Abstract

The boundary-value problem of the propagation of Dyakonov–Tamm waves localized to a central twist defect in a structurally chiral material was formulated and numerically solved. The angular magnitude of the twist defect and the orientation of the twist defect relative to the direction of propagation were varied. Detailed analysis showed that either two or three different Dyakonov–Tamm waves can propagate, depending on the angular magnitude and the orientation of the twist defect. These waves have different phase speeds and degrees of localization to the twist–defect interface. The most localized Dyakonov–Tamm waves are essentially confined to within two structural periods of the twist–defect interface on either side.

© 2009 Optical Society of America

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    [CrossRef]
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2009 (3)

J. Gao, A. Lakhtakia, J. A. Polo, Jr., and M. K. Lei, “Dyakonov-Tamm wave guided by a twist defect in a structurally chiral material,” J. Opt. Soc. Am. A 26, 1615-1621 (2009). Replace zn+/-+/-γ by ΠΩzn+/-+/-γ in Eq. .
[CrossRef]

K. Agarwal, J. A. Polo, Jr., and A. Lakhtakia, “Theory of Dyakonov-Tamm waves at the planar interface of a sculptured nematic thin film and an isotropic dielectric material,” J. Opt. A 11, 074003 (2009).
[CrossRef]

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of Dyakonov surface waves,” Phys. Rev. Lett. 102, 043903 (2009).
[CrossRef] [PubMed]

2008 (4)

A. M. Furs and L. M. Barkovsky, “Surface polaritons at the planar interface of twinned gyrotropic dielectric media,” Electromagnetics 28, 146-161 (2008).
[CrossRef]

S. R. Nelatury, J. A. Polo Jr., and A. Lakhtakia, “Electrical control of surface-wave propagation at the planar interface of a linear electro-optic material and an isotropic dielectric material,” Electromagnetics 28, 162-174 (2008).
[CrossRef]

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126-145 (2008).
[CrossRef]

S. R. Nelatury, J. A. Polo Jr., and A. Lakhtakia, “On widening the angular existence domain for Dyakonov surface waves using the Pockels effect,” Microwave Opt. Technol. Lett. 50, 2360-2362 (2008).
[CrossRef]

2007 (6)

A. M. Merzlikin, A. P. Vinogradov, A. V. Dorofeenko, M. Inoue, M. Levy, and A. B. Granovsky, “Controllable Tamm states in magnetophotonic crystal,” Physica B 394, 277-280 (2007).
[CrossRef]

J. A. Polo, Jr., S. R. Nelatury, and A. Lakhtakia, “Propagation of surface waves at the planar interface of a columnar thin film and an isotropic substrate,” J. Nanophotonics 1, 013501 (2007).
[CrossRef]

J. A. Polo, Jr., S. R. Nelatury, and A. Lakhtakia, “Surface waves at a biaxial bicrystalline interface,” J. Opt. Soc. Am. A 24, 2974-2979 (2007).
[CrossRef]

A. Lakhtakia and J. A. Polo, Jr., “Dyakonov-Tamm wave at the planar interface of a chiral sculptured thin film and an isotropic dielectric material,” J. Eur. Opt. Soc. Rapid Publ. 2, 07021 (2007).
[CrossRef]

A. Lakhtakia, “Generation of spectral holes by inserting central structurally chiral layer defects in periodic structurally chiral materials,” Opt. Commun. 275, 283-287 (2007).
[CrossRef]

A. H. Gevorgyan and M. Z. Harutyunyan, “Chiral photonic crystals with an anisotropic defect layer,” Phys. Rev. E 76, 031701 (2007).
[CrossRef]

2006 (3)

J. A. Polo, Jr., S. Nelatury, and A. Lakhtakia, “Surface electromagnetic wave at a tilted uniaxial bicrystalline interface,” Electromagnetics 26, 629-642 (2006).
[CrossRef]

J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals,” J. Opt. A 8, 630-638 (2006).
[CrossRef]

A. Namdar, I. V. Shadrivov, and Y. S. Kivshar, “Backward Tamm states in left-handed metamaterials,” Appl. Phys. Lett. 89, 114104 (2006).
[CrossRef]

2005 (2)

F. Wang and A. Lakhtakia, “Optical crossover phenomenon due to a central 90°-twist defect in a chiral sculptured thin film or chiral liquid crystal,” Proc. R. Soc. London Ser. A 461, 2985-3004 (2005).
[CrossRef]

L.-C. Crasovan, D. Artigas, D. Mihalache, and L. Torner, “Optical Dyakonov surface waves at magnetic interfaces,” Opt. Lett. 30, 3075-3077 (2005).
[CrossRef] [PubMed]

2004 (2)

J. A. Polo, Jr. and A. Lakhtakia, “Comparison of two methods for oblique propagation in helicoidal bianisotropic mediums,” Opt. Commun. 230, 369-386 (2004).
[CrossRef]

M. Becchi, S. Ponti, J. A. Reyes, and C. Oldano, “Defect modes in helical photonic crystals: an analytic approach,” Phys. Rev. B 70, 033103 (2004).
[CrossRef]

2003 (1)

J. Schmidtke, W. Stille, and H. Finkelmann, “Defect mode emission of a dye-doped cholesteric polymer network,” Phys. Rev. Lett. 90, 083902 (2003).
[CrossRef] [PubMed]

2002 (2)

V. I. Kopp and A. Z. Genack, “Twist defect in chiral photonic structures,” Phys. Rev. Lett. 89, 033901 (2002).
[CrossRef] [PubMed]

A. Lakhtakia, “Sculptured thin films: accomplishments and emerging uses,” Mater. Sci. Eng. C 19, 427-434 (2002).
[CrossRef]

2001 (3)

A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculptured thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33-46 (2001).
[CrossRef]

A. N. Darinskii, “Dispersionless polaritons on a twist boundary in optically uniaxial crystals,” Crystallogr. Rep. 46, 842-844 (2001).
[CrossRef]

M. Schubert and C. M. Herzinger, “Ellipsometry on anisotropic materials: Bragg conditions and phonons in dielectric helical thin films,” Phys. Status Solidi A 188, 1563-1575 (2001).
[CrossRef]

2000 (3)

V. C. Venugopal and A. Lakhtakia, “Electromagnetic plane-wave response characteristics of non-axially excited slabs of dielectric thin-film helicoidal bianisotropic mediums,” Proc. R. Soc. London Ser. A 456, 125-161 (2000).
[CrossRef]

Q. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circular polarization filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863-1868 (2000).
[CrossRef]

I. J. Hodgkinson, Q. H. Wu, K. E. Thorn, A. Lakhtakia, andM. W. McCall, “Spacerless circular-polarization spectral-hole filters using chiral sculptured thin films: theory and experiment,” Opt. Commun. 184, 57-66 (2000).
[CrossRef]

1999 (1)

A. Lakhtakia and V. C. Venugopal, “On Bragg reflection by helicoidal bianisotropic mediums,” Arch. Elektr. Üebertrag. 53, 287-290 (1999).

1998 (1)

1997 (1)

A. Lakhtakia and W. S. Weiglhofer, “Further results on light propagation in helicoidal bianisotropic mediums: oblique propagation,” Proc. R. Soc. London Ser. A 453, 93-105 (1997).
[CrossRef]

1995 (1)

L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, “Hybrid waves guided by ultrathin films,” J. Lightwave Technol. 13, 2027-2033 (1995).
[CrossRef]

1994 (1)

G. P. Agrawal and S. Radic, “Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photon. Technol. Lett. 6, 995-997 (1994).
[CrossRef]

1993 (1)

L. Torner, J. P. Torres, and D. Mihalache, “New type of guided waves in birefringent media,” IEEE Photonics Technol. Lett. 5, 201-203 (1993).
[CrossRef]

1990 (2)

N. S. Averkiev and M. I. Dyakonov, “Electromagnetic waves localized at the interface of transparent anisotropic media,” Opt. Spectrosc. 68, 653-655 (1990).

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, “Observation of 'Tamm states' in superlattices,” Phys. Rev. Lett. 64, 2555-2558 (1990).
[CrossRef] [PubMed]

1988 (1)

M. I. D'yakonov, “New type of electromagnetic wave propagating at an interface,” Sov. Phys. JETP 67, 714-716 (1988).

1985 (1)

I. Abdulhalim, L. Benguigui, and R. Weil, “Selective reflection by helicoidal liquid crystals, results of an exact calculation using the 4 × 4 characteristic matrix method,” J. Phys. 46, 815-825 (1985).
[CrossRef]

1983 (1)

W. E. Haas, “Liquid crystal display research: the first fifteen years,” Mol. Cryst. Liq. Cryst. 94, 1-31 (1983).
[CrossRef]

1976 (1)

H. A. Haus and C. V. Shank, “Asymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. 12, 532-539 (1976).
[CrossRef]

1932 (1)

I. Tamm, “Über eine mögliche Art der Elektronenbindung an Kristalloberflächen,” Z. Phys. A 76, 849-850 (1932).

Abdulhalim, I.

I. Abdulhalim, L. Benguigui, and R. Weil, “Selective reflection by helicoidal liquid crystals, results of an exact calculation using the 4 × 4 characteristic matrix method,” J. Phys. 46, 815-825 (1985).
[CrossRef]

Agarwal, K.

K. Agarwal, J. A. Polo, Jr., and A. Lakhtakia, “Theory of Dyakonov-Tamm waves at the planar interface of a sculptured nematic thin film and an isotropic dielectric material,” J. Opt. A 11, 074003 (2009).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal and S. Radic, “Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photon. Technol. Lett. 6, 995-997 (1994).
[CrossRef]

Agulló-Rueda, F.

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, “Observation of 'Tamm states' in superlattices,” Phys. Rev. Lett. 64, 2555-2558 (1990).
[CrossRef] [PubMed]

Artigas, D.

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of Dyakonov surface waves,” Phys. Rev. Lett. 102, 043903 (2009).
[CrossRef] [PubMed]

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126-145 (2008).
[CrossRef]

L.-C. Crasovan, D. Artigas, D. Mihalache, and L. Torner, “Optical Dyakonov surface waves at magnetic interfaces,” Opt. Lett. 30, 3075-3077 (2005).
[CrossRef] [PubMed]

Averkiev, N. S.

N. S. Averkiev and M. I. Dyakonov, “Electromagnetic waves localized at the interface of transparent anisotropic media,” Opt. Spectrosc. 68, 653-655 (1990).

Barkovsky, L. M.

A. M. Furs and L. M. Barkovsky, “Surface polaritons at the planar interface of twinned gyrotropic dielectric media,” Electromagnetics 28, 146-161 (2008).
[CrossRef]

Baumeister, P. W.

P. W. Baumeister, Optical Coating Technology (SPIE Press, 2004).
[CrossRef]

Becchi, M.

M. Becchi, S. Ponti, J. A. Reyes, and C. Oldano, “Defect modes in helical photonic crystals: an analytic approach,” Phys. Rev. B 70, 033103 (2004).
[CrossRef]

Benguigui, L.

I. Abdulhalim, L. Benguigui, and R. Weil, “Selective reflection by helicoidal liquid crystals, results of an exact calculation using the 4 × 4 characteristic matrix method,” J. Phys. 46, 815-825 (1985).
[CrossRef]

Brum, J. A.

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, “Observation of 'Tamm states' in superlattices,” Phys. Rev. Lett. 64, 2555-2558 (1990).
[CrossRef] [PubMed]

Chang, L. L.

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, “Observation of 'Tamm states' in superlattices,” Phys. Rev. Lett. 64, 2555-2558 (1990).
[CrossRef] [PubMed]

Chen, H. C.

H. C. Chen, Theory of Electromagnetic Waves--A Coordinate-free Approach (McGraw-Hill, 1983).

Crasovan, L.

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of Dyakonov surface waves,” Phys. Rev. Lett. 102, 043903 (2009).
[CrossRef] [PubMed]

Crasovan, L. C.

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126-145 (2008).
[CrossRef]

Crasovan, L.-C.

Darinskii, A. N.

A. N. Darinskii, “Dispersionless polaritons on a twist boundary in optically uniaxial crystals,” Crystallogr. Rep. 46, 842-844 (2001).
[CrossRef]

de Gennes, P. G.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Clarendon, 1993).

Dorofeenko, A. V.

A. M. Merzlikin, A. P. Vinogradov, A. V. Dorofeenko, M. Inoue, M. Levy, and A. B. Granovsky, “Controllable Tamm states in magnetophotonic crystal,” Physica B 394, 277-280 (2007).
[CrossRef]

Dyakonov, M. I.

N. S. Averkiev and M. I. Dyakonov, “Electromagnetic waves localized at the interface of transparent anisotropic media,” Opt. Spectrosc. 68, 653-655 (1990).

D'yakonov, M. I.

M. I. D'yakonov, “New type of electromagnetic wave propagating at an interface,” Sov. Phys. JETP 67, 714-716 (1988).

Esaki, L.

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, “Observation of 'Tamm states' in superlattices,” Phys. Rev. Lett. 64, 2555-2558 (1990).
[CrossRef] [PubMed]

Finkelmann, H.

J. Schmidtke, W. Stille, and H. Finkelmann, “Defect mode emission of a dye-doped cholesteric polymer network,” Phys. Rev. Lett. 90, 083902 (2003).
[CrossRef] [PubMed]

Furs, A. M.

A. M. Furs and L. M. Barkovsky, “Surface polaritons at the planar interface of twinned gyrotropic dielectric media,” Electromagnetics 28, 146-161 (2008).
[CrossRef]

Gao, J.

Gaylord, T. K.

Genack, A. Z.

V. I. Kopp and A. Z. Genack, “Twist defect in chiral photonic structures,” Phys. Rev. Lett. 89, 033901 (2002).
[CrossRef] [PubMed]

Gevorgyan, A. H.

A. H. Gevorgyan and M. Z. Harutyunyan, “Chiral photonic crystals with an anisotropic defect layer,” Phys. Rev. E 76, 031701 (2007).
[CrossRef]

Glytsis, E. N.

Granovsky, A. B.

A. M. Merzlikin, A. P. Vinogradov, A. V. Dorofeenko, M. Inoue, M. Levy, and A. B. Granovsky, “Controllable Tamm states in magnetophotonic crystal,” Physica B 394, 277-280 (2007).
[CrossRef]

Haas, W. E.

W. E. Haas, “Liquid crystal display research: the first fifteen years,” Mol. Cryst. Liq. Cryst. 94, 1-31 (1983).
[CrossRef]

Harutyunyan, M. Z.

A. H. Gevorgyan and M. Z. Harutyunyan, “Chiral photonic crystals with an anisotropic defect layer,” Phys. Rev. E 76, 031701 (2007).
[CrossRef]

Haus, H. A.

H. A. Haus and C. V. Shank, “Asymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. 12, 532-539 (1976).
[CrossRef]

Herzinger, C. M.

M. Schubert and C. M. Herzinger, “Ellipsometry on anisotropic materials: Bragg conditions and phonons in dielectric helical thin films,” Phys. Status Solidi A 188, 1563-1575 (2001).
[CrossRef]

Hodgkinson, I. J.

A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculptured thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33-46 (2001).
[CrossRef]

Q. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circular polarization filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863-1868 (2000).
[CrossRef]

I. J. Hodgkinson, Q. H. Wu, K. E. Thorn, A. Lakhtakia, andM. W. McCall, “Spacerless circular-polarization spectral-hole filters using chiral sculptured thin films: theory and experiment,” Opt. Commun. 184, 57-66 (2000).
[CrossRef]

I. J. Hodgkinson and Q. H. Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, 1997).
[CrossRef]

Hong, J. M.

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, “Observation of 'Tamm states' in superlattices,” Phys. Rev. Lett. 64, 2555-2558 (1990).
[CrossRef] [PubMed]

Inoue, M.

A. M. Merzlikin, A. P. Vinogradov, A. V. Dorofeenko, M. Inoue, M. Levy, and A. B. Granovsky, “Controllable Tamm states in magnetophotonic crystal,” Physica B 394, 277-280 (2007).
[CrossRef]

Jaluria, Y.

Y. Jaluria, Computer Methods for Engineering (Brunner-Routledge, 1996).

Johansen, S. K.

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126-145 (2008).
[CrossRef]

Kivshar, Y. S.

A. Namdar, I. V. Shadrivov, and Y. S. Kivshar, “Backward Tamm states in left-handed metamaterials,” Appl. Phys. Lett. 89, 114104 (2006).
[CrossRef]

Kopp, V. I.

V. I. Kopp and A. Z. Genack, “Twist defect in chiral photonic structures,” Phys. Rev. Lett. 89, 033901 (2002).
[CrossRef] [PubMed]

Lakhtakia, A.

J. Gao, A. Lakhtakia, J. A. Polo, Jr., and M. K. Lei, “Dyakonov-Tamm wave guided by a twist defect in a structurally chiral material,” J. Opt. Soc. Am. A 26, 1615-1621 (2009). Replace zn+/-+/-γ by ΠΩzn+/-+/-γ in Eq. .
[CrossRef]

K. Agarwal, J. A. Polo, Jr., and A. Lakhtakia, “Theory of Dyakonov-Tamm waves at the planar interface of a sculptured nematic thin film and an isotropic dielectric material,” J. Opt. A 11, 074003 (2009).
[CrossRef]

S. R. Nelatury, J. A. Polo Jr., and A. Lakhtakia, “Electrical control of surface-wave propagation at the planar interface of a linear electro-optic material and an isotropic dielectric material,” Electromagnetics 28, 162-174 (2008).
[CrossRef]

S. R. Nelatury, J. A. Polo Jr., and A. Lakhtakia, “On widening the angular existence domain for Dyakonov surface waves using the Pockels effect,” Microwave Opt. Technol. Lett. 50, 2360-2362 (2008).
[CrossRef]

J. A. Polo, Jr., S. R. Nelatury, and A. Lakhtakia, “Surface waves at a biaxial bicrystalline interface,” J. Opt. Soc. Am. A 24, 2974-2979 (2007).
[CrossRef]

J. A. Polo, Jr., S. R. Nelatury, and A. Lakhtakia, “Propagation of surface waves at the planar interface of a columnar thin film and an isotropic substrate,” J. Nanophotonics 1, 013501 (2007).
[CrossRef]

A. Lakhtakia and J. A. Polo, Jr., “Dyakonov-Tamm wave at the planar interface of a chiral sculptured thin film and an isotropic dielectric material,” J. Eur. Opt. Soc. Rapid Publ. 2, 07021 (2007).
[CrossRef]

A. Lakhtakia, “Generation of spectral holes by inserting central structurally chiral layer defects in periodic structurally chiral materials,” Opt. Commun. 275, 283-287 (2007).
[CrossRef]

J. A. Polo, Jr., S. Nelatury, and A. Lakhtakia, “Surface electromagnetic wave at a tilted uniaxial bicrystalline interface,” Electromagnetics 26, 629-642 (2006).
[CrossRef]

F. Wang and A. Lakhtakia, “Optical crossover phenomenon due to a central 90°-twist defect in a chiral sculptured thin film or chiral liquid crystal,” Proc. R. Soc. London Ser. A 461, 2985-3004 (2005).
[CrossRef]

J. A. Polo, Jr. and A. Lakhtakia, “Comparison of two methods for oblique propagation in helicoidal bianisotropic mediums,” Opt. Commun. 230, 369-386 (2004).
[CrossRef]

A. Lakhtakia, “Sculptured thin films: accomplishments and emerging uses,” Mater. Sci. Eng. C 19, 427-434 (2002).
[CrossRef]

A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculptured thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33-46 (2001).
[CrossRef]

I. J. Hodgkinson, Q. H. Wu, K. E. Thorn, A. Lakhtakia, andM. W. McCall, “Spacerless circular-polarization spectral-hole filters using chiral sculptured thin films: theory and experiment,” Opt. Commun. 184, 57-66 (2000).
[CrossRef]

Q. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circular polarization filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863-1868 (2000).
[CrossRef]

V. C. Venugopal and A. Lakhtakia, “Electromagnetic plane-wave response characteristics of non-axially excited slabs of dielectric thin-film helicoidal bianisotropic mediums,” Proc. R. Soc. London Ser. A 456, 125-161 (2000).
[CrossRef]

A. Lakhtakia and V. C. Venugopal, “On Bragg reflection by helicoidal bianisotropic mediums,” Arch. Elektr. Üebertrag. 53, 287-290 (1999).

A. Lakhtakia and W. S. Weiglhofer, “Further results on light propagation in helicoidal bianisotropic mediums: oblique propagation,” Proc. R. Soc. London Ser. A 453, 93-105 (1997).
[CrossRef]

A. Lakhtakia and R. Messier, Sculptured Thin Films: Nanoengineered Morphology and Optics (SPIE Press, 2005).
[CrossRef]

Lei, M. K.

Levy, M.

A. M. Merzlikin, A. P. Vinogradov, A. V. Dorofeenko, M. Inoue, M. Levy, and A. B. Granovsky, “Controllable Tamm states in magnetophotonic crystal,” Physica B 394, 277-280 (2007).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin-film Optical Filters, 3rd ed. (Institute of Physics, 2001).
[CrossRef]

Martorell, J.

J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals,” J. Opt. A 8, 630-638 (2006).
[CrossRef]

McCall, M. W.

A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculptured thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33-46 (2001).
[CrossRef]

I. J. Hodgkinson, Q. H. Wu, K. E. Thorn, A. Lakhtakia, andM. W. McCall, “Spacerless circular-polarization spectral-hole filters using chiral sculptured thin films: theory and experiment,” Opt. Commun. 184, 57-66 (2000).
[CrossRef]

Mendez, E. E.

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, “Observation of 'Tamm states' in superlattices,” Phys. Rev. Lett. 64, 2555-2558 (1990).
[CrossRef] [PubMed]

Merzlikin, A. M.

A. M. Merzlikin, A. P. Vinogradov, A. V. Dorofeenko, M. Inoue, M. Levy, and A. B. Granovsky, “Controllable Tamm states in magnetophotonic crystal,” Physica B 394, 277-280 (2007).
[CrossRef]

Messier, R.

A. Lakhtakia and R. Messier, Sculptured Thin Films: Nanoengineered Morphology and Optics (SPIE Press, 2005).
[CrossRef]

Mihalache, D.

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126-145 (2008).
[CrossRef]

L.-C. Crasovan, D. Artigas, D. Mihalache, and L. Torner, “Optical Dyakonov surface waves at magnetic interfaces,” Opt. Lett. 30, 3075-3077 (2005).
[CrossRef] [PubMed]

L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, “Hybrid waves guided by ultrathin films,” J. Lightwave Technol. 13, 2027-2033 (1995).
[CrossRef]

L. Torner, J. P. Torres, and D. Mihalache, “New type of guided waves in birefringent media,” IEEE Photonics Technol. Lett. 5, 201-203 (1993).
[CrossRef]

Morozov, G. V.

J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals,” J. Opt. A 8, 630-638 (2006).
[CrossRef]

Namdar, A.

A. Namdar, I. V. Shadrivov, and Y. S. Kivshar, “Backward Tamm states in left-handed metamaterials,” Appl. Phys. Lett. 89, 114104 (2006).
[CrossRef]

Nelatury, S.

J. A. Polo, Jr., S. Nelatury, and A. Lakhtakia, “Surface electromagnetic wave at a tilted uniaxial bicrystalline interface,” Electromagnetics 26, 629-642 (2006).
[CrossRef]

Nelatury, S. R.

S. R. Nelatury, J. A. Polo Jr., and A. Lakhtakia, “Electrical control of surface-wave propagation at the planar interface of a linear electro-optic material and an isotropic dielectric material,” Electromagnetics 28, 162-174 (2008).
[CrossRef]

S. R. Nelatury, J. A. Polo Jr., and A. Lakhtakia, “On widening the angular existence domain for Dyakonov surface waves using the Pockels effect,” Microwave Opt. Technol. Lett. 50, 2360-2362 (2008).
[CrossRef]

J. A. Polo, Jr., S. R. Nelatury, and A. Lakhtakia, “Propagation of surface waves at the planar interface of a columnar thin film and an isotropic substrate,” J. Nanophotonics 1, 013501 (2007).
[CrossRef]

J. A. Polo, Jr., S. R. Nelatury, and A. Lakhtakia, “Surface waves at a biaxial bicrystalline interface,” J. Opt. Soc. Am. A 24, 2974-2979 (2007).
[CrossRef]

Ohno, H.

H. Ohno, E. E. Mendez, J. A. Brum, J. M. Hong, F. Agulló-Rueda, L. L. Chang, and L. Esaki, “Observation of 'Tamm states' in superlattices,” Phys. Rev. Lett. 64, 2555-2558 (1990).
[CrossRef] [PubMed]

Ojeda, C.

L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, “Hybrid waves guided by ultrathin films,” J. Lightwave Technol. 13, 2027-2033 (1995).
[CrossRef]

Oldano, C.

M. Becchi, S. Ponti, J. A. Reyes, and C. Oldano, “Defect modes in helical photonic crystals: an analytic approach,” Phys. Rev. B 70, 033103 (2004).
[CrossRef]

Polo, J. A.

K. Agarwal, J. A. Polo, Jr., and A. Lakhtakia, “Theory of Dyakonov-Tamm waves at the planar interface of a sculptured nematic thin film and an isotropic dielectric material,” J. Opt. A 11, 074003 (2009).
[CrossRef]

J. Gao, A. Lakhtakia, J. A. Polo, Jr., and M. K. Lei, “Dyakonov-Tamm wave guided by a twist defect in a structurally chiral material,” J. Opt. Soc. Am. A 26, 1615-1621 (2009). Replace zn+/-+/-γ by ΠΩzn+/-+/-γ in Eq. .
[CrossRef]

A. Lakhtakia and J. A. Polo, Jr., “Dyakonov-Tamm wave at the planar interface of a chiral sculptured thin film and an isotropic dielectric material,” J. Eur. Opt. Soc. Rapid Publ. 2, 07021 (2007).
[CrossRef]

J. A. Polo, Jr., S. R. Nelatury, and A. Lakhtakia, “Surface waves at a biaxial bicrystalline interface,” J. Opt. Soc. Am. A 24, 2974-2979 (2007).
[CrossRef]

J. A. Polo, Jr., S. R. Nelatury, and A. Lakhtakia, “Propagation of surface waves at the planar interface of a columnar thin film and an isotropic substrate,” J. Nanophotonics 1, 013501 (2007).
[CrossRef]

J. A. Polo, Jr., S. Nelatury, and A. Lakhtakia, “Surface electromagnetic wave at a tilted uniaxial bicrystalline interface,” Electromagnetics 26, 629-642 (2006).
[CrossRef]

J. A. Polo, Jr. and A. Lakhtakia, “Comparison of two methods for oblique propagation in helicoidal bianisotropic mediums,” Opt. Commun. 230, 369-386 (2004).
[CrossRef]

Polo Jr., J. A.

S. R. Nelatury, J. A. Polo Jr., and A. Lakhtakia, “Electrical control of surface-wave propagation at the planar interface of a linear electro-optic material and an isotropic dielectric material,” Electromagnetics 28, 162-174 (2008).
[CrossRef]

S. R. Nelatury, J. A. Polo Jr., and A. Lakhtakia, “On widening the angular existence domain for Dyakonov surface waves using the Pockels effect,” Microwave Opt. Technol. Lett. 50, 2360-2362 (2008).
[CrossRef]

Ponti, S.

M. Becchi, S. Ponti, J. A. Reyes, and C. Oldano, “Defect modes in helical photonic crystals: an analytic approach,” Phys. Rev. B 70, 033103 (2004).
[CrossRef]

Prost, J.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Clarendon, 1993).

Radic, S.

G. P. Agrawal and S. Radic, “Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photon. Technol. Lett. 6, 995-997 (1994).
[CrossRef]

Reyes, J. A.

M. Becchi, S. Ponti, J. A. Reyes, and C. Oldano, “Defect modes in helical photonic crystals: an analytic approach,” Phys. Rev. B 70, 033103 (2004).
[CrossRef]

Schmidtke, J.

J. Schmidtke, W. Stille, and H. Finkelmann, “Defect mode emission of a dye-doped cholesteric polymer network,” Phys. Rev. Lett. 90, 083902 (2003).
[CrossRef] [PubMed]

Schubert, M.

M. Schubert and C. M. Herzinger, “Ellipsometry on anisotropic materials: Bragg conditions and phonons in dielectric helical thin films,” Phys. Status Solidi A 188, 1563-1575 (2001).
[CrossRef]

Shadrivov, I. V.

A. Namdar, I. V. Shadrivov, and Y. S. Kivshar, “Backward Tamm states in left-handed metamaterials,” Appl. Phys. Lett. 89, 114104 (2006).
[CrossRef]

Shank, C. V.

H. A. Haus and C. V. Shank, “Asymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. 12, 532-539 (1976).
[CrossRef]

Sherwin, J. A.

A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculptured thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33-46 (2001).
[CrossRef]

Sprung, D. W. L.

J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals,” J. Opt. A 8, 630-638 (2006).
[CrossRef]

Starzhinskii, V. M.

V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients (Wiley, 1975).

Stille, W.

J. Schmidtke, W. Stille, and H. Finkelmann, “Defect mode emission of a dye-doped cholesteric polymer network,” Phys. Rev. Lett. 90, 083902 (2003).
[CrossRef] [PubMed]

Takayama, O.

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of Dyakonov surface waves,” Phys. Rev. Lett. 102, 043903 (2009).
[CrossRef] [PubMed]

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126-145 (2008).
[CrossRef]

Tamm, I.

I. Tamm, “Über eine mögliche Art der Elektronenbindung an Kristalloberflächen,” Z. Phys. A 76, 849-850 (1932).

Thorn, K. E.

I. J. Hodgkinson, Q. H. Wu, K. E. Thorn, A. Lakhtakia, andM. W. McCall, “Spacerless circular-polarization spectral-hole filters using chiral sculptured thin films: theory and experiment,” Opt. Commun. 184, 57-66 (2000).
[CrossRef]

Torner, L.

O. Takayama, L. Crasovan, D. Artigas, and L. Torner, “Observation of Dyakonov surface waves,” Phys. Rev. Lett. 102, 043903 (2009).
[CrossRef] [PubMed]

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126-145 (2008).
[CrossRef]

L.-C. Crasovan, D. Artigas, D. Mihalache, and L. Torner, “Optical Dyakonov surface waves at magnetic interfaces,” Opt. Lett. 30, 3075-3077 (2005).
[CrossRef] [PubMed]

L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, “Hybrid waves guided by ultrathin films,” J. Lightwave Technol. 13, 2027-2033 (1995).
[CrossRef]

L. Torner, J. P. Torres, and D. Mihalache, “New type of guided waves in birefringent media,” IEEE Photonics Technol. Lett. 5, 201-203 (1993).
[CrossRef]

Torres, J. P.

L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, “Hybrid waves guided by ultrathin films,” J. Lightwave Technol. 13, 2027-2033 (1995).
[CrossRef]

L. Torner, J. P. Torres, and D. Mihalache, “New type of guided waves in birefringent media,” IEEE Photonics Technol. Lett. 5, 201-203 (1993).
[CrossRef]

Venugopal, V. C.

V. C. Venugopal and A. Lakhtakia, “Electromagnetic plane-wave response characteristics of non-axially excited slabs of dielectric thin-film helicoidal bianisotropic mediums,” Proc. R. Soc. London Ser. A 456, 125-161 (2000).
[CrossRef]

A. Lakhtakia and V. C. Venugopal, “On Bragg reflection by helicoidal bianisotropic mediums,” Arch. Elektr. Üebertrag. 53, 287-290 (1999).

Vinogradov, A. P.

A. M. Merzlikin, A. P. Vinogradov, A. V. Dorofeenko, M. Inoue, M. Levy, and A. B. Granovsky, “Controllable Tamm states in magnetophotonic crystal,” Physica B 394, 277-280 (2007).
[CrossRef]

Walker, D. B.

Wang, F.

F. Wang and A. Lakhtakia, “Optical crossover phenomenon due to a central 90°-twist defect in a chiral sculptured thin film or chiral liquid crystal,” Proc. R. Soc. London Ser. A 461, 2985-3004 (2005).
[CrossRef]

Weiglhofer, W. S.

A. Lakhtakia and W. S. Weiglhofer, “Further results on light propagation in helicoidal bianisotropic mediums: oblique propagation,” Proc. R. Soc. London Ser. A 453, 93-105 (1997).
[CrossRef]

Weil, R.

I. Abdulhalim, L. Benguigui, and R. Weil, “Selective reflection by helicoidal liquid crystals, results of an exact calculation using the 4 × 4 characteristic matrix method,” J. Phys. 46, 815-825 (1985).
[CrossRef]

Wu, Q.

Q. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circular polarization filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863-1868 (2000).
[CrossRef]

Wu, Q. H.

A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculptured thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33-46 (2001).
[CrossRef]

I. J. Hodgkinson, Q. H. Wu, K. E. Thorn, A. Lakhtakia, andM. W. McCall, “Spacerless circular-polarization spectral-hole filters using chiral sculptured thin films: theory and experiment,” Opt. Commun. 184, 57-66 (2000).
[CrossRef]

I. J. Hodgkinson and Q. H. Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, 1997).
[CrossRef]

Yakubovich, V. A.

V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients (Wiley, 1975).

Appl. Phys. Lett. (1)

A. Namdar, I. V. Shadrivov, and Y. S. Kivshar, “Backward Tamm states in left-handed metamaterials,” Appl. Phys. Lett. 89, 114104 (2006).
[CrossRef]

Arch. Elektr. Üebertrag. (1)

A. Lakhtakia and V. C. Venugopal, “On Bragg reflection by helicoidal bianisotropic mediums,” Arch. Elektr. Üebertrag. 53, 287-290 (1999).

Crystallogr. Rep. (1)

A. N. Darinskii, “Dispersionless polaritons on a twist boundary in optically uniaxial crystals,” Crystallogr. Rep. 46, 842-844 (2001).
[CrossRef]

Electromagnetics (4)

J. A. Polo, Jr., S. Nelatury, and A. Lakhtakia, “Surface electromagnetic wave at a tilted uniaxial bicrystalline interface,” Electromagnetics 26, 629-642 (2006).
[CrossRef]

A. M. Furs and L. M. Barkovsky, “Surface polaritons at the planar interface of twinned gyrotropic dielectric media,” Electromagnetics 28, 146-161 (2008).
[CrossRef]

S. R. Nelatury, J. A. Polo Jr., and A. Lakhtakia, “Electrical control of surface-wave propagation at the planar interface of a linear electro-optic material and an isotropic dielectric material,” Electromagnetics 28, 162-174 (2008).
[CrossRef]

O. Takayama, L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics 28, 126-145 (2008).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. A. Haus and C. V. Shank, “Asymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. 12, 532-539 (1976).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

G. P. Agrawal and S. Radic, “Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photon. Technol. Lett. 6, 995-997 (1994).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

L. Torner, J. P. Torres, and D. Mihalache, “New type of guided waves in birefringent media,” IEEE Photonics Technol. Lett. 5, 201-203 (1993).
[CrossRef]

J. Eur. Opt. Soc. Rapid Publ. (1)

A. Lakhtakia and J. A. Polo, Jr., “Dyakonov-Tamm wave at the planar interface of a chiral sculptured thin film and an isotropic dielectric material,” J. Eur. Opt. Soc. Rapid Publ. 2, 07021 (2007).
[CrossRef]

J. Lightwave Technol. (1)

L. Torner, J. P. Torres, C. Ojeda, and D. Mihalache, “Hybrid waves guided by ultrathin films,” J. Lightwave Technol. 13, 2027-2033 (1995).
[CrossRef]

J. Nanophotonics (1)

J. A. Polo, Jr., S. R. Nelatury, and A. Lakhtakia, “Propagation of surface waves at the planar interface of a columnar thin film and an isotropic substrate,” J. Nanophotonics 1, 013501 (2007).
[CrossRef]

J. Opt. A (2)

K. Agarwal, J. A. Polo, Jr., and A. Lakhtakia, “Theory of Dyakonov-Tamm waves at the planar interface of a sculptured nematic thin film and an isotropic dielectric material,” J. Opt. A 11, 074003 (2009).
[CrossRef]

J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals,” J. Opt. A 8, 630-638 (2006).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Phys. (1)

I. Abdulhalim, L. Benguigui, and R. Weil, “Selective reflection by helicoidal liquid crystals, results of an exact calculation using the 4 × 4 characteristic matrix method,” J. Phys. 46, 815-825 (1985).
[CrossRef]

Mater. Sci. Eng. C (1)

A. Lakhtakia, “Sculptured thin films: accomplishments and emerging uses,” Mater. Sci. Eng. C 19, 427-434 (2002).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

S. R. Nelatury, J. A. Polo Jr., and A. Lakhtakia, “On widening the angular existence domain for Dyakonov surface waves using the Pockels effect,” Microwave Opt. Technol. Lett. 50, 2360-2362 (2008).
[CrossRef]

Mol. Cryst. Liq. Cryst. (1)

W. E. Haas, “Liquid crystal display research: the first fifteen years,” Mol. Cryst. Liq. Cryst. 94, 1-31 (1983).
[CrossRef]

Opt. Commun. (4)

A. Lakhtakia, “Generation of spectral holes by inserting central structurally chiral layer defects in periodic structurally chiral materials,” Opt. Commun. 275, 283-287 (2007).
[CrossRef]

I. J. Hodgkinson, Q. H. Wu, K. E. Thorn, A. Lakhtakia, andM. W. McCall, “Spacerless circular-polarization spectral-hole filters using chiral sculptured thin films: theory and experiment,” Opt. Commun. 184, 57-66 (2000).
[CrossRef]

A. Lakhtakia, M. W. McCall, J. A. Sherwin, Q. H. Wu, and I. J. Hodgkinson, “Sculptured thin-film spectral holes for optical sensing of fluids,” Opt. Commun. 194, 33-46 (2001).
[CrossRef]

J. A. Polo, Jr. and A. Lakhtakia, “Comparison of two methods for oblique propagation in helicoidal bianisotropic mediums,” Opt. Commun. 230, 369-386 (2004).
[CrossRef]

Opt. Eng. (1)

Q. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circular polarization filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863-1868 (2000).
[CrossRef]

Opt. Lett. (1)

Opt. Spectrosc. (1)

N. S. Averkiev and M. I. Dyakonov, “Electromagnetic waves localized at the interface of transparent anisotropic media,” Opt. Spectrosc. 68, 653-655 (1990).

Phys. Rev. B (1)

M. Becchi, S. Ponti, J. A. Reyes, and C. Oldano, “Defect modes in helical photonic crystals: an analytic approach,” Phys. Rev. B 70, 033103 (2004).
[CrossRef]

Phys. Rev. E (1)

A. H. Gevorgyan and M. Z. Harutyunyan, “Chiral photonic crystals with an anisotropic defect layer,” Phys. Rev. E 76, 031701 (2007).
[CrossRef]

Phys. Rev. Lett. (4)

V. I. Kopp and A. Z. Genack, “Twist defect in chiral photonic structures,” Phys. Rev. Lett. 89, 033901 (2002).
[CrossRef] [PubMed]

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[CrossRef]

Physica B (1)

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[CrossRef]

Proc. R. Soc. London Ser. A (3)

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Figures (9)

Fig. 1
Fig. 1

Schematic of the helical morphology of a structurally right-handed chiral sculptured thin film with a central twist defect.

Fig. 2
Fig. 2

Sets of solutions κ k 0 of Eq. (18) for different combinations of the angular offsets γ + and γ ; ε a = 2.514 , ε b = 3.943 , ε c = 3.153 , χ = 46.367°, h = 1 , Ω = 197 nm, and λ 0 = 633 nm . (a) First, (b) second, (c) third, and (d) fourth sets.

Fig. 3
Fig. 3

Values of κ k 0 for the second and the third sets of solutions at γ + = π . See Fig. 2 for the constitutive parameters of the chiral STFs on either side of the twist–defect interface.

Fig. 4
Fig. 4

Ranges of γ + and γ for the existence of the fourth set of solutions. See Fig. 2 for the constitutive parameters of the chiral STFs on either side of the twist–defect interface.

Fig. 5
Fig. 5

Profiles of the magnitudes of field components of the first solution ( κ k 0 = 0.73394 ) of Eq. (18) for γ + = 75 ° and γ = 135 ° . Electric field magnitudes are in V/m and magnetic field magnitudes are in A/m, with A 1 = 1 V m . Field components in the half-space z > 0 are superscripted +, whereas those in the half-space z < 0 are superscripted −. See Fig. 2 for the values of the constitutive and geometric parameters used.

Fig. 6
Fig. 6

Same as Fig. 5, but for the second solution ( κ k 0 = 1.54011 ) of Eq. (18) for γ + = 75 ° and γ = 135 ° .

Fig. 7
Fig. 7

Same as Fig. 5, but for the third solution ( κ k 0 = 1.58769 ) of Eq. (18) for γ + = 75 ° and γ = 135 ° .

Fig. 8
Fig. 8

Same as Fig. 5, but for the fourth solution ( κ k 0 = 1.84119 ) of Eq. (18) for γ + = 75 ° and γ = 135 ° .

Fig. 9
Fig. 9

Variations of decay constants exp ( u 1 ) = exp ( v 1 ) and exp ( u 2 ) = exp ( v 2 ) with the angular offsets γ ± . See Fig. 2 for the values of the constitutive and geometric parameters used.

Equations (24)

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ε ͇ ( z ) = ε 0 S ͇ z ( z , h , Ω , γ + ) S ͇ y ( χ ) ε ͇ ref S ͇ y T ( χ ) S ͇ z T ( z , h , Ω , γ + ) , z > 0 ,
ε ͇ ( z ) = ε 0 S ͇ z ( z , h , Ω , γ ) S ͇ y ( χ ) ε ͇ ref S ͇ y T ( χ ) S ͇ z T ( z , h , Ω , γ ) , z < 0 ,
ε ͇ ref = ε a u ̱ z u ̱ z + ε b u ̱ x u ̱ x + ε c u ̱ y u ̱ y
S ͇ z ( z , h , Ω , γ ± , ) = ( u ̱ x u ̱ x + u ̱ y u ̱ y ) cos ζ ± + h ( u ̱ y u ̱ x u ̱ x u ̱ y ) sin ζ ± + u ̱ z u ̱ z ,
ζ ± = π z Ω + γ ± ,
S ͇ y ( χ ) = ( u ̱ x u ̱ x + u ̱ z u ̱ z ) cos χ + ( u ̱ z u ̱ x u ̱ x u ̱ z ) sin χ + u ̱ y u ̱ y
{ E ̱ ( r ̱ ) = e ̱ ( z ) exp ( i κ x ) H ̱ ( r ̱ ) = h ̱ ( z ) exp ( i κ x ) } ,
[ f ̱ ( z ) ] = [ e x ( z ) e y ( z ) h x ( z ) h y ( z ) ] T .
d d z [ f ̱ ( z ) ] = i [ P ͇ ± ( z , κ ) ] [ f ̱ ( z ) ] , z > 0 z < 0 ,
[ P ͇ ± ( z , κ ) ] = ω [ 0 0 0 μ 0 0 0 μ 0 0 h ε 0 ( ε c ε d ) cos ζ ± sin ζ ± ε 0 ( ε c cos 2 ζ ± + ε d sin 2 ζ ± ) 0 0 ε 0 ( ε c sin 2 ζ ± + ε d cos 2 ζ ± ) h ε 0 ( ε c ε d ) cos ζ ± sin ζ ± 0 0 ] + κ ε d ( ε a ε b ) ε a ε b sin χ cos χ [ cos ζ ± h sin ζ ± 0 0 0 0 0 0 0 0 0 h sin ζ ± 0 0 0 cos ζ ± ] + [ 0 0 0 κ 2 ω ε 0 ε d ε a ε b 0 0 0 0 0 κ 2 ω μ 0 0 0 0 0 0 0 ] ,
ε d = ε a ε b ε a cos 2 χ + ε b sin 2 χ .
{ [ f ̱ ( 2 Ω ) ] = [ N ͇ + ] [ f ̱ ( 0 + ) ] [ f ̱ ( 2 Ω ) ] = [ N ͇ ] [ f ̱ ( 0 ) ] }
{ [ N ͇ + ] = exp { i 2 Ω [ Q ͇ + ] } [ N ͇ ] = exp { i 2 Ω [ Q ͇ ] } } .
α n ± = i ln σ n ± 2 Ω .
[ f ̱ ( 0 + ) ] = [ [ t ̱ + ] ( 1 ) [ t ̱ + ] ( 2 ) ] [ A 1 A 2 ] ,
[ f ̱ ( 0 ) ] = [ [ t ̱ ] ( 1 ) [ t ̱ ] ( 2 ) ] [ B 1 B 2 ] ,
[ M ͇ ] [ A 1 A 2 B 1 B 2 ] = [ 0 0 0 0 ] .
det [ M ͇ ] = 0
[ W ͇ n ± ] = exp { ± i [ P ͇ ± ( z n 1 ± + z n ± 2 , κ ) ] 2 Ω N } , n [ 1 , N ] ,
[ N ͇ ± ] [ W ͇ N ± ] [ W ͇ N 1 ± ] [ W ͇ 2 ± ] [ W ͇ 1 ± ] .
[ f ̱ ( z n ± ) ] = [ e x ( z n ± ) e y ( z n ± ) h x ( z n ± ) h y ( z n ± ) ] [ W ͇ n ± ] [ W ͇ n 1 ± ] [ W ͇ 2 ± ] [ W ͇ 1 ± ] [ f ( 0 ± ) ] ,
n [ 1 , ) ,
h z ( z n ± ) = ( κ ω μ o ) e y ( z n ± ) , n [ 1 , ) ,
e z ( z n ± ) = ( ε d ε a ε b ) { ( κ ω ε o ) h y ( z n ± ) + ( ε a ε b ) sin 2 χ 2 [ e x ( z n ± ) cos ( Π Ω z n ± + γ ± ) + h e y ( z n ± ) sin ( Π Ω z n ± + γ ± ) ] } , n [ 1 , ) .

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