Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Longitudinal coherence and interferometry in dispersive media

W. A. Hamilton, A. G. Klein, G. I. Opat

Published Nov 1, 1983• 35 citations
Publisher

Abstract

For the nondispersive propagation of waves in one dimension, there is no essential difference between the concepts of longitudinal and temporal coherence, and these terms are often used interchangeably. For the dispersive propagation of waves, such as electrons or neutrons in vacuo, or light in a medium, this is no longer the case. We analyze the coherence properties of a dispersively propagating beam of radiation, and discuss the observation of its spatial and temporal coherence properties by means of a two-beam interferometer.

DOI
10.1103/physreva.28.3149

Related papers

Coherence properties of one-dimensional pulses in dispersive media

Weijian Wang, E. Wolf

In recent years longitudinal coherence of electron and neutron wave packets has been investigated,1,2 and it was shown that their coherence length remains unchanged even though the length of the wave packet increases on propagation.3,4 As pointed out in Ref. 3, one may expect that a similar result will hold for light that propagates in a dispersive medium. We present some new general theorems relating to an ensemble of identical 1-D optical pulses which propagate in a linear homogeneous medium of any given dispersive properties. In particular we derive a general expression for the mutual coherence function and for the cross-spectral density function of the pulse field in the medium in terms of the Fourier spectrum of a single pulse shape. The analysis brings out clearly the distinction (already noted in Ref. 4) between the coherence length and the coherence time of fields in dispersive media. We also show that the pulse field is spatially completely coherent at each frequency, even though the shape of each pulse changes on propagation. The results have potential application to interferometry with optical pulses and with de Broglie wave packets of elementary particles.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations

Nonstationary electromagnetics of controllably dispersive media

Douglas H. Bradshaw, Michael D. Di Rosa

Recent experiments have demonstrated that it is possible to alter the dispersion of a medium without significantly altering its absorption or refractive index and that this may be done while a wave propagates through the medium. This possibility opens up a new set of potential experiments to the field of nonstationary optics. We consider the basic kinetics of waves propagating through a medium whose group and phase velocities are a function of position and time. We compare the dynamics of waves propagating through two homogeneous media, one a nondispersive medium with a time dependent phase velocity, and one a dispersive medium with a time dependent group velocity and show that new dynamic effects accompany new kinetic ones.

arXiv:1006.1700•Jun 9, 2010•0 citations

Invariance properties of random pulses and of other random fields in dispersive media

Weijian Wang, E. Wolf

This paper is concerned with one-dimensional random fields consisting of randomly distributed identical light pulses which propagate in a linear dispersive medium. It is shown that such fields are necessarily stationary and that their power spectra and their longitudinal coherence properties do not change on propagation. The invariance of the power spectrum and of the coherence properties are shown to apply more generally to any one-dimensional stationary field of any state of coherence, propagating in a linear dispersive medium. Some invariance properties of nondiffracting partially coherent fields in dispersive media and of partially coherent fields in lossless fibers are also discussed.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Nov 1, 1995•4 citations

Coherent and Incoherent Radiation

Yanhua H. Shih

This chapter introduces the concept of coherence and discuss the coherent property of radiation. The author starts from Einstein’s granularity picture of light to introduce two category of superpositions in terms of Einstein’s subfields and Maxwell’s Fourier-modes. Einstein’s picture of light is still in the framework of electromagnetic theory of radiation, except the concept of “bundle of ray” added additional freedom to the superposition of Fourier mode. The physics the authors consider now is the coherent or incoherent superposition among these subfields that are created from these spatially separated sub-sources. If these subfields are able to superpose coherently people consider the radiation spatially coherent; otherwise, the radiation is spatially incoherent. It is interesting to see the similarities between temporal wavepacket in the longitudinal dimension and the spatial wavepacket in the transverse dimension. The temporal coherence of the radiation produces temporal wavepackets, implying temporal constructive-destructive interference; and the spatial coherence of the radiation results in spatial wavepackets, implying spatial constructive-destructive interference.

CRC Press eBooks•Dec 16, 2020•0 citations

Longitudinal Coherence in Neutron Interferometry

A. G. Klein, G. I. Opat, W. A. Hamilton

The proposition that the coherence length of de Broglie wave packets remains unchanged even though the length of the packets increases upon propagation is discussed and demonstrated.Received 27 December 1982DOI:https://doi.org/10.1103/PhysRevLett.50.563©1983 American Physical Society

Physical Review Letters•Feb 21, 1983•94 citations

An Introduction to Quantum Optics: Photon and Biphoton Physics

Yanhua H. Shih

Electromagnetic Wave Theory and Measurement of Light Electromagnetic Wave Theory of Light Classical Superposition Measurement of Light Intensity of Light: Expectation and Fluctuation Measurement of Intensity: Ensemble Average and Time Average Coherence Property of Light-The State of the Radiation Coherence Property of Light Temporal Coherence Spatial Coherence Diffraction and Propagation Diffraction Field Propagation Optical Imaging A Classic Imaging System Fourier Transform via a Lens First-Order Coherence of Light First-Order Temporal Coherence First-Order Spatial Coherence Second-Order Coherence of Light Second-Order Coherence of Coherent Light Second-Order Correlation of Chaotic-Thermal Radiation and the HBT Interferometer The Physical Cause of the HBT Phenomenon Near-Field Second-Order Spatial Coherence of Thermal Light Nth-Order Coherence of Light Nth-Order Near-Field Spatial Coherence of Thermal Light Homodyne Detection and Heterodyne Detection of Light Optical Homodyne and Heterodyne Detection Balanced Homodyne and Heterodyne Detection Balanced Homodyne Detection of Independent and Coupled Thermal Fields Quantum Theory of Light: Field Quantization and Measurement The Experimental Foundation-Part I: Blackbody Radiation The Experimental Foundation-Part II: Photoelectric Effect The Light Quantum and the Field Quantization Photon Number State of Radiation Field Coherent State of Radiation Field Density Operator and Density Matrix Composite System and Two-Photon State of Radiation Field A Simple Model of Incoherent and Coherent Radiation Source Pure State and Mixed State Product State, Entangled State, and Mixed State of Photon Pairs Time-Dependent Perturbation Theory Measurement of Light: Photon Counting Measurement of Light: Joint Detection of Photons Field Propagation in Space-Time Quantum Theory of Optical Coherence Quantum Degree of First-Order Coherence Photon and Effective Wavefunction Measurement of the First-Order Coherence or Correlation Quantum Degree of Second-Order Coherence Two-Photon Interference vs. Statistical Correlation of Intensity Fluctuations Second-Order Spatial Correlation of Thermal Light Photon Counting and Measurement of G(2) Quantum Entanglement EPR Experiment and EPR State Product State, Entangled State, and Classically Correlated State Entangled States in Spin Variables Entangled Biphoton State EPR Correlation of Entangled Biphoton System Subsystem in an Entangled Two-Photon State Biphoton in Dispersive Media Quantum Imaging Biphoton Imaging Ghost Imaging Ghost Imaging and Uncertainty Relation Thermal Light Ghost Imaging Classical Simulation of Ghost Imaging Turbulence-Free Ghost Imaging Two-Photon Interferometry I: Biphoton Interference Is Two-Photon Interference the Interference of Two Photons? Two-Photon Interference with Orthogonal Polarization Franson Interferometer Two-Photon Ghost Interference Delayed Choice Quantum Eraser Two-Photon Interferometry II: Quantum Interference of Chaotic Light Two-Photon Young's Interference Two-Photon Anticorrelation with Incoherent Chaotic Light Two-Photon Interference with Incoherent Orthogonal Polarized Chaotic Light Bell's Theorem and Bell's Inequality Measurement Hidden Variable Theory and Quantum Calculation for the Measurement of Spin 1/2 Bohm State Bell's Theorem and Bell's Inequality Bell States Bell State Preparation

•Jan 24, 2011•40 citations
For the nondispersive propagation of waves in one dimension, there is no essential difference between the concepts of longitudinal and temporal coherence, and these terms are often used interchangeably. For the dispersive propagation of waves, such as electrons or neutrons in vacuo, or light in a medium, this is no longer the case. We analyze the coherence properties of a dispersively propagating beam of radiation, and discuss the observation of its spatial and temporal coherence properties by means of a two-beam interferometer.
In recent years longitudinal coherence of electron and neutron wave packets has been investigated,1,2 and it was shown that their coherence length remains unchanged even though the length of the wave packet increases on propagation.3,4 As pointed out in Ref. 3, one may expect that a similar result will hold for light that propagates in a dispersive medium. We present some new general theorems relating to an ensemble of identical 1-D optical pulses which propagate in a linear homogeneous medium of any given dispersive properties. In particular we derive a general expression for the mutual coherence function and for the cross-spectral density function of the pulse field in the medium in terms of the Fourier spectrum of a single pulse shape. The analysis brings out clearly the distinction (already noted in Ref. 4) between the coherence length and the coherence time of fields in dispersive media. We also show that the pulse field is spatially completely coherent at each frequency, even though the shape of each pulse changes on propagation. The results have potential application to interferometry with optical pulses and with de Broglie wave packets of elementary particles.
Recent experiments have demonstrated that it is possible to alter the dispersion of a medium without significantly altering its absorption or refractive index and that this may be done while a wave propagates through the medium. This possibility opens up a new set of potential experiments to the field of nonstationary optics. We consider the basic kinetics of waves propagating through a medium whose group and phase velocities are a function of position and time. We compare the dynamics of waves propagating through two homogeneous media, one a nondispersive medium with a time dependent phase velocity, and one a dispersive medium with a time dependent group velocity and show that new dynamic effects accompany new kinetic ones.
This paper is concerned with one-dimensional random fields consisting of randomly distributed identical light pulses which propagate in a linear dispersive medium. It is shown that such fields are necessarily stationary and that their power spectra and their longitudinal coherence properties do not change on propagation. The invariance of the power spectrum and of the coherence properties are shown to apply more generally to any one-dimensional stationary field of any state of coherence, propagating in a linear dispersive medium. Some invariance properties of nondiffracting partially coherent fields in dispersive media and of partially coherent fields in lossless fibers are also discussed.
This chapter introduces the concept of coherence and discuss the coherent property of radiation. The author starts from Einstein’s granularity picture of light to introduce two category of superpositions in terms of Einstein’s subfields and Maxwell’s Fourier-modes. Einstein’s picture of light is still in the framework of electromagnetic theory of radiation, except the concept of “bundle of ray” added additional freedom to the superposition of Fourier mode. The physics the authors consider now is the coherent or incoherent superposition among these subfields that are created from these spatially separated sub-sources. If these subfields are able to superpose coherently people consider the radiation spatially coherent; otherwise, the radiation is spatially incoherent. It is interesting to see the similarities between temporal wavepacket in the longitudinal dimension and the spatial wavepacket in the transverse dimension. The temporal coherence of the radiation produces temporal wavepackets, implying temporal constructive-destructive interference; and the spatial coherence of the radiation results in spatial wavepackets, implying spatial constructive-destructive interference.
Electromagnetic Wave Theory and Measurement of Light Electromagnetic Wave Theory of Light Classical Superposition Measurement of Light Intensity of Light: Expectation and Fluctuation Measurement of Intensity: Ensemble Average and Time Average Coherence Property of Light-The State of the Radiation Coherence Property of Light Temporal Coherence Spatial Coherence Diffraction and Propagation Diffraction Field Propagation Optical Imaging A Classic Imaging System Fourier Transform via a Lens First-Order Coherence of Light First-Order Temporal Coherence First-Order Spatial Coherence Second-Order Coherence of Light Second-Order Coherence of Coherent Light Second-Order Correlation of Chaotic-Thermal Radiation and the HBT Interferometer The Physical Cause of the HBT Phenomenon Near-Field Second-Order Spatial Coherence of Thermal Light Nth-Order Coherence of Light Nth-Order Near-Field Spatial Coherence of Thermal Light Homodyne Detection and Heterodyne Detection of Light Optical Homodyne and Heterodyne Detection Balanced Homodyne and Heterodyne Detection Balanced Homodyne Detection of Independent and Coupled Thermal Fields Quantum Theory of Light: Field Quantization and Measurement The Experimental Foundation-Part I: Blackbody Radiation The Experimental Foundation-Part II: Photoelectric Effect The Light Quantum and the Field Quantization Photon Number State of Radiation Field Coherent State of Radiation Field Density Operator and Density Matrix Composite System and Two-Photon State of Radiation Field A Simple Model of Incoherent and Coherent Radiation Source Pure State and Mixed State Product State, Entangled State, and Mixed State of Photon Pairs Time-Dependent Perturbation Theory Measurement of Light: Photon Counting Measurement of Light: Joint Detection of Photons Field Propagation in Space-Time Quantum Theory of Optical Coherence Quantum Degree of First-Order Coherence Photon and Effective Wavefunction Measurement of the First-Order Coherence or Correlation Quantum Degree of Second-Order Coherence Two-Photon Interference vs. Statistical Correlation of Intensity Fluctuations Second-Order Spatial Correlation of Thermal Light Photon Counting and Measurement of G(2) Quantum Entanglement EPR Experiment and EPR State Product State, Entangled State, and Classically Correlated State Entangled States in Spin Variables Entangled Biphoton State EPR Correlation of Entangled Biphoton System Subsystem in an Entangled Two-Photon State Biphoton in Dispersive Media Quantum Imaging Biphoton Imaging Ghost Imaging Ghost Imaging and Uncertainty Relation Thermal Light Ghost Imaging Classical Simulation of Ghost Imaging Turbulence-Free Ghost Imaging Two-Photon Interferometry I: Biphoton Interference Is Two-Photon Interference the Interference of Two Photons? Two-Photon Interference with Orthogonal Polarization Franson Interferometer Two-Photon Ghost Interference Delayed Choice Quantum Eraser Two-Photon Interferometry II: Quantum Interference of Chaotic Light Two-Photon Young's Interference Two-Photon Anticorrelation with Incoherent Chaotic Light Two-Photon Interference with Incoherent Orthogonal Polarized Chaotic Light Bell's Theorem and Bell's Inequality Measurement Hidden Variable Theory and Quantum Calculation for the Measurement of Spin 1/2 Bohm State Bell's Theorem and Bell's Inequality Bell States Bell State Preparation