Abstract

A theoretical analysis of incoherent intermode light power diffusion in multimode dielectric waveguides with rough (corrugated) surfaces is presented. The correlation length a of the surface-profile variations is assumed to be sufficiently large (aλ2π) to permit light scattering into the outer space only from the modes close to the critical angles of propagation and yet sufficiently small (ad, where d is the average width of the waveguide) to permit direct interaction between a given mode and a large number of neighboring ones. The cases of a one-dimensional (1D) slab waveguide and a two-dimensional cylindrical waveguide (optical fiber) are analyzed, and we find that in both cases the partial differential equations that govern the evolution of the angular light power profile propagating along the waveguide are 1D and of the diffusion type. However, whereas in the former case the effective conductivity coefficient proves to be linearly dependent on the transverse-mode wave number, in the latter one the linear dependence is for the effective diffusion coefficient. The theoretical predictions are in reasonable agreement with experimental results for the intermode power diffusion in multimode (700×700) optical fibers with etched surfaces. The characteristic length of dispersion of a narrow angular power profile evaluated from the correlation length and standard deviation of heights of the surface profile proved to be in good agreement with the experimentally observed changes in the output angular power profiles.

© 2005 Optical Society of America

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  1. J. T. Boyd, D. B. Anderson, “Effect of waveguide optical scattering on the integrated optical spectrum analyzer dynamic range,” IEEE J. Quantum Electron. QE-14, 437–443 (1978).
    [CrossRef]
  2. E. Bradley, D. G. Hall, “Out-of-plane scattering from glass waveguides: comparison of theory and experiment,” Opt. Lett. 7, 235–237 (1982).
    [CrossRef] [PubMed]
  3. D. Gloge, A. Tynes, M. Duguay, J. Hansen, “Picosecond pulse distortion in optical fibers,” IEEE J. Quantum Electron. QE-8, 217–221 (1972).
    [CrossRef]
  4. D. Marcuse, “Mode conversion caused by surface imperfections of a dielectric slab waveguide,” Bell Syst. Tech. J. 48, 3187–3215 (1969).
    [CrossRef]
  5. D. Marcuse, “Radiation losses of dielectric waveguides in terms of the power spectrum of the wall distortion function,” Bell Syst. Tech. J. 48, 3233–3242 (1969).
    [CrossRef]
  6. D. G. Hall, “Comparison of two approaches to the waveguide scattering problem,” Appl. Opt. 19, 1732–1734 (1980).
    [CrossRef] [PubMed]
  7. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, Boston, Mass. 1991).
  8. D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).
    [CrossRef]
  9. F. G. Bass, V. D. Freulicher, I. M. Fuks, “Damping of proper waves in a plate with rough walls,” JETP Lett. 7, 373–375 (1968).
  10. F. G. Bass, V. D. Freulicher, I. M. Fuks, “The average field of a point source in a waveguide with rough walls,” Izv. Vyssh. Uchebn. Zaved., Radiofiz. 12, 1521–1531 (1969) (in Russian).
  11. F. G. Bass, V. D. Freulicher, I. M. Fuks, “Radiation transfer equation in waveguide with statistically rough walls,” Ukr. Phys. J. 14, 1548–1551 (1969) (in Russian).
  12. F. G. Bass, V. D. Freulicher, I. M. Fuks, “Propagation in statistically irregular waveguides—Part II: Second order statistical moments,” IEEE Trans. Antennas Propag. AP-22, 288–295 (1974).
    [CrossRef]
  13. F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, New York, 1979).
  14. P. Shen, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, San Diego, Calif., 1995).
  15. A. Z. Genack, N. Garcia, “Observation of photon localization in a three-dimensional disordered system,” Phys. Rev. Lett. 66, 2064–2067 (1991).
    [CrossRef] [PubMed]
  16. M. S. Stoychev, A. Z. Genack, “Observation of non-Rayleigh statistics in the approach to photon localization,” Opt. Lett. 24, 262–264 (1999).
    [CrossRef]
  17. A. García-Martin, J. A. Torres, J. J. Sáenz, M. Nieto-Vesperinas, “Transition from diffusive to localized regimes in surface corrugated optical waveguides,” Appl. Phys. Lett. 71, 1912–1914 (1997).
    [CrossRef]
  18. A. García-Martin, J. J. Sáenz, M. Nieto-Vesperinas, “Spatial field distributions in the transition from ballistic to diffusive transport in randomly corrugated waveguides,” Phys. Rev. Lett. 84, 3578–3581 (2000).
    [CrossRef] [PubMed]
  19. J. A. Sánchez-Gil, V. Freilikher, I. V. Yurkevich, A. A. Maradudin, “Coexistence of ballistic transport, diffusion, and localization in surface disordered waveguides,” Phys. Rev. Lett. 80, 948–951 (1998).
    [CrossRef]
  20. J. A. Sánchez-Gil, V. Freilikher, A. A. Maradudin, I. V. Yurkevich, “Reflection and transmission of waves in surface-disordered waveguides,” Phys. Rev. B 59, 5915–5925 (1999).
    [CrossRef]
  21. D. W. Lynch, W. R. Hunter, “Optical properties of metals,” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, San Diego, Calif., 1998), pp. 341–419.
    [CrossRef]
  22. F. Scheffold, R. Lenke, R. Tweer, G. Maret, “Localization or classical diffusion of light?” Nature (London) 398, 206–207 (1999).
    [CrossRef]
  23. E. I. Chaikina, N. Puente, T. A. Leskova, E. R. Méndez, “Redistribution of modes in a surface disordered waveguide,” in Surface Scattering and Diffraction for Advanced Metrology, Z. H. Gu and A. A. Maradudin, eds., Proc. SPIE4447, 122–129 (2002).
  24. E. I. Chaikina, S. Stepanov, T. A. Leskova, E. R. Méndez, A. G. Navarrete, “Intermode power transfer in a multimode optical fiber with a rough surface,” in Surface Scattering and Diffraction III, Z. H. Gu and A. A. Maradudin, eds., Proc. SPIE5189, 50–58 (2003).
  25. E. I. Chaikina, A. G. Navarette, S. Stepanov, E. R. Méndez, T. A. Leskova, “Light diffusion in a multimode optical fiber with rough surface,” in Proceedings of PIERS, Pisa, March 18–31, 2004), pp. 727–730. http://emacademy.org/piers2k6Cambridge/index.html.
  26. E. I. Chaikina, S. Stepanov, G. Navarrete, T. A. Leskova, E. R. Méndez, “Formation of angular power profile via ballistic light transport in a multimode optical fiber with a corrugated surface,” Phys. Rev. B 71, 085419 (1–9) (2005).
    [CrossRef]
  27. V. Ruiz-Cortés, E. R. Méndez, Z. H. Gu, A. A. Maradudin, “Light scattering from gold-coated ground glass and chemically etched surfaces,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed., Proc. SPIE1558, 222–232 (1991).

2005 (1)

E. I. Chaikina, S. Stepanov, G. Navarrete, T. A. Leskova, E. R. Méndez, “Formation of angular power profile via ballistic light transport in a multimode optical fiber with a corrugated surface,” Phys. Rev. B 71, 085419 (1–9) (2005).
[CrossRef]

2000 (1)

A. García-Martin, J. J. Sáenz, M. Nieto-Vesperinas, “Spatial field distributions in the transition from ballistic to diffusive transport in randomly corrugated waveguides,” Phys. Rev. Lett. 84, 3578–3581 (2000).
[CrossRef] [PubMed]

1999 (3)

J. A. Sánchez-Gil, V. Freilikher, A. A. Maradudin, I. V. Yurkevich, “Reflection and transmission of waves in surface-disordered waveguides,” Phys. Rev. B 59, 5915–5925 (1999).
[CrossRef]

F. Scheffold, R. Lenke, R. Tweer, G. Maret, “Localization or classical diffusion of light?” Nature (London) 398, 206–207 (1999).
[CrossRef]

M. S. Stoychev, A. Z. Genack, “Observation of non-Rayleigh statistics in the approach to photon localization,” Opt. Lett. 24, 262–264 (1999).
[CrossRef]

1998 (1)

J. A. Sánchez-Gil, V. Freilikher, I. V. Yurkevich, A. A. Maradudin, “Coexistence of ballistic transport, diffusion, and localization in surface disordered waveguides,” Phys. Rev. Lett. 80, 948–951 (1998).
[CrossRef]

1997 (1)

A. García-Martin, J. A. Torres, J. J. Sáenz, M. Nieto-Vesperinas, “Transition from diffusive to localized regimes in surface corrugated optical waveguides,” Appl. Phys. Lett. 71, 1912–1914 (1997).
[CrossRef]

1991 (1)

A. Z. Genack, N. Garcia, “Observation of photon localization in a three-dimensional disordered system,” Phys. Rev. Lett. 66, 2064–2067 (1991).
[CrossRef] [PubMed]

1982 (1)

1980 (1)

1978 (1)

J. T. Boyd, D. B. Anderson, “Effect of waveguide optical scattering on the integrated optical spectrum analyzer dynamic range,” IEEE J. Quantum Electron. QE-14, 437–443 (1978).
[CrossRef]

1974 (1)

F. G. Bass, V. D. Freulicher, I. M. Fuks, “Propagation in statistically irregular waveguides—Part II: Second order statistical moments,” IEEE Trans. Antennas Propag. AP-22, 288–295 (1974).
[CrossRef]

1972 (2)

D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).
[CrossRef]

D. Gloge, A. Tynes, M. Duguay, J. Hansen, “Picosecond pulse distortion in optical fibers,” IEEE J. Quantum Electron. QE-8, 217–221 (1972).
[CrossRef]

1969 (4)

D. Marcuse, “Mode conversion caused by surface imperfections of a dielectric slab waveguide,” Bell Syst. Tech. J. 48, 3187–3215 (1969).
[CrossRef]

D. Marcuse, “Radiation losses of dielectric waveguides in terms of the power spectrum of the wall distortion function,” Bell Syst. Tech. J. 48, 3233–3242 (1969).
[CrossRef]

F. G. Bass, V. D. Freulicher, I. M. Fuks, “The average field of a point source in a waveguide with rough walls,” Izv. Vyssh. Uchebn. Zaved., Radiofiz. 12, 1521–1531 (1969) (in Russian).

F. G. Bass, V. D. Freulicher, I. M. Fuks, “Radiation transfer equation in waveguide with statistically rough walls,” Ukr. Phys. J. 14, 1548–1551 (1969) (in Russian).

1968 (1)

F. G. Bass, V. D. Freulicher, I. M. Fuks, “Damping of proper waves in a plate with rough walls,” JETP Lett. 7, 373–375 (1968).

Anderson, D. B.

J. T. Boyd, D. B. Anderson, “Effect of waveguide optical scattering on the integrated optical spectrum analyzer dynamic range,” IEEE J. Quantum Electron. QE-14, 437–443 (1978).
[CrossRef]

Bass, F. G.

F. G. Bass, V. D. Freulicher, I. M. Fuks, “Propagation in statistically irregular waveguides—Part II: Second order statistical moments,” IEEE Trans. Antennas Propag. AP-22, 288–295 (1974).
[CrossRef]

F. G. Bass, V. D. Freulicher, I. M. Fuks, “Radiation transfer equation in waveguide with statistically rough walls,” Ukr. Phys. J. 14, 1548–1551 (1969) (in Russian).

F. G. Bass, V. D. Freulicher, I. M. Fuks, “The average field of a point source in a waveguide with rough walls,” Izv. Vyssh. Uchebn. Zaved., Radiofiz. 12, 1521–1531 (1969) (in Russian).

F. G. Bass, V. D. Freulicher, I. M. Fuks, “Damping of proper waves in a plate with rough walls,” JETP Lett. 7, 373–375 (1968).

F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, New York, 1979).

Boyd, J. T.

J. T. Boyd, D. B. Anderson, “Effect of waveguide optical scattering on the integrated optical spectrum analyzer dynamic range,” IEEE J. Quantum Electron. QE-14, 437–443 (1978).
[CrossRef]

Bradley, E.

Chaikina, E. I.

E. I. Chaikina, S. Stepanov, G. Navarrete, T. A. Leskova, E. R. Méndez, “Formation of angular power profile via ballistic light transport in a multimode optical fiber with a corrugated surface,” Phys. Rev. B 71, 085419 (1–9) (2005).
[CrossRef]

E. I. Chaikina, S. Stepanov, T. A. Leskova, E. R. Méndez, A. G. Navarrete, “Intermode power transfer in a multimode optical fiber with a rough surface,” in Surface Scattering and Diffraction III, Z. H. Gu and A. A. Maradudin, eds., Proc. SPIE5189, 50–58 (2003).

E. I. Chaikina, A. G. Navarette, S. Stepanov, E. R. Méndez, T. A. Leskova, “Light diffusion in a multimode optical fiber with rough surface,” in Proceedings of PIERS, Pisa, March 18–31, 2004), pp. 727–730. http://emacademy.org/piers2k6Cambridge/index.html.

E. I. Chaikina, N. Puente, T. A. Leskova, E. R. Méndez, “Redistribution of modes in a surface disordered waveguide,” in Surface Scattering and Diffraction for Advanced Metrology, Z. H. Gu and A. A. Maradudin, eds., Proc. SPIE4447, 122–129 (2002).

Duguay, M.

D. Gloge, A. Tynes, M. Duguay, J. Hansen, “Picosecond pulse distortion in optical fibers,” IEEE J. Quantum Electron. QE-8, 217–221 (1972).
[CrossRef]

Freilikher, V.

J. A. Sánchez-Gil, V. Freilikher, A. A. Maradudin, I. V. Yurkevich, “Reflection and transmission of waves in surface-disordered waveguides,” Phys. Rev. B 59, 5915–5925 (1999).
[CrossRef]

J. A. Sánchez-Gil, V. Freilikher, I. V. Yurkevich, A. A. Maradudin, “Coexistence of ballistic transport, diffusion, and localization in surface disordered waveguides,” Phys. Rev. Lett. 80, 948–951 (1998).
[CrossRef]

Freulicher, V. D.

F. G. Bass, V. D. Freulicher, I. M. Fuks, “Propagation in statistically irregular waveguides—Part II: Second order statistical moments,” IEEE Trans. Antennas Propag. AP-22, 288–295 (1974).
[CrossRef]

F. G. Bass, V. D. Freulicher, I. M. Fuks, “Radiation transfer equation in waveguide with statistically rough walls,” Ukr. Phys. J. 14, 1548–1551 (1969) (in Russian).

F. G. Bass, V. D. Freulicher, I. M. Fuks, “The average field of a point source in a waveguide with rough walls,” Izv. Vyssh. Uchebn. Zaved., Radiofiz. 12, 1521–1531 (1969) (in Russian).

F. G. Bass, V. D. Freulicher, I. M. Fuks, “Damping of proper waves in a plate with rough walls,” JETP Lett. 7, 373–375 (1968).

Fuks, I. M.

F. G. Bass, V. D. Freulicher, I. M. Fuks, “Propagation in statistically irregular waveguides—Part II: Second order statistical moments,” IEEE Trans. Antennas Propag. AP-22, 288–295 (1974).
[CrossRef]

F. G. Bass, V. D. Freulicher, I. M. Fuks, “Radiation transfer equation in waveguide with statistically rough walls,” Ukr. Phys. J. 14, 1548–1551 (1969) (in Russian).

F. G. Bass, V. D. Freulicher, I. M. Fuks, “The average field of a point source in a waveguide with rough walls,” Izv. Vyssh. Uchebn. Zaved., Radiofiz. 12, 1521–1531 (1969) (in Russian).

F. G. Bass, V. D. Freulicher, I. M. Fuks, “Damping of proper waves in a plate with rough walls,” JETP Lett. 7, 373–375 (1968).

F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, New York, 1979).

Garcia, N.

A. Z. Genack, N. Garcia, “Observation of photon localization in a three-dimensional disordered system,” Phys. Rev. Lett. 66, 2064–2067 (1991).
[CrossRef] [PubMed]

García-Martin, A.

A. García-Martin, J. J. Sáenz, M. Nieto-Vesperinas, “Spatial field distributions in the transition from ballistic to diffusive transport in randomly corrugated waveguides,” Phys. Rev. Lett. 84, 3578–3581 (2000).
[CrossRef] [PubMed]

A. García-Martin, J. A. Torres, J. J. Sáenz, M. Nieto-Vesperinas, “Transition from diffusive to localized regimes in surface corrugated optical waveguides,” Appl. Phys. Lett. 71, 1912–1914 (1997).
[CrossRef]

Genack, A. Z.

M. S. Stoychev, A. Z. Genack, “Observation of non-Rayleigh statistics in the approach to photon localization,” Opt. Lett. 24, 262–264 (1999).
[CrossRef]

A. Z. Genack, N. Garcia, “Observation of photon localization in a three-dimensional disordered system,” Phys. Rev. Lett. 66, 2064–2067 (1991).
[CrossRef] [PubMed]

Gloge, D.

D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).
[CrossRef]

D. Gloge, A. Tynes, M. Duguay, J. Hansen, “Picosecond pulse distortion in optical fibers,” IEEE J. Quantum Electron. QE-8, 217–221 (1972).
[CrossRef]

Gu, Z. H.

V. Ruiz-Cortés, E. R. Méndez, Z. H. Gu, A. A. Maradudin, “Light scattering from gold-coated ground glass and chemically etched surfaces,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed., Proc. SPIE1558, 222–232 (1991).

Hall, D. G.

Hansen, J.

D. Gloge, A. Tynes, M. Duguay, J. Hansen, “Picosecond pulse distortion in optical fibers,” IEEE J. Quantum Electron. QE-8, 217–221 (1972).
[CrossRef]

Hunter, W. R.

D. W. Lynch, W. R. Hunter, “Optical properties of metals,” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, San Diego, Calif., 1998), pp. 341–419.
[CrossRef]

Lenke, R.

F. Scheffold, R. Lenke, R. Tweer, G. Maret, “Localization or classical diffusion of light?” Nature (London) 398, 206–207 (1999).
[CrossRef]

Leskova, T. A.

E. I. Chaikina, S. Stepanov, G. Navarrete, T. A. Leskova, E. R. Méndez, “Formation of angular power profile via ballistic light transport in a multimode optical fiber with a corrugated surface,” Phys. Rev. B 71, 085419 (1–9) (2005).
[CrossRef]

E. I. Chaikina, A. G. Navarette, S. Stepanov, E. R. Méndez, T. A. Leskova, “Light diffusion in a multimode optical fiber with rough surface,” in Proceedings of PIERS, Pisa, March 18–31, 2004), pp. 727–730. http://emacademy.org/piers2k6Cambridge/index.html.

E. I. Chaikina, S. Stepanov, T. A. Leskova, E. R. Méndez, A. G. Navarrete, “Intermode power transfer in a multimode optical fiber with a rough surface,” in Surface Scattering and Diffraction III, Z. H. Gu and A. A. Maradudin, eds., Proc. SPIE5189, 50–58 (2003).

E. I. Chaikina, N. Puente, T. A. Leskova, E. R. Méndez, “Redistribution of modes in a surface disordered waveguide,” in Surface Scattering and Diffraction for Advanced Metrology, Z. H. Gu and A. A. Maradudin, eds., Proc. SPIE4447, 122–129 (2002).

Lynch, D. W.

D. W. Lynch, W. R. Hunter, “Optical properties of metals,” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, San Diego, Calif., 1998), pp. 341–419.
[CrossRef]

Maradudin, A. A.

J. A. Sánchez-Gil, V. Freilikher, A. A. Maradudin, I. V. Yurkevich, “Reflection and transmission of waves in surface-disordered waveguides,” Phys. Rev. B 59, 5915–5925 (1999).
[CrossRef]

J. A. Sánchez-Gil, V. Freilikher, I. V. Yurkevich, A. A. Maradudin, “Coexistence of ballistic transport, diffusion, and localization in surface disordered waveguides,” Phys. Rev. Lett. 80, 948–951 (1998).
[CrossRef]

V. Ruiz-Cortés, E. R. Méndez, Z. H. Gu, A. A. Maradudin, “Light scattering from gold-coated ground glass and chemically etched surfaces,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed., Proc. SPIE1558, 222–232 (1991).

Marcuse, D.

D. Marcuse, “Mode conversion caused by surface imperfections of a dielectric slab waveguide,” Bell Syst. Tech. J. 48, 3187–3215 (1969).
[CrossRef]

D. Marcuse, “Radiation losses of dielectric waveguides in terms of the power spectrum of the wall distortion function,” Bell Syst. Tech. J. 48, 3233–3242 (1969).
[CrossRef]

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, Boston, Mass. 1991).

Maret, G.

F. Scheffold, R. Lenke, R. Tweer, G. Maret, “Localization or classical diffusion of light?” Nature (London) 398, 206–207 (1999).
[CrossRef]

Méndez, E. R.

E. I. Chaikina, S. Stepanov, G. Navarrete, T. A. Leskova, E. R. Méndez, “Formation of angular power profile via ballistic light transport in a multimode optical fiber with a corrugated surface,” Phys. Rev. B 71, 085419 (1–9) (2005).
[CrossRef]

V. Ruiz-Cortés, E. R. Méndez, Z. H. Gu, A. A. Maradudin, “Light scattering from gold-coated ground glass and chemically etched surfaces,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed., Proc. SPIE1558, 222–232 (1991).

E. I. Chaikina, A. G. Navarette, S. Stepanov, E. R. Méndez, T. A. Leskova, “Light diffusion in a multimode optical fiber with rough surface,” in Proceedings of PIERS, Pisa, March 18–31, 2004), pp. 727–730. http://emacademy.org/piers2k6Cambridge/index.html.

E. I. Chaikina, N. Puente, T. A. Leskova, E. R. Méndez, “Redistribution of modes in a surface disordered waveguide,” in Surface Scattering and Diffraction for Advanced Metrology, Z. H. Gu and A. A. Maradudin, eds., Proc. SPIE4447, 122–129 (2002).

E. I. Chaikina, S. Stepanov, T. A. Leskova, E. R. Méndez, A. G. Navarrete, “Intermode power transfer in a multimode optical fiber with a rough surface,” in Surface Scattering and Diffraction III, Z. H. Gu and A. A. Maradudin, eds., Proc. SPIE5189, 50–58 (2003).

Navarette, A. G.

E. I. Chaikina, A. G. Navarette, S. Stepanov, E. R. Méndez, T. A. Leskova, “Light diffusion in a multimode optical fiber with rough surface,” in Proceedings of PIERS, Pisa, March 18–31, 2004), pp. 727–730. http://emacademy.org/piers2k6Cambridge/index.html.

Navarrete, A. G.

E. I. Chaikina, S. Stepanov, T. A. Leskova, E. R. Méndez, A. G. Navarrete, “Intermode power transfer in a multimode optical fiber with a rough surface,” in Surface Scattering and Diffraction III, Z. H. Gu and A. A. Maradudin, eds., Proc. SPIE5189, 50–58 (2003).

Navarrete, G.

E. I. Chaikina, S. Stepanov, G. Navarrete, T. A. Leskova, E. R. Méndez, “Formation of angular power profile via ballistic light transport in a multimode optical fiber with a corrugated surface,” Phys. Rev. B 71, 085419 (1–9) (2005).
[CrossRef]

Nieto-Vesperinas, M.

A. García-Martin, J. J. Sáenz, M. Nieto-Vesperinas, “Spatial field distributions in the transition from ballistic to diffusive transport in randomly corrugated waveguides,” Phys. Rev. Lett. 84, 3578–3581 (2000).
[CrossRef] [PubMed]

A. García-Martin, J. A. Torres, J. J. Sáenz, M. Nieto-Vesperinas, “Transition from diffusive to localized regimes in surface corrugated optical waveguides,” Appl. Phys. Lett. 71, 1912–1914 (1997).
[CrossRef]

Puente, N.

E. I. Chaikina, N. Puente, T. A. Leskova, E. R. Méndez, “Redistribution of modes in a surface disordered waveguide,” in Surface Scattering and Diffraction for Advanced Metrology, Z. H. Gu and A. A. Maradudin, eds., Proc. SPIE4447, 122–129 (2002).

Ruiz-Cortés, V.

V. Ruiz-Cortés, E. R. Méndez, Z. H. Gu, A. A. Maradudin, “Light scattering from gold-coated ground glass and chemically etched surfaces,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed., Proc. SPIE1558, 222–232 (1991).

Sáenz, J. J.

A. García-Martin, J. J. Sáenz, M. Nieto-Vesperinas, “Spatial field distributions in the transition from ballistic to diffusive transport in randomly corrugated waveguides,” Phys. Rev. Lett. 84, 3578–3581 (2000).
[CrossRef] [PubMed]

A. García-Martin, J. A. Torres, J. J. Sáenz, M. Nieto-Vesperinas, “Transition from diffusive to localized regimes in surface corrugated optical waveguides,” Appl. Phys. Lett. 71, 1912–1914 (1997).
[CrossRef]

Sánchez-Gil, J. A.

J. A. Sánchez-Gil, V. Freilikher, A. A. Maradudin, I. V. Yurkevich, “Reflection and transmission of waves in surface-disordered waveguides,” Phys. Rev. B 59, 5915–5925 (1999).
[CrossRef]

J. A. Sánchez-Gil, V. Freilikher, I. V. Yurkevich, A. A. Maradudin, “Coexistence of ballistic transport, diffusion, and localization in surface disordered waveguides,” Phys. Rev. Lett. 80, 948–951 (1998).
[CrossRef]

Scheffold, F.

F. Scheffold, R. Lenke, R. Tweer, G. Maret, “Localization or classical diffusion of light?” Nature (London) 398, 206–207 (1999).
[CrossRef]

Shen, P.

P. Shen, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, San Diego, Calif., 1995).

Stepanov, S.

E. I. Chaikina, S. Stepanov, G. Navarrete, T. A. Leskova, E. R. Méndez, “Formation of angular power profile via ballistic light transport in a multimode optical fiber with a corrugated surface,” Phys. Rev. B 71, 085419 (1–9) (2005).
[CrossRef]

E. I. Chaikina, A. G. Navarette, S. Stepanov, E. R. Méndez, T. A. Leskova, “Light diffusion in a multimode optical fiber with rough surface,” in Proceedings of PIERS, Pisa, March 18–31, 2004), pp. 727–730. http://emacademy.org/piers2k6Cambridge/index.html.

E. I. Chaikina, S. Stepanov, T. A. Leskova, E. R. Méndez, A. G. Navarrete, “Intermode power transfer in a multimode optical fiber with a rough surface,” in Surface Scattering and Diffraction III, Z. H. Gu and A. A. Maradudin, eds., Proc. SPIE5189, 50–58 (2003).

Stoychev, M. S.

Torres, J. A.

A. García-Martin, J. A. Torres, J. J. Sáenz, M. Nieto-Vesperinas, “Transition from diffusive to localized regimes in surface corrugated optical waveguides,” Appl. Phys. Lett. 71, 1912–1914 (1997).
[CrossRef]

Tweer, R.

F. Scheffold, R. Lenke, R. Tweer, G. Maret, “Localization or classical diffusion of light?” Nature (London) 398, 206–207 (1999).
[CrossRef]

Tynes, A.

D. Gloge, A. Tynes, M. Duguay, J. Hansen, “Picosecond pulse distortion in optical fibers,” IEEE J. Quantum Electron. QE-8, 217–221 (1972).
[CrossRef]

Yurkevich, I. V.

J. A. Sánchez-Gil, V. Freilikher, A. A. Maradudin, I. V. Yurkevich, “Reflection and transmission of waves in surface-disordered waveguides,” Phys. Rev. B 59, 5915–5925 (1999).
[CrossRef]

J. A. Sánchez-Gil, V. Freilikher, I. V. Yurkevich, A. A. Maradudin, “Coexistence of ballistic transport, diffusion, and localization in surface disordered waveguides,” Phys. Rev. Lett. 80, 948–951 (1998).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. García-Martin, J. A. Torres, J. J. Sáenz, M. Nieto-Vesperinas, “Transition from diffusive to localized regimes in surface corrugated optical waveguides,” Appl. Phys. Lett. 71, 1912–1914 (1997).
[CrossRef]

Bell Syst. Tech. J. (3)

D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).
[CrossRef]

D. Marcuse, “Mode conversion caused by surface imperfections of a dielectric slab waveguide,” Bell Syst. Tech. J. 48, 3187–3215 (1969).
[CrossRef]

D. Marcuse, “Radiation losses of dielectric waveguides in terms of the power spectrum of the wall distortion function,” Bell Syst. Tech. J. 48, 3233–3242 (1969).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. T. Boyd, D. B. Anderson, “Effect of waveguide optical scattering on the integrated optical spectrum analyzer dynamic range,” IEEE J. Quantum Electron. QE-14, 437–443 (1978).
[CrossRef]

D. Gloge, A. Tynes, M. Duguay, J. Hansen, “Picosecond pulse distortion in optical fibers,” IEEE J. Quantum Electron. QE-8, 217–221 (1972).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

F. G. Bass, V. D. Freulicher, I. M. Fuks, “Propagation in statistically irregular waveguides—Part II: Second order statistical moments,” IEEE Trans. Antennas Propag. AP-22, 288–295 (1974).
[CrossRef]

Izv. Vyssh. Uchebn. Zaved., Radiofiz. (1)

F. G. Bass, V. D. Freulicher, I. M. Fuks, “The average field of a point source in a waveguide with rough walls,” Izv. Vyssh. Uchebn. Zaved., Radiofiz. 12, 1521–1531 (1969) (in Russian).

JETP Lett. (1)

F. G. Bass, V. D. Freulicher, I. M. Fuks, “Damping of proper waves in a plate with rough walls,” JETP Lett. 7, 373–375 (1968).

Nature (London) (1)

F. Scheffold, R. Lenke, R. Tweer, G. Maret, “Localization or classical diffusion of light?” Nature (London) 398, 206–207 (1999).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (2)

J. A. Sánchez-Gil, V. Freilikher, A. A. Maradudin, I. V. Yurkevich, “Reflection and transmission of waves in surface-disordered waveguides,” Phys. Rev. B 59, 5915–5925 (1999).
[CrossRef]

E. I. Chaikina, S. Stepanov, G. Navarrete, T. A. Leskova, E. R. Méndez, “Formation of angular power profile via ballistic light transport in a multimode optical fiber with a corrugated surface,” Phys. Rev. B 71, 085419 (1–9) (2005).
[CrossRef]

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A. Z. Genack, N. Garcia, “Observation of photon localization in a three-dimensional disordered system,” Phys. Rev. Lett. 66, 2064–2067 (1991).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

J. A. Sánchez-Gil, V. Freilikher, I. V. Yurkevich, A. A. Maradudin, “Coexistence of ballistic transport, diffusion, and localization in surface disordered waveguides,” Phys. Rev. Lett. 80, 948–951 (1998).
[CrossRef]

Ukr. Phys. J. (1)

F. G. Bass, V. D. Freulicher, I. M. Fuks, “Radiation transfer equation in waveguide with statistically rough walls,” Ukr. Phys. J. 14, 1548–1551 (1969) (in Russian).

Other (8)

F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, New York, 1979).

P. Shen, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, San Diego, Calif., 1995).

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, Boston, Mass. 1991).

V. Ruiz-Cortés, E. R. Méndez, Z. H. Gu, A. A. Maradudin, “Light scattering from gold-coated ground glass and chemically etched surfaces,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed., Proc. SPIE1558, 222–232 (1991).

D. W. Lynch, W. R. Hunter, “Optical properties of metals,” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, San Diego, Calif., 1998), pp. 341–419.
[CrossRef]

E. I. Chaikina, N. Puente, T. A. Leskova, E. R. Méndez, “Redistribution of modes in a surface disordered waveguide,” in Surface Scattering and Diffraction for Advanced Metrology, Z. H. Gu and A. A. Maradudin, eds., Proc. SPIE4447, 122–129 (2002).

E. I. Chaikina, S. Stepanov, T. A. Leskova, E. R. Méndez, A. G. Navarrete, “Intermode power transfer in a multimode optical fiber with a rough surface,” in Surface Scattering and Diffraction III, Z. H. Gu and A. A. Maradudin, eds., Proc. SPIE5189, 50–58 (2003).

E. I. Chaikina, A. G. Navarette, S. Stepanov, E. R. Méndez, T. A. Leskova, “Light diffusion in a multimode optical fiber with rough surface,” in Proceedings of PIERS, Pisa, March 18–31, 2004), pp. 727–730. http://emacademy.org/piers2k6Cambridge/index.html.

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Figures (11)

Fig. 1
Fig. 1

(a) Intermode scattering and leakage of the light outside a 1D slab waveguide via scattering from a rough wall. (b) Diagram illustrating the introduction of normalized longitudinal k and transverse κ wave numbers. Boundary areas are shown by dashed boxes. The piece of parabola demonstrates the applicability of a parabolic approximation for small values of transverse wave numbers.

Fig. 2
Fig. 2

(a) First three eigensolutions K β ( κ ) = J 0 ( 2 β κ ) of the diffusion equation for a 1D slab waveguide, which have finite values at κ = 0 and zero values at κ = 1 (with eigenvalues β: (1) 1.45, (2) 7.6, and (3) 18.8, respectively).

Fig. 3
Fig. 3

Evolution of initial light power profiles (a) p ( 0 , κ ) = exp [ ( κ 0.3 ) 4 ] and (b) p ( 0 , κ ) = exp { [ ( κ 0.3 ) 0.15 ] 2 } in a corrugated 1D slab waveguide shown for normalized propagation distances z L D = 0 , 0.1 , 0.2 , 0.5 , 1 , 2 (from the uppermost curve to the lowest curve).

Fig. 4
Fig. 4

(a) Evolution of an initial light power profile p ( 0 , κ ) = exp [ ( κ 0.3 ) 4 ] in a corrugated 1D slab waveguide in the case of the modified boundary condition p ( z , 0.005 ) κ = 0 , shown for normalized propagation lengths z L D = 0 , 0.1 , 0.2 , 0.5 , 1 , 2 (from the uppermost curve to the lowest curve). (b) Initial power density profile p ( 0 , κ ) = exp [ ( κ 0.3 ) 4 ] and those after propagation distances z L D = 0.5 as calculated for different boundary conditions p ( z , κ min ) κ = 0 at κ min = 0.001 , 0.002 , 0.005 , 0.01 (from the uppermost curve to the lowest curve).

Fig. 5
Fig. 5

Diagram showing propagation and radiation of light from an optical fiber with a rough surface.

Fig. 6
Fig. 6

l m diagram for an optical fiber, showing the triangle of permitted guided-mode indexes. Dashed lines show mode groups with fixed transverse wave number κ. Dashed parallelogram shows the mode area that contributes to intermode power exchange effectively.

Fig. 7
Fig. 7

(a) Reduction in average intermode connection number f as a function of the ratio between maximal angular mode indexes in initial and final mode groups l max l max = 1 + Δ κ κ , calculated for different values of l max ( d 2 a ) = 4 θ a λ = 5 , 10 , 20 (from the lowest curve to the uppermost curve). The approximate f factor used in the calculations [expression (27)] is shown by a solid line. (b) First three eigensolutions of the diffusion equation for a corrugated optical fiber, which have finite values at κ = 0 and zero values at κ = 1 [with eigenvalues β: (1) 3.7, (2) 12, and (3) 26, respectively].

Fig. 8
Fig. 8

Evolution of initial power profiles (a) p ( 0 , κ ) = exp [ ( κ 0.3 ) 4 ] and (b) p ( 0 , κ ) = exp { [ ( κ 0.3 ) 0.75 ] 2 } in a corrugated optical fiber, as shown for normalized propagation distances z L D = 0 , 0.1 , 0.2 , 0.5 , 1 (from the uppermost curve to the lowest curve).

Fig. 9
Fig. 9

Comparison of the diffusion spreading of a narrow Gaussian profile p ( 0 , κ ) = exp { [ ( κ 0.7 ) 0.75 ] 2 } excited at a high incidence angle (a) in a corrugated 1D slab waveguide and (b) in a corrugated fiber. Both families of curves are plotted for propagation distances z L D = 0 , 0.01 , 0.02 , 0.05 , 0.1 , 0.2 (from the uppermost curve to the lowest curve).

Fig. 10
Fig. 10

(a) Family of experimentally observed angular distributions of the output light intensity obtained at an initial excitation angle θ 25 ° after propagation through different lengths of the corrugated fiber z: 0, 11, 18, 24, 33, 64, 96, and 181 mm (from the uppermost curve to the lowest curve). (b) Family of theoretical curves calculated from Eq. (29) for an initial power profile similar to the one presented in (a) and for propagation distances z L D = 0.025 , 0.05 , 0.075 , 0.1 , 0.2 (from the uppermost curve to the lowest curve).

Fig. 11
Fig. 11

(a) Propagation-distance dependence of the maximum amplitude of the detected power profile [Fig. 10a]. (b) Propagation-length dependence of the profile width at a level of 0.7 of the maximum (circles and squares present data obtained for two different fiber samples with similar roughness). Solid curves show displaced inverse and direct square-root dependencies, respectively.

Equations (34)

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g ( k ) = π a k 0 exp ( a 2 k 0 2 4 k 2 ) ,
κ 2 = n 2 k 2 2 n ( n k ) 2 k ( n k ) .
T i j = Δ z 2 δ 2 k 0 κ i 2 κ j 2 d 2 ( 1 + 2 γ i d ) ( 1 + 2 γ j d ) k i k j g ( k i k j ) .
T i j Δ z 2 δ 2 k 0 κ i 2 κ j 2 d 2 k i k j g ( k i k j ) ,
T i i = 1 j i T i j = 1 Δ z l i .
l i 1 = j i 2 δ 2 k 0 κ i 2 κ j 2 d 2 k i k j g ( k i k j ) .
ρ ( k ) = d k 0 π n 2 1 n k .
T i j = T ( k i , k j ) Δ z 8 δ 2 k 0 ( n k i ) ( n k j ) d 2 g ( k i k j ) ,
l i { d ( Δ k ) ρ ( k i + Δ k ) 8 δ 2 k 0 ( n k i ) [ n ( k i + Δ k ) ] d 2 g ( Δ k ) } 1 = 1 8 2 n d δ 2 k 0 2 1 ( n k i ) 3 2 n d κ i 1 4 δ 2 k 0 2 κ i 2 .
Δ p i ( z ) = p i ( z + Δ z ) p i ( z ) = j i p j ( z ) T j i j i p i ( z ) T i j .
Δ p ( z , k ) = d ( Δ k ) ρ ( k + Δ k ) p ( z , k + Δ k ) T ( k + Δ k , k ) d ( Δ k ) ρ ( k + Δ k ) p ( z , k ) T ( k , k + Δ k ) = d ( Δ k ) ρ ( k + Δ k ) T ( k , k + Δ k ) [ p ( z , k + Δ k ) p ( z , k ) ] ,
p ( z , k + Δ k ) p ( z , k ) Δ k p ( z , k ) k + ( Δ k ) 2 2 2 p ( z , k ) k 2 .
ρ ( k + Δ k ) T ( k , k + Δ k ) Δ z 4 2 n δ 2 k 0 2 π d ( n k ) [ n ( k + Δ k ) ] 1 2 g ( Δ k ) Δ z 4 2 n δ 2 k 0 2 π d [ ( n k ) 3 2 Δ k ( n k ) 1 2 2 ] g ( Δ k ) .
Δ p ( z , k ) Δ z 8 δ 2 k 0 2 π d ( n 2 ) 1 2 [ ( n k ) 3 2 2 2 p ( z , k ) k 2 ( n k ) 1 2 2 p ( z , k ) k ] + d ( Δ k ) ( Δ k ) 2 g ( Δ k ) .
p ( z , k ) z = 8 2 n δ 2 d a 2 [ ( n k ) 3 2 2 p ( z , k ) k 2 ( n k ) 1 2 p ( z , k ) k ] ,
p ( z , κ ) z = κ [ κ L D p ( z , κ ) κ ] ,
L D = d a 2 4 n δ 2 .
K β ( κ ) = J 0 ( 2 β κ ) ,
Z β ( z ) = exp ( β z L D ) .
E z , l m ( r , φ ) = J l ( κ l m k 0 r ) exp ( i l φ ) .
κ l m = π M k 0 d ,
M = l + 2 m .
g ( Δ k , Δ k ) = { π a k 0 exp [ ( Δ k a k 0 2 ) 2 ] } { π a k 0 exp [ ( Δ k a k 0 2 ) 2 ] } ,
T l m , l m = Δ z 4 δ 2 k 0 κ l m 2 κ l m 2 d 2 k l m k l m g ( k l m k l m ) .
T l m , l m = Δ z 4 δ 2 k 0 κ l m 2 κ l m 2 d 2 k l m k l m g ( k l m k l m ) [ 1 π d k 0 g ( k l k l ) ] .
k 0 d 2 + d ( Δ k ) π a k 0 exp [ ( Δ k a k 0 2 ) 2 ] = π k 0 d ,
f ( k , k + Δ k ) { 1 for Δ k 0 κ + Δ κ κ n ( k + Δ k ) n k for Δ k > 0 } ,
p ( z , k ) z = 8 2 n δ 2 d a 2 [ ( n k ) 3 2 2 p ( z , k ) k 2 3 2 ( n k ) 1 2 p ( z , k ) k ] = 8 2 n δ 2 d a 2 k [ ( n k ) 3 2 p ( z , k ) k ] .
p ( z , κ ) z = 1 L D κ κ [ κ 2 p ( z , κ ) κ ] .
K β ( κ ) = ( 1 β κ ) J 1 ( 2 β κ ) .
P ( z , κ ) z = 1 L D κ [ κ P ( z , κ ) κ P ( z , κ ) ] = κ L D 2 P ( z , κ ) κ 2 .
p ( z , κ ) = 1 ( z κ 0 L D ) 1 2 exp [ ( κ κ 0 ) 2 4 z κ 0 L D ] ,
L G L D Δ κ 2 κ .
L G l a 2 k 0 2 κ 2 Δ κ 2 n 2 = 4 ( Δ κ 2 n a k 0 κ ) 2

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