DBR and all-dielectric-DBR. Although both types exhibited satisfactory performance during continuous-wave (CW) operation in conjunction with current injection as early as 2008, GaN-VCSELs have not yet been mass produced for several reasons. These include the difficulty in controlling the thicknesses of nitride semiconductor layers in hybrid-DBR type devices and issues related to the cavity dimensions in all-dielectric-DBR units. Two novel all-dielectric GaN-based VCSEL concepts based on different structures are examined herein. In one, the device incorporates dielectric DBRs at both ends of the cavity, with one DBR embedded in n-type GaN grown using the epitaxial lateral overgrowth technique. The other concept incorporates a curved mirror fabricated on (000-1) GaN. Both designs are intended to mitigate challenges regarding industrial-scale processing that are related to the difficulty in controlling the cavity length, which have thus far prevented practical applications of all-dielectric GaN-based VCSELs.

Broadband interferometric subtraction of optical fields

We present a Mach-Zehnder-like interferometer capable of simultaneous super-octave (950 - 2100 nm) destructive interference with an intensity extinction of 4 × 10^-4. Achromatic nulling is achieved by unbalancing the number of Fresnel reflections off optically denser media in the two interferometer arms. With a methane gas sample in one interferometer arm, we isolate the coherent molecular vibrational emission from the broadband, impulsive excitation and quantitatively examine the potential improvement in detectable concentration, compared to direct transmission geometry. The novel concept will benefit sensing applications requiring high detection sensitivity and dynamic range, including time-domain and frequency-domain spectroscopy.

Long-Term Stable Online Acetylene Detection by a CEAS System with Suppression of Cavity Length Drift

A trace acetylene (C₂H₂) detection system was demonstrated using the cavity-enhanced absorption spectroscopy (CEAS) technique and a near-infrared distributed feedback (NIR-DFB) laser. A Fabry–Perot (F–P) cavity with an effective optical path length of 49.7 m was sealed and employed as a gas absorption cell. Co-axis cavity alignment geometry was adopted to acquire a larger transmitted light intensity and a higher sensitivity compared with off-axis geometry. The laser frequency was locked to the cavity fundamental mode (TEM₀₀ mode) by using the Pound–Drever–Hall (PDH) technique continuously. By introducing a cavity length-locking loop, the drift of the cavity length was suppressed, and the stability of the system was enhanced. To demonstrate the efficacy of the system, a C₂H₂ absorption spectrum near 6534.36 cm⁻¹ was acquired by tuning the laser operation temperature. Measurements of C₂H₂ samples with different concentrations were carried out, and a good linear relationship between C₂H₂ concentration and the cavity-transmitted signal voltage was observed. The measurement results showed the system could work stably for more than 2 h without major fluctuations. The Allan variance analysis results demonstrated a detection limit of 9 parts-per-billion (ppb) with an averaging time of 11 s corresponding to a minimum detectable absorption coefficient of 1.1 × 10⁻⁸ cm⁻¹.

Squeezed vacuum states of light for gravitational wave detectors

A century after Einstein's formulation of general relativity, the detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) made the first direct detection of gravitational waves. This historic achievement was the culmination of a world-wide effort and decades of instrument research. While sufficient for this monumental discovery, the current generation of gravitational-wave detectors represent the least sensitive devices necessary for the task; improved detectors will be required to fully exploit this new window on the Universe. In this paper, we review the application of squeezed vacuum states of light to gravitational-wave detectors as a way to reduce quantum noise, which currently limits their performance in much of the detection band.

Orbital angular momentum of an elliptic beam after an elliptic spiral phase plate

We obtain a simple closed expression for the normalized orbital angular momentum (OAM) (OAM per unit power) of an arbitrary paraxial light beam with an elliptic shape, diffracted by an elliptic spiral phase plate (SPP), rotated by an arbitrary angle around the optical axis. Moreover, ellipticities of the beam and of the SPP can be different. It is shown that when an elliptic beam illuminates an elliptic SPP, the normalized OAM of the output beam is maximal (minimal) when both the beam and the SPP are oriented in the same (orthogonal) directions. The results can be used in optical trapping, e.g., for continuous change of the OAM transferred to a particle by rotating the SPP around the optical axis.

Efficiency signal conversion parameter to evaluate astigmatic femtosecond-optical parametric oscillator cavities

In this work, we define the efficiency signal conversion numerical parameter, V_eff, useful to evaluate the operation efficiency of femtosecond-Optical Parametric Oscillator (fs-OPO) cavities considering the astigmatism effect. For the validation of the V_eff, we have performed experimental measurements. We present different high efficiency home-made singly resonant fs-OPO cavities, with signal tuneability from 1.1 µm to 1.6 µm based on a 0.5 mm Periodically Poled Lithium Niobate doped with MgO (MgO:PPLN) crystal. We have also defined the pump energy threshold per crystal unit length, ζ_p,th. Pump threshold, achieved by following the V_eff, was 142 mW at 810 nm, and ζ_p,th = 2.10 nJ/mm, the lowest value, in comparison with other studies. The V_eff is based on an ABCD matrix Gaussian beam propagation method, which calculates the mode coupling between the pump and signal beams along the crystal under different cavity configurations taking into account the astigmatism. The model was compared and tested with 3 different experimental singly resonant fs-OPO ring cavity configurations that we have defined as single-folded, two-folded, and direct-pump cavity.

Multipass amplifiers with self-compensation of the thermal lens

We present an architecture for a multipass amplifier based on a succession of optical Fourier transforms and short propagations that shows a superior stability for variations of the thermal lens compared to state-of-the-art 4f-based amplifiers. We found that the proposed multipass amplifier is robust to variations of the active medium dioptric power. The superiority of the proposed architecture is demonstrated by analyzing the variations of the size and divergence of the output beam in the form of a Taylor expansion around the design value for variations of the thermal lens in the active medium. The dependence of the output beam divergence and size is investigated also for variations of the number of passes, for aperture effects in the active medium, and as a function of the size of the beam on the active medium. This architecture makes efficient use of the transverse beam filtering inherent in the active medium to deliver a beam with excellent quality (TEM00).

Degeneracy in the diffraction of orbital angular momentum carrying beams

Symmetry constraints on the far-field diffraction of Laguerre-Gauss vortex beams by planar aperture arrays with N-fold rotational symmetry are considered. The experiments reveal a simple structure for the diffraction pattern and high degree of degeneracy in its dependence on the orbital angular momentum index of the incident beam in agreement with analytical and numerical results.

Analysis of Design and Fabrication Parameters for Lensed Optical Fibers as Pertinent Probes for Sensing and Imaging

A method for adjusting the working distance and spot size of a fiber probe while suppressing or enhancing the back-coupling to the lead-in fiber is presented. As the optical fiber probe, a lensed optical fiber (LOF) was made by splicing a short piece of coreless silica fiber (CSF) on a single-mode fiber and forming a lens at the end of the CSF. By controlling the length of the CSF and the radius of lens curvature, the optical properties of the LOF were adjusted. The evolution of the beam in the LOF was analyzed by using the Gaussian ABCD matrix method. To confirm the idea experimentally, 17 LOF samples were fabricated and analyzed theoretically and also experimentally. The results show that it is feasible in designing the LOF to be more suitable for specific or dedicated applications. Applications in physical sensing and biomedical imaging fields are expected.

Vector beam generation from vertical cavity surface emitting lasers

Radially and azimuthally polarized beams in a single transverse mode are generated from a commercially available vertical cavity surface emitting laser (VCSEL) in an external cavity with a birefringent rutile lens, of which the c axis is parallel to the optical axis of the cavity, to select favorable polarization. Additionally, a vector Bessel-Gaussian beam is generated from a VCSEL, which is fabricated to oscillate with a linear polarization in a fixed direction in free running, in the same way. These results clearly show the potential ability of VCSELs to generate vector beams, which will be essential to space-division multiplexing in the future optical communication.

Modeling method of a ladar scene projector based on physically based rendering technology

The ladar scene projector is a key device in the hardware-in-the-loop (HWIL) simulation system. Ladar scene modeling is a fundamental work of developing a ladar scene projector. A modeling method based on physically based rendering technology and OpenGL is proposed in this paper. This modeling method can quickly generate delay, amplitude, and pulse width data for all return signals in a large-array-scale ladar scene. A 100×100-array-sized ladar scene model with a distance range of 0-3 km is simulated. The average data generation time is only 5.31 ms. Distance resolution is 1.5 m, and the peak-valley error is less than 0.15 m. This method achieves efficient modeling and fast hardware update rates, which greatly improves the real-time performance of the ladar scene projector. It has strong practicality and can be directly applied in the HWIL simulation system.

Relativistic coupling of phase and amplitude noise in optical interferometry

Extraneous motion of optical elements in an interferometer leads to excess noise. Typically, fluctuations in the effective path length lead to phase noise, while beam pointing fluctuations lead to apparent amplitude noise. For a transmissive optic moving along the optical axis, neither effect should exist. However, relativity of motion suggests that, even in this case, small corrections of order v/c (v the velocity of the optic) give rise to phase and amplitude noise on the light. Here we calculate the effect of this relativistic mechanism of noise coupling and discuss when such an effect would limit the sensitivity of optical interferometers.

Regression-based technique for improved optical rangefinding using tunable focus lenses

In this paper, we present a novel method of target range estimation by tuning the spot size of a Gaussian beam at the plane of a reflective target. The beam spot size tuning is achieved through the use of a tunable focus lens (TFL). Using a carefully aligned sensor assembly, the diameter of the reflected beam is recorded at the plane of an imaging detector for different TFL focal length settings. This dataset is then used to estimate the distance of the target from the TFL. The proposed rangefinder is compact and requires minimal post-data-acquisition signal processing resulting in a fast response time compared to other spatial signal processing-based sensor designs. The estimation of target distance through a multiple data-point measurement dataset also ensures that the proposed method is robust to errors associated with obtaining range estimates from a single measurement data point. Experimental results demonstrate an excellent agreement with theory. With our proposed estimation method, we show a significant improvement in the measurement dynamic range of the sensor as well as its resolution compared to similar sensing schemes in prior art. We also experimentally demonstrate the possibility to extend the measurement dynamic range by incorporating a bias lens of a fixed focal length with the sensor module. The proposed sensor module is electronically controlled and consequently can be fully automated and compactly packaged with the use of commercially available miniature optical components.

Lateral optical confinement of GaN-based VCSEL using an atomically smooth monolithic curved mirror

We demonstrate the lateral optical confinement of GaN-based vertical-cavity surface-emitting lasers (GaN-VCSELs) with a cavity containing a curved mirror that is formed monolithically on a GaN wafer. The output wavelength of the devices is 441–455 nm. The threshold current is 40 mA (J_th = 141 kA/cm²) under pulsed current injection (W_p = 100 ns; duty = 0.2%) at room temperature. We confirm the lateral optical confinement by recording near-field images and investigating the dependence of threshold current on aperture size. The beam profile can be fitted with a Gaussian having a theoretical standard deviation of σ = 0.723 µm, which is significantly smaller than previously reported values for GaN-VCSELs with plane mirrors. Lateral optical confinement with this structure theoretically allows aperture miniaturization to the diffraction limit, resulting in threshold currents far lower than sub-milliamperes. The proposed structure enabled GaN-based VCSELs to be constructed with cavities as long as 28.3 µm, which greatly simplifies the fabrication process owing to longitudinal mode spacings of less than a few nanometers and should help the implementation of these devices in practice.

Gamma and gamma-coupled beams

A new class of scalar, rotationally symmetric Gaussian-like beams is introduced. The slowly varying amplitudes of such beams are represented as analytical solutions to the paraxial wave equation, described in terms of the incomplete gamma functions and their products with quadratic exponential and power functions of different kinds. The specific functional forms of these solutions give rise to such names as gamma, gamma-Gaussian, gamma-parabolic, and gamma-anti-Gaussian beams. It is established that, within a focal volume specified by a waist size and the depth of field of about three Rayleigh lengths of the fundamental Gaussian beam of the same waist size, the parametrically optimized zero-order gamma and gamma-coupled beams possess more stabilized transverse sizes, very weak transverse irradiance sidelobes, more uniform axial irradiance distributions, and more steep controllable fall-offs of the last distributions relative to those that are inherent in the above fundamental Gaussian beam and the Bessel-Gauss beams with linear and quadratic radial dependence and the same waist size.

Radial-angular entanglement in Laguerre-Gaussian mode superpositions

Classical optic entanglement between the radial and angular degrees of freedom in Laguerre-Gaussian mode superpositions is explored within the framework of symmetric first-order optical systems. The Gouy phase picked by a Laguerre-Gaussian mode on free propagation is seen to be of consequence to the radial-angular entanglement in the mode superpositions. We illustrate examples of mode superpositions for which radial-angular entanglement is preserved on passage through symmetric first-order optical systems. An indicator of radial-angular entanglement in two-mode Laguerre-Gaussian superpositions is demonstrated to be a robust free space signaler in the presence of atmospheric turbulence, through examples.

Temperature-scanning saturation cavity ring-down spectrometry for Doppler-free spectroscopy

Saturation cavity ring-down spectroscopy (SCRDS) is a powerful Doppler-free spectroscopy means for measuring absolute frequencies of transitions at the ultra-low uncertainties. We report in this paper a simple way to implement it by temperature scanning the cavity length, which circumvents the need for a complex optical cavity-length stabilization system based upon a piezoelectric actuator (PZT). To demonstrate this approach, the absolute frequencies of the two transitions, R6F1 of the 2v₃ and Q9A1 of the 2v₂ + v₃ bands, of ¹²CH₄, are determined to be 182 185 269.362(20) MHz and 182 187 617.543(39) MHz. The accuracy of measurements is improved by about 3-4 orders of magnitude when compared to those obtained with conventional spectroscopic methods.

Anisotropic diffraction induced by orbital angular momentum during propagations of optical beams

It is demonstrated that the orbital angular momentum (OAM) carried by the elliptic beam without the phase-singularity can induce the anisotropic diffraction (AD). The quantitative relation between the OAM and its induced AD is analytically obtained by a comparison of two different kinds of (1+2)-dimensional beam propagations: the linear propagations of the elliptic beam without the OAM in an anisotropic medium and that with the OAM in an isotropic one. In the former case, the optical beam evolves as the fundamental mode of the eigenmodes when its ellipticity is the square root of the anisotropic parameter defined in the paper; while in the latter case, the fundamental mode exists only when the OAM carried by the optical beam equals a specific one called a critical OAM. The OAM always enhances the beam-expanding in the major-axis direction and weakens that in the minor-axis direction no matter the sign of the OAM, and the larger the OAM, the stronger the AD induced by it. Besides, the OAM can also make the elliptic beam rotate, and the absolute value of the rotation angle is no larger than π/2 during the propagation.

Design and characterization of a dead-time regime enhanced early photon projection imaging system

Scattering of visible and near-infrared light in biological tissue reduces spatial resolution for imaging of tissues thicker than 100 μm. In this study, an optical projection imaging system is presented and characterized that exploits the dead-time characteristics typical of photon counting modules based on single photon avalanche diodes (SPADs). With this system, it is possible to attenuate the detection of more scattered late-arriving photons, such that detection of less scattered early-arriving photons can be enhanced with increased light intensity, without being impeded by the maximum count rate of the SPADs. The system has the potential to provide transmittance-based anatomical information or fluorescence-based functional information (with slight modification in the instrumentation) of biological samples with improved resolution in the mesoscopic domain (0.1-2 cm). The system design, calibration, stability, and performance were evaluated using simulation and experimental phantom studies. The proposed system allows for the detection of very-rare early-photons at a higher frequency and with a better signal-to-noise ratio. The experimental results demonstrated over a 3.4-fold improvement in the spatial resolution using early photon detection vs. conventional detection, and a 1000-fold improvement in imaging time using enhanced early detection vs. conventional early photon detection in a 4-mm thick phantom with a tissue-equivalent absorption coefficient of μa = 0.05 mm-1 and a reduced scattering coefficient of μs' = 5 mm-1.

Circular-Polarization-Dependent Study of Microwave-Induced Conductivity Oscillations in a Two-Dimensional Electron Gas on Liquid Helium

The polarization dependence of the photoconductivity response at cyclotron-resonance harmonics in a nondegenerate two-dimensional (2D) electron system formed on the surface of liquid helium is studied using a setup in which a circular polarization of opposite directions can be produced. Contrary to the results of similar investigations reported for semiconductor 2D electron systems, for electrons on liquid helium, a strong dependence of the amplitude of magnetoconductivity oscillations on the direction of circular polarization is observed. This observation is in accordance with theoretical models based on photon-assisted scattering, and, therefore, it presents a principal argument in the dispute over the origin of microwave-induced conductivity oscillations.

Sorting Photons by Radial Quantum Number

The Laguerre-Gaussian (LG) modes constitute a complete basis set for representing the transverse structure of a paraxial photon field in free space. Earlier workers have shown how to construct a device for sorting a photon according to its azimuthal LG mode index, which describes the orbital angular momentum (OAM) carried by the field. In this paper we propose and demonstrate a mode sorter based on the fractional Fourier transform to efficiently decompose the optical field according to its radial profile. We experimentally characterize the performance of our implementation by separating individual radial modes as well as superposition states. The reported scheme can, in principle, achieve unit efficiency and thus can be suitable for applications that involve quantum states of light. This approach can be readily combined with existing OAM mode sorters to provide a complete characterization of the transverse profile of the optical field.

Realization of first-order optical systems using thin lenses of positive focal length

An explicit decomposition of the most general first-order optical system characterized by an Sp(4,R) matrix is obtained in terms of free propagation, thin convex lenses, and thin cylindrical lenses of positive focal length. The Euler decomposition of an Sp(4,R) matrix is used in arriving at the decomposition. It is shown that not more than four convex lenses and 14 cylindrical lenses of positive focal length are required to realize the same. Explicit decompositions for the case of differential free and inverse free propagation, differential magnifiers, and differential fractional Fourier transform are provided.

Gouy phase induced polarization transition of focused vector vortex beams

We propose a common criterion for the effect of Gouy phase on the distinct polarization transition of focused vector vortex beams (VVBs). Such polarization transition is strongly dependent on the parity of the smaller modulus between VVB's polarization order and topological charge. Significantly, the cross polarization transitions are observed at areas where the two spin components with equi-intensity are exactly overlapping and the Gouy phase difference (GPD) between them equals to (2k + 1)π, k is an integer. As a whole, the focal field shows radially variant polarization distributions resulting from the unequal intensity proportion of the two spin components. This polarization transition holds potential in modifying the patterns of periodic surface structure induced by femtosecond vector beams.

Diffraction of partially-coherent light beams by microlens arrays

The synthesis method including wave-optics and ray-tracing for the acceleration of the simulation of micro-optical systems has been developed. The effects of the spatial coherence and randomization of microlens array (MLA) parameters have been considered. The method based on coherent states representation for the calculation of the optical efficiency of microlens arrays taking into account the light source polarization has been developed. Numerical simulations of the intensity distributions and spreading angle of a diffracted beam have been carried out.

Simple method for efficient reconfigurable optical vortex beam splitting

In recent years, singular light beams with orbital angular momentum are one of the most striking examples of structured light that have been widely applied in modern science. The transition from the generation of a single vortex beam to the generation of multiple such beams progressed the development of singular optics. This paper presents a new efficient method of vortex laser beam splitting using a two-level pure-phase diffractive optical element. The proposed compact element, which can be easily implemented with a low-cost binary spatial light modulator or fabricated by electron beam lithography or photolithography, is a useful tool for the reconfigurable generation of multiple closed-packed vortex beams. Furthermore, the proposed splitter can efficiently operate in the wavelength range of approximately 8% of the central wavelength, thus providing an efficient method to generate optical vortex arrays with various potential applications in modern optics and photonics.

Improved laser-based triangulation sensor with enhanced range and resolution through adaptive optics-based active beam control

Various existing target ranging techniques are limited in terms of the dynamic range of operation and measurement resolution. These limitations arise as a result of a particular measurement methodology, the finite processing capability of the hardware components deployed within the sensor module, and the medium through which the target is viewed. Generally, improving the sensor range adversely affects its resolution and vice versa. Often, a distance sensor is designed for an optimal range/resolution setting depending on its intended application. Optical triangulation is broadly classified as a spatial-signal-processing-based ranging technique and measures target distance from the location of the reflected spot on a position sensitive detector (PSD). In most triangulation sensors that use lasers as a light source, beam divergence-which severely affects sensor measurement range-is often ignored in calculations. In this paper, we first discuss in detail the limitations to ranging imposed by beam divergence, which, in effect, sets the sensor dynamic range. Next, we show how the resolution of laser-based triangulation sensors is limited by the interpixel pitch of a finite-sized PSD. In this paper, through the use of tunable focus lenses (TFLs), we propose a novel design of a triangulation-based optical rangefinder that improves both the sensor resolution and its dynamic range through adaptive electronic control of beam propagation parameters. We present the theory and operation of the proposed sensor and clearly demonstrate a range and resolution improvement with the use of TFLs. Experimental results in support of our claims are shown to be in strong agreement with theory.

Concave silicon micromirrors for stable hemispherical optical microcavities

A detailed study of the fabrication of silicon concave micromirrors for hemispherical microcavities is presented that includes fabrication yield, surface quality, surface roughness, cavity depth, radius of curvature, and the aspect ratio between the cavity depth and radius of curvature. Most importantly, it is shown that much larger cavity depths are possible than previously reported while achieving desirable aspect ratios and nanometer-level roughness. This should result in greater frequency stability and improved insensitivity to fabrication variations for the mode coupling optics. Spectral results for an assembled hemispherical microcavity are presented, demonstrating that high finesse and quality factor are achieved with these micromirrors, F = 1524 and Q = 3.78 x 10⁵, respectively.

Nonlinear imaging of nanostructures using beams with binary phase modulation

We demonstrate nonlinear microscopy of oriented nanowires using excitation beams with binary phase modulation. A simple and intuitive optical scheme comprising a spatial light modulator gives us the possibility to control the phase across an incident Hermite-Gaussian beam of order (1,0) (HG₁₀ mode). This technique allows us to gradually vary the spatial distribution of the longitudinal electric fields in the focal volume, as demonstrated by second-harmonic generation from vertically-aligned GaAs nanowires. These results open new opportunities for the full control of polarization in the focal volume to enhance light interaction with nanostructured materials.

Conservation of extremal ellipticity and analytical expressions for astigmatism and asymmetry in Gaussian beam transformations

A Gaussian beam with initial astigmatism, waist, and M² asymmetry propagates through a simple optical system consisting of a single thin, aberration-free lens. We derive simple analytical expressions for the asymmetry, astigmatism, and ellipticity of the beam after the lens, and show that the maximal ellipticity of the beam is a conserved quantity that is solely dependent on these input parameters. This appears to still hold for general astigmatic Gaussian beams. Our simple, analytical results conveniently determine the trade-off between astigmatism and asymmetry of a laser for a given output maximum ellipticity requirement pre- or post-lenses.