OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 30, Iss. 8 — Aug. 1, 2013
  • pp: 2199–2205

Solution of the Bethe–Salpeter equation in a nondiffusive random medium having large scatterers

Vaibhav Gaind, Dergan Lin, and Kevin J. Webb  »View Author Affiliations

JOSA B, Vol. 30, Issue 8, pp. 2199-2205 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (490 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present a formalism for solving the scalar Bethe–Salpeter equation (BSE) in the nondiffusive regime under the ladder approximation and for an infinite randomly scattering medium having scatterers of size on the order of or larger than the wavelength. We compare the information content in a wave transport model (the BSE) with that in energy-based transport, the Boltzmann transport equation (BTE), in the spatial frequency domain. Our results suggest that when absorption dominates scatter, the intensity Green’s function from a BTE model is similar to the field correlation Green’s function from a BSE solution. When scatter dominates loss, there are significant differences between the BTE and BSE representations, and the BTE solutions appear to be smoothed versions of those from the BSE. Therefore, field correlation measurements, perhaps extracted from intensity correlations over frequency and space, offer significantly more information than a mean-intensity measurement in the weakly scattering and nondiffusive regime. Our work provides a mathematical framework for electric field correlation-based imaging methods based on the BSE that hold promise in, for example, near-surface tissue imaging.

© 2013 Optical Society of America

OCIS Codes
(030.1670) Coherence and statistical optics : Coherent optical effects
(030.6140) Coherence and statistical optics : Speckle
(030.6600) Coherence and statistical optics : Statistical optics
(290.5825) Scattering : Scattering theory

ToC Category:
Coherence and Statistical Optics

Original Manuscript: November 21, 2012
Revised Manuscript: February 24, 2013
Manuscript Accepted: May 12, 2013
Published: July 19, 2013

Virtual Issues
Vol. 8, Iss. 9 Virtual Journal for Biomedical Optics

Vaibhav Gaind, Dergan Lin, and Kevin J. Webb, "Solution of the Bethe–Salpeter equation in a nondiffusive random medium having large scatterers," J. Opt. Soc. Am. B 30, 2199-2205 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1977), Vol. 2.
  2. J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, 1976).
  3. U. Frisch, “Wave propagation in random media,” in Probability Methods in Applied Mathematics, A. T. Bharucha-Reid, ed. (Academic, 1968), Vol. 1, pp. 76–198.
  4. E. Salpeter and H. Bethe, “A relativistic equation for bound-state problems,” Phys. Rev. 84, 1232 (1951). [CrossRef]
  5. P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (Springer, 2006).
  6. L. Florescu and S. John, “Theory of photon statistics and optical coherence in a multiple-scattering random-laser medium,” Phys. Rev. E 69, 046603 (2004). [CrossRef]
  7. M. B. van der Mark, M. P. van Albada, and A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988). [CrossRef]
  8. E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2007).
  9. H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, “Optical image reconstruction using frequency domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996). [CrossRef]
  10. S. R. Arridge and J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997). [CrossRef]
  11. A. B. Milstein, S. Oh, J. S. Reynolds, K. J. Webb, C. A. Bouman, and R. P. Millane, “Three-dimensional Bayesian optical diffusion tomography with experimental data,” Opt. Lett. 27, 95–97 (2002). [CrossRef]
  12. A. B. Milstein, J. J. Stott, S. Oh, D. A. Boas, R. P. Millane, C. A. Bouman, and K. J. Webb, “Fluorescence optical diffusion tomography using multiple-frequency data,” J. Opt. Soc. Am. A 21, 1035–1049 (2004). [CrossRef]
  13. Y. Kim, Y. Liu, V. Turzhitsky, H. Roy, R. Wali, and V. Backman, “Coherent backscattering spectroscopy,” Opt. Lett. 29, 1906–1908 (2004). [CrossRef]
  14. Y. Kim, Y. Liu, V. Turzhitsky, R. Wali, H. Roy, and V. Backman, “Depth-resolved low-coherence enhanced backscattering,” Opt. Lett. 30, 741–743 (2005). [CrossRef]
  15. H. Subramanian, P. Pradhan, Y. Kim, and V. Backman, “Penetration depth of low-coherence enhanced backscattered light in subdiffusion regime,” Phys. Rev. E 75, 41914 (2007). [CrossRef]
  16. D. Huang, E. Swanson, C. Lin, J. Schuman, W. Stinson, W. Chang, M. Hee, T. Flotte, D. Gregory, C. Puliafito, and J. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991). [CrossRef]
  17. J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999). [CrossRef]
  18. Z. Q. Zhang, I. P. Jones, H. P. Schriemer, J. H. Page, D. A. Weitz, and P. Sheng, “Wave transport in random media: the ballistic to diffusive transition,” Phys. Rev. E 60, 4843–4850 (1999). [CrossRef]
  19. X. Zhang and Z.-Q. Zhang, “Wave transport through thin slabs of random media with internal reflection: ballistic to diffusive transition,” Phys. Rev. E 66, 016612 (2002). [CrossRef]
  20. D. Livdan and A. Lisyanki, “Transport properties of waves in absorbing random media with microstructure,” Phys. Rev. B 53, 14843 (1996). [CrossRef]
  21. A. Lubatsch, J. Kroha, and K. Busch, “Theory of light diffusion in disordered media with linear absorption or gain,” Phys. Rev. B 71, 184201 (2005). [CrossRef]
  22. S. John, G. Pang, and Y. Yang, “Optical coherence propagation and imaging in a multiple scattering medium,” J. Biomed. Opt. 1, 180–191 (1996). [CrossRef]
  23. A. Hielscher and A. Klose, “Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698 (1999). [CrossRef]
  24. A. D. Klose and A. H. Hielscher, “Optical tomography using the time-independent equation of radiative transfer-part 2: inverse model,” J. Quant. Spectrosc. Radiat. Transfer 72, 715–732 (2002). [CrossRef]
  25. A. Lagendijk and B. Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996). [CrossRef]
  26. V. S. Podolsky and A. A. Lisyansky, “Transfer matrix of a spherical scatterer,” Phys. Rev. B 54, 12125–12128 (1996). [CrossRef]
  27. M. A. Webster, T. D. Gerke, K. J. Webb, and A. M. Weiner, “Spectral and temporal speckle field measurements of a random medium,” Opt. Lett. 29, 1491–1493 (2004). [CrossRef]
  28. Z. Wang, M. A. Webster, A. M. Weiner, and K. J. Webb, “Polarized temporal impulse response for scattering media from third-order frequency correlations of speckle intensity patterns,” J. Opt. Soc. Am. A 23, 3045–3053 (2006). [CrossRef]
  29. I. S. Reed, “On a moment theorem for complex Gaussian processes,” IRE Trans. Inf. Theory 8, 194–195 (1962). [CrossRef]
  30. J. W. Goodman, Statistical Optics (Wiley, 1985).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1. Fig. 2. Fig. 3.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited