UNDERSTANDING HALF-WAVE LOSS,PHASE SHIFT IN A SYMMETRIC BEAM SPLITTER,AND SECOND-ORDER INTERFERENCE FROM THE PERSPECTIVE OF THE BARRIER MODEL
DU Chunguang;
Abstract：
When a light wave is reflected at the interface between two semi-infinite media,the relative phase between the reflected and incident amplitudes is a fundamental optical effect.Another fundamental phase relation arises in a symmetric beam splitter between its reflection and transmission amplitudes.Both effects originate from the phase structure of wave scattering,although their underlying connection is not always clearly understood.As a pedagogical investigation,this paper systematically analyzes these phase relations using simple one-dimensional potential models in quantum mechanics and provides intuitive physical explanations.For asymmetricsquarebarrier,the reflected and transmitted amplitudes necessarily differ in phase by±π/2,with the reflection phase referenced at the interface on the incident side and the transmission phase referenced at the interface on the exit side.The result is further extended to general symmetric barriers,for which the detailed form of the barrier determines only whether the phase difference is+π/2 or-π/2.The role of this phase structure in the second-order interference of two identical particles is then examined.Through this sequence of analysis,half-wave loss at a reflecting interface,the phase relation in a symmetric beam splitter,and multiparticle quantum interference are incorporated into a unified wave-scattering framework.This treatment provides a useful pedagogical reference for related topics in quantum mechanics and optics courses.
Key Words： half-wave loss;one-dimensional potential barrier;beam splitter phase shift;second-order interference
Foundation:
Authors: DU Chunguang;
DOI: 10.27024/j.wlygc.2026.06.29.01
References：
- [1] 牟绪程，邓新元，董文达.波动与光学下册[M].北京：清华大学出版社，1994.MOU X C,DENG X Y,DONG W D.Wave and optics Volume 2[M].Beijing:Tsinghua University Press,1994.(in Chinese)
- [2] 赵凯华.新概念物理教程光学[M].北京：高等教育出版社，2004.ZHAO K H.New concept physics tutorial:Optics[M].Beijing:Higher Education Press,2004.(in Chinese)
- [3] JACKSON J D.经典电动力学[M].3版.影印版.北京：高等教育出版社，2004.JACKSON J D.Classical electrodynamics[M].3rd ed.Reprint.Beijing:Higher Education Press,2004.(in English)
- [4] 郭硕鸿.电动力学[M].北京：高等教育出版社，1979.GUO S H.Electrodynamics[M].Beijing:Higher Education Press,1979.(in Chinese)
- [5] OU Z Y,HONG C K,MANDEL L.Relation between input and output states for a beam splitter[J].Optics Communications,1987,63(2):118-122.
- [6] RICHARD A C,BAHAA E A S,MALVIN C T.Quantum-mechanical lossless beam splitter:SU(2) symmetry and photon statistics[J].Physical Review A,1989,40(3):1371-1384.
- [7] OU Z Y,MANDEL L.Further evidence of nonclassical behavior in optical interference[J].Physical review letters,1989,62(25):2941-2944.
- [8] SCULLY M O,ZUBAIRY M S.Quantum optics[M].Cambridge University Press,1997.
- [9] GERRY C,KNIGHT P.Introductory quantum optics[M].Cambridge University Press,2005.
- [10] 周世勋原著，陈灏修订.量子力学教程[M].2版.北京：高等教育出版社，2009.ZHOU S X (original author),CHEN H (revised edition).Quantum mechanics tutorial[M].2nd ed.Beijing:Higher Education Press,2009.(in Chinese)