II: Dispersion Relations and Phase Retrieval in Optical Spectroscopy
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The Kramers-Kronig relations are bidirectional complex relations based on causality that connect the real and imaginary parts of a response function, typically the optical permittivity.
“The Kramers-Kronig relations are bidirectional complex relations that work on the principle of causality and are commonly used in optics to connect the real and imaginary parts of a response function, typically the optical permittivity.”
From Robust phase correction techniques for terahertz time-domain reflection spectroscopy (2024) · cites this paper as [35]
The phase of the reflection coefficient can be extracted from its amplitude and, conversely, the amplitude can be extracted from its phase via the Kramers-Kronig relations.
“These two equations state that the phase of the reflection coefficient can be extracted from its amplitude and, conversely, the amplitude of the reflection coefficient can be extracted from its phase.”
From Robust phase correction techniques for terahertz time-domain reflection spectroscopy (2024) · cites this paper as [35]
Cites
Kramers-Kronig analysis of reflection data
Roessler, D. M. (1965) · British Journal of Applied Physics · doi:10.1088/0508-3443/16/8/310 · Cited by 264
Dispersion relations for complex reflectivities
Smith, D. Y. (1977) · Journal of the Optical Society of America · doi:10.1364/josa.67.000570 · Cited by 31
On the Kramers-Kronig Relation for the Phase Spectrum
Nash, P. L., Bell, R. J., & Alexander, R. (1995) · Journal of Modern Optics · doi:10.1080/09500349514551601 · Cited by 21
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Generalized Kramers–Kronig relations in nonlinear optical- and THz-spectroscopy
Peiponen, K., & Saarinen, J. (2009) · Reports on Progress in Physics · doi:10.1088/0034-4885/72/5/056401 · Cited by 86 · see citing works
Self-citationNumerical phase correction method for terahertz time-domain reflection spectroscopy
Vartiainen, E. M., Ino, Y., Shimano, R., Kuwata-Gonokami, M., Svirko, Y. P., & Peiponen, K.-E. (2004) · Journal of Applied Physics · doi:10.1063/1.1786345 · Cited by 79 · see citing works
Self-citationThe Nonlinear Optical Susceptibility
Boyd, R. (2020) · Nonlinear Optics · doi:10.1016/b978-0-12-369470-6.00001-0 · Cited by 65 · see citing works
Contribution of Semi-Quantum Dielectric Function Models to the Analysis of Infrared Spectra
Meneses, D. D. S., Brun, J., Echegut, P., & Simon, P. (2004) · Applied Spectroscopy · doi:10.1366/0003702041655467 · Cited by 64
Alternative approach to the derivation of dispersion relations for optical constants
King, F. W. (2006) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/39/33/012 · Cited by 41 · see citing works
Reflectance Study of Milk in the UV-Visible Range
Räty, J., & Peiponen, K. (1999) · doi:10.1366/0003702991947919 · Cited by 40
Self-citationKramers—Kronig Relations and Sum Rules in Nonlinear Optical Spectroscopy
Peiponen, K., Lucarini, V., Saarinen, J., & Vartiainen, E. (2004) · Applied Spectroscopy · doi:10.1366/000370204774103309 · Cited by 33 · see citing works
Self-citationXiao, H., & Oughstun, K. (1999) · Journal of the Optical Society of America B · doi:10.1364/josab.16.001773 · Cited by 31 · see citing works
Dispersion Relations and Phase Retrieval in Infrared Reflection Spectra Analysis
Brun, J., Meneses, D. D. S., Rousseau, B., & Echegut, P. (2001) · doi:10.1366/0003702011952479 · Cited by 20
Resolving Optical Constants from Reflectance of Liquids in the UV-Visible Range
Räty, J., Vartiainen, E., & Peiponen, K. (1999) · doi:10.1366/0003702991945272 · Cited by 18
Self-citationDispersion Theory of Liquids Containing Optically Linear and Nonlinear Maxwell Garnett Nanoparticles
Peiponen, K., Mx00E4kinen, M. O. A., Saarinen, J., & Asakura, T. (2001) · Optical Review · doi:10.1007/s10043-001-0009-5 · Cited by 13 · see citing works
Self-citationSaarinen, J., Vartiainen, E., & Peiponen, K. (2009) · Sensors and Actuators B Chemical · doi:10.1016/j.snb.2009.02.033 · Cited by 12 · see citing works
Self-citationMeneses, D. D. S., Rousseau, B., Echegut, P., & Matzen, G. (2007) · Applied Spectroscopy · doi:10.1366/000370207781269710 · Cited by 11 · see citing works
Peiponen, K., Jääskeläinen, A., Vartiainen, E., Räty, J., Tapper, U., Richard, O., Kauppinen, E., & Lumme, K. (2001) · Applied Optics · doi:10.1364/ao.40.005482 · Cited by 9 · see citing works
Self-citationDispersion theory of effective meromorphic nonlinear susceptibilities of nanocomposites
Peiponen, K., Vartiainen, E., & Asakura, T. (1998) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/10/11/012 · Cited by 8 · see citing works
Self-citationRetrieval of Linear Optical Functions from Finite Range Spectra
Meneses, D. D. S., Rousseau, B., Echegut, P., & Simon, P. (2007) · Applied Spectroscopy · doi:10.1366/000370207783292163 · Cited by 7 · see citing works
Retrieval of Optical Constants from Magnetoreflectance by Maximum Entropy Model
Vartiainen, E., Peiponen, K., & Asakura, T. (1998) · doi:10.1007/s10043-998-0271-x · Cited by 1
Self-citationRobust phase correction techniques for terahertz time-domain reflection spectroscopy
Jatkar, K. D., Yeh, T.-T., Pancaldi, M., & Bonetti, S. (2024) · arXiv · doi:10.48550/arxiv.2412.18662
“[31, 34, 35].”
Peiponen, K., Räty, J., Vartiainen, E., Sugiura, T., & Kawata, S. (1999) · Measurement Science and Technology · doi:10.1088/0957-0233/10/12/404
Self-citationVartiainen, E., Peiponen, K., & Asakura, T. (1999) · Other Conferences · doi:10.1117/12.347838
“However, since X3eff (0)=0)+co—0)) is to be retrieved from its ME model (v) = IflIexp[-i(v)]/[l + >ak exp(-i2rkv)], (6) w 10 — laI”
BackgroundSelf-citationThe Group Velocity Approximation
Oughstun, K. (2019) · Springer Series in Optical Sciences · doi:10.1007/978-1-4419-0149-1_3
- Authors
- Peiponen, K.-E., Vartiainen, E. M., & Asakura, T.
- Affiliations
- Hokkaido University (JP)
- ORCID
- Asakura, Toshimitsu
- Venue
- Progress in Optics
- Publisher
- Elsevier
- Published
- 1997
- Pages
- 57-94
- ISSN
- 0079-6638 (ISSN-L)
- OpenAlex
- W1503958166
- Cited by
- 21
- References
- 0
- Citations by year
- 2020: 1 · 2019: 1
- FWCI
- 9.60
- Type
- book chapter
- Language
- en
- Open access
- closed
- Locations
- Progress in optics (publishedVersion)
- Funders
- Academy of Finland
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Photorefractive and Nonlinear Optics
- Physical Sciences › Chemistry › Analytical Chemistry › Spectroscopy and Chemometric Analyses
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Optical and Acousto-Optic Technologies
- Keywords
- Kramers-Kronig relations, dispersion relation, phase retrieval, causality, optical constants, nonlinear spectroscopy, maximum entropy method, sum rules, reflectance spectroscopy, optical spectrum analysis, data inversion
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