Unified operator approach for deriving Hermite-Gaussian and Laguerre-Gaussian laser modes

A unified operator approach is described for deriving Hermite-Gaussian and Laguerre-Gaussian laser beams by using as a starting point a plane-wave-spectrum representation of the electromagnetic field. We show that by using the plane-wave representation of the fundamental Gaussian mode as a seed function, all higher-order beam modes can be derived by acting with differential operators on this fundamental solution. The approach presented can be easily generalized to nonparaxial situations and to include vector effects of the electromagnetic field.     

Nonlinear modes in optical fibers

It is shown that the electromagnetic field generated in an optical fiber operating in a nonlinear regime has the form of nonlinear guided modes—cnoidal (periodic) waves which transform into monochromatic fiber modes in the linear operating regime. The cnoidal modes are generated due to nonlinear polarization effects in the dielectric medium. These effects can be described by equations with sinusoidal nonlinearity.     

Acoustic modes in optical fiberlike waveguides

A perturbation analysis of guided and leaky modes in fiber acoustic waveguides with core and cladding parameters that are slightly different is presented. The perturbing parameter is the shear-velocity difference between the core and cladding material epsilon(s). Acoustic fields and eigenvalues are expanded in power series of epsilon (s)(1/2) for radial and flexural modes and in powers of epsilon(3) for torsional modes. Expansion of leaky longitudinal modes is also in terms of epsilon(s), but the nature of perturbation analysis for these modes is somewhat different from that of guided modes. Zero-order solutions for all types of modes are obtained, and some important higher-order effects are discussed. Common features of optical and acoustic modes in weakly guiding fibers are addressed. It is shown that with respect to zero-order solutions of guided modes, optical and acoustic fibers have identical propagation characteristics. Exact and zero-order propagation characteristics for several lower-order shear-type modes are calculated and compared.     

Propagating modes in gain-guided optical fibers

Optical fibers in which gain-guiding effects are significant or even dominant compared with conventional index guiding may become of practical interest for future high-power single-mode fiber lasers. I derive the propagation characteristics of symmetrical slab waveguides and cylindrical optical fibers having arbitrary amounts of mixed gain and index guiding, assuming a single uniform transverse profile for both the gain and the refractive-index steps. Optical fibers of this type are best characterized by using a complex-valued v-squared parameter in place of the real-valued v parameter commonly used to describe conventional index-guided optical fibers.     

Propagation of optical vortices embedded with multiple wavefront singularities

Optical vortices with the embedded wavefront singularities have attracted intensive attentions in many branches of modern physics, due to their important applications in optical tweezers, quantum entangles, optical testing, atmospheric propagations, etc. In this paper, optical vortices are generated by new types of custom designed wavefronts and their propagation in free-space is reported. Huygens–Fresnel diffraction integral is directly solved using the Gauss–Legendre quadrature method to estimate the diffraction pattern at some arbitrary plane. The variation of vorticity is demonstrated under diffraction. Evolution of phase singularities in wavefronts as the wavefront propagate is predicted for various near field distances. Simulations reveal that the exchange of the nature of topological charge occurs at a finite distance. Experimentally, the wavefronts have been generated using the phase-only spatial light modulator and their far-field diffraction patterns are recorded. The experimental result has been validated with the numerical simulation.     

Diffractive optical Hough transform implemented with phase singularities

The conventional Hough transform is implemented with a computer-generated hologram. The transmission function of the computer-generated hologram is computed with an extension of Bryngdahl's technique, which incorporates branch-point phase singularities. With this implementation it is shown that the branch-point technique can be used to implement point transforms successfully with an implicit transformation equation such as the Hough transform. This is done first by expression of the implicit transform in terms of several explicit transforms. After computation of the complex-valued transmission functions of the explicit transform, the functions are added together to form the transmission function for the implicit transform. Results are obtained by computation of Fresnel diffraction patterns of the Hough-transform computer-generated hologram, illuminated by different input images.     

Conversion of Hermite-Gaussian and Laguerre-Gaussian beams in an astigmatic optical system. 1. Experiment

The workings of a mode converter providing energy-effective conversion of an Hermite-Gaussian beam to a Laguerre-Gaussian beam and vice versa are analyzed experimentally. The converter is an astigmatic Fourier transformer consisting of a system of two cylindrical lenses with perpendicular principal planes lying between two spherical lenses. It is shown that this device is less sensitive to the mating of the astigmatic elements. Pis’ma Zh. Tekh. Fiz. 24, 68–73 (September 12, 1998)     

Propagation of Laguerre-Gaussian and elegant Laguerre-Gaussian beams in apertured fractional Hankel transform systems

On the basis of the fact that a hard-edged-aperture function can be expanded into a finite sum of complex Gaussian functions, approximate analytical expressions for the output field distribution of a Laguerre-Gaussian beam and an elegant Laguerre-Gaussian beam passing through apertured fractional Hankel transform systems are derived. Some numerical simulation comparisons are done, by using the approximate analytical formulas and diffraction integral formulas, and it is shown that our method can significantly improve the numerical calculation efficiency.     

Experimental study of a perforated coaxial exciter of high-order modes in a barrel-shaped cavity

A method proposed previously [1], according to which high-order modes in a barrel-shaped cavity are selectively excited using a coaxial waveguide with a double periodic perforation of the wall, has been experimentally realized. A rotating H₁₁ waveguide mode has been converted into a rotating H₅₃₁ eigenmode with a conversion efficiency of about 98%.     

Characterization of surface-plasmon modes in metal-clad optical waveguides

Finite-element analysis, based on the vector H-field formulation and incorporating the perturbation technique, is used to calculate the complex propagation characteristics of metal-coated dielectric waveguides. The propagation and attenuation characteristics of the surface-plasmon modes at the metal/dielectric interfaces are presented. The effects on the optical properties of metal-clad optical fibers with infinite and finite cladding thickness and the formation of the supermodes due to the coupling between the surface-plasmon modes in the presence of different surrounding materials are also investigated.     

Quantization of coupled modes propagation in integrated optical waveguides

Abstract

A quantum mechanical analysis of the propagation of coupled modes in integrated optical waveguides is given. The modal orthonormalization property on a cross-section of an optical waveguide, the vector structure of the guided optical modes and the reversal-time symmetry are taken into account to derive the quantum momentum operator and Heisenberg's equations giving a quantum-consistent formulation of the coupled mode propagation as a function of forward and backward creation and annihilation operators.     

一种离轴使用的同轴三反射系统的设计和装调

本文设计了一种视场角为3.的离轴使用的同轴三反射系统,并从理论上分析了焦平面如何离焦补偿像差、反射镜倾斜和偏心之间的补偿关系.通过采取离焦、折镜的平动或转动、反射镜本身的偏心和倾斜相互补偿的方法,来补偿反射镜的装调误差.事实证明,比普通离轴三反射系统的装调容易实现,精确度高.     

Axial interface optical phonon modes in a double-nanoshell system

Within the framework of the dielectric continuum (DC) model, we analyze the axial interface optical phonon modes in a double system of nanoshells. This system is constituted by two identical equidistant nanoshells which are embedded in an insulating medium. To illustrate our results, typical II-VI semiconductors are used as constitutive polar materials of the nanoshells. Resolution of Laplace's equation in bispherical coordinates for the potentials derived from the interface vibration modes is made. By imposing the usual electrostatic boundary conditions at the surfaces of the two-nanoshell system, recursion relations for the coefficients appearing in the potentials are obtained, which entails infinite matrices. The problem of deriving the interface frequencies is reduced to the eigenvalue problem on infinite matrices. A truncating method for these matrices is used to obtain the interface phonon branches. Dependences of the interface frequencies on the ratio of inter-nanoshell separation to core size are obtained for different systems with several values of nanoshell interdistance. Effects due to the change of shell and embedding materials are also investigated in interface phonon modes.     

Introducing secure modes of operation for optical encryption

We analyze optical encryption systems using the techniques of conventional cryptography. All conventional block encryption algorithms are vulnerable to attack, and often they employ secure modes of operation as one way to increase security. We introduce the concept of conventional secure modes to optical encryption and analyze the results in the context of known conventional and optical attacks. We consider only the optical system "double random phase encoding," which forms the basis for a large number of optical encryption, watermarking, and multiplexing systems. We consider all attacks proposed to date in one particular scenario. We analyze only the mathematical algorithms themselves and do not consider the additional security that arises from employing these algorithms in physical optical systems.     

Nonlinear optical interactions of laser modes in quantum cascade lasers

We overview the results of recent experimental and theoretical studies of nonlinear dynamics of mid-infrared quantum cascade lasers (QCLs) associated with nonlinear interactions of laser modes. Particular attention is paid to phase-sensitive nonlinear mode mixing which turns out to be quite prominent in QCLs of different kinds and which gives rise to frequency and phase locking of laser modes. Nonlinear phase coupling of laser modes in QCLs leads to a variety of ultrafast and coherent phenomena: synchronization of transverse modes, beam steering, the RNGH multimode instability, and generation of mode-locked ultrashort pulses.     

Potential and vortex features of optical speckle fields and visualization of wave-front singularities

The feasibility of noninterferometric methods to measure phase distribution in a laser beam cross section for visualization of the vortex dislocations of an optical speckle-field wave front is analyzed. Peculiarities of the phase retrieved from the measured intensity distribution (the phase problem in optics) and from the wave-front slopes measured by a Hartmann sensor are discussed. A concept of the vortex and the potential parts of the phase is introduced. An analytic formula to retrieve the potential phase from the measured intensity has been obtained. We show that the considered means of measurements allow the positions of the dislocation centers to be sensed and the spatial configuration of the intensity zero lines to be reconstructed.     

Diffractive optical elements for intra-cavity beam-shaping of laser modes

Abstract

Diffractive optical elements (DOE) are applied as intra-cavity mode selection devices for customizing the fundamental mode of laser resonators for high power laser systems. Using a phase-conjugating mode selecting element (MSE) in a laser oscillator, we are able to produce a good approximation to a super-Gaussian mode with a near flat intensity profile. This offers higher energy extraction from any following laser amplifiers compared to an unmodified Gaussian TEM₀₀ mode. Two different designs for operation in a 1 m cavity length Nd:YAG master oscillator are presented. Both designs are surface relief phase elements fabricated in fused silica using photolithography with reactive-ion etching to produce 16 level elements for use in transmission. One element is designed to replace the cavity end mirror, while the other stands off an arbitrary distance from the end mirror. A novel iterated design for these transmissive elements is introduced. Numerical results and experimental measurements are presented and discussed.     

Coupling characteristics of cladding modes in tilted optical fiber bragg gratings

We have studied both theoretically and experimentally the effect of grating tilting on the coupling between the fundamental core mode and the cladding modes in an optical fiber Bragg grating. The coupling is shown to be very sensitive on the tilting angle. It is also shown that tilting angle has to be minimized in fibers with designs to suppress the coupling between the fundamental core mode and the cladding modes. We have also studied the single, strong loss peak accompanying the Bragg reflection peak in depressed-cladding fibers, thus showing a good agreement between behavior that is measured and that is predicted theoretically.     

Hyperspectral nanoscale imaging on dielectric substrates with coaxial optical antenna scan probes

We have demonstrated hyperspectral tip-enhanced Raman imaging on dielectric substrates using linearly polarized light and nanofabricated coaxial antenna tips. A full Raman spectrum was acquired at each pixel of a 256 by 256 pixel contact-mode atomic force microscope image of carbon nanotubes grown on a fused silica microscope coverslip, allowing D and G mode intensity and D-mode peak shifts to be measured with ～20 nm spatial resolution. Tip enhancement was sufficient to acquire useful Raman spectra in 50-100 ms. Coaxial scan probes combine the efficiency and enhanced, ultralocalized optical fields of plasmonically coupled antennae with the superior topographical imaging properties of sharp metal tips. The yield of the coaxial tip fabrication process is close to 100%, and the tips are sufficiently durable to support hours of contact-mode force microscope imaging. Our coaxial probes avoid the limitations associated with the "gap-mode" imaging geometry used in most tip-enhanced Raman studies to date, where a sharp metal tip is held ～1 nm above a metallic substrate with the sample located in the gap.