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

doi:10.1364/JOSAA.29.001252

Generation of J₀-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 »View Author Affiliations

JOSA A, Vol. 29, Issue 7, pp. 1252-1258 (2012)
http://dx.doi.org/10.1364/JOSAA.29.001252

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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.

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(260.1960) Physical optics : Diffraction theory
(290.3200) Scattering : Inverse scattering

ToC Category:
Physical Optics

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

Citation
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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-7-1252

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References

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]

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

[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]

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

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

[5] 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]

[6] 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]

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

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

[9] 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]

[10] 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]

[11] 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.

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

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

[14] 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]

[15] 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]

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

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

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

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

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

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

[22] 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]

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

[24] 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]

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

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

[27] 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]

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

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

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

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

[32] 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]

[33] 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]

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

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

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Generation of J₀-Bessel-Gauss beam by a heterogeneous refractive index map