OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: G. I. Stegeman
  • Vol. 23, Iss. 8 — Aug. 1, 2006
  • pp: 1506–1510

Nonstationary time-domain statistics of multiply scattered broadband terahertz pulses

Jeremy Pearce, Kevin Doyle, Zhongping Jian, Jason Deibel, and Daniel M. Mittleman  »View Author Affiliations

JOSA B, Vol. 23, Issue 8, pp. 1506-1510 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (98 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We examine the time-domain statistics of randomly varying electric fields generated by multiple scattering of single-cycle electromagnetic pulses in a random medium. This analysis emphasizes the fact that these measured random fields are not stationary, as is commonly assumed for diffusing photons generated with a narrowband light source. We demonstrate that the nonstationarity is a consequence of the time dependence of the configurationally averaged intensity, and that the statistical properties of the random field can be predicted if this quantity is known. We also discuss an approach for describing the transition from nonstationary to stationary behavior by investigating the degree of stationarity during a short time window. A parameterization of the statistics using a gamma distribution provides a quantifiable measure of the approach to stationarity. Our predictions are in good agreement with experimental observations.

© 2006 Optical Society of America

OCIS Codes
(030.6600) Coherence and statistical optics : Statistical optics
(290.4210) Scattering : Multiple scattering
(320.7100) Ultrafast optics : Ultrafast measurements

ToC Category:
Coherence and Statistical Optics

Original Manuscript: January 23, 2006
Manuscript Accepted: March 30, 2006

Virtual Issues
Vol. 1, Iss. 9 Virtual Journal for Biomedical Optics

Jeremy Pearce, Kevin Doyle, Zhongping Jian, Jason Deibel, and Daniel M. Mittleman, "Nonstationary time-domain statistics of multiply scattered broadband terahertz pulses," J. Opt. Soc. Am. B 23, 1506-1510 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, "Experimental images of heterogeneous turbid media by frequency-domain diffusing tomography," Opt. Lett. 20, 426-428 (1995). [CrossRef] [PubMed]
  2. D. A. Boas, L. E. Campbell, and A. G. Yodh, "Scattering and imaging with diffusing temporal field correlations," Phys. Rev. Lett. 75, 1855-1858 (1995). [CrossRef] [PubMed]
  3. D. A. Boas and A. G. Yodh, "Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation," J. Opt. Soc. Am. A 14, 192-215 (1997). [CrossRef]
  4. D. L. Lasocki, C. L. Matson, and P. J. Collins, "Analysis of forward scattering of diffuse photon-density waves in turbid media: a diffraction tomography approach to an analytic solution," Opt. Lett. 23, 558-560 (1998). [CrossRef]
  5. J. D. McKinney, M. A. Webster, K. J. Webb, and A. M. Weiner, "Characterization and imaging in optically scattering media by use of laser speckle and a variable-coherence source," Opt. Lett. 25, 4-6 (2000). [CrossRef]
  6. J. C. Schotland and V. A. Markel, "Inverse scattering with diffusing waves," J. Opt. Soc. Am. A 18, 2767-2777 (2001). [CrossRef]
  7. R. Berkovits and S. Feng, "Correlations in coherent multiple scattering," Phys. Rep. 238, 135-172 (1994). [CrossRef]
  8. C. A. Thompson, K. J. Webb, and A. M. Weiner, "Diffusive media characterization with laser speckle," Appl. Opt. 36, 3726-3734 (1997). [CrossRef] [PubMed]
  9. M. A. Webster, K. J. Webb, and A. M. Weiner, "Temporal response of a random medium from third-order laser speckle frequency correlations," Phys. Rev. Lett. 88, 033901 (2002). [CrossRef] [PubMed]
  10. B. A. van Tiggelen, P. Sebbah, M. Stoytchev, and A. Z. Genack, "Delay-time statistics for diffuse waves," Phys. Rev. E 59, 7166-7172 (1999). [CrossRef]
  11. J. Rivas, R. Sprik, and A. Lagendijk, "Static and dynamic transport of light close to the Anderson localization transition," Phys. Rev. E 63, 046613 (2001). [CrossRef]
  12. J. Pearce, Z. Jian, and D. Mittleman, "Statistics of multiply scattered broadband terahertz pulses," Phys. Rev. Lett. 91, 043903 (2003). [CrossRef] [PubMed]
  13. S. Mujumdar, K. J. Chau, and A. Y. Elezzabi, "Experimental and numerical investigation of terahertz transmission through strongly scattering sub-wavelength size spheres," Appl. Phys. Lett. 85, 6284-6286 (2004). [CrossRef]
  14. J. Pearce, Z. Jian, and D. Mittleman, "Spectral shifts as a signature of the onset of diffusion of broadband terahertz pulses," Opt. Lett. 29, 2926-2928 (2004). [CrossRef]
  15. A. A. Chabanov, B. Hu, and A. Z. Genack, "Dynamic correlation in wave propagation in random media," Phys. Rev. Lett. 93, 123901 (2004). [CrossRef] [PubMed]
  16. K. J. Chau, G. D. Dice, and A. Y. Elezzabi, "Coherent plasmonic enhanced terahertz transmission through random metallic media," Phys. Rev. Lett. 94, 173904 (2005). [CrossRef] [PubMed]
  17. K. J. Chau and A. Y. Elezzabi, "Terahertz transmission through ensembles of subwavelength-size metallic particles," Phys. Rev. B 72, 075110 (2005). [CrossRef]
  18. J. Pearce and D. Mittleman, "Bayesian approach to non-Gaussian field statistics for diffuse broadband terahertz pulses," Opt. Lett. 30, 2843-2845 (2005). [CrossRef] [PubMed]
  19. J. W. Goodman, Statistical Optics (Wiley, 2000).
  20. A. Z. Genack, P. Sebbah, M. Stoytchev, and B. A. van Tiggelen, "Statistics of wave dynamics in random media," Phys. Rev. Lett. 82, 715-718 (1999). [CrossRef]
  21. A. A. Chabanov and A. Z. Genack, "Field distributions in the crossover from ballistic to diffusive wave propagation," Phys. Rev. E 56, R1338-R1341 (1997). [CrossRef]
  22. K. M. Yoo and R. R. Alfano, "Time resolved depolarization of multiple back scattered light from random media," Phys. Lett. A 142, 531-536 (1989). [CrossRef]
  23. M. S. Patterson, B. Chance, and B. C. Wilson, "Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties," Appl. Opt. 28, 2331-2336 (1989). [CrossRef] [PubMed]
  24. D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, "Time-resolved experiments on light diffusion in anisotropic random media," Phys. Rev. E 62, 6681-6687 (2000). [CrossRef]
  25. J. Pearce and D. Mittleman, "The propagation of single-cycle THz pulses in random media," Opt. Lett. 26, 2002-2004 (2001). [CrossRef]
  26. M. A. Webster, T. D. Gerke, A. M. Weiner, and K. J. Webb, "Spectral and temporal speckle field measurements of a random medium," Opt. Lett. 29, 1491-1493 (2004). [CrossRef] [PubMed]
  27. M. Bondani, D. Redaelli, A. Spinelli, A. Andreoni, G. Roberti, P. Riccio, and R. Liuzzi, "Photon time-of-flight distributions through turbid media directly measured with single-photon avalanche diodes," J. Opt. Soc. Am. B 20, 2383-2388 (2003). [CrossRef]
  28. Z. Jian, J. Pearce, and D. Mittleman, "Characterizing individual scattering events by measuring the amplitude and phase of the electric field diffusing through a random medium," Phys. Rev. Lett. 91, 033903 (2003). [CrossRef] [PubMed]

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
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited