قارن الطرق

	طريقة انتشار الحزمة	مصفوفة ABCD
المجال	علم البصريات	علم البصريات
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1978	1966
صاحب الطريقة	Michael Feit and John Fleck	Herwig Kogelnik and Tingye Li
النوع	Paraxial propagation algorithm	Ray optics formalism
المصدر التأسيسي	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.
الأسماء البديلة	BPM, paraxial approximation method	ray transfer matrix, ABCD method, system matrix
ذات صلة	3	3
الملخص	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.