Fraunhofer diffraction of laser beams with amplitude modulations and phase fluctuations by a lens with a central obscure aperture

Abstract

By using the statistical-optics model and generalized Huygens-Fresnel diffraction integral, Fraunhofer diffraction of high-power laser beams with amplitude modulations (AMs) and phase fluctuations (PFs) focused by a lens with a central obscure aperture has been studied. Detailed numerical calculation results have been given, showing the dependence of the intensity distribution at the geometrical focal position and the power (energy) focus-ability of high-power laser beams not only on the obscure ratio, but also on the truncation parameter, AMs and PFs of beams.     

Rigorous theory of the diffraction of Gaussian beams by finite gratings: TE polarization

A rigorous modal theory for the diffraction of Gaussian beams from N equally spaced slits (finite grating) in a planar perfectly conducting thin screen is presented. The case of normal incidence and TE polarization state is considered; i.e., the electric field is parallel to the slits. The characteristics of the far-field diffraction patterns, the transmission coefficient, and the normally diffracted energy as a function of several optogeometrical parameters are analyzed within the so-called vectorial region, where the polarization effects are important. The diffraction pattern of an aperiodic grating is also considered. In addition, one diffraction property known to be valid in the scalar region is generalized to the vectorial region: the existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits. The classical grating equation is tested for incident Gaussian beams under several conditions.     

Orthogonal planar laser polarization spectroscopy

Planar laser polarization spectroscopy has recently been used to image the hydroxyl radical in combustion for small intersection angles of pump and probe beams. We report an experimental configuration that allows planar laser polarization imaging for perpendicular intersection of pump and probe beams. We demonstrate what to our knowledge is the first planar laser polarization spectroscopy imaging at a 90 degree intersection of pump and probe beams for both linearly and circularly polarized pump beams.     

Intensity limitation for a self-focusing femtosecond laser pulse propagating in a medium with cubic nonlinearity

The self-focusing of an axisymmetric beam propagating in a cubically nonlinear medium has been studied by computer simulation with allowance for the temporal dispersion of the nonlinear response, which is manifested for femtosecond laser pulses. It shown that, depending on the ratio of the medium length and the diffraction length, the dispersion of the nonlinear response can lead either to limitation of the intensity growth rate in the nonlinear focus or its absence (for weakly diffracting beams), to an increase in the range of the nonlinear focus formation (for beams with a diffraction length 2.5–25 times the medium length), or to a decrease in this range (for beams with a diffraction length approximately equal to or shorter than the medium length). These phenomena are related to the dependence of the group velocity of pulse propagation on its intensity.     

Scalar diffraction field calculation from curved surfaces via Gaussian beam decomposition

We introduce a local signal decomposition method for the analysis of three-dimensional (3D) diffraction fields involving curved surfaces. We decompose a given field on a two-dimensional curved surface into a sum of properly shifted and modulated Gaussian-shaped elementary signals. Then we write the 3D diffraction field as a sum of Gaussian beams, each of which corresponds to a modulated Gaussian window function on the curved surface. The Gaussian beams are propagated according to a derived approximate expression that is based on the Rayleigh-Sommerfeld diffraction model. We assume that the given curved surface is smooth enough that the Gaussian window functions on it can be treated as written on planar patches. For the surfaces that satisfy this assumption, the simulation results show that the proposed method produces quite accurate 3D field solutions.     

Gaussian beams in hollow metal waveguides: experiment

Gaussian beams have been widely used for propagating electromagnetic waves in free space and in certain other optical systems. It has been suggested that recurring forms of such beams might also be useful for propagation in planar or rectangular metal waveguides. Experimental verification of the recurrence of the Gaussian field distribution in metal waveguides is reported here.     

Microspectrometer with slab-waveguide transmission gratings

An integrated transmission diffraction grating in a planar optical waveguide is presented for broadband spectroscopic analysis of liquids and gases. Silicon oxynitride slab waveguides on silicon substrates with low optical loss in the visible range are combined with a phase transmission grating exhibiting a blaze effect at 500 nm to achieve high-efficiency diffraction and high spectral dispersion. Collimated white light propagates through the waveguide and couples into air at a stepped formed planar grating. The beams of each adjacent step interfere constructively at the focal line of a cylindrical lens, its focal line positioned perpendicular to the waveguide plane. We used a common silicon photodiode array to detect the spectral data. Our approach is to develop a compact and economic spectrometer without moving parts that can be applied for UV-visible analysis and near-infrared industrial process control as well.     

The Beam Ratio in Volume Holography

Abstract

Holograms for potential use as optical interconnects in micro-electronic circuits can be recorded optically by either sequential or simultaneous exposures. It is desirable that these holograms have the highest possible diffraction efficiency. In this paper, we investigate the role of the beam ratio, in both recording modes, in achieving the maximum diffraction efficiency. In the study to determine the optimum beam ratio that is needed in order to obtain the maximum diffraction efficiency on reconstruction, it is usually assumed that either the reference beam intensity, the total object beam intensity, or the average light intensity have been fixed and that the interference fringes have the highest theoretically possible contrast. According to the properties of volume phase holograms, we suggest that the total intensity of all the component beams should be the fixed parameter and that the main refractive index modulation should reach a maximum. Expressions are derived using these assumptions.     

Bowtie limited diffraction beams for low-sidelobe and large depthof field imaging

Limited diffraction beams such as Bessel beams and X waves have a large depth of field and thus could have many applications. However, these beams have higher sidelobes as compared to conventional focused beams in their focal planes. In this paper, a new class of limited diffraction beams is developed. These beams are termed bowtie limited diffraction beams because they have bowtie shapes in a plane perpendicular to the beam axis. To obtain pulse-echo images of low sidelobes and a large depth of field, a bowtie limited diffraction beam is used in transmission and its 90° rotated response (around the beam axis) is used in reception. Unlike the summation-subtraction method developed previously, this method does not reduce image frame rate or dynamic range of signals and is not motion sensitive. The theory of the bowtie limited diffraction beams is developed. Computer simulation of the theoretical beams under practical conditions, such as finite aperture, finite bandwidth, and causal excitation, is performed with the Rayleigh-Sommerfeld diffraction formula. The simulated beams are very close to those predicted analytically over a large depth of field     

Gaussian beams in hollow metal waveguides

Various families of Gaussian beams have been explored previously to represent the propagation of nearly plane electromagnetic waves in media having at most quadratic transverse variations of the index of refraction and the gain or loss in the vicinity of the beam. However, such beams cannot directly represent the wave solutions for propagation in planar or rectangular waveguides, and sinusoidal mode functions are more commonly used for such waveguides. On the other hand, it is also useful to consider the possibility of recurring Gaussian beams that have an approximately Gaussian transverse profile at certain distinct planes along the propagation path. It is shown here that under some conditions recurring Gaussian beams can describe wave propagation in hollow metal waveguides, and they can also lead to efficient coupling between the waveguide fields and free-space beams.     

A study of two-dimensional array transducers for limited diffraction beams

The newly developed limited diffraction beams such as the Bessel beams and X waves have a large depth of field and approximate depth-independent property. They have possible applications in medical imaging, color Doppler imaging, tissue characterization, and nondestructive evaluation of materials, and in other wave related physical branches such as electromagnetics and optics. However, limited diffraction beams are currently produced with an annular array transducer that has to be steered mechanically. In this paper, we study the feasibility of steering these beams with a two-dimensional array, and show that there will be almost no distortion of beams if the effective aperture reduction of the array is properly compensated so that the beams have a constant transverse profile as they are steered. In addition, methods for reducing the complexity of the electronic multiplexing of the array elements are proposed. We also investigate the influences of the interelement distance and the size of array elements on the sidelobes and grating lobes of limited diffraction beams as the beams are steered. They are similar to those previously reported for conventional beams.     

Designing limited diffraction beams

Theoretically, limited diffraction beams can only be produced with an infinite aperture. In practice, they can be closely approximated with a finite aperture over a large depth of field. Because of this property, these beams could have applications in medical imaging, tissue characterization, Doppler velocity estimation, and nondestructive evaluation (NDE) of materials, as well as other physics-related areas such as electromagnetics and optics. In this paper, a new method is developed to design limited diffraction beams of desired beam shapes within a finite aperture of interest. It uses previously discovered limited diffraction beams such as Bessel beams and X waves as basis functions, and constructs new beams with linear superpositions of the bases. To construct a new beam of a desired shape, coefficients of the basis functions in the linear superposition are chosen so that the difference between the new beam and a desired beam is minimized under the criterion of least-squares error within the aperture. This procedure is implemented by digitizing both the basis beams and desired beams in the aperture and solving a system of linear equations from its normal equation. The method is applied to several desired beams that are limited diffraction beams known previously. Results show that the designed beams and the desired beams are virtually identical. If the desired beams are not solutions to the wave equation, the designed beams are new limited diffraction beams that are similar in shapes to the desired beams. This suggests that the method may be a powerful and practical tool for developing new limited diffraction beams of desired properties.     

Diffraction-attenuation resistant beams: their higher-order versions and finite-aperture generations

Recently, a method for obtaining diffraction-attenuation resistant beams in absorbing media has been developed in terms of suitable superposition of ideal zero-order Bessel beams. In this work, we show that such beams keep their resistance to diffraction and absorption even when generated by finite apertures. Moreover, we shall extend the original method to allow a higher control over the transverse intensity profile of the beams. Although the method is developed for scalar fields, it can be applied to paraxial vector wave fields, as well. These new beams have many potential applications, such as in free-space optics, medical apparatus, remote sensing, and optical tweezers.     

An X wave transform

Limited diffraction beams such as X waves can propagate to an infinite distance without spreading if they are produced with an infinite aperture and energy. In practice, when the aperture and energy are finite, these beams have a large depth of field with only limited diffraction. Because of this property, limited diffraction beams could have applications in medical imaging, tissue characterization, blood flow velocity vector imaging, nondestructive evaluation of materials, communications, and other areas such as optics and electromagnetics. In this paper, a new transform, called X wave transform, is developed. In the transform, any well behaved solutions to the isotropic-homogeneous wave equation or limited diffraction beams can he expanded using X waves as basis functions. The coefficients of the expansions can be calculated with the properties that X waves are orthogonal. Examples are given to demonstrate the efficacy of the X wave transform. The X wave transform reveals an intrinsic relationship between any well behaved solutions to the wave equation and X waves, including limited diffraction beams. This provides a theoretical foundation to develop new limited diffraction beams or solutions to the wave equation that may have practical usefulness.     

Angular tolerant resonant grating filters under oblique incidence

Resonant grating filters have been proposed as a promising alternative to multilayer stacks for narrowband free-space filtering. The efficiency of such filters under normal incidence has been demonstrated. Unfortunately, under oblique incidence, the limited angular tolerance of the resonance forbids any filtering applications with use of standard collimated incident beams. Using a multimode planar waveguide and a bi-atom grating, we show how to increase the angular tolerance up to the divergence of standard beams (0.2 deg) without modifying the spectral bandwidth (0.1 nm), under any oblique angle of incidence.     

Cosmic Microwave Background Polarization Detector with High Efficiency, Broad Bandwidth, and Highly Symmetric Coupling to Transition Edge Sensor Bolometers

We describe a prototype detector system designed for precise measurements of Cosmic Microwave Background polarization. The design combines a quasi-optical polarization modulator, a metal feedhorn, a superconducting planar microwave circuit, and a pair of transition-edge sensor (TES) bolometers operating at <100 mK. The circular feedhorn produces highly symmetric beams with very low cross-polarization. The planar circuit preserves symmetry in coupling to bolometers measuring orthogonal polarizations. We implement the circuit with superconducting niobium transmission lines. Three-dimensional interfaces between the planar circuit and waveguides leading to feedhorn and backshort have been carefully designed with electromagnetic simulations. Power is thermalized in resistors and conducted to bolometers via normal electrons. Our system is designed for a 29–43 GHz signal band. We have tested individual circuit elements in this frequency range. Fabrication of a full single-pixel system is underway.      

The Spatial Coherence Properties of Gaussian Schell-model Beams

The transverse and longitudinal spatial coherence properties of the light beams generated by planar gaussian Schell-model sources are discussed. It is found that for all gaussian Schell-model beams the ratio of the transverse coherence length to the beam width remains invariant upon propagation. An examination of the longitudinal coherence for both on-axis and off-axis pairs of points indicates that the longitudinal coherence will not, in general, die out as the separation between the points is increased. Rather, the degree of longitudinal coherence will approach a finite (non-zero) value as long as the source contains a finite coherence area, regardless of how small this area may be. Gaussian quasihomogeneous beams are studied as a limiting case. The relation of the present work to the analysis of speckle size is briefly discussed.     

Observation of self-diffraction effect in acid blue 7 dye soaked gelatin films

Abstract

Permanent self-diffraction gratings are formed in red sensitive Acid blue 7 dye soaked gelatin films under illumination of an interference pattern by two linearly polarized beams from a He-Ne laser at 632.8 nm. Growth of the self-diffraction grating is monitored by measuring intensities of various diffraction orders. Systematic studies are carried out to investigate the influence of various parameters involved in diffraction efficiency of the grating such as time of exposure, concentration of dye in the gelatin-coated plate, intensity of interfering beams and intensity ratio of interfering beams. Efficient gratings with ten diffracted orders are formed. Several interesting observations are made by blocking one of the writing beams and an attempt is made to analyse these results.     

Producing bowtie limited diffraction beams with synthetic arrayexperiment

Limited diffraction beams have a large depth of field and could have applications in medical ultrasound and other wave related areas such as electromagnetics and optics. However, these beams have higher sidelobes than conventional focused beams at their focuses. Recently, a new type of beam, called bowtie limited diffraction beams, was developed. These beams can achieve both low sidelobes and a large depth of field in medical imaging. In this paper, the production of bowtie beams in water with a synthetic array experiment is reported. A broad-band PZT ceramic/polymer composite transducer of about 1 mm diameter and 2.5 MHz central frequency was scanned in a raster format and placed at the centers of elements of an equivalent two-dimensional array of 50 mm diameter aperture. A polyvinylidene fluoride (PVDF) needle hydrophone of 0.5 mm diameter was used to receive the waves produced by the transducer. Proper weighting functions were applied to the received signals to produce various beams. Results show that the bowtie beams produced with the synthetic array experiment are in good agreement with those derived from theory and obtained by computer simulations. The depth of field of these beams is about 216 mm and sidelobes of a tenth derivative bowtie X wave in pulse-echo imaging are about 30 dB lower than those of rotary symmetric limited diffraction beams such as the zeroth-order X wave discovered previously     

Broad band focusing and demultiplexing of in-plane propagating surface plasmons

On the basis of a novel phase modulation method by in-plane diffraction processes, a well-designed nanoarray on metal surface is proposed to realize a broad band focusing (bandwidth ～100 nm) and a demultiplexing element (resolution ～12 nm) of surface plasmon polariton (SPP) waves. Moreover, sublattice arrays are developed to achieve an improved demultiplexer and confocal SPP beams. The proposed scheme with implemented functionalities is designed totally in planar dimension, which is free of the SPP coupling process and indicates more practical application in photonic integrations.