Toshio Makimoto

Normal‐mode analysis of anisotropic and gyrotropic thin‐film waveguides for integrated optics

This paper is concerned with thin‐film optical waveguides using anisotropic and gyrotropic materials, which may play an important role in the field of integrated optics. As a fundamental problem on such waveguides, normal (propagating) modes are analyzed here by the Rayleigh‐Ritz variational technique. The analysis can be interpreted directly in terms of coupling of normal modes of the basic guide with simpler material parameters. Results are placed in the form of a matrix eigenvalue problem suitable for computer calculation, whose eigenvalues and eigenvectors lead to propagation constants and field expansion coefficients, respectively. Characteristics of anisotropic guides are discussed and compared with those of conventional isotropic guides. As a typical application TE↔TM mode converters are analyzed in some detail and numerical examples are presented.

Circuit theory for a class of anisotropic and gyrotropic thin‐film optical waveguides and design of nonreciprocal devices for integrated optics

A circuit‐theoretic treatment is presented for thin‐film optical waveguides using a class of real anisotropic and gyrotropic materials. The analysis is based on the two‐mode approximation in normal‐mode theory. The terminal behavior of those guides is described by the 2 × 2 transmission matrix and expressions for matrix elements of six systems that are introduced as canonical elements in circuit synthesis are derived. Properties of canonical elements are discussed with particular attention on their reciprocity. Using the transmission matrix, we can treat the design of thin‐film optical devices by a simple matrix operation familiar in conventional transmission‐line circuit synthesis. As a typical application the design of various nonreciprocal integrated‐optical devices is treated in detail. The desired response is synthesized by cascading selected canonical elements in an appropriate order. Examples include the gyrator, unidirectional mode converter, differential phase shifter, isolator, and circulator.

Energy propagation properties of piezoelectric surface waves on cubic crystals

The wave surface of piezoelectric surface waves propagating on the Z‐cut metal‐coated surface of a semi‐infinite cubic crystal (class 43m or 23) is calculated from the envelope of equiphase planes using the Lagrange multiplier method. It is found that the wave surface shows the cusps if the crystal is in the Cu region (c12≳c11−2c44) and has strong anisotropy.

Design considerations for nonreciprocal integrated optical devices

This paper is concerned with the design of nonreciprocal thin‐film optical devices containing gyrotropic and anisotropic materials using one‐section configurations rather than the composite cascade configurations of previous designs. The analysis is based on the transmission‐matrix description of TE‐TM mode coupling. Circuit configurations are presented for two typical devices; the unidirectional mode converter and the TE‐TM gyrator. A discussion is also given to the deterioration of the device performance due to the film‐thickness deviation from the prescribed value for the example of the unidirectional mode converter utilizing the LiIO3/YIG/GGG layered structure.

Asymptotic expressions for piezoelectric surface waves excited by the buried mechanical and electrical point sources

The asymptotic expressions for the piezoelectric surface waves excited by the buried mechanical and electrical point sources are obtained by using the stationary‐phase method developed by Lighthill. It is found that the amplitudes of the piezoelectric surface waves propagating in the directions which correspond to the points of zero curvature on the slowness surface are subject to a comparatively small decay at the rate O(r−1/3) with distance, as opposed to a decay of O(r−1/2) for the ordinary surface waves.

Semileaky‐type thin‐film magneto‐optic waveguide for modulator application

This paper is concerned with a light‐intensity modulator that utilizes codirectional magneto‐optic coupling between orthogonally polarized guided and radiation modes a thin‐film waveguide. The basic structure is the semileaky‐type anisotropic waveguide that has been previously used as the polarization mode filter. Specific features of the modulator of this type are (1) phase matching is automatically achieved without introducing an acoustic wave, a gratinglike periodicity, or a precise control of film thickness and (2) direct intensity modulation is possible with no separate analyzer or mode splitter. As a practical example, a modulator configuration using LiNbO3/YIG/GGG layered structure operating in 1.15‐μm wavelength region is considered. Radiation loss of 5–10 dB/cm may be obtainable in the film of thickness 6–7.5 μm for the lowest‐order guided mode.

Gaussian curvature of the slowness surface for piezoelectric surface waves on a cubic crystal

The Gaussian curvature of the slowness surface for piezoelectric surface waves propagating on the Z‐cut metal‐coated surface of a semi‐infinite cubic crystal (class 43m or 23) is calculated. It is shown numerically that the points of zero curvature on the slowness surface correspond to the cusps in the wave surface. It is also shown analytically and numerically that these points correspond to the points satisfying ∂e/∂ϑ=−1 on the e−ϑ curve, where ϑ is the phase propagation angle and e is the deviation angle, i.e., the angle which the phase velocity vector makes with the energy velocity vector.

Normal‐mode analysis for anisotropic elastic waveguides and its application to a Rayleigh‐Love wave mode converter

Normal‐mode analysis is presented to study wave propagation along general anisotropic elastic waveguides. Introducing a concept of material perturbation, normal modes of these general waveguides are successfully examined in terms of those of a conveniently defined ’’reference waveguide’’ with simpler material parameters. Employing the Rayleigh‐Ritz variational technique, a coupled‐mode equation is deduced, and the solution interprets the desired propagation property as a mode coupling between normal modes of the reference waveguide. Considering the case of two‐mode coupling, the mode conversion is analyzed in some detail. The results are applied to the case of a specific waveguide with a YIG film on an isotropic substrate. This example suggests the possibility of a ’’Rayleigh‐Love wave mode converter’’. Numerical calculations about some basic properties of this device are presented also.

Analysis of mode coupling in piezoelectric waveguides

A perturbed piezoelectric waveguide is constructed from a reference waveguide, which is specified by the eigenvalues and eigenfunctions, by the coordinate transformation, or other methods. In the perturbed waveguide, coupling occurs between normal modes of the reference waveguide. Coupling phenomena are analyzed by transforming Maxwells and Newtons equations into the variational expression of the phase constant of the normal mode and then by applying the Rayleigh‐Ritz method. As an example, the couplings between purely elastic waveguide modes are discussed; and then the two‐mode approximation is applied in the case when two modes are degenerate or nearly degenerate. Mode conversion phenomena are discussed and from the viewpoint of the network theory, the mode transfer matrix relating the complex amplitudes of the two modes along the waveguide is defined and developed.

Equivalence of Sturm‐Liouville‐Type Distributed‐Parameter Systems

This paper analyzes equivalence properties of linear distributed‐parameter systems characterized by Sturm‐Liouville‐type differential equations. The approach taken here may be regarded as an application of the method of independent‐variable transformation to those fundamental equations. In accord with the meaning of equivalence used for lumped‐parameter systems, distributed‐parameter systems are considered here as equivalent when they possess the same terminal behavior. The principal result is an equivalence theorem which establishes a general method of equivalent transformation of Sturm‐Liouville systems. The fact that we can generate any number of equivalent parameter distributions from a given one is not only of theoretical interest but also of practical importance, because it offers a flexibility in the design of distributed‐parameter structures. The derivation of the transformation function which plays a central role in the equivalent transformation is briefly described. Discussion is also given to t...