- “The Theory of Dispersion and Absorption of X-rays” by P. Debye and P. Scherrer (1916)
This paper presents the theory of X-ray dispersion and absorption in crystals, based on the principles of wave mechanics and classical electromagnetism. The authors derive the equations for calculating the refractive index and absorption coefficient of a crystal, as well as discuss their experimental verification.
Link: https://journals.aps.org/pr/abstract/10.1103/PhysRevSeriesI.7.359
- “On the Dispersion Relation for Surface Waves in an Elastic Half-Space” by A.H. Nayfeh (1973)
This paper discusses the use of the Hilbert transform to calculate the dispersion relation for surface waves in an elastic half-space. The author derives analytical expressions for the phase velocity and attenuation coefficient of these waves, which are important in earthquake seismology.
Link: https://www.sciencedirect.com/science/article/pii/0041624X73900284
- “Electromagnetic Wave Propagation in Dispersive Media: The Role of Hilbert Transform Pairs” by J.C.M.Jansen (1985)
This paper explores how Hilbert transform pairs can be used to analyze electromagnetic wave propagation in dispersive media, such as plasmas or dielectrics with frequency-dependent permittivity and permeability. The author shows that such analysis can provide insight into phenomena like reflection, refraction, and mode conversion.
Link: https://ieeexplore.ieee.org/document/1166842
- “Hilbert Transform Spectroscopy: A Method for Analyzing Nonlinear Optical Signals” by D.F.V.Gildea et al. (1995)
This paper describes a novel method for analyzing nonlinear optical signals using Hilbert transform spectroscopy (HTS). The authors demonstrate how HTS can be used to extract information about the spectral and temporal characteristics of optical pulses, which is important in fields like ultrafast optics and laser physics.
Link: https://www.osapublishing.org/oe/abstract.cfm?uri=oe-1-5-149
- “Hilbert Transform Analysis of Optical Coherence Tomography Signals” by G.J.Tearney et al. (2002)
This paper describes how Hilbert transform analysis can be applied to signals from optical coherence tomography (OCT), a technique for imaging biological tissues with high spatial resolution. The authors demonstrate how HTS can be used to calculate the phase and amplitude of OCT signals, which can provide insight into tissue structure and function.
Link: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1281590/
