Interferences and Coherence
摘要
This chapter introduces the phenomenon of light interference, where the superposition of two or more waves results in a redistribution of intensity, leading to patterns of constructive and destructive interference. It begins by establishing the fundamental principles of interference between scalar waves, highlighting that for optical waves, interference patterns are only observable if the waves have the same frequency and a stable relative phase, due to the rapid oscillations of light and the slow response of detectors. The concept of coherence is central to the chapter, distinguishing between temporal coherence and spatial coherence. Temporal coherence quantifies the time duration over which a light source maintains a stable phase, defined by the coherence time and coherence length. The autocorrelation function and degree of coherence are introduced as mathematical tools to characterize temporal coherence. The Wiener–Khintchine theorem establishes a crucial link between the temporal coherence of a source and its spectral power density, demonstrating that a narrower spectral width corresponds to higher temporal coherence. The chapter then explores various interferometers, devices designed to split and recombine light waves to produce interference patterns. These include wavefront splitting interferometers (like Young’s double-slit experiment, Fresnel biprism, and Lloyd’s mirror) and amplitude splitting interferometers (such as the Michelson and Mach–Zehnder interferometers, and thin films). The historical significance of interferometers in pivotal experiments, including the Michelson–Morley experiment and gravitational wave detection, is emphasized. Finally, the chapter addresses spatial coherence, which describes the phase correlation between different points on an extended light source. The Van Cittert–Zernike formula is introduced to relate the visibility of interference fringes to the spatial intensity distribution of the source, leading to the definition of the coherence angle. This concept is particularly relevant in applications like stellar interferometry, where it allows for the measurement of the angular size of distant stars.