Linganisha mbinu

	Njia ya Uenezaji wa Mfumo (Beam Propagation Method - BPM)	Matriki ya ABCD	Mofolojia ya Fourier
Nyanja	Optiki	Optiki	Optiki
Familia	Process / pipeline	Process / pipeline	Process / pipeline
Mwaka wa asili	1978	1966	1822
Mwanzilishi	Michael Feit and John Fleck	Herwig Kogelnik and Tingye Li	Joseph Fourier and Ernst Abbe
Aina	Paraxial propagation algorithm	Ray optics formalism	Spectral decomposition method
Chanzo asilia	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.	Goodman, J. W. (1968). Introduction to Fourier Optics. McGraw-Hill.
Majina mbadala	BPM, paraxial approximation method	ray transfer matrix, ABCD method, system matrix	frequency-domain optics, wave optics, diffraction theory
Zinazohusiana	3	3	3
Muhtasari	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.	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.