手法を比較

	ビーム伝搬法	ABCD行列	有限差分時間領域法	フーリエ光学
分野	光学	光学	光学	光学
系統	Process / pipeline	Process / pipeline	Process / pipeline	Process / pipeline
提唱年	1978	1966	1966	1822
提唱者	Michael Feit and John Fleck	Herwig Kogelnik and Tingye Li	Kane Yee	Joseph Fourier and Ernst Abbe
種類	Paraxial propagation algorithm	Ray optics formalism	Finite-difference algorithm	Spectral decomposition method
原典	Feit, M. D., & Fleck, J. A. (1978). Light propagation in graded-index optical fibers. Applied Optics, 17(24), 3990-3998.	Kogelnik, H., & Li, T. (1966). Laser beams and resonators. Applied Optics, 5(10), 1550-1567.	Yee, K. S. (1966). Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Transactions on Antennas and Propagation, 14(3), 302-307.	Goodman, J. W. (1968). Introduction to Fourier Optics. McGraw-Hill.
別名	BPM, paraxial approximation method	ray transfer matrix, ABCD method, system matrix	FDTD, Yee scheme	frequency-domain optics, wave optics, diffraction theory
関連	3	3	3	3
概要	The Beam Propagation Method is a computational technique for simulating the propagation of optical beams through slowly varying, weakly guiding structures. Developed by Feit and Fleck in 1978, BPM exploits the paraxial approximation to reduce the full vector wave equation to a scalar or vector envelope equation, enabling efficient simulation of waveguides, integrated optics, and photonic devices.	The ABCD matrix, or ray transfer matrix method, is a compact algebraic framework for analyzing optical systems. Introduced by Kogelnik and Li in 1966, it represents the linear transformation of ray position and angle (or Gaussian beam parameters) through optical elements. This method is foundational in laser physics, Gaussian optics, and optical design, enabling rapid calculation of resonator stability, beam propagation, and system performance.	The Finite-Difference Time-Domain method is a computational technique for solving Maxwell's equations by discretizing space and time on a grid. Introduced by Kane Yee in 1966, FDTD is a foundational approach in computational electrodynamics and optical simulation, enabling direct modeling of electromagnetic wave propagation through complex media.	Fourier optics is a mathematical framework that analyzes optical systems and phenomena using Fourier transforms and frequency-domain methods. Grounded in Joseph Fourier's 1822 work on heat diffusion and Ernst Abbe's microscopy theory, this approach decomposes optical fields into plane waves or spatial frequencies, revealing how optical systems manipulate and filter these components to produce images and transmit information.