Abstract

Using complete modal expansions for the electromagnetic fields above and below a rough interface between free space and chiral media and on imposing exact boundary conditions at the interface, Maxwell’s equations are converted into generalized telegraphists’ equations for the wave amplitudes of different species of waves (radiation far fields, lateral, and surface waves). The local basis functions, used in the complete modal expansions, are functions of the fluctuating surface height and medium parameters. The generalized telegraphists’ equations are coupled first-order differential equations for the forward- and backward-traveling wave amplitudes. The coupling between the different species of waves is due to the fluctuations of the rough surface height and medium parameters. A Taylor series expansion of the surface element scattering matrix in terms of the chiral parameter is used to distinguish between depolarization due to surface roughness and the chiral properties of the medium. The analysis has applications in remote sensing and identification of biological and chemical materials through their optical activity.

© 2013 Optical Society of America

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  1. P. E. Crittenden and E. Bahar, “Electromagnetic wave scattering from a rough interface above a chiral medium: generalized field transforms,” J. Opt. Soc. Am. A30, 325–334 (2012).
  2. S. A. Schelkunoff, “Generalized telegraphists’ equations for waveguides,” Bell Syst. Tech. J. 31, 784–801 (1952).
  3. S. A. Schelkunoff, “Conversions of Maxwell’s equations into generalized telegraphists’ equations,” Bell Syst. Tech. J. 34, 995–1045 (1955).
  4. P. E. Crittenden, “Electromagnetic sensing of chiral materials,” Ph.D. thesis (University of Nebraska Lincoln, 2002).
  5. P. E. Crittenden and E. Bahar, “A modal solution for reflection and transmission at a chiral–chiral interface,” Can. J. Phys. 83, 1267–1290 (2005).
    [CrossRef]
  6. E. Bahar, “Like and cross polarized scatter cross sections for two dimensional, multiscale rough surface based on a full wave variational technique,” Radio Sci. 46, 1–12 (2011).
    [CrossRef]
  7. W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [CrossRef]
  8. S. L. Jacques and R. J. Ramella-Roman, “Propagation of polarized light beams through biological tissues,” Proc. SPIE 3914, 345–352 (2000).
    [CrossRef]
  9. V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7, 300–306 (2002).
    [CrossRef]
  10. L. Wang and S. Jacques, “Non-invasive detection of skin cancers by measuring optical properties of tissue,” Proc. SPIE 2395, 548–558 (1995).
    [CrossRef]
  11. E. Bahar, “Generalized Fourier transform for stratified media,” Can. J. Phys. 50, 3123–3131 (1972).
    [CrossRef]
  12. E. Bahar, “Radio wave propagation in stratified media and non-uniform boundaries and varying electromagnetic parameters—full wave analysis,” Can. J. Phys. 50, 3132–3142 (1972).
    [CrossRef]
  13. E. Bahar and G. G. Rajan, “Depolarization and scattering of electromagnetic waves by irregular boundaries for arbitrary incident and scatter angles—full wave solutions,” IEEE Trans. Antennas Propag. ITA-27, 214–225 (1979).
    [CrossRef]
  14. E. Bahar, “Full wave solutions for the depolarization of the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Antennas Propag. ITA-29, 443–454 (1981).
    [CrossRef]
  15. E. Bahar and Y. Zhang, “Numerical solutions for the scattered fields from rough surfaces using the full wave generalized telegraphists’ equations,” Int. J. Numer. Model. 10, 83–99 (1997).
    [CrossRef]
  16. E. Bahar and B. S. Lee, “Full wave solutions for rough surface bi-static radar cross sections: Comparison with small perturbation, physical optics, numerical, and experimental results,” Radio Sci. 29, 407–429 (1994).
    [CrossRef]
  17. E. Bahar and M. El-Shenawee, “Full wave single and double scatter from rough surfaces,” J. Comput. Phys. 115, 390–398 (1994).
    [CrossRef]
  18. E. Bahar and M. El-Shenawee, “Numerical method to compute TE and TM multiple scatter from rough surfaces exhibiting backscatter enhancement,” IEEE Trans. Magn. 30, 3140–3143 (1994).
    [CrossRef]
  19. E. Bahar and M. El-Shenawee, “Double scatter cross sections for two dimensional random rough surfaces that exhibit backscatter enhancement,” J. Opt. Soc. Am. A 18, 108–109 (2001).
    [CrossRef]
  20. S. O. Rice, “Reflection of electromagnetic waves from a slightly rough surface,” Commun. Pure Appl. Math. 4, 351–378 (1951).
    [CrossRef]
  21. A. Ishmaru, Wave Propagation and Scattering in Random Media (Academic, 1978).
  22. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves From Rough Surfaces (Pergamon, 1963).
  23. P. Beckmann, The Depolarization of Electromagnetic Waves (Golem, 1968).
  24. G. T. Ruek, D. E. Barrick, W. D. Stuart, and C. K. Krechbaum, Radar Cross Section Handbook (Plenum, 1970).
  25. E. Bahar, “Optimum electromagnetic wave excitations of complex media characterized by positive or negative reflective indices and chiral properties,” J. Opt. Soc. Am. 24, 2807–2813 (2007).
    [CrossRef]
  26. E. Bahar, “Cross polarization of lateral waves propagating along a free space-chiral planar interface: application to identification of optically active materials,” J. Opt. Soc. Am. B 28, 1194–1199 (2011).
    [CrossRef]
  27. E. Bahar, “Guided surface waves over a freespace-chiral interface: applications to identification of optically active materials,” J. Opt. Soc. Am. B 28, 868–872 (2011).
    [CrossRef]
  28. E. Bahar, “Comparison of polarimetric techniques for the identification of biological and chemical materials using Mueller matrices, lateral waves and surface waves,” J. Opt. Soc. Am. A 28, 2139–2147 (2011).
    [CrossRef]
  29. E. Bahar, “Coupling between guided surface waves, lateral waves and the radiation fields by rough surfaces—full wave solutions,” IEEE Trans. Microwave Theor. Tech. MTT-25, 923–931 (1977).
    [CrossRef]
  30. E. Bahar, “Excitation of surface waves and the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Microwave Theor. Tech. MTT-28, 999–1006 (1980).
    [CrossRef]
  31. E. Bahar, “Excitation of lateral waves and the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Antennas Propag. ITA-29, 443–454 (1981).
    [CrossRef]
  32. E. Bahar, “Radio waves propagation over a rough variable impedance boundary, part I—full wave analysis,” IEEE Trans. Antennas Propag. ITA-20, 362–368 (1972).
    [CrossRef]

2011

E. Bahar, “Like and cross polarized scatter cross sections for two dimensional, multiscale rough surface based on a full wave variational technique,” Radio Sci. 46, 1–12 (2011).
[CrossRef]

E. Bahar, “Guided surface waves over a freespace-chiral interface: applications to identification of optically active materials,” J. Opt. Soc. Am. B 28, 868–872 (2011).
[CrossRef]

E. Bahar, “Cross polarization of lateral waves propagating along a free space-chiral planar interface: application to identification of optically active materials,” J. Opt. Soc. Am. B 28, 1194–1199 (2011).
[CrossRef]

E. Bahar, “Comparison of polarimetric techniques for the identification of biological and chemical materials using Mueller matrices, lateral waves and surface waves,” J. Opt. Soc. Am. A 28, 2139–2147 (2011).
[CrossRef]

2007

E. Bahar, “Optimum electromagnetic wave excitations of complex media characterized by positive or negative reflective indices and chiral properties,” J. Opt. Soc. Am. 24, 2807–2813 (2007).
[CrossRef]

2005

P. E. Crittenden and E. Bahar, “A modal solution for reflection and transmission at a chiral–chiral interface,” Can. J. Phys. 83, 1267–1290 (2005).
[CrossRef]

2002

V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7, 300–306 (2002).
[CrossRef]

2001

2000

S. L. Jacques and R. J. Ramella-Roman, “Propagation of polarized light beams through biological tissues,” Proc. SPIE 3914, 345–352 (2000).
[CrossRef]

1997

E. Bahar and Y. Zhang, “Numerical solutions for the scattered fields from rough surfaces using the full wave generalized telegraphists’ equations,” Int. J. Numer. Model. 10, 83–99 (1997).
[CrossRef]

1995

L. Wang and S. Jacques, “Non-invasive detection of skin cancers by measuring optical properties of tissue,” Proc. SPIE 2395, 548–558 (1995).
[CrossRef]

1994

E. Bahar and B. S. Lee, “Full wave solutions for rough surface bi-static radar cross sections: Comparison with small perturbation, physical optics, numerical, and experimental results,” Radio Sci. 29, 407–429 (1994).
[CrossRef]

E. Bahar and M. El-Shenawee, “Full wave single and double scatter from rough surfaces,” J. Comput. Phys. 115, 390–398 (1994).
[CrossRef]

E. Bahar and M. El-Shenawee, “Numerical method to compute TE and TM multiple scatter from rough surfaces exhibiting backscatter enhancement,” IEEE Trans. Magn. 30, 3140–3143 (1994).
[CrossRef]

1990

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

1981

E. Bahar, “Full wave solutions for the depolarization of the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Antennas Propag. ITA-29, 443–454 (1981).
[CrossRef]

E. Bahar, “Excitation of lateral waves and the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Antennas Propag. ITA-29, 443–454 (1981).
[CrossRef]

1980

E. Bahar, “Excitation of surface waves and the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Microwave Theor. Tech. MTT-28, 999–1006 (1980).
[CrossRef]

1979

E. Bahar and G. G. Rajan, “Depolarization and scattering of electromagnetic waves by irregular boundaries for arbitrary incident and scatter angles—full wave solutions,” IEEE Trans. Antennas Propag. ITA-27, 214–225 (1979).
[CrossRef]

1977

E. Bahar, “Coupling between guided surface waves, lateral waves and the radiation fields by rough surfaces—full wave solutions,” IEEE Trans. Microwave Theor. Tech. MTT-25, 923–931 (1977).
[CrossRef]

1972

E. Bahar, “Radio waves propagation over a rough variable impedance boundary, part I—full wave analysis,” IEEE Trans. Antennas Propag. ITA-20, 362–368 (1972).
[CrossRef]

E. Bahar, “Generalized Fourier transform for stratified media,” Can. J. Phys. 50, 3123–3131 (1972).
[CrossRef]

E. Bahar, “Radio wave propagation in stratified media and non-uniform boundaries and varying electromagnetic parameters—full wave analysis,” Can. J. Phys. 50, 3132–3142 (1972).
[CrossRef]

1955

S. A. Schelkunoff, “Conversions of Maxwell’s equations into generalized telegraphists’ equations,” Bell Syst. Tech. J. 34, 995–1045 (1955).

1952

S. A. Schelkunoff, “Generalized telegraphists’ equations for waveguides,” Bell Syst. Tech. J. 31, 784–801 (1952).

1951

S. O. Rice, “Reflection of electromagnetic waves from a slightly rough surface,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

Bahar, E.

E. Bahar, “Cross polarization of lateral waves propagating along a free space-chiral planar interface: application to identification of optically active materials,” J. Opt. Soc. Am. B 28, 1194–1199 (2011).
[CrossRef]

E. Bahar, “Comparison of polarimetric techniques for the identification of biological and chemical materials using Mueller matrices, lateral waves and surface waves,” J. Opt. Soc. Am. A 28, 2139–2147 (2011).
[CrossRef]

E. Bahar, “Like and cross polarized scatter cross sections for two dimensional, multiscale rough surface based on a full wave variational technique,” Radio Sci. 46, 1–12 (2011).
[CrossRef]

E. Bahar, “Guided surface waves over a freespace-chiral interface: applications to identification of optically active materials,” J. Opt. Soc. Am. B 28, 868–872 (2011).
[CrossRef]

E. Bahar, “Optimum electromagnetic wave excitations of complex media characterized by positive or negative reflective indices and chiral properties,” J. Opt. Soc. Am. 24, 2807–2813 (2007).
[CrossRef]

P. E. Crittenden and E. Bahar, “A modal solution for reflection and transmission at a chiral–chiral interface,” Can. J. Phys. 83, 1267–1290 (2005).
[CrossRef]

E. Bahar and M. El-Shenawee, “Double scatter cross sections for two dimensional random rough surfaces that exhibit backscatter enhancement,” J. Opt. Soc. Am. A 18, 108–109 (2001).
[CrossRef]

E. Bahar and Y. Zhang, “Numerical solutions for the scattered fields from rough surfaces using the full wave generalized telegraphists’ equations,” Int. J. Numer. Model. 10, 83–99 (1997).
[CrossRef]

E. Bahar and B. S. Lee, “Full wave solutions for rough surface bi-static radar cross sections: Comparison with small perturbation, physical optics, numerical, and experimental results,” Radio Sci. 29, 407–429 (1994).
[CrossRef]

E. Bahar and M. El-Shenawee, “Numerical method to compute TE and TM multiple scatter from rough surfaces exhibiting backscatter enhancement,” IEEE Trans. Magn. 30, 3140–3143 (1994).
[CrossRef]

E. Bahar and M. El-Shenawee, “Full wave single and double scatter from rough surfaces,” J. Comput. Phys. 115, 390–398 (1994).
[CrossRef]

E. Bahar, “Full wave solutions for the depolarization of the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Antennas Propag. ITA-29, 443–454 (1981).
[CrossRef]

E. Bahar, “Excitation of lateral waves and the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Antennas Propag. ITA-29, 443–454 (1981).
[CrossRef]

E. Bahar, “Excitation of surface waves and the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Microwave Theor. Tech. MTT-28, 999–1006 (1980).
[CrossRef]

E. Bahar and G. G. Rajan, “Depolarization and scattering of electromagnetic waves by irregular boundaries for arbitrary incident and scatter angles—full wave solutions,” IEEE Trans. Antennas Propag. ITA-27, 214–225 (1979).
[CrossRef]

E. Bahar, “Coupling between guided surface waves, lateral waves and the radiation fields by rough surfaces—full wave solutions,” IEEE Trans. Microwave Theor. Tech. MTT-25, 923–931 (1977).
[CrossRef]

E. Bahar, “Radio wave propagation in stratified media and non-uniform boundaries and varying electromagnetic parameters—full wave analysis,” Can. J. Phys. 50, 3132–3142 (1972).
[CrossRef]

E. Bahar, “Generalized Fourier transform for stratified media,” Can. J. Phys. 50, 3123–3131 (1972).
[CrossRef]

E. Bahar, “Radio waves propagation over a rough variable impedance boundary, part I—full wave analysis,” IEEE Trans. Antennas Propag. ITA-20, 362–368 (1972).
[CrossRef]

P. E. Crittenden and E. Bahar, “Electromagnetic wave scattering from a rough interface above a chiral medium: generalized field transforms,” J. Opt. Soc. Am. A30, 325–334 (2012).

Barrick, D. E.

G. T. Ruek, D. E. Barrick, W. D. Stuart, and C. K. Krechbaum, Radar Cross Section Handbook (Plenum, 1970).

Beckmann, P.

P. Beckmann, The Depolarization of Electromagnetic Waves (Golem, 1968).

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves From Rough Surfaces (Pergamon, 1963).

Cheong, W. F.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Crittenden, P. E.

P. E. Crittenden and E. Bahar, “A modal solution for reflection and transmission at a chiral–chiral interface,” Can. J. Phys. 83, 1267–1290 (2005).
[CrossRef]

P. E. Crittenden, “Electromagnetic sensing of chiral materials,” Ph.D. thesis (University of Nebraska Lincoln, 2002).

P. E. Crittenden and E. Bahar, “Electromagnetic wave scattering from a rough interface above a chiral medium: generalized field transforms,” J. Opt. Soc. Am. A30, 325–334 (2012).

El-Shenawee, M.

E. Bahar and M. El-Shenawee, “Double scatter cross sections for two dimensional random rough surfaces that exhibit backscatter enhancement,” J. Opt. Soc. Am. A 18, 108–109 (2001).
[CrossRef]

E. Bahar and M. El-Shenawee, “Full wave single and double scatter from rough surfaces,” J. Comput. Phys. 115, 390–398 (1994).
[CrossRef]

E. Bahar and M. El-Shenawee, “Numerical method to compute TE and TM multiple scatter from rough surfaces exhibiting backscatter enhancement,” IEEE Trans. Magn. 30, 3140–3143 (1994).
[CrossRef]

Ishmaru, A.

A. Ishmaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

Jacques, S.

L. Wang and S. Jacques, “Non-invasive detection of skin cancers by measuring optical properties of tissue,” Proc. SPIE 2395, 548–558 (1995).
[CrossRef]

Jacques, S. L.

S. L. Jacques and R. J. Ramella-Roman, “Propagation of polarized light beams through biological tissues,” Proc. SPIE 3914, 345–352 (2000).
[CrossRef]

Krechbaum, C. K.

G. T. Ruek, D. E. Barrick, W. D. Stuart, and C. K. Krechbaum, Radar Cross Section Handbook (Plenum, 1970).

Lee, B. S.

E. Bahar and B. S. Lee, “Full wave solutions for rough surface bi-static radar cross sections: Comparison with small perturbation, physical optics, numerical, and experimental results,” Radio Sci. 29, 407–429 (1994).
[CrossRef]

Maitland, D. J.

V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7, 300–306 (2002).
[CrossRef]

Prahl, S. A.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Rajan, G. G.

E. Bahar and G. G. Rajan, “Depolarization and scattering of electromagnetic waves by irregular boundaries for arbitrary incident and scatter angles—full wave solutions,” IEEE Trans. Antennas Propag. ITA-27, 214–225 (1979).
[CrossRef]

Ramella-Roman, R. J.

S. L. Jacques and R. J. Ramella-Roman, “Propagation of polarized light beams through biological tissues,” Proc. SPIE 3914, 345–352 (2000).
[CrossRef]

Rice, S. O.

S. O. Rice, “Reflection of electromagnetic waves from a slightly rough surface,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

Ruek, G. T.

G. T. Ruek, D. E. Barrick, W. D. Stuart, and C. K. Krechbaum, Radar Cross Section Handbook (Plenum, 1970).

Sankaran, V.

V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7, 300–306 (2002).
[CrossRef]

Schelkunoff, S. A.

S. A. Schelkunoff, “Conversions of Maxwell’s equations into generalized telegraphists’ equations,” Bell Syst. Tech. J. 34, 995–1045 (1955).

S. A. Schelkunoff, “Generalized telegraphists’ equations for waveguides,” Bell Syst. Tech. J. 31, 784–801 (1952).

Spizzichino, A.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves From Rough Surfaces (Pergamon, 1963).

Stuart, W. D.

G. T. Ruek, D. E. Barrick, W. D. Stuart, and C. K. Krechbaum, Radar Cross Section Handbook (Plenum, 1970).

Walsh, J. T.

V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7, 300–306 (2002).
[CrossRef]

Wang, L.

L. Wang and S. Jacques, “Non-invasive detection of skin cancers by measuring optical properties of tissue,” Proc. SPIE 2395, 548–558 (1995).
[CrossRef]

Welch, A. J.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Zhang, Y.

E. Bahar and Y. Zhang, “Numerical solutions for the scattered fields from rough surfaces using the full wave generalized telegraphists’ equations,” Int. J. Numer. Model. 10, 83–99 (1997).
[CrossRef]

Bell Syst. Tech. J.

S. A. Schelkunoff, “Generalized telegraphists’ equations for waveguides,” Bell Syst. Tech. J. 31, 784–801 (1952).

S. A. Schelkunoff, “Conversions of Maxwell’s equations into generalized telegraphists’ equations,” Bell Syst. Tech. J. 34, 995–1045 (1955).

Can. J. Phys.

P. E. Crittenden and E. Bahar, “A modal solution for reflection and transmission at a chiral–chiral interface,” Can. J. Phys. 83, 1267–1290 (2005).
[CrossRef]

E. Bahar, “Generalized Fourier transform for stratified media,” Can. J. Phys. 50, 3123–3131 (1972).
[CrossRef]

E. Bahar, “Radio wave propagation in stratified media and non-uniform boundaries and varying electromagnetic parameters—full wave analysis,” Can. J. Phys. 50, 3132–3142 (1972).
[CrossRef]

Commun. Pure Appl. Math.

S. O. Rice, “Reflection of electromagnetic waves from a slightly rough surface,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

IEEE J. Quantum Electron.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

IEEE Trans. Antennas Propag.

E. Bahar and G. G. Rajan, “Depolarization and scattering of electromagnetic waves by irregular boundaries for arbitrary incident and scatter angles—full wave solutions,” IEEE Trans. Antennas Propag. ITA-27, 214–225 (1979).
[CrossRef]

E. Bahar, “Full wave solutions for the depolarization of the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Antennas Propag. ITA-29, 443–454 (1981).
[CrossRef]

E. Bahar, “Excitation of lateral waves and the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Antennas Propag. ITA-29, 443–454 (1981).
[CrossRef]

E. Bahar, “Radio waves propagation over a rough variable impedance boundary, part I—full wave analysis,” IEEE Trans. Antennas Propag. ITA-20, 362–368 (1972).
[CrossRef]

IEEE Trans. Magn.

E. Bahar and M. El-Shenawee, “Numerical method to compute TE and TM multiple scatter from rough surfaces exhibiting backscatter enhancement,” IEEE Trans. Magn. 30, 3140–3143 (1994).
[CrossRef]

IEEE Trans. Microwave Theor. Tech.

E. Bahar, “Coupling between guided surface waves, lateral waves and the radiation fields by rough surfaces—full wave solutions,” IEEE Trans. Microwave Theor. Tech. MTT-25, 923–931 (1977).
[CrossRef]

E. Bahar, “Excitation of surface waves and the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Microwave Theor. Tech. MTT-28, 999–1006 (1980).
[CrossRef]

Int. J. Numer. Model.

E. Bahar and Y. Zhang, “Numerical solutions for the scattered fields from rough surfaces using the full wave generalized telegraphists’ equations,” Int. J. Numer. Model. 10, 83–99 (1997).
[CrossRef]

J. Biomed. Opt.

V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7, 300–306 (2002).
[CrossRef]

J. Comput. Phys.

E. Bahar and M. El-Shenawee, “Full wave single and double scatter from rough surfaces,” J. Comput. Phys. 115, 390–398 (1994).
[CrossRef]

J. Opt. Soc. Am.

E. Bahar, “Optimum electromagnetic wave excitations of complex media characterized by positive or negative reflective indices and chiral properties,” J. Opt. Soc. Am. 24, 2807–2813 (2007).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

E. Bahar, “Cross polarization of lateral waves propagating along a free space-chiral planar interface: application to identification of optically active materials,” J. Opt. Soc. Am. B 28, 1194–1199 (2011).
[CrossRef]

E. Bahar, “Guided surface waves over a freespace-chiral interface: applications to identification of optically active materials,” J. Opt. Soc. Am. B 28, 868–872 (2011).
[CrossRef]

Proc. SPIE

L. Wang and S. Jacques, “Non-invasive detection of skin cancers by measuring optical properties of tissue,” Proc. SPIE 2395, 548–558 (1995).
[CrossRef]

S. L. Jacques and R. J. Ramella-Roman, “Propagation of polarized light beams through biological tissues,” Proc. SPIE 3914, 345–352 (2000).
[CrossRef]

Radio Sci.

E. Bahar, “Like and cross polarized scatter cross sections for two dimensional, multiscale rough surface based on a full wave variational technique,” Radio Sci. 46, 1–12 (2011).
[CrossRef]

E. Bahar and B. S. Lee, “Full wave solutions for rough surface bi-static radar cross sections: Comparison with small perturbation, physical optics, numerical, and experimental results,” Radio Sci. 29, 407–429 (1994).
[CrossRef]

Other

A. Ishmaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves From Rough Surfaces (Pergamon, 1963).

P. Beckmann, The Depolarization of Electromagnetic Waves (Golem, 1968).

G. T. Ruek, D. E. Barrick, W. D. Stuart, and C. K. Krechbaum, Radar Cross Section Handbook (Plenum, 1970).

P. E. Crittenden, “Electromagnetic sensing of chiral materials,” Ph.D. thesis (University of Nebraska Lincoln, 2002).

P. E. Crittenden and E. Bahar, “Electromagnetic wave scattering from a rough interface above a chiral medium: generalized field transforms,” J. Opt. Soc. Am. A30, 325–334 (2012).

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Equations (74)

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EyxExy=γ2β1Ezjωμ(γk)2HzKz2(γ1k+γ2k),
HyxHxy=γ2β1Hz+jωϵ(γk)2EzjζKz2(γ1kγ2k).
γ1=k1kβ,γ2=k1+kβ
K=Kδ(xx)δ(yy)az=Kzaz.
H=Q1+Q2andE=jη(Q1Q2).
Q1x=1γ1Q1zy,Q1y=1γ1Q1zx,
Q2x=1γ2Q2zy,Q2y=1γ2Q2zx.
Q1yx=1γ12Q1zy2+γ1Q1zjζKγ12kδ(xx)δ(yy),
Q2yx=1γ22Q2zy2+γ2Q2zjζKγ22kδ(xx)δ(yy).
[ψijR+ψijL]hh+=0,[ηψijRηψijL]hh+=0,
[ηγ1ψijRy+ηγ2ψijLy]hh+=0,[1γ1ψijRy1γ2ψijLy]hh+=0,
[kγ1ΨijR+kγ2ΨijL]hh+=0,[ηkγ1ΨijRηkγ2ΨijL]hh+=0,
[ηkγ12ΨijRy+ηkγ22ΨijLy]hh+=0,[kγ12ΨijRykγ22ΨijLy]hh+=0.
Hz(x,h+)=Hz(x,h),Ez(x,h+)=Ez(x,h),
Ey(x,h+)sinθ+Ex(x,h+)cosθ=Ey(x,h)sinθ+Ex(x,h)cosθ,
Hy(x,h+)sinθ+Hx(x,h+)cosθ=Hy(x,h)sinθ+Hx(x,h)cosθ.
[Q1z+Q2z]hh+=0,[η(Q1zQ2z)]=0,
[η(Q1yQ2y)sinθ+η(Q1xQ2x)cosθ]hh+=0,
[(Q1y+Q2y)sinθ+(Q1x+Q2x)cosθ]hh+=0.
[η(Q1yQ2y)h(x)+ηy(Q1zγ1+Q2zγ2)]hh+=0,
[(Q1y+Q2y)h(x)+y(Q1zγ1Q2zγ2)]hh+=0.
ddxϕ1(x)ϕ2(x)f(x,y)dy=ϕ1(x)ϕ2(x)f(x,y)xdy+f(x,ϕ2(x))ϕ2(x)f(x,ϕ1(x))ϕ2(x).
[ΨijRyηkγ12Q1z+ΨijLyηkγ22Q2z]hh+=0,
[(ΨijRηkγ1Q1yΨijLηkγ2Q2y)h(x)+ΨijRηkγ12Q1zy+ΨijLηkγ22Q2zy]hh+=0.
jηkγ1Q1yxΨijRdy=ddxjηkγ1Q1yΨijRdyjQ1yx(ηkγ1ΨijR)dy+[jηkγ1Q1yΨijR]hh+h(x).
ddxE^yij(x,u)ψmnR(u,y)ΨijR(u,y)YR(u,y)dy+mnGmnijR(u,u)E^ymn(x,u).
GmnijR(u,u)=qγ1ψmnR(u,y)x[ηkγ1ΨijR(u,y)]dy.
xdhdxh+dϵdxμ+dμdxμ+dβdxβ.
jηkγ122Q1zy2ΨijR(u,y)dy=jηkγ12Q1z(x,y)2ΨijRy2dy[jηkγ12{Q1z(x,y)yΨijR(u,y)Q1z(x,y)ΨijR(u,y)y}]hh+.
jηkγ12Q1z(x,y)2ΨijR(u,y)y2dy=Q1z(x,y)jqΨijR(u,y)YR(u,y)dyjηkQ1z(x,y)ΨijR(u,y)dy.
jmnH^zmn(x,u)qψmnRΨijR(uy)YR(uy)dy.
K2δ(xx)δ(yy)ΨijR(u,y)dy=K2δ(xx)ΨijR(u,y)KijR(x,u)2.
ddxmnE^ymnψmnR(u,y)ΨijR(u,y)YR(u,y)dy=mnGmnijR(u,u)E^ymn(x,u)+jmnH^zmn(x,u)qψmnR(u,y)ΨijR(u,y)YR(u,y)dy+KijR(x,u)2j[ηkγ1Q1yΨijR]hh+h(x)j[ηkγ12Q1zyΨijR]hh++j[ηkγ12Q1zΨijRy]hh+.
ddxmnE^ymnψmnL(u,y)ΨijL(u,y)YL(u,y)dy=mnGmnijL(u,u)E^ymn(x,u)+jmnH^zmn(x,u)qψmnL(u,y)ΨijL(u,y)YL(u,y)dy+KijL(x,u)2j[ηkγ2Q2yΨijL]hh+h(x)j[ηkγ22Q2zyΨijL]hh++j[ηkγ22Q2zΨijLy]hh+.
GmnijL(u,u)qγ2ψmnL(u,y)x[ηkγ2ΨijL(u,y)]dy
KijLKδ(xx)ΨijL(u,y).
ddxE^yij(x,u)=jqH^ij(x,u)mnGmnij(u,u)E^ymn(x,u)+Kij(x,u)2.
Gmnij(u,u)=GmnijR(u,u)+GmnijL(u,u),
Kij(x,u)=KijR(x,u)+KijL(x,u).
ddxmnH^zmn(x,u)ψmnR(u,y)ΨijR(u,y)YR(u,y)dy=jmnE^ymn(x,u)qψmnR(u,y)ΨijR(u,y)YR(u,y)dyH^zmn(x,u)ψmnR(u,y)x[ΨijR(u,y)YR(u,y)]dy+[Q1zΨijRYR]hh+h(x)
ddxmnH^zmn(x,u)ψmnL(u,y)ΨijL(u,y)YL(u,y)dy=jmnE^ymn(x,u)qψmnL(u,y)ΨijL(u,y)YL(u,y)dyH^zmn(x,u)ψmnL(u,y)x[ΨijL(u,y)YL(u,y)]dy+[Q2zΨijLYL]hh+h(x).
ddxH^zij(x,u)jqE^yij(x,u)=mnGmnij(u,u)H^zmn(x,u).
ddxE^yij(x,u)jqH^zij(x,u)=mnGmnij(u,u)E^ymn(x,u)+Kij(x,u)2,
ddxH^zij(x,u)jqE^yij(x,u)=mnGijmn(u,u)H^zmn(x,u).
H^zij(x,u)=aij(x,u)+bij(x,u)
E^yij(x,u)=aij(x,y)bij(x,u).
ddxaij(x,u)jqaij(x,u)=mnSijmnaa(u,u)amn(x,u)+mnSijmnab(u,u)bmn(x,u)+Kij(x,u)4
ddxbij(x,u)+jqbij(x,u)=mnSijmnba(u,u)amn(x,u)+mnSijmnbb(u,u)bmn(x,u)Kij(x,u)4.
Sijmncd(u,u)=12[Gijmn(u,u)Gmnij(u,u)].
Gmnij(u,u)=(qγ1ψmnR(u,y)x[ηkγ1ΨijR(u,y)]+qγ2ψmnL(u,y)x[ηkγ1ΨijL(u,y)])dy=GmnijR+GmnijL.
[S]=[S]0+k1β1[S]0.
[S(kr,ki)]=2cosθ0rcosθ0i[R0(kr,ki)].
R0(kr,ki)=[R0VVR0VHR0HVR0HH].
R0VV=[μrC1rC1icos(ϕrϕi)S0rS0i](11εr)+(1μr)cos(ϕrϕi)(C0r+ηrC1r)(C0i+ηrC1i),
R0HH=[εrC1rC1icos(ϕrϕi)S0rS0i](11μr)+(1εr)cos(ϕrϕi)(C0r+C1r/ηr)(C0i+C1i/ηr),
R0HV=ηr[(11μr)C1r(11εr)C1i]sin(ϕrϕi)(C0r+C1r/ηr)(C0i+ηrC1i),
R0VH=ηr[(11εr)C1r(11μr)C1i]sin(ϕrϕi)(C0r+ηrC1r)(C0i+C1i/ηr).
k0rk0nr=k0(sinθ0rcosϕrax+cosθ0ray+sinθ0rcosϕraz)
k0ik0ni=k0(sinθ0icosϕiaxcosθ0iay+sinθ0icosϕiaz).
[ErVErH]=G0llLL[S(kf,ki)][exp(iv·rs)exp(iv·rt)]dxsdzs[EiVEiH]=GfGDf.
rs=xsax+hay+zsaz,r=xax+yay+zaz=rnr.
rt=rs(h=0),
v=k0(nrni)=vxax+vyay+vzaz,
G0=k02exp(ik0r)/2πivyr.
n=(hxax+ayhzaz)/(1+hx2ax+hz2az),
nr·ay=cosθ0randni·ay=cosθ0i
nr·n=cosθ0nrandni·n=cosθ0ni
cos(ϕrϕi)=(ni×ay)·(nr×ay)
cos(ϕnrϕni)==(ni×n)·(nr×n).
ns=v/v=(krki)|krki|.
R0n=[R0nVV00R0nHH].
k1β1[S]0=2cosθ0nicosθ0nr[0R0nVHR0nHV0].
R0nVH=R0nHV=12jk1β1T01nHHT10nVVtanθ1n2.
T01nVVT10nHH=T01nHHT10nVV=4cosθ0ncosθ1n[(Y0cosθ0n+Y1cosθ1n)(Z0cosθ0n+Z1cosθ1n)].

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