Free-space Light Propagation Research Articles

Orbital angular momentum spectrum of model partially coherent beams in turbulence

The use of partial coherence has been extensively studied as a potential solution to mitigate the destructive effects of atmospheric turbulence in optical applications involving the free space propagation of light. However, in OAM-based optical systems, reducing coherence leads to the broadening of the orbital angular momentum (OAM) spectrum, consequently increasing the cross-talk between adjacent modes. In this paper, we have investigated three fundamental classes of partially coherent OAM beams under the influence of turbulence. The aim is to identify a distinct type of partially coherent beam (PCB) in which the reduction in coherence results in higher resistance of the OAM spectrum against atmospheric disturbances. It is demonstrated that, for a specific propagation distance, we can prepare a PCB in which the benefits of reducing coherence outweigh its drawbacks.

Combined finite-element and scalar diffraction simulation of light scattering on zone edges of diffractive intraocular lenses.

A method has been developed to simulate the effects of scattered light on the image quality of optical systems. The coherent model is based on geometrical optics to take account of wavefront aberrations caused by lenses, applies finite-element calculation to solve Maxwell's equations around small scattering structures such as edges of diffractive surface zones, and uses scalar diffraction for free-space light propagation. The implementation is discussed in detail, and the operation is demonstrated on diffractive intraocular lenses. Point spread and modulation transfer functions are evaluated for an axial object point, taking account of scattered light as a function of slant angle and round radius of diffractive zone edges. Results show that, at a distance of ±200 Airy radius (i.e.,±2.1∘) from the axis, scattered irradiance is about 5 times more than without considering edge effects. Optimum round radius was found to be 7% of the step height, which agrees with simple geometrical optical estimations.

First steps into coherent object classification using convolutional deep diffractive neural networks

Abstract As artificial intelligence and deep learning becomes more important, new approaches for photonic neural computing arise. We investigate the concept of deep diffractive neural networks. First proposed in 2018, deep diffractive neural network operate passively, using coherent images and diffractive optics to do image-to-image regression and object classification. In this article we shortly review current approaches, give a brief introduction into the mathematical description of such diffractive networks using the Angular Spectrum method and show the first results of our own developments of convolutional diffractive networks with an experimental accuracy of approximately 84 %. The objective of this article is to give an introduction into the field of optical computing with neural networks using diffraction and free-space propagation of light.

Imaging optical fields below metal films and metal-dielectric waveguides by a scanning microscope.

Laser scanning confocal fluorescence microscopy (LSCM) is now an important method for tissue and cell imaging when the samples are located on the surfaces of glass slides. In the past decade, there has been extensive development of nano-optical structures that display unique effects on incident and transmitted light, which will be used with novel configurations for medical and consumer products. For these applications, it is necessary to characterize the light distribution within short distances from the structures for efficient detection and elimination of bulky optical components. These devices will minimize or possibly eliminate the need for free-space light propagation outside of the device itself. We describe the use of the scanning function of a LSCM to obtain 3D images of the light intensities below the surface of nano-optical structures. More specifically, we image the spatial distributions inside the substrate of fluorescence emission coupled to waveguide modes after it leaks through thin metal films or dielectric-coated metal films. The observed spatial distribution were in general agreement with far-field calculations, but the scanning images also revealed light intensities at angles not observed with classical back focal plane imaging. Knowledge of the subsurface optical intensities will be crucial in the combination of nano-optical structures with rapidly evolving imaging detectors.

Three-dimensional analysis of free-space light propagation based on quantum mechanical scattering theory of light

In this paper, a free-space light propagation analysis between 3-dimensional (3-D) volumetric spaces is proposed. In contrast to conventional scalar diffraction, the proposed theory is based on quantum mechanical scattering providing a general volumetric analysis for the free-space light propagation. Assuming a plane wave light incidence, we obtained a new analytic formula for 3-D volumetric convolution, which provided a transfer function in a closed form used for caculating the electric fields at the observation points. The proposed method was consistent with the conventional numerical methods for a 2-dimensional aperture and can be further applied to exact calculation of diffraction fields from 3-D surfaces, providing a compact reconstruction algorithm for 3-D images in a computer generated hologram.

Light propagation analysis using a translated plane angular spectrum method with the oblique plane wave incidence.

A novel angular spectrum method was proposed to numerically analyze off-axis free-space light propagation on a translated plane to an arbitrary angle. Utilizing a shifted angular spectrum method based on an oblique incident plane wave assumption, a generalized light propagation formulation was obtained in a wide range of both tilt angles and sampling intervals, which overcame the limitations of prior attempts. A detailed comparison of the proposed angular spectrum method with prior methods is numerically presented for diffractive optics and computer-generated holograms. The validity of the proposed method was confirmed experimentally by reconstructing a digital holographic image using a spatial light modulator.

Ammonia sensing system based on wavelength modulation spectroscopy

A sensing system in the near infrared region has been developed for ammonia sensing based on the wavelength modulation spectroscopy (WMS) principle. The WMS is a rather sensitive technique for detecting atomic/molecular species, presenting the advantage that it can be used in the near-infrared region by using the optical telecommunications technology. In this technique, the laser wavelength and intensity were modulated by applying a sine wave signal through the injection current, which allowed the shift of the detection bandwidth to higher frequencies where laser intensity noise was typically lower. Two multi-pass cells based on free space light propagation with 160 cm and 16 cm of optical path length were used, allowing the redundancy operation and technology validation. This system used a diode laser with an emission wavelength at 1512.21 nm, where NH3 has a strong absorption line. The control of the NH3 gas sensing system, as well as acquisition, processing and data presentation was performed.

Safe range of free space light propagation calculation in single precision.

Calculations of free space light propagation, such as those used in digital holography, deal with distances much longer than a wavelength. Computer representation of real numbers must therefore provide enough precision to handle this situation. We show that single precision must be used with the utmost care, which is especially important in GPU calculations. We also show that Fresnel approximation significantly improves single precision calculations for distances bigger than about one metre.

The Fresnel Diffraction: A Story of Light and Darkness

In a first part of the paper we give a simple introduction to the free space propagation of light at the level of a Master degree in Physics. The presentation promotes linear filtering aspects at the expense of fundamental physics. Following the Huygens-Fresnel approach, the propagation of the wave writes as a convolution relationship, the impulse response being a quadratic phase factor. We give the corresponding filter in the Fourier plane. As an illustration, we describe the propagation of wave with a spatial sinusoidal amplitude, introduce lenses as quadratic phase transmissions, discuss their Fourier transform properties and give some properties of Soret screens. Classical diffractions of rectangular diaphragms are also given here. In a second part of the paper, the presentation turns into the use of external occulters in coronagraphy for the detection of exoplanets and the study of the solar corona. Making use of Lommel series expansions, we obtain the analytical expression for the diffraction of a circular opaque screen, giving thereby the complete formalism for the Arago-Poisson spot. We include there shaped occulters. The paper ends up with a brief application to incoherent imaging in astronomy.

Beam-quality measurements using a spatial light modulator

We present a fast and easy technique for measuring the beam propagation ratio, M(2), of laser beams using a spatial light modulator. Our technique is based on digitally simulating the free-space propagation of light, thus eliminating the need for the traditional scan in the propagation direction. We illustrate two approaches to achieving this, neither of which requires any information of the laser beam under investigation nor necessitates any moving optical components. The comparison with theoretical predictions reveals excellent agreement and proves the accuracy of the technique.

Micromachined Fabry–Perot resonator combining submillimeter cavity length and high quality factor

We demonstrate experimentally optical quality factor of nearly 9000 in a micromachined Fabry–Pérot resonator based on free space propagation of light and direct coupling to optical fibers. This result is obtained on long cavity resonators (L>250 μm), a usually difficult case in terms of power loss, but very useful configuration for experiments requiring either long optical path or enough space for manipulation. The resonator architecture includes two multilayered silicon-air Bragg mirrors of cylindrical shape, combined with a fiber rod lens. The specific stability criteria are derived for the proposed resonator architecture. Dimensions of the fabricated devices are chosen accordingly.

A Fluorescence Molecular Tomography In-vivo Imaging System for Macro/Meso-Scale Subjects

A novel quantitative fluorescence molecular tomography (FMT) imager for both macro and meso-scale animal experiments is developed. The image reconstruction algorithms are implemented in the framework of finite element method, while the experimental system is constructed using a non-contact, multi-angle full 360 degree transmission scheme. Shape-from-silhouette based volume carving approach is used to render the 3D models of the actual samples. With a free-space light propagation model, the readout from the CCD is converted into the photon density normal to sample surface in order to match the model-based tomographic reconstruction. For meso-scale subjects, a radiative transfer equation (RTE) based FMT reconstruction algorithm is adopted. For macro-scale subjects, a diffusion approximation (DA) based FMT reconstruction algorithm is adopted. Imaging results for both macro-scale and meso- scale subjects are presented to valid system performance.

Diffusive reflectance for the free-space light propagation theory

Based on the free-space light propagation theory, the noncontact measurement technique for optical tomography provides high quality data sets by using charge coupled device camera for light detection. The free-space theory was originally formulated for a single object but did not take into account the reflection among object surfaces. However, complex geometries of small animals can induce multiple light reflections on surfaces. A major issue is how to model the surface reflectance to work with the free-space light propagation theory. In this letter, we utilize the Monte Carlo simulation technique to evaluate the performance of the free-space theory with multiple light reflections. Two types of surface reflectance have been simulated, including the specular or diffuse reflectance, respectively. It is found that for tissuelike objects the diffusive reflectance works the best with the free-space theory and a discrepancy occurs when the surface exhibits specular reflectance.

Speckles and their dynamics for structured target illumination: optical spatial filtering velocimetry

This contribution analyses the dynamics of laser speckle patterns, designed for sensing with a receiver, based on spatial filtering. Speckle translation is probed after free-space propagation of light scattered from non-specular moving surfaces. By structuring the target illumination the speckle patterns can be modulated with a fine structure, enhancing the performance of the spatial filter. The space-time normalized cross-covariance function of speckle patterns incident on the spatial filter is presented for a simple structure of the field distribution on the target. This function provides the corresponding statistical parameters, i.e. structural size, velocity and decorrelation length, for both the speckles and the fine structure. The analysis also reveals that the speckles and the fine structure do not necessarily translate as a rigid structure. The spatial power spectrum for the speckle patterns and the spatial filter defines the optimum geometry for the structured illumination. The temporal power spectrum of the photocurrent from the optical spatial filter illustrates the direct influence of the speckle statistics on the sensor performance. Experimentally, a significant increase in signal level is obtained when illuminating the target with a structured field distribution, rather than using a single Gaussian beam. Moreover, the option of improving the signal quality by manipulating the target illumination will be discussed theoretically and experimentally.

Speckle dynamics for intensity-modulated illumination

We analyze the dynamics of laser speckle patterns, designed for sensing with a receiver, based on spatial filtering. The speckle translation arises after free-space propagation of light scattered from nonspecular surfaces of a solid object in motion. The speckle pattern is manipulated by modulating the intensity of the coherent light, illuminating the target. The space-time normalized cross covariance of speckle patterns incident on the spatial sensor is calculated for the field distribution of three Gaussian beams having arbitrary directions and separations when incident on the target. The modulation of the intensity distribution at the target introduce a higher spatial frequency component in the speckle pattern. The theoretical analysis provides the statistical parameters for both the speckles and the higher spatial frequency component. The analysis reveals that the speckles and the higher spatial frequency component do not necessarily translate as a rigid structure. The theoretical findings are supported by measurements.

Optical kicked system exhibiting localization in the spatial frequency domain

An optical kicked system with free-space light propagation along a sequence of equally spaced thin phase gratings is presented and investigated. We show, to our knowledge for the first time in optics, the occurrence of the localization effect in the spatial frequency domain, which suppresses the spreading of diffraction orders formed by the repeated modulation by the gratings of the propagating wave. Resonances and antiresonances of the optical system are described and are shown to be related to the Talbot effect. The system is similar in some aspects to the quantum kicked rotor, which is the standard system in the theoretical studies of the suppression of classical (corresponding to Newtonian mechanics) chaos by interference effects. Our experimental verification was done in a specific regime, where the grating spacing was near odd multiples of half the Talbot length. It is shown that this corresponds to the vicinity of antiresonance in the kicked system. The crucial alignment of the gratings in-phase positioning in the experiment was based on a diffraction elimination property at antiresonance. In the present study we obtain new theoretical and experimental results concerning the localization behavior in the vicinity of antiresonance. The behavior in this regime is related to that of electronic motion in incommensurate potentials, a subject that was extensively studied in condensed matter physics.

Far zone spectral shifts in light propagation from the exit face of a few-mode fibre waveguide guiding the frequency-dependent linearly polarized modes

Far zone spectral shifts, including free space propagation of light from a planar secondary, partially coherent source represented by the exit face of a few-mode fibre waveguide, are investigated in the paraxial regime by using frequency-dependent linearly polarized (LP) modes guided by the fibre waveguide. The origin of the far zone blue or red spectral shift of individual frequency-dependent LP modes, as well as of their superposition at the particular observation point, is clarified. In particular, the dependence of the wavelength shifts of spectra on the position of the observation point in the far zone plane and the primary source linewidth is studied for the two-mode, weakly guiding, step-index fibre waveguide.

Coherence of Light at the Output of a Fibre Waveguide Analysed in the Space-Frequency Domain

Abstract Coherence of light in the space-frequency domain is investigated at the exit face of a weakly guiding fibre waveguide as well as in its far zone by using the coherent mode representation. Two limiting cases of fibre waveguide excitation by cross-spectrally pure, quasimonochromatic, spatially incoherent and coherent sources are considered in the evaluation of spectral changes occurring in the free space propagation of light in the paraxial regime from the exit face of the fibre waveguide to its far zone. In particular, the blue and the red shifts as well as the spectra modifications in the far zone of two-mode, weakly guiding, step-index fibre waveguide are presented for both spatially incoherent and coherent exciting sources. A frequency dependence of the modes is also considered which leads to a substantial reduction in spectral shifts. Moreover, it is revealed that a variable spectral modulation is present in the case of the fibre waveguide excitation by a spatially coherent source.