Abstract

A vector-wave analysis of nondiffracting beams propagating along a birefringent chiral crystal for the case of tensor character of both the optical activity and linear birefringence is presented. We have written characteristic equations and found propagation constants and amplitude parameters of the eigenmodes. The characteristic curves have anomalous zones described by an isotropic point or a gap-point, provided that the elements of an optical activity tensor obey the requirement g11g33<0, |g33|>|g11|. In the anomalous zone, a nondiffracting beam can propagate through a purely chiral crystal as if through an isotropic medium. We have shown that the field of eigenmodes is nonuniformly polarized in the beam cross section, while the field with the initially uniform polarization distribution experiences periodic transformations. We have revealed that even a purely chiral crystal without linear birefringence can generate optical vortices in an initially vortex-free Bessel beam.

© 2009 Optical Society of America

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    [CrossRef]

2009 (1)

T. A. Fadeyeva, A. F. Rubass, and A. V. Volyar, “Transverse shift of a high-order paraxial vortex-beam induced by a homogeneous anisotropic medium,” Phys. Rev. A 79, 053815.1-12 (2009).
[CrossRef]

2008 (1)

2007 (2)

A. Volyar, A. Rubass, V. Shvedov, T. Fadeyeva, and K. Kotlyarov, “Optical vortices and Airy' spiral in chiral crystals,” Ukr. J. Phys. Opt. 8, 166-181 (2007), http://www.ifo.lviv.ua/journal/2007/2007_3_8_05.html.
[CrossRef]

V. Kotlyar, A. Kovalev, R. Skidanov, O. Moiseev, and V. Soifer, “Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate,” J. Opt. Soc. Am. A 24, 1955-1964 (2007).
[CrossRef]

2006 (2)

A. Volyar, and T. Fadeyeva, “Laguerre-Gaussian beams with complex and real arguments in uniaxial crystals,” Opt. Spectrosc. 101, 297-304 (2006).
[CrossRef]

M. V. Berry and M. R. Jeffray, “Chiral conical diffraction,” J. Opt. A, Pure Appl. Opt. 8, 363-372 (2006).
[CrossRef]

2005 (3)

F. Flossman, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901-4 (2005).
[CrossRef]

D. McGoloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15-28 (2005).
[CrossRef]

C. López-Mariscal, M. Bandres, J. C. Gutiérrez-Vega, S. Chávez-Cerda, “Observation of parabolic nondiffracting optical fields,” Opt. Express 13, 2364-2369 (2005).
[CrossRef] [PubMed]

2004 (2)

M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett. 29, 44-46 (2004).
[CrossRef] [PubMed]

S. Orlov and A. Stabinis, “Propagation of superpositions of coaxial optical Bessel beams carrying vortices,” J. Opt. A, Pure Appl. Opt. 6, S259-S262 (2004).
[CrossRef]

2003 (2)

M. Berry and M. Dennis, “The optical singularities of birefringent dichroic chiral crystals,” Proc. R. Soc. London, Ser. A 459, 1261-1292 (2003).
[CrossRef]

A. Ciattoni, G. Cincotti, and C. Palma, “Circular polarized beams and vortex generation in uniaxial media,” J. Opt. Soc. Am. A 20, 163-171 (2003).
[CrossRef]

2002 (5)

G. Cincotti, A. Ciatoni, and C. Palma, “Laguerre-Gaussian and Bessel-Gaussian beams in uniaxial crystals,” J. Opt. Soc. Am. A 19, 1680-1688 (2002).
[CrossRef]

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O'Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbit angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52-S57 (2002).
[CrossRef]

J. Molloy and M. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

E. S. Petrova, “The influence of the natural and magnetic gyrotropy on the polarization and energy of the vector Bessel light beams,” Proc. of Natl. Acad. Sci. Belarus. Series of physicsmath. 1, 95-100 (2002).

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155-165 (2002).
[CrossRef]

2001 (1)

V. Belyi, T. King, N. Kazak, N. Khilo, A. Ryzhevich, and E. Katranji, “Methods of formation and nonlinear conversion of Bessel optical vortices,” Proc. SPIE 4403, 229-240 (2001).
[CrossRef]

2000 (1)

1999 (1)

N. Kazak, N. Khilo, and A. Ryzhevich, “Generation of Bessel beams under the conditions of internal conical refraction,” Quantum Electron. 29, 1020-1024 (1999).
[CrossRef]

1998 (1)

1997 (1)

B. Z. Katsenelenbaum, E. N. Korshunova, A. N. Sivov, and A. D. Shatrov, “Chiral electromagnetic objects,” Phys. Usp. 40, 1149-1160 (1997).
[CrossRef]

1995 (1)

Z. Bouchali and M. Olvik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555-1566 (1995).
[CrossRef]

1993 (1)

1991 (1)

R. Mishra, “A vector analysis of a Bessel beam,” Opt. Commun. 85, 159-161 (1991).
[CrossRef]

1989 (1)

1988 (1)

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1968).

Allison, I.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O'Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbit angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52-S57 (2002).
[CrossRef]

Bandres, M.

Bandres, M. A.

Bassiri, S.

Belyi, V.

V. Belyi, T. King, N. Kazak, N. Khilo, A. Ryzhevich, and E. Katranji, “Methods of formation and nonlinear conversion of Bessel optical vortices,” Proc. SPIE 4403, 229-240 (2001).
[CrossRef]

Berry, M.

M. Berry and M. Dennis, “The optical singularities of birefringent dichroic chiral crystals,” Proc. R. Soc. London, Ser. A 459, 1261-1292 (2003).
[CrossRef]

Berry, M. V.

M. V. Berry and M. R. Jeffray, “Chiral conical diffraction,” J. Opt. A, Pure Appl. Opt. 8, 363-372 (2006).
[CrossRef]

M. V. Berry and M. R. Jeffray, “Conical diffraction: Hamilton's diabolical points at the heart of crystal optics,” in Progress in Optics, Vol. 50, E.Wolf, ed. (Elsevier, 2007), pp. 11-50.
[CrossRef]

Bouchali, Z.

Z. Bouchali and M. Olvik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555-1566 (1995).
[CrossRef]

Chávez-Cerda, S.

Chipman, R. A.

Ciatoni, A.

Ciattoni, A.

Cincotti, G.

Courtial, J.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O'Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbit angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52-S57 (2002).
[CrossRef]

Dennis, M.

M. Berry and M. Dennis, “The optical singularities of birefringent dichroic chiral crystals,” Proc. R. Soc. London, Ser. A 459, 1261-1292 (2003).
[CrossRef]

Dennis, M. R.

F. Flossman, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901-4 (2005).
[CrossRef]

Dholakia, K.

D. McGoloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15-28 (2005).
[CrossRef]

Egorov, Y.

Engheta, N.

Fadeyeva, T.

T. Fadeyeva, A. Rubass, Y. Egorov, A. Volyar, and G. Swartzlander, “Quadrefringence of optical vortices in a uniaxial crystal,” J. Opt. Soc. Am. A 25, 1634-1641 (2008).
[CrossRef]

A. Volyar, A. Rubass, V. Shvedov, T. Fadeyeva, and K. Kotlyarov, “Optical vortices and Airy' spiral in chiral crystals,” Ukr. J. Phys. Opt. 8, 166-181 (2007), http://www.ifo.lviv.ua/journal/2007/2007_3_8_05.html.
[CrossRef]

A. Volyar, and T. Fadeyeva, “Laguerre-Gaussian beams with complex and real arguments in uniaxial crystals,” Opt. Spectrosc. 101, 297-304 (2006).
[CrossRef]

Fadeyeva, T. A.

T. A. Fadeyeva, A. F. Rubass, and A. V. Volyar, “Transverse shift of a high-order paraxial vortex-beam induced by a homogeneous anisotropic medium,” Phys. Rev. A 79, 053815.1-12 (2009).
[CrossRef]

Flossman, F.

F. Flossman, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901-4 (2005).
[CrossRef]

Gutierrez-Vega, J. C.

Gutiérrez-Vega, J. C.

C. López-Mariscal, M. Bandres, J. C. Gutiérrez-Vega, S. Chávez-Cerda, “Observation of parabolic nondiffracting optical fields,” Opt. Express 13, 2364-2369 (2005).
[CrossRef] [PubMed]

M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett. 29, 44-46 (2004).
[CrossRef] [PubMed]

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O'Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbit angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52-S57 (2002).
[CrossRef]

Hillman, L. W.

Indebetouw, G.

Iturbe-Castillo, M. D.

Jeffray, M. R.

M. V. Berry and M. R. Jeffray, “Chiral conical diffraction,” J. Opt. A, Pure Appl. Opt. 8, 363-372 (2006).
[CrossRef]

M. V. Berry and M. R. Jeffray, “Conical diffraction: Hamilton's diabolical points at the heart of crystal optics,” in Progress in Optics, Vol. 50, E.Wolf, ed. (Elsevier, 2007), pp. 11-50.
[CrossRef]

Katranji, E.

V. Belyi, T. King, N. Kazak, N. Khilo, A. Ryzhevich, and E. Katranji, “Methods of formation and nonlinear conversion of Bessel optical vortices,” Proc. SPIE 4403, 229-240 (2001).
[CrossRef]

Katsenelenbaum, B. Z.

B. Z. Katsenelenbaum, E. N. Korshunova, A. N. Sivov, and A. D. Shatrov, “Chiral electromagnetic objects,” Phys. Usp. 40, 1149-1160 (1997).
[CrossRef]

Kazak, N.

V. Belyi, T. King, N. Kazak, N. Khilo, A. Ryzhevich, and E. Katranji, “Methods of formation and nonlinear conversion of Bessel optical vortices,” Proc. SPIE 4403, 229-240 (2001).
[CrossRef]

N. Kazak, N. Khilo, and A. Ryzhevich, “Generation of Bessel beams under the conditions of internal conical refraction,” Quantum Electron. 29, 1020-1024 (1999).
[CrossRef]

Khilo, N.

V. Belyi, T. King, N. Kazak, N. Khilo, A. Ryzhevich, and E. Katranji, “Methods of formation and nonlinear conversion of Bessel optical vortices,” Proc. SPIE 4403, 229-240 (2001).
[CrossRef]

N. Kazak, N. Khilo, and A. Ryzhevich, “Generation of Bessel beams under the conditions of internal conical refraction,” Quantum Electron. 29, 1020-1024 (1999).
[CrossRef]

King, T.

V. Belyi, T. King, N. Kazak, N. Khilo, A. Ryzhevich, and E. Katranji, “Methods of formation and nonlinear conversion of Bessel optical vortices,” Proc. SPIE 4403, 229-240 (2001).
[CrossRef]

Korshunova, E. N.

B. Z. Katsenelenbaum, E. N. Korshunova, A. N. Sivov, and A. D. Shatrov, “Chiral electromagnetic objects,” Phys. Usp. 40, 1149-1160 (1997).
[CrossRef]

Kotlyar, V.

Kotlyarov, K.

A. Volyar, A. Rubass, V. Shvedov, T. Fadeyeva, and K. Kotlyarov, “Optical vortices and Airy' spiral in chiral crystals,” Ukr. J. Phys. Opt. 8, 166-181 (2007), http://www.ifo.lviv.ua/journal/2007/2007_3_8_05.html.
[CrossRef]

Kovalev, A.

Leizer, A.

López-Mariscal, C.

MacVicar, I.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O'Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbit angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52-S57 (2002).
[CrossRef]

Maier, M.

F. Flossman, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901-4 (2005).
[CrossRef]

McClain, S. C.

McGoloin, D.

D. McGoloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15-28 (2005).
[CrossRef]

Mishra, R.

R. Mishra, “A vector analysis of a Bessel beam,” Opt. Commun. 85, 159-161 (1991).
[CrossRef]

Moiseev, O.

Molloy, J.

J. Molloy and M. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

New, G. H. C.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O'Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbit angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52-S57 (2002).
[CrossRef]

Olvik, M.

Z. Bouchali and M. Olvik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555-1566 (1995).
[CrossRef]

O'Neil, A. T.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O'Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbit angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52-S57 (2002).
[CrossRef]

Orlov, S.

S. Orlov and A. Stabinis, “Propagation of superpositions of coaxial optical Bessel beams carrying vortices,” J. Opt. A, Pure Appl. Opt. 6, S259-S262 (2004).
[CrossRef]

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155-165 (2002).
[CrossRef]

Padgett, M.

J. Molloy and M. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

Padgett, M. J.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O'Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbit angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52-S57 (2002).
[CrossRef]

Palma, C.

Papas, C. H.

Petrova, E. S.

E. S. Petrova, “The influence of the natural and magnetic gyrotropy on the polarization and energy of the vector Bessel light beams,” Proc. of Natl. Acad. Sci. Belarus. Series of physicsmath. 1, 95-100 (2002).

Regelskis, K.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155-165 (2002).
[CrossRef]

Rubass, A.

T. Fadeyeva, A. Rubass, Y. Egorov, A. Volyar, and G. Swartzlander, “Quadrefringence of optical vortices in a uniaxial crystal,” J. Opt. Soc. Am. A 25, 1634-1641 (2008).
[CrossRef]

A. Volyar, A. Rubass, V. Shvedov, T. Fadeyeva, and K. Kotlyarov, “Optical vortices and Airy' spiral in chiral crystals,” Ukr. J. Phys. Opt. 8, 166-181 (2007), http://www.ifo.lviv.ua/journal/2007/2007_3_8_05.html.
[CrossRef]

Rubass, A. F.

T. A. Fadeyeva, A. F. Rubass, and A. V. Volyar, “Transverse shift of a high-order paraxial vortex-beam induced by a homogeneous anisotropic medium,” Phys. Rev. A 79, 053815.1-12 (2009).
[CrossRef]

Ruschin, S.

Ryzhevich, A.

V. Belyi, T. King, N. Kazak, N. Khilo, A. Ryzhevich, and E. Katranji, “Methods of formation and nonlinear conversion of Bessel optical vortices,” Proc. SPIE 4403, 229-240 (2001).
[CrossRef]

N. Kazak, N. Khilo, and A. Ryzhevich, “Generation of Bessel beams under the conditions of internal conical refraction,” Quantum Electron. 29, 1020-1024 (1999).
[CrossRef]

Schwarz, U. T.

F. Flossman, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901-4 (2005).
[CrossRef]

Shatrov, A. D.

B. Z. Katsenelenbaum, E. N. Korshunova, A. N. Sivov, and A. D. Shatrov, “Chiral electromagnetic objects,” Phys. Usp. 40, 1149-1160 (1997).
[CrossRef]

Shvedov, V.

A. Volyar, A. Rubass, V. Shvedov, T. Fadeyeva, and K. Kotlyarov, “Optical vortices and Airy' spiral in chiral crystals,” Ukr. J. Phys. Opt. 8, 166-181 (2007), http://www.ifo.lviv.ua/journal/2007/2007_3_8_05.html.
[CrossRef]

Sivov, A. N.

B. Z. Katsenelenbaum, E. N. Korshunova, A. N. Sivov, and A. D. Shatrov, “Chiral electromagnetic objects,” Phys. Usp. 40, 1149-1160 (1997).
[CrossRef]

Skidanov, R.

Smilgevicius, V.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155-165 (2002).
[CrossRef]

Soifer, V.

Soskin, M.

M. Soskin and M. Vasnetsov, “Singular optics,” in Progress in Optics, Vol. 42, E.Wolf, ed. (North-Holland, 2001), pp. 219-276.
[CrossRef]

Stabinis, A.

S. Orlov and A. Stabinis, “Propagation of superpositions of coaxial optical Bessel beams carrying vortices,” J. Opt. A, Pure Appl. Opt. 6, S259-S262 (2004).
[CrossRef]

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155-165 (2002).
[CrossRef]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1968).

Swartzlander, G.

Vasnetsov, M.

M. Soskin and M. Vasnetsov, “Singular optics,” in Progress in Optics, Vol. 42, E.Wolf, ed. (North-Holland, 2001), pp. 219-276.
[CrossRef]

Volyar, A.

T. Fadeyeva, A. Rubass, Y. Egorov, A. Volyar, and G. Swartzlander, “Quadrefringence of optical vortices in a uniaxial crystal,” J. Opt. Soc. Am. A 25, 1634-1641 (2008).
[CrossRef]

A. Volyar, A. Rubass, V. Shvedov, T. Fadeyeva, and K. Kotlyarov, “Optical vortices and Airy' spiral in chiral crystals,” Ukr. J. Phys. Opt. 8, 166-181 (2007), http://www.ifo.lviv.ua/journal/2007/2007_3_8_05.html.
[CrossRef]

A. Volyar, and T. Fadeyeva, “Laguerre-Gaussian beams with complex and real arguments in uniaxial crystals,” Opt. Spectrosc. 101, 297-304 (2006).
[CrossRef]

Volyar, A. V.

T. A. Fadeyeva, A. F. Rubass, and A. V. Volyar, “Transverse shift of a high-order paraxial vortex-beam induced by a homogeneous anisotropic medium,” Phys. Rev. A 79, 053815.1-12 (2009).
[CrossRef]

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A. Yariv and P. Yeh, Optical Waves of Crystals (Wiley, 1984).

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[CrossRef]

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M. V. Berry and M. R. Jeffray, “Chiral conical diffraction,” J. Opt. A, Pure Appl. Opt. 8, 363-372 (2006).
[CrossRef]

S. Orlov and A. Stabinis, “Propagation of superpositions of coaxial optical Bessel beams carrying vortices,” J. Opt. A, Pure Appl. Opt. 6, S259-S262 (2004).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt. (1)

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O'Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbit angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52-S57 (2002).
[CrossRef]

J. Opt. Soc. Am. A (8)

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S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155-165 (2002).
[CrossRef]

R. Mishra, “A vector analysis of a Bessel beam,” Opt. Commun. 85, 159-161 (1991).
[CrossRef]

Opt. Express (1)

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A. Volyar, and T. Fadeyeva, “Laguerre-Gaussian beams with complex and real arguments in uniaxial crystals,” Opt. Spectrosc. 101, 297-304 (2006).
[CrossRef]

Phys. Rev. A (1)

T. A. Fadeyeva, A. F. Rubass, and A. V. Volyar, “Transverse shift of a high-order paraxial vortex-beam induced by a homogeneous anisotropic medium,” Phys. Rev. A 79, 053815.1-12 (2009).
[CrossRef]

Phys. Rev. Lett. (1)

F. Flossman, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901-4 (2005).
[CrossRef]

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A. Volyar, A. Rubass, V. Shvedov, T. Fadeyeva, and K. Kotlyarov, “Optical vortices and Airy' spiral in chiral crystals,” Ukr. J. Phys. Opt. 8, 166-181 (2007), http://www.ifo.lviv.ua/journal/2007/2007_3_8_05.html.
[CrossRef]

Other (4)

A. Yariv and P. Yeh, Optical Waves of Crystals (Wiley, 1984).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1968).

M. V. Berry and M. R. Jeffray, “Conical diffraction: Hamilton's diabolical points at the heart of crystal optics,” in Progress in Optics, Vol. 50, E.Wolf, ed. (Elsevier, 2007), pp. 11-50.
[CrossRef]

M. Soskin and M. Vasnetsov, “Singular optics,” in Progress in Optics, Vol. 42, E.Wolf, ed. (North-Holland, 2001), pp. 219-276.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Dispersive curves for (a),(b) the mode parameters B ± ( 1 , 2 , 3 ) and (b),(c) the propagation constants β ± ( 1 , 2 , 3 ) k in a purely chiral medium with n o = n 3 = 1.55 : (1) g = 3 × 10 10 , g 3 = 8 × 10 10 ; (2) g = g 3 = 3 × 10 10 ; (3) g = 3 × 10 10 , g 3 = 8 × 10 10 ; (d) [ g ] = m .

Fig. 2
Fig. 2

Dispersive curves (a),(b) B ± ( U ) and (c),(d) δ β ± 2 ( U ) of nondiffracting beams in an optically active medium perturbed by a weak linear birefringence Δ ϵ , g = 3 × 10 10 , g 3 = 8 × 10 10 .

Fig. 3
Fig. 3

Maps of the polarization states and integral curves on the background of the intensity distribution: U = 1.56 × 10 7 m 1 , Δ g = 0 , g = 3 × 10 10 .

Fig. 4
Fig. 4

Dispersive curves for (a),(b) the mode parameters B ± ( 1 , 2 , 3 ) and (c),(d) the propagation constants β ± ( 1 , 2 , 3 ) k in a chiral birefringent crystal with n o = 1.544 , n 3 = 1.553 : (1) g = 3 × 10 10 , g 3 = 8 × 10 10 ; (2) g = g 3 = 3 × 10 10 ; (3) g = 3 × 10 10 , g 3 = 9 × 10 10 .

Fig. 5
Fig. 5

Intensity distributions in the x-directed linearly polarized components E x of the vortex Bessel beam ( l = 1 ) and the zeroth order ( l = 0 ) Bessel beam: g = 3 × 10 10 , g 3 = 9 × 10 10 , U = 1.3 × 10 7 m 1 .

Equations (52)

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( a ) × E = i k B , ( b ) × H = i k D ,
( c ) D = 0 , ( d ) B = 0 ,
D = ϵ ̂ E i γ ̂ H , B = H + i γ ̂ E ,
( E ) 2 E k 2 ( ϵ ̂ 2 γ 2 I ̂ ) E = 2 k γ × E + k Δ γ ( × e z E z ) + e z Δ γ [ k ( × E ) z k 2 ( γ + γ 3 ) E z ] ,
H = [ i ( × E ) k ] i γ E i Δ γ e z E z ,
D = ( ϵ γ 2 ) E + ( Δ γ k ) ( × z E ) z + [ Δ ϵ Δ γ ( γ + γ 3 ) ] z E z = 0 .
z E z = [ ( ϵ γ 2 ) / ϵ γ ] E ( Δ γ k ϵ γ ) ( × z E ) z ,
E = α E ( Δ γ k ϵ γ ) ( × z E ) z ,
2 E + k 2 ( ϵ ̂ I ̂ γ 2 ) E + 2 k γ ( × E ) + ( Δ γ k ϵ γ ) ( × z E ) z = α ( E ) k Δ γ ( × e z E z ) + e z k Δ γ [ k ( γ + γ 3 ) E z ( × E ) z ] .
E ( x , y , z ) = E ( x , y ) exp ( i β z ) ,
2 E x + U ¯ 2 E x + 2 k γ ( × E ) x + Δ γ [ k ( × e z E z ) x i ( β k ϵ γ ) x ( × E ) z ] = α x ( E ) ,
2 E y + U ¯ 2 E y + 2 k γ ( × E ) y + Δ γ [ k ( × e z E z ) y i ( β k ϵ γ ) y ( × E ) z ] = α y ( E ) ,
E z = i E ( ϵ γ 2 ) ( ϵ γ β ) ( × E ) z Δ γ ( ϵ γ k ) ,
u = x + i y , v = x i y ,
2 u = x i y , 2 v = x + i y ,
E = v E + + u E , and 2 4 u v 2 ,
E + = E x i E y , E = E x + i E y .
2 E + + ( U ¯ 2 2 k β γ ) E + i 2 ( κ β + θ ) u ( × E ) z = 2 ( α Ω β ) u ( E ) ,
2 E + ( U ¯ 2 + 2 k β γ ) E i 2 ( κ β θ ) v ( × E ) z = 2 ( α + Ω β ) v ( E ) ,
E = A ( u Ψ v Ψ ) + B ( u Ψ v Ψ ) ,
2 Ψ + U 1 2 Ψ = 0 , 2 Ψ + U 2 2 Ψ = 0 ,
U 1 2 = ( U ¯ 2 2 k β γ ) ( A + B ) A ( 1 + κ β + θ ) + B [ 1 + ( Ω β ) α ] ,
U 2 2 = ( U ¯ 2 + 2 k β γ ) ( A B ) A ( 1 κ β + θ ) B [ 1 ( Ω β ) α ] .
2 Ψ + U 2 Ψ = 0 ,
[ U ¯ 2 U 2 ( 1 + θ ) ] A [ 2 k β γ + ( Ω β ) U 2 ] B = 0 ,
β ( 2 k γ + κ U 2 ) A + [ U ¯ 2 U 2 ( 1 α ) ] B = 0 .
[ k 2 ( ϵ γ 2 ) β 2 U 2 ( 1 + θ ) [ 2 k β γ + ( Ω β ) U 2 ] β ( 2 k γ + κ U 2 ) k 2 ( ϵ γ 2 ) β 2 U 2 ( 1 α ) ] = 0 .
β ± 2 = k 2 ( ϵ + γ 2 ) [ ( ϵ 3 + ϵ 2 γ γ 3 ) ( 2 ϵ γ ) U 2 ] ± D ,
B ± = ( β ± k ) [ k 2 ( ϵ γ 2 ) β ± 2 U 2 ( ϵ 3 γ 2 ) ϵ γ ] [ 2 β ± 2 γ + U 2 ( ϵ γ 2 ) ( γ + γ 3 ) ϵ γ ] 1 .
β ± = k ( n ± γ ) ,
β ± k ( n ± γ ) [ 1 ( U k ϵ ) 2 2 ] , B ± [ 1 ( U k ϵ ) 2 2 ] .
U is 2 = 2 k 2 ( γ Δ γ ) ϵ γ , β + ( U is ) = β ( U is ) .
g 3 g < 0 , | g 3 | > | g | .
E ( + ) = ( ( 1 + B + ) u Ψ ( 1 B + ) v Ψ ) exp ( i β + z ) ,
E ( ) = ( ( 1 + B ) u Ψ ( 1 B ) v Ψ ) exp ( i β z ) ,
Ψ l = J l ( U r ) exp ( ± i l φ ) .
u e i φ [ r ( i r ) φ ] , v e i φ [ r + ( i r ) φ ] ,
E + , 1 ( ± ) = ( 1 + B ± ) e i β ± z e i φ [ r ( i r ) φ ] Ψ 0 ,
E , 1 ( ± ) = ( 1 B ± ) e i β ± z e i φ [ r + ( i r ) φ ] Ψ 0 ,
E | m 1 | ( ± ) = v m E , 1 ( ± ) = { e i φ [ r + ( i r ) φ ] } ( m ) E , 1 ( ± ) .
J m 1 ( x ) = J m ( x ) + ( m x ) J m ( x ) , J m + 1 ( x ) = J m ( x ) + ( m x ) J m ( x ) ,
E + , | m 1 | ( ± ) = ( 1 + B ± ) e i β ± z e i ( m 1 ) φ J m 1 ( U r ) ,
E , | m 1 | ( ± ) = ( 1 B ± ) e i β ± z e i ( m + 1 ) φ J m + 1 ( U r ) ,
E ̑ , | m + 1 | ( ± ) = u m E .1 ( ± ) = { e i φ [ r ( i r ) φ ] } ( m ) E , 1 ( ± ) ,
E ̃ + , | m + 1 | ( ± ) = ( 1 + B ± ) e i β ± z e i ( m + 1 ) φ J m + 1 ( U r ) ,
E ̃ , | m + 1 | ( ± ) = ( 1 B ± ) e i β ± z e i ( m 1 ) φ J m 1 ( U r ) .
E m = a E | m 1 | ( + ) + b E | m 1 | ( ) .
E = 2 i ( 1 B ) e i φ e i β ̃ z sin ( δ β z ) J 1 ( U r ) ,
U g 2 = 2 k 2 ( γ Δ γ ) ϵ γ , Δ β 2 = β + 2 β 2 = k 2 ( 2 γ Δ γ ) Δ ϵ .
E ( L ) = c 1 E ( B + , β + , m = 0 ) + c 2 E ( B , β , m = 0 ) + c 3 E ( B + , β + , m = 2 ) + c 4 E ( B , β , m = 2 ) .
E + ( L ) = J 1 ( U r ) e i β ̃ z 2 ( 1 B ) { 2 i ( 1 + B ) ( 1 + B + ) sin ( δ β z ) e i φ + [ ( 1 + B ) ( 1 B + ) e i δ β z ( 1 B ) ( 1 + B + ) e i δ β z ] e i φ } ,
E ( L ) = e i β ̃ z 2 ( 1 B ) { 2 i ( 1 B ) ( 1 B + ) sin ( δ β z ) e i 3 φ J 3 ( U r ) + [ ( 1 + B ) ( 1 B + ) e i δ β z ( 1 B ) ( 1 + B + ) e i δ β z ] e i φ J 1 ( U r ) } .

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