Hanbury Brown-Twiss effect with electromagnetic waves.

The classic Hanbury Brown-Twiss experiment is analyzed in the space-frequency domain by taking into account the vectorial nature of the radiation. We show that as in scalar theory, the degree of electromagnetic coherence fully characterizes the fluctuations of the photoelectron currents when a random vector field with Gaussian statistics is incident onto the detectors. Interpretation of this result in terms of the modulations of optical intensity and polarization state in two-beam interference is discussed. We demonstrate that the degree of cross-polarization may generally diverge. We also evaluate the effects of the state of polarization on the correlations of intensity fluctuations in various circumstances.

Connection between electric and magnetic coherence in free electromagnetic fields.

We introduce quantitative measures for the description of the electric and magnetic coherence in a stationary, random electromagnetic field at two points, in a volume, and in the Fourier space. These quantities are applied to free electromagnetic fields, and several theorems regarding the relationship between the two types of coherences in such fields are established. Fields which are statistically homogeneous, and those which, in addition, are statistically isotropic are considered separately. Furthermore, the connection between the electric and magnetic coherence is exemplified for some specific statistically homogeneous fields.

Universality of electromagnetic-field correlations within homogeneous and isotropic sources.

We investigate the structure of second-order correlations in electromagnetic fields produced by statistically stationary, homogeneous, and isotropic current distributions. We show that the coherence properties of such fields within a low-loss or nondissipative medium do not depend on the source characteristics, but are solely determined by the propagation properties, and that the degree of coherence of the field is given by the sinc law. Our analysis reproduces the known results for blackbody fields, but it applies to a wider class of sources, not necessarily in thermal equilibrium. We discuss the physics behind the universal behavior of the correlations by comparing the results with those obtained by an electromagnetic plane-wave model.

Degree of polarization for optical near fields.

We investigate an extension to the concept of degree of polarization that applies to arbitrary electromagnetic fields, i.e., fields whose wave fronts are not necessarily planar. The approach makes use of generalized spectral Stokes parameters that appear as coefficients, when the full 3 x 3 spectral coherence matrix is expanded in terms of the Gell-Mann matrices. By defining the degree of polarization in terms of these parameters in a manner analogous to the conventional planar-field case, we are led to a formula that consists of scalar invariants of the spectral coherence matrix only. We show that attractive physical insight is gained by expressing the three-dimensional degree of polarization explicitly with the help of the correlations between the three orthogonal spectral components of the electric field. Furthermore, we discuss the fundamental differences in characterizing the polarization state of a field by employing either the two- or the three-dimensional coherence-matrix formalism. The extension of the concept of the degree of polarization to include electromagnetic fields having structures of arbitrary form is expected to be particularly useful, for example, in near-field optics.

Radiation efficiency of partially coherent electromagnetic beams.

We present a general definition of the radiation efficiency of stationary electromagnetic fields and prove that it is bounded between zero and unity for beams of any state of coherence and polarization. The radiation efficiency may be interpreted as a measure of how directed the radiated fields are, and therefore it can be used to assess the allowed spatial coherence and intensity variations across a beam. We consider a class of partially coherent electromagnetic fields that were recently introduced in the literature and evaluate the radiation efficiencies for two particular examples, namely, the azimuthally polarized symmetric beams and the dipolar beams that are nearly linearly polarized in the central region. The results show that the radiation efficiency is fairly insensitive to the state of polarization and that it differs appreciably from unity for only small values of source and correlation widths.

Eye-safe actively Q-switched microchip laser with an electro-absorbing semiconductor modulator.

We present what we believe to be the first actively Q -switched monolithic microchip laser with a wavelength of 1.55 microm that uses an electro-absorbing semiconductor modulator. At an absorbed pump power of 130 mW and a switching voltage of 2.2 V, the laser produces 470-nJ pulses at a repetition rate of 10 kHz. The output is a stable single longitudinal mode with a center wavelength of 1.553 microm, and the transverse beam profile is close to an ideal Gaussian, with an M(2) value of 1.15.

Synthesis of diffractive axicons for partially coherent light based on asymptotic wave theory.

A general, noniterative method for designing diffractive axicons is derived. This new technique clarifies the earlier phenomenological design principle that was used for coherent light and extends it to the domain of partial coherence. The approach is based on the method of stationary phase in fluctuating diffracted wave fields, and it applies to arbitrary axially symmetric radiation of the Schell-model type. It is shown that the general design equation can be solved numerically, in a straightforward way, for any reasonable illumination and image specifications.

Canonical perturbative approach to nonlinear systems with application to optical waves in layered Kerr media.

We investigate electromagnetic wave reflection and propagation in layered Kerr structures by introducing a method based on the application of canonical perturbation theory to fields in nonlinear media. Via the Hamilton-Jacobi formalism of classical mechanics, the waves in linear layers are expressed with constant canonical variables. The nonlinearity is treated as a small perturbation that modifies the constant invariants. We explicitly evaluate the nonlinear fields correct to first order by perturbation and compare the results to a rigorous nonlinear thin-layer model. Both polarizations, TE and TM, are considered separately. An exact quadrature solution of the nonlinear field in TM polarization is derived. We show that with weak nonlinearities the perturbative technique yields simple and accurate analytical expressions for the nonlinear fields. The results give physical insight into the use of nonlinear media for controlling the scattered fields in layered structures.

A reciprocity inequality for Gaussian Schell-model beams and some of its consequences.

A reciprocity inequality is derived, involving the effective size of a planar, secondary, Gaussian Schell-model source and the effective angular spread of the beam that the source generates. The analysis is shown to imply that a fully spatially coherent source of that class (which generates the lowest-order Hermite-Gaussian laser mode) has certain minimal properties.

Conoscopic interferometry of surface-acoustic-wave substrate crystals.

Conoscopic interferometry is applied for determining the crystal orientation of lithium niobate and other commonly employed substrate wafers for integrated-optic and surface-acoustic-wave devices. The method is particularly applicable for detecting the orientation of the optic axes of the strongly birefringent niobate but is less sensitive for lithium tantalate or quartz. Conoscopic interference is a low-cost and easy-to-use method that is especially suitable for laboratory usage.

Design of diffractive axicons for partially coherent light.

We propose a novel method of designing diffractive axicons for use in spatially partially coherent illumination. The design procedure is based on the results obtained by the stationary-phase method. The technique leads to a coherence-dependent differential equation with appropriate boundary conditions for the axicon phase function. We demonstrate the method with annular-aperture axicons generating extended focal line segments of uniform on-axis intensity.

SAW diffraction using the thin-element decomposition method.

We adapt the angular spectrum of plane waves (ASPW) decomposition to numerical simulations of the diffraction of surface-acoustic waves (SAWs) on anisotropic model substrate, such as YZ lithium niobate. We utilize the thin-element decomposition (TED) method, appropriately modified for an anisotropic substrate; we also introduce a novel "average-wavenumber" variation of this scheme; these are numerically found to be mutually consistent. We apply the TED method to simulate wave propagation both in infinite periodic structures of metallized gratings and also in finite gratings. We demonstrate that the ASPW provides a convenient and numerically fast tool for precise diffraction calculations in practical SAW devices which also display structural variations in the lateral direction, perpendicular to the principal direction of wave propagation. Additionally, we compare the present TED method to waveguide theory in an analysis of the role of SAW reflections from the electrodes.

Decrease in spatial coherence of light propagating in free space.

It is shown that a highly spatially incoherent light distribution may be generated from a highly coherent one on propagation in free space. This result essentially demonstrates that there exists an inverse of a classic result of optical coherence theory, namely, the van Cittert-Zernike theorem. The analysis also indicates that the technique of phase conjugation may be used to reverse changes in the coherence properties of light, at least those which are generated on propagation in free space.

Radiometric description of intensity and coherence in generalized holographic axicon images.

The characteristics of extended-range focal-line images generated in partially coherent light by annular-aperture logarithmic axicons are analyzed in terms of a certain generalized radiometric model. This radiometric description, which makes use of radiance propagation along geometric rays, is valid in the asymptotic short-wavelength limit, and it yields both the spectral density and the spatial coherence distributions of the images. The radio metrically obtained values on the image axis and in transverse planes are assessed against direct partially coherent wave-theoretical calculations. It is shown that the radiometric technique produces remarkably accurate results for the intensity and the spatial coherence profiles. Compared with diffraction calculations, the radiometric method is much faster, especially in conditions of relatively incoherent illumination.

Relationships between the complex degrees of coherence in the space-time and in the space-frequency domains.

A relationship is established between two correlation coefficients (complex degrees of coherence) frequently used in the theory of partially coherent optical fields. One of them characterizes correlation in the space-time domain, the other in the space-frequency domain. Some relations obtained previously by ad hoc methods are shown to readily follow from our general formula.

Reconstruction of optical-source profiles from fixed-baseline two-pinhole spectral measurements.

Source masking by a cosine amplitude grating is shown to render possible the reconstruction of the intensity distribution associated with globally incoherent optical sources from spectral measurements performed with a Young's two-pinhole fixed-baseline interferometer. The effect of the mask is to map the low spatial frequencies of the source intensity onto accessible optical frequencies. The permissible parameter regimes are studied, and the feasibility of the technique is demonstrated by numerical simulations.

Programmable optical interconnections by multilevel synthetic acousto-optic holograms.

Reconfigurable high-fidelity, high-efficiency weighted optical interconnection patterns are demonstrated for the first time to our knowledge with the aid of optimized multilevel phase gratings achieved electronically as phase-modulated sinusoidal refractive-index variations propagating in an acousto-optic Bragg cell.

Propagation of a generalized radiance in paraxial optical systems.

It is demonstrated that the symmetric form of the generalized radiance remains invariant on propagation along rays through lossless paraxial optical systems described by their ABCD matrices. This result is derived directly on the basis of the cascaded Huygens-Fresnel integral, and it holds for all states of the field coherence. When combined with quasihomogeneous sources the result leads to a fully consistent wave theory of radiometry with partially coherent light.

Realization of general nondiffracting beams with computer-generated holograms.

A new class of solutions to the scalar wave equation was introduced recently that represents transversely localized but totally nondiffracting fields. We show by the method of stationary phase that any of these wave fields can be realized approximately with a laser and a single computer-generated hologram. We briefly discuss various techniques for coding and fabrication of the required hologram and the associated diffraction efficiencies. Using both binary-amplitude and four-level phase holograms, we demonstrate experimentally the formation of arbitrary-order Bessel beams and rotationally nonsymmetric beams.

Coherence theoretic algorithm to determine the transverse-mode structure of lasers.

We introduce an algorithm to determine the relative modal weights of a laser beam with Hermite-Gaussian modes. The method is based on coherence theory of stable resonator modes in the space-frequency domain. Numerical simulations are presented that show that the algorithm is not sensitive to moderate levels of noise.