Generation of J<sub>0</sub>-Bessel-Gauss beam by a heterogeneous refractive index map

Damian P. San-Roman-Alerigi; Tien K. Ng; Yaping Zhang; Ahmed Ben Slimane; Mohammad Alsunaidi; Boon S. Ooi

doi:10.1364/JOSAA.29.001252

Generation of $J_{0}$ -Bessel-Gauss beam by a heterogeneous refractive index map

Damian P. San-Roman-Alerigi, Tien K. Ng, Yaping Zhang, Ahmed Ben Slimane, Mohammad Alsunaidi, and Boon S. Ooi

Journal of the Optical Society of America A
Vol. 29,
Issue 7,
pp. 1252-1258
(2012)
•https://doi.org/10.1364/JOSAA.29.001252

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Damian P. San-Roman-Alerigi, Tien K. Ng, Yaping Zhang, Ahmed Ben Slimane, Mohammad Alsunaidi, and Boon S. Ooi, "Generation of J₀-Bessel-Gauss beam by a heterogeneous refractive index map," J. Opt. Soc. Am. A 29, 1252-1258 (2012)

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Related Topics
Table of Contents Category
- Physical Optics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Diffraction (050.1940)
- Diffraction theory (260.1960)
- Inverse scattering (290.3200)

About this Article
History
- Original Manuscript: January 17, 2012
- Revised Manuscript: March 13, 2012
- Manuscript Accepted: March 14, 2012
- Published: June 6, 2012

Accessible

Open Access

Abstract

In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to a $J_{0}$ -Bessel-Gauss convertor. We theoretically demonstrate the viability of a device that could be fabricated on a $Si / {Si}_{1 - y} O_{y} / {Si}_{1 - x - y} {Ge}_{x} C_{y}$ platform or by photo-refractive media. The proposed device is 200 μm in length and 25 μm in width, and its refractive index varies in controllable steps across the light propagation and transversal directions. The computed conversion efficiency and loss are 90%, and $- 0.457 dB$ , respectively. The theoretical results, obtained from the beam conversion efficiency, self-regeneration, and propagation through an opaque obstruction, demonstrate that a two-dimensional (2D) graded index map of the refractive index can be used to transform a Gauss beam into a $J_{0}$ -Bessel-Gauss beam. To the best of our knowledge, this is the first demonstration of such beam transformation by means of a 2D index-mapping that is fully integrable in silicon photonics based planar lightwave circuits (PLCs). The concept device is significant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and nonlinear beam diode lasers.

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References

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|
Author
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Publication

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[Crossref]
W. Cong, N. Chen, and B. Gu, “Generation of nondiffracting beams by diffractive phase elements,” J. Opt. Soc. Am. 15, 2362–2364 (1998).
[Crossref]
S. Chavez-Cerda, “A new approach to Bessel beams,” J. Mod. Opt. 46, 923–930 (1999).
F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[Crossref]
Y. Lin, W. Seka, J. H. Eberly, H. Huang, and D. L. Brown, “Experimental investigation of Bessel beam characteristics,” Appl. Opt. 31, 2708–2713 (1992).
[Crossref]
R. M. Herman and T. A. Wiggins, “Propagation and focusing of Bessel-Gauss, generalized Bessel-Gauss and modified Bessel-Gauss beams,” J. Opt. Soc. Am. A 18, 170–176 (2001).
[Crossref]
I. A. Litvin, M. G. McLaren, and A. Forbes, “Propagation of obstructed Bessel and Bessel-Gauss beams,” Proc. SPIE 7062, 706218 (2008).
[Crossref]
J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]
F. Wu, Y. Chen, and D. Guo, “Nanosecond pulsed Bessel-Gauss beam generated directly from Nd:YAG axicon-based resonator,” Appl. Opt. 46, 4943–4947 (2007).
[Crossref]
V. Arrizón, D. Sánchez-de-la-Llave, U. Ruiz, and G. Méndez, “Efficient generation of an arbitrary nondiffracting Bessel beam employing its phase modulation,” Opt. Lett. 34, 1456–1458 (2009).
[Crossref]
M. M. Méndez Otero, G. C. Martínez Jimnez, M. L. Arroyo Carrasco, M. D. Iturbe Castillo, and E. A. Mart Panameño, “Generation of Bessel-Gauss beams by means of computed generated holograms for Bessel Beams,” in Frontiers in Optics, Technical Digest (CD) (Optical Society of America, 2006), paper JWD129.
Q. Zhan, “Evanescent Bessel beam generation via surface plasmon resonance excitation by radially polrized beam,” Opt. Lett. 31, 1726–1728 (2006).
[Crossref]
J. Canning, “Diffraction-free mode generation and propagation in optical waveguides,” Opt. Commun. 207, 35–39 (2002).
[Crossref]
V. S. Ilchenko, M. Mohageg, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Efficient generation of truncated Bessel beams using cylindrical waveguides,” Opt. Express 15, 5866–5871 (2007).
[Crossref]
T. Tsai, E. McLeod, and C. B. Arnold, “Generating Bessel beams with a tunable acoustic gradient index of refraction lens,” Proc. SPIE 6326, 63261F (2006).
[Crossref]
F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photon. 4, 780–785 (2010).
[Crossref]
M. Lei and B. Yao, “Characteristics of beam profiles of Gaussian beam passing through an axicon,” Opt. Commun. 239, 367–372 (2004).
[Crossref]
K. Hayata, “Are Bessel beams supportable in graded-index media?” Opt. Rev. 3, 299–300 (1996).
[Crossref]
B. Gang and L. Peijun, “Inverse medium scattering problems for electromagnetic waves,” SIAM J. Appl. Math. 65, 2049–2066 (2005).
[Crossref]
A. J. Devaney, “A filtered backprojection algorithm for diffraction tomography,” Ultrason. Imag. 4, 336–350 (1982).
[Crossref]
R. M. Lewis, “Physical optics inverse diffraction,” IEEE Trans. Antennas Propag. 17, 308–314 (1969).
[Crossref]
Y. Lai, J. Ng, H. Yang, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chang, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[Crossref]
M. Piana, “On uniqueness for anisotropic inhomogeneous inverse scattering problems,” Inverse Probl. 14, 1565–1579 (1998).
[Crossref]
O. Dorn, H. Bertete-Aguirre, J. G. Berryman, and G. C. Papanicolaou, “A nonlinear inversion method for 3D electromagnetic imaging using adjoint fields,” Inverse Probl. 15, 1523–1558 (1999).
[Crossref]
A. J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. Biomed. Eng. BME-30, 377–386 (1983).
[Crossref]
H. Hadar and P. Monk, “The linear sampling method for solving the electromagnetic inverse medium problem,” Inverse Probl. 18, 891–906 (2002).
[Crossref]
H. Hadar, “The interior transmission problem for anisotropic Maxwell’s equations and its applications to the inverse problem,” Math. Methods Appl. Sci. 27, 2111–2129 (2004).
[Crossref]
F. Cakoni, “A variational approach for the solution of the electromagnetic interior transmission problem for anisotropic media,” Inverse Probl. Imaging 1, 443–456 (2007).
J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref]
U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2008).
[Crossref]
H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref]
H. J. Lee, C. H. Henry, K. J. Orlowsky, R. F. Kazarinov, and T. Y. Kometani, “Refractive-index dispersion of phospho-silicate glass, thermal oxide, and silicon nitride films on silicon,” Appl. Opt. 27, 4104–4109 (1988).
[Crossref]
W. Fenga, W. K. Choia, L. K. Beraa, M. Jib, and C. Y. Yangb, “Optical characterization of as-prepared and rapid thermal oxidized partially strain compensated Si1xyGexCy films,” Mater. Sci. Semicond. Process. 4, 655–659 (2001).
[Crossref]
A. Zakery, “Optical properties and applications of chalcogenide glasses: a review,” J. Non-Cryst. Solids 330, 1–12 (2003).
[Crossref]
S. B. Kang, “Optical and dielectric properties of chalcogenide glasses at terahertz frequencies,” ETRI J. 31, 667–674(2009).
[Crossref]

2010 (2)

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photon. 4, 780–785 (2010).
[Crossref]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref]

2009 (3)

S. B. Kang, “Optical and dielectric properties of chalcogenide glasses at terahertz frequencies,” ETRI J. 31, 667–674(2009).
[Crossref]

Y. Lai, J. Ng, H. Yang, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chang, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[Crossref]

V. Arrizón, D. Sánchez-de-la-Llave, U. Ruiz, and G. Méndez, “Efficient generation of an arbitrary nondiffracting Bessel beam employing its phase modulation,” Opt. Lett. 34, 1456–1458 (2009).
[Crossref]

2008 (2)

I. A. Litvin, M. G. McLaren, and A. Forbes, “Propagation of obstructed Bessel and Bessel-Gauss beams,” Proc. SPIE 7062, 706218 (2008).
[Crossref]

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2008).
[Crossref]

2007 (3)

F. Wu, Y. Chen, and D. Guo, “Nanosecond pulsed Bessel-Gauss beam generated directly from Nd:YAG axicon-based resonator,” Appl. Opt. 46, 4943–4947 (2007).
[Crossref]

F. Cakoni, “A variational approach for the solution of the electromagnetic interior transmission problem for anisotropic media,” Inverse Probl. Imaging 1, 443–456 (2007).

V. S. Ilchenko, M. Mohageg, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Efficient generation of truncated Bessel beams using cylindrical waveguides,” Opt. Express 15, 5866–5871 (2007).
[Crossref]

2006 (3)

T. Tsai, E. McLeod, and C. B. Arnold, “Generating Bessel beams with a tunable acoustic gradient index of refraction lens,” Proc. SPIE 6326, 63261F (2006).
[Crossref]

Q. Zhan, “Evanescent Bessel beam generation via surface plasmon resonance excitation by radially polrized beam,” Opt. Lett. 31, 1726–1728 (2006).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref]

2005 (1)

B. Gang and L. Peijun, “Inverse medium scattering problems for electromagnetic waves,” SIAM J. Appl. Math. 65, 2049–2066 (2005).
[Crossref]

2004 (2)

M. Lei and B. Yao, “Characteristics of beam profiles of Gaussian beam passing through an axicon,” Opt. Commun. 239, 367–372 (2004).
[Crossref]

H. Hadar, “The interior transmission problem for anisotropic Maxwell’s equations and its applications to the inverse problem,” Math. Methods Appl. Sci. 27, 2111–2129 (2004).
[Crossref]

2003 (1)

A. Zakery, “Optical properties and applications of chalcogenide glasses: a review,” J. Non-Cryst. Solids 330, 1–12 (2003).
[Crossref]

2002 (2)

H. Hadar and P. Monk, “The linear sampling method for solving the electromagnetic inverse medium problem,” Inverse Probl. 18, 891–906 (2002).
[Crossref]

J. Canning, “Diffraction-free mode generation and propagation in optical waveguides,” Opt. Commun. 207, 35–39 (2002).
[Crossref]

2001 (2)

R. M. Herman and T. A. Wiggins, “Propagation and focusing of Bessel-Gauss, generalized Bessel-Gauss and modified Bessel-Gauss beams,” J. Opt. Soc. Am. A 18, 170–176 (2001).
[Crossref]

W. Fenga, W. K. Choia, L. K. Beraa, M. Jib, and C. Y. Yangb, “Optical characterization of as-prepared and rapid thermal oxidized partially strain compensated Si1xyGexCy films,” Mater. Sci. Semicond. Process. 4, 655–659 (2001).
[Crossref]

1999 (2)

O. Dorn, H. Bertete-Aguirre, J. G. Berryman, and G. C. Papanicolaou, “A nonlinear inversion method for 3D electromagnetic imaging using adjoint fields,” Inverse Probl. 15, 1523–1558 (1999).
[Crossref]

S. Chavez-Cerda, “A new approach to Bessel beams,” J. Mod. Opt. 46, 923–930 (1999).

1998 (2)

W. Cong, N. Chen, and B. Gu, “Generation of nondiffracting beams by diffractive phase elements,” J. Opt. Soc. Am. 15, 2362–2364 (1998).
[Crossref]

M. Piana, “On uniqueness for anisotropic inhomogeneous inverse scattering problems,” Inverse Probl. 14, 1565–1579 (1998).
[Crossref]

1996 (1)

K. Hayata, “Are Bessel beams supportable in graded-index media?” Opt. Rev. 3, 299–300 (1996).
[Crossref]

1992 (1)

Y. Lin, W. Seka, J. H. Eberly, H. Huang, and D. L. Brown, “Experimental investigation of Bessel beam characteristics,” Appl. Opt. 31, 2708–2713 (1992).
[Crossref]

1988 (1)

H. J. Lee, C. H. Henry, K. J. Orlowsky, R. F. Kazarinov, and T. Y. Kometani, “Refractive-index dispersion of phospho-silicate glass, thermal oxide, and silicon nitride films on silicon,” Appl. Opt. 27, 4104–4109 (1988).
[Crossref]

1987 (3)

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[Crossref]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[Crossref]

1983 (1)

A. J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. Biomed. Eng. BME-30, 377–386 (1983).
[Crossref]

1982 (1)

A. J. Devaney, “A filtered backprojection algorithm for diffraction tomography,” Ultrason. Imag. 4, 336–350 (1982).
[Crossref]

1969 (1)

R. M. Lewis, “Physical optics inverse diffraction,” IEEE Trans. Antennas Propag. 17, 308–314 (1969).
[Crossref]

Arnold, C. B.

T. Tsai, E. McLeod, and C. B. Arnold, “Generating Bessel beams with a tunable acoustic gradient index of refraction lens,” Proc. SPIE 6326, 63261F (2006).
[Crossref]

Arrizón, V.

Arroyo Carrasco, M. L.

M. M. Méndez Otero, G. C. Martínez Jimnez, M. L. Arroyo Carrasco, M. D. Iturbe Castillo, and E. A. Mart Panameño, “Generation of Bessel-Gauss beams by means of computed generated holograms for Bessel Beams,” in Frontiers in Optics, Technical Digest (CD) (Optical Society of America, 2006), paper JWD129.

Beraa, L. K.

Berryman, J. G.

Bertete-Aguirre, H.

Brown, D. L.

Y. Lin, W. Seka, J. H. Eberly, H. Huang, and D. L. Brown, “Experimental investigation of Bessel beam characteristics,” Appl. Opt. 31, 2708–2713 (1992).
[Crossref]

Cakoni, F.

F. Cakoni, “A variational approach for the solution of the electromagnetic interior transmission problem for anisotropic media,” Inverse Probl. Imaging 1, 443–456 (2007).

Canning, J.

J. Canning, “Diffraction-free mode generation and propagation in optical waveguides,” Opt. Commun. 207, 35–39 (2002).
[Crossref]

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref]

Chang, C. T.

Chavez-Cerda, S.

S. Chavez-Cerda, “A new approach to Bessel beams,” J. Mod. Opt. 46, 923–930 (1999).

Chen, H.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref]

Chen, N.

W. Cong, N. Chen, and B. Gu, “Generation of nondiffracting beams by diffractive phase elements,” J. Opt. Soc. Am. 15, 2362–2364 (1998).
[Crossref]

Chen, Y.

F. Wu, Y. Chen, and D. Guo, “Nanosecond pulsed Bessel-Gauss beam generated directly from Nd:YAG axicon-based resonator,” Appl. Opt. 46, 4943–4947 (2007).
[Crossref]

Choia, W. K.

Cong, W.

W. Cong, N. Chen, and B. Gu, “Generation of nondiffracting beams by diffractive phase elements,” J. Opt. Soc. Am. 15, 2362–2364 (1998).
[Crossref]

Devaney, A. J.

A. J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. Biomed. Eng. BME-30, 377–386 (1983).
[Crossref]

A. J. Devaney, “A filtered backprojection algorithm for diffraction tomography,” Ultrason. Imag. 4, 336–350 (1982).
[Crossref]

Dorn, O.

Durnin, J.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[Crossref]

Eberly, J. H.

Y. Lin, W. Seka, J. H. Eberly, H. Huang, and D. L. Brown, “Experimental investigation of Bessel beam characteristics,” Appl. Opt. 31, 2708–2713 (1992).
[Crossref]

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Fahrbach, F. O.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photon. 4, 780–785 (2010).
[Crossref]

Fenga, W.

Forbes, A.

I. A. Litvin, M. G. McLaren, and A. Forbes, “Propagation of obstructed Bessel and Bessel-Gauss beams,” Proc. SPIE 7062, 706218 (2008).
[Crossref]

Gang, B.

B. Gang and L. Peijun, “Inverse medium scattering problems for electromagnetic waves,” SIAM J. Appl. Math. 65, 2049–2066 (2005).
[Crossref]

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[Crossref]

Gu, B.

W. Cong, N. Chen, and B. Gu, “Generation of nondiffracting beams by diffractive phase elements,” J. Opt. Soc. Am. 15, 2362–2364 (1998).
[Crossref]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[Crossref]

Guo, D.

F. Wu, Y. Chen, and D. Guo, “Nanosecond pulsed Bessel-Gauss beam generated directly from Nd:YAG axicon-based resonator,” Appl. Opt. 46, 4943–4947 (2007).
[Crossref]

Hadar, H.

H. Hadar, “The interior transmission problem for anisotropic Maxwell’s equations and its applications to the inverse problem,” Math. Methods Appl. Sci. 27, 2111–2129 (2004).
[Crossref]

H. Hadar and P. Monk, “The linear sampling method for solving the electromagnetic inverse medium problem,” Inverse Probl. 18, 891–906 (2002).
[Crossref]

Han, D.

Hayata, K.

K. Hayata, “Are Bessel beams supportable in graded-index media?” Opt. Rev. 3, 299–300 (1996).
[Crossref]

Henry, C. H.

Herman, R. M.

R. M. Herman and T. A. Wiggins, “Propagation and focusing of Bessel-Gauss, generalized Bessel-Gauss and modified Bessel-Gauss beams,” J. Opt. Soc. Am. A 18, 170–176 (2001).
[Crossref]

Huang, H.

Y. Lin, W. Seka, J. H. Eberly, H. Huang, and D. L. Brown, “Experimental investigation of Bessel beam characteristics,” Appl. Opt. 31, 2708–2713 (1992).
[Crossref]

Ilchenko, V. S.

Iturbe Castillo, M. D.

Jib, M.

Kang, S. B.

S. B. Kang, “Optical and dielectric properties of chalcogenide glasses at terahertz frequencies,” ETRI J. 31, 667–674(2009).
[Crossref]

Kazarinov, R. F.

Kometani, T. Y.

Lai, Y.

Lee, H. J.

Lei, M.

M. Lei and B. Yao, “Characteristics of beam profiles of Gaussian beam passing through an axicon,” Opt. Commun. 239, 367–372 (2004).
[Crossref]

Leonhardt, U.

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2008).
[Crossref]

Lewis, R. M.

R. M. Lewis, “Physical optics inverse diffraction,” IEEE Trans. Antennas Propag. 17, 308–314 (1969).
[Crossref]

Lin, Y.

Y. Lin, W. Seka, J. H. Eberly, H. Huang, and D. L. Brown, “Experimental investigation of Bessel beam characteristics,” Appl. Opt. 31, 2708–2713 (1992).
[Crossref]

Litvin, I. A.

I. A. Litvin, M. G. McLaren, and A. Forbes, “Propagation of obstructed Bessel and Bessel-Gauss beams,” Proc. SPIE 7062, 706218 (2008).
[Crossref]

Maleki, L.

Mart Panameño, E. A.

Martínez Jimnez, G. C.

Matsko, A. B.

McLaren, M. G.

I. A. Litvin, M. G. McLaren, and A. Forbes, “Propagation of obstructed Bessel and Bessel-Gauss beams,” Proc. SPIE 7062, 706218 (2008).
[Crossref]

McLeod, E.

T. Tsai, E. McLeod, and C. B. Arnold, “Generating Bessel beams with a tunable acoustic gradient index of refraction lens,” Proc. SPIE 6326, 63261F (2006).
[Crossref]

Méndez, G.

Méndez Otero, M. M.

Miceli, J.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Mohageg, M.

Monk, P.

H. Hadar and P. Monk, “The linear sampling method for solving the electromagnetic inverse medium problem,” Inverse Probl. 18, 891–906 (2002).
[Crossref]

Ng, J.

Orlowsky, K. J.

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[Crossref]

Papanicolaou, G. C.

Peijun, L.

B. Gang and L. Peijun, “Inverse medium scattering problems for electromagnetic waves,” SIAM J. Appl. Math. 65, 2049–2066 (2005).
[Crossref]

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref]

Philbin, T. G.

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2008).
[Crossref]

Piana, M.

M. Piana, “On uniqueness for anisotropic inhomogeneous inverse scattering problems,” Inverse Probl. 14, 1565–1579 (1998).
[Crossref]

Rohrbach, A.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photon. 4, 780–785 (2010).
[Crossref]

Ruiz, U.

Sánchez-de-la-Llave, D.

Savchenkov, A. A.

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref]

Seka, W.

Y. Lin, W. Seka, J. H. Eberly, H. Huang, and D. L. Brown, “Experimental investigation of Bessel beam characteristics,” Appl. Opt. 31, 2708–2713 (1992).
[Crossref]

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref]

Simon, P.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photon. 4, 780–785 (2010).
[Crossref]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref]

Tsai, T.

T. Tsai, E. McLeod, and C. B. Arnold, “Generating Bessel beams with a tunable acoustic gradient index of refraction lens,” Proc. SPIE 6326, 63261F (2006).
[Crossref]

Wiggins, T. A.

R. M. Herman and T. A. Wiggins, “Propagation and focusing of Bessel-Gauss, generalized Bessel-Gauss and modified Bessel-Gauss beams,” J. Opt. Soc. Am. A 18, 170–176 (2001).
[Crossref]

Wu, F.

F. Wu, Y. Chen, and D. Guo, “Nanosecond pulsed Bessel-Gauss beam generated directly from Nd:YAG axicon-based resonator,” Appl. Opt. 46, 4943–4947 (2007).
[Crossref]

Xiao, J.

Yang, H.

Yangb, C. Y.

Yao, B.

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Fig. 1.

Schematic representation of a Gauss to $J_{0}$ -Bessel-Gauss transformation via a heterogeneous medium; the transformation device in region $A$ has a refractive index map that needs to be calculated in order to achieve the desired beam transformation. The device is embedded in a homogeneous medium $B$ , where Bessel and Gauss beams are known solutions to the Helmholtz equation.

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Fig. 2.

Illustration of (a) superposition of transition stages in the transformation of Gauss to $J_{0}$ -Bessel-Gauss beams, and (b) the transformation functions $f$ and $g$ .

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Fig. 3.

Sketch of the proposed refractive index map for the converter as defined by the transformation functions $f$ and $g$ , with a device length of 200 μm and a width 25 μm. Albeit here shown in 11 steps, the refractive index varies smoothly between 1 and 2.57 in controllable steps. The device is rotationally symmetric around the propagation axis $z$ .

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Fig. 4.

Fine resolution refractive index map for the converter, with minimum feature size $d = 1 nm$ , as defined by the transformation functions $f$ and $g$ . Device length is 200 μm and width is 25 μm. The refractive index varies smoothly between 1 and 2.57 in 50 controllable steps. A practical device could be fabricated on a $Si / {Si}_{1 y} O_{y} / {Si}_{1 x y} {Ge}_{x} C_{y}$ slab and the refractive index steps achieved by controlled oxidation or with photo-refractive materials. The device is rotationally symmetric around the propagation axis $z$ .

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Fig. 5.

Transverse electric field intensity of the converted beam: (a) simulated near field computed at 5 μm from the output of the device (green), and fit, 95% confidence, to $J_{0}$ -Bessel-Gauss (red). Its far field profile (b), and (c) zoom to principal peak.

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Fig. 6.

Transverse electric field intensity profile for the converted beam for two different grid sizes: (a) shows the optimal grid size of 1 nm (green) and modified grid size of 10 nm (blue), both computed at the near fields, 5 μm from the output of the device. The far fields for both output beams (b), for optimal grid size (green) and modified grid (blue), and (c) magnification of the near field around the principal peak.

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Fig. 7.

Transverse electric field intensity profile for (a) the converted beam (green), its fit (red), and the scattered field profile (blue), computed at 50 μm from the scattering region. The far field for the undisturbed and perturbed beams are shown in (b), and (c) shows magnification of the fields around the principal peak.

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Equations (8)

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\nabla^{2} E⃗ - μ ε (r⃗) \frac{\partial^{2} E⃗}{\partial t^{2}} = - \nabla (\frac{1}{ε} E⃗ \cdot \nabla ε),

ε_{\min} \leq ε (r⃗) \leq ε_{\max}, \forall r⃗ \in A .

\nabla^{2} ϑ⃗ (r⃗) - ω^{2} μ ε (r⃗) ϑ⃗ (r⃗) = \nabla (ϑ⃗ (r⃗) \cdot \nabla \ln ε (r⃗)) .

ϑ⃗ (r⃗) = {\begin{array}{l} ϕ⃗ (r⃗) & \forall & r⃗ \in S_{i}, \\ ψ⃗ (r⃗) & \forall & r⃗ \in A, \\ ζ⃗ (r⃗) & \forall & r⃗ \in S_{o}, \end{array}

ψ⃗ (r⃗) = f (r⃗) ϕ⃗ (r⃗) + g (r⃗) ζ⃗ (r⃗) + γ⃗ (r⃗),

\overset{ϖ⃗}{\overset{︷}{\nabla^{2} (f (r⃗) ϕ⃗ (r⃗) + g (r⃗) ζ⃗ (r⃗))}} - \overset{ω^{2} μ ψ⃗}{\overset{︷}{ω^{2} μ \cdot (f (r⃗) ϕ⃗ (r⃗) + g (r⃗) ζ⃗ (r⃗))}} \cdot ε (r⃗) = \nabla [(f (r⃗) ϕ⃗ (r⃗) + g (r⃗) ζ⃗ (r⃗)) \cdot \nabla \ln ε (\vec{r})] .

\nabla [(f (r⃗) ϕ⃗ (r⃗) + g (r⃗) ζ⃗ (r⃗)) \cdot \nabla \ln ε (r⃗)] = (ψ⃗ \cdot \nabla) \nabla \ln ε (r⃗) + \nabla_{ψ} (\nabla \ln ε (r⃗) \cdot ψ⃗) .

ω^{2} μ ψ⃗ ε (r⃗) + (ψ⃗ \cdot \nabla) \nabla \ln ε (r⃗) + \nabla_{ψ} (\nabla \ln ε (r⃗) \cdot ψ⃗) = ϖ⃗ .