Otozo Fukumitsu

Propagation of light beams beyond the paraxial approximation

Light beams extending beyond the paraxial region are investigated by the correction scheme of Lax et al. [ Phys. Rev. A11, 1365 ( 1975)] All higher-order corrections for the Laguerre–Gaussian and Hermite–Gaussian beams are obtained explicity. It is shown that the corrections for both Gaussian beams are described in the same form. When the field distribution of a light beam is specified at some transverse plane, we can deal with its propagation beyond the paraxial approximation by superposing the corrected beams.

Scattering of a Hermite–Gaussian beam mode by parallel dielectric circular cylinders

The scattering of a two-dimensional conventional beam mode by an arbitrary configuration of parallel circular cylinders is considered. A relation is derived between a real-argument Hermite–Gaussian beam mode and the fields excited by multipoles with complex source points. Using this relation, the scattered field by a beam mode is represented in terms of those scattered by a finite number of multipole fields. The total scattered fields are examined numerically for a Gaussian beam incident upon an array of eight cylinders.

Signal-to-noise ratio in optical heterodyne detection for Gaussian fields.

The signal-to-noise ratio of optical heterodyne detection is discussed for Gaussian fields. The ratio of the aperture radius a of the detector to the smallest spot size w(s) of the signal has serious effects on the SNR. The conditions that maximize the SNR are obtained for a given signal or local oscillator field. The effects of field mismatching or misalignment are also discussed. Numerical analyses show that when such mismatching or misalignment exists, the spot size of the local oscillator field should be larger than that of the signal with a ratio of a/w(s) approximately 1.2. Then the heterodyne efficiency is rather insensitive to the errors and yet takes reasonable values (above 0.8).

Asymptotic representation of the boundary-diffraction wave for a three-dimensional Gaussian beam incident upon a Kirchhoff half-screen

Diffraction of a Gaussian beam with a circular spot size normally incident upon a Kirchhoff half-screen is investigated based on the boundary-diffraction-wave (BDW) theory. The evaluation of the boundary-diffraction wave by the steepest-descent method yields the uniform asymptotic representation of the total diffracted field consisting of the geometrical-optics and diffraction components. The use of complex rays to construct the diffraction component is also shown by applying the geometrical theory of diffraction (GTD) to the problem. Comparison of the representation of the diffraction component by the BDW theory with that by the GTD gives the diffraction coefficient for the Gaussian beam that ensures the continuity of the diffracted field at the shadow boundary.

Diffraction of a Gaussian beam through a finite aperture lens and the resulting heterodyne efficiency

The diffraction field of a Gaussian beam through a finite aperture lens is investigated. The field distributions at the position where the field is most focused are shown and compared with those obtained by an infinite aperture lens. The results are applied to an optical heterodyne detection system with Gaussian fields, and the optimum conditions that maximize the heterodyne efficiency are obtained numerically.

Asymptotic representation of the boundary diffraction wave for a Gaussian beam incident on a circular aperture

The diffraction of a Gaussian beam normally incident on a circular aperture is investigated by using the boundary-diffraction-wave theory. With the help of the steepest-descent method, an asymptotic representation of the boundary diffraction wave is obtained. The diffracted field, which is the sum of the geometrical-optics component and the diffraction component, is shown to be continuous at the shadow boundary. The diffraction coefficient is compared with that used in Keller’s geometrical theory of diffraction for a plane wave. The error of the asymptotic approximation is also estimated.

Transmission of an Optical Wave Beam Through a System of Two Aperture Stops

The beam-mode expansion method used in the discussions of the diffraction of a Gaussian wave beam through an aperture is applied to a system of two circular or square aperture stops, and the analytical expressions of the power transmission and conversion coefficients of a fundamental mode through the system are obtained. By using these expressions, the optimum incidence conditions that maximize the power transmission coefficient of the fundamental mode can be known. These conditions coincide formally with those obtained by Kogelnik and Yariv for an incident wave having a prolate spheroidal-wave function distribution. Both circular and square geometries can be analyzed in the same way.

Use of complex ray theory in the design of a laser diode module

Use of complex ray theory in the design of optical devices with a thick lens is presented. As a thick lens consists of convex and concave interfaces, the transmission characteristics of an optical beam through a curved dielectric interface is investigated using complex ray theory and the mode expansion method. As an example, this procedure is applied to the design of a laser diode module with a spherical lens.

Application of the Beam Mode Expansion to the Analysis of Noise Reduction Structure (Short Papers)

The beam mode expansion method used to discuss the distraction problem by an aperture is applied to the analysis of the noise reduction structure consisting of two aperture stops. The incident field is a fundamental wave beam whose amplitude distribution is Gaussian. The transmitted field through the structure can be represented as a sum of beam mode functions and is regarded as a signal. The noise which is originated from the spontaneous emission is added to the incident Gaussian wave beam. The signal-to-noise ratio (SNR) in the output is discussed and optimum conditions are obtained numerically.