本文选自“清华物理系百年庆专刊”——《物理与工程》2026年第5期

杜春光，清华大学物理系副教授。长期从事基础物理教学，主讲量子与统计、量子光学与原子光学、大学物理等课程。主要研究方向是量子光学，并从事负折射材料、表面等离子体、强激光等离子体等。

摘要

光波在两个半无限大介质的界面上反射时，反射与入射振幅之间的相移，以及在对称分束器中反射与透射振幅之间的相移，都是光学中的基本物理效应。它们在本质上都源于波的散射相位结构，但它们之间的内在关系需要深入理解。本文对相关教学问题进行了探索，用量子力学中简单的一维势模型对上述相位规律进行系统分析，并给出简单直观的解释。本文分析发现，对于对称方势垒（即对称双界面结构），反射波与透射波两种成分之间必然有相位差（其中反射波相位取自入射一侧的界面，而透射波相位取自透射一侧的界面），并进一步推广到一般对称势垒，发现势垒的具体形式仅影响以上相位差的正负号。在此基础上，本文进一步讨论了这一相位结构在全同双粒子二级干涉实验中的关键作用。通过这一分析链条，本文将界面反射中的半波损失、对称分束器中的相移规律以及多粒子量子干涉现象纳入同一波动散射框架加以理解，为量子力学和光学类课程中的相关问题提供了教学参考。

关键词 半波损失；一维势垒；分束器相移；二级干涉

DOI 10.27024/j.wlygc.2026.06.29.01

UNDERSTANDING HALF-WAVE LOSS, PHASE SHIFT IN A SYMMETRIC BEAM SPLITTER, AND SECOND-ORDER INTERFERENCE FROM THE PERSPECTIVE OF THE BARRIER MODEL DU Chunguang

(Department of Physics, Tsinghua University, Beijing 100084)

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 a symmetric square barrier, 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

点击标题阅读原文：杜春光｜从势垒模型出发理解半波损失、对称分束器相移及二级干涉

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通信作者： 杜春光，ducg@mail.tsinghua.edu.cn。

引文格式： 杜春光. 从势垒模型出发理解半波损失、对称分束器相移及二级干涉[J]. 物理与工程，2026，46（5）：79-85.

Cite this article: DU C G. Understanding half-wave loss, phase shift in a symmetric beam splitter, and second-order interference from the perspective of the barrier model[J]. Physics and Engineering, 2026， 46（5）： 79-85. (in Chinese)

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