Electromagnetic equivalent model for phase conjugate mirror based on the utilization of left-handed material

doi:10.1364/OE.15.013877

Electromagnetic equivalent model for phase conjugate mirror based on the utilization of left-handed material

Guoan Zheng, Lixin Ran, and Changhuei Yang »View Author Affiliations

Optics Express, Vol. 15, Issue 21, pp. 13877-13885 (2007)
http://dx.doi.org/10.1364/OE.15.013877

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Abstract

An electromagnetic equivalent model for the phase conjugate mirror (PCM) is proposed in this paper. The model is based on the unique property of the isotropic left-handed material (LHM) - the ability of LHM to reverse the phase factors of propagative waves. We show that a PCM interface can be substituted with a LHM-RHM (right-handed material) interface and associated image sources and objects in the LHM. This equivalent model is fully equivalent in the treatment of propagative wave components. However, we note that the presence of evanescent wave components can lead to undesirably surface resonance at the LHM-RHM interface. This artefact can be kept well bounded by introducing a small refractive index mismatch between the LHM and RHM. We demonstrate the usefulness of this model by modelling several representative scenarios of light patterns interacting with a PCM. The simulations were performed by applying the equivalent model to a commercial finite element method (FEM) software. This equivalent model also points to the intriguing possibility of realizing some unique LHM based systems in the optical domain by substituting a PCM in place of a LHM-RHM interface.

OCIS Codes
(190.5040) Nonlinear optics : Phase conjugation
(260.2110) Physical optics : Electromagnetic optics

ToC Category:
Physical Optics

History
Original Manuscript: July 26, 2007
Revised Manuscript: September 11, 2007
Manuscript Accepted: September 12, 2007
Published: October 8, 2007

Citation
Guoan Zheng, Lixin Ran, and Changhuei Yang, "Electromagnetic equivalent model for phase conjugate mirror based on the utilization of left-handed material," Opt. Express 15, 13877-13885 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-21-13877

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References

B. Ya. Zel’dovich, R. F. Pilipetskii, and V. V. Shkunov, Principles of Phase Conjugation (Springer, Berlin, 1985).
R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).
R. Mittra and T. M. Habashy, "Theory of wave-front-distortion correction by phase conjugation," J. Opt. Soc. Am. A 1, 1103-1109 (1984). [CrossRef]
S. I. Bozhevolnyi, O. Keller, and I. I. Smolyaninov, "Scattered light enhancement near a phase conjugating mirror," Opt. Commun. 115, 115-120 (1995). [CrossRef]
P. Mathey, S. Odoulov, and D. Rytz, "Instability of single-frequency operation in semilinear photorefractive coherent oscillators," Phys. Rev. Lett. 89, 053901 (2002). [CrossRef] [PubMed]
J. de Rosny and M. Fink, "Overcoming the diffraction limit in wave physics using a time-reversal mirror and a novel acoustic sink," Phys. Rev. Lett. 89, 124301 (2002). [CrossRef] [PubMed]
B. E. Henty and D. D. Stancil, "Multipath-enabled super-resolution for rf and microwave communication using phase-conjugate arrays," Phys. Rev. Lett. 93, 243904 (2004). [CrossRef]
G. Lerosey, J.de Rosny, A. Tourin, M. Fink, "Focusing Beyond the Diffraction Limit with Far-Field Time Reversal," Science 315, 1120-1122 (2007). [CrossRef] [PubMed]
M. Cronin-Golomb, J. O. White, A. Yariv, B. Fischer, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. 20, 12-30 (1984). [CrossRef]
A. A. Zozulya, and V. T. Tikhonchuk, "Investigation of stability of four-wave mixing in photorefractive media," Phys. Lett. A 135, 447-452 (1989). [CrossRef]
P. C. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, "Optical phase conjugation for turbidity suppression in biological samples," submitted toNature Photonic.
D. R. Smith and N. Kroll, "Negative Refractive Index in Left-Handed Materials," Phys. Rev. Lett. 84, 4184 (2000). [CrossRef] [PubMed]
J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966 (2000). [CrossRef] [PubMed]
J. Pacheco, T. M. Grzegorczyk, B. I. Wu, Y. Zhang, and J. A. Kong, "Power Propagation in Homogeneous Isotropic Frequency-Dispersive Left-Handed Media," Phys. Rev. Lett. 89, 257401 (2002). [CrossRef] [PubMed]
M. Nieto-V. and E. Wolf, "Phase conjugation and symmetries with wave fields in free space containing evanescent components," J. Opt. Soc. Am. A 2, 1429-1434 (1985). [CrossRef]
J. A. Kong, Electromagnetic Wave Theory, (EMW Publishing, 2005) Chaps. 3, 5.
N. Engheta, "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Antennas Wireless Propag. Lett. 1, 10-13 (2002). [CrossRef]
Y. Li, L. Ran, H. Chen, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Experimental realization of a one dimensional LHM-RHM Resonator," IEEE Trans. Microwave Theory and Tech. special issue on Metamaterials 53, 1522-1526 (2005).
S. He, Y. Jin, Z. Ruan and J. Kuang, "On subwavelength and open resonators involving metamaterials of negative refraction index," New J. Phys. 7, 210 (2005). [CrossRef]
T. J. Cui, Q. Cheng, W. B. Lu, Q. Jiang and J. A. Kong, "Localization of electromagnetic energy using a left-handed-medium slab," Phys. Rev. B 71, 045114 (2005). [CrossRef]
COMSOL Multiphysics 3.3 (2007), COMSOL INC. (http://www.comsol.com/)

Bozhevolnyi, S. I.
Cheng, Q.
Cronin-Golomb, M.
Cui, T. J.
de Rosny, J.
Engheta, N.
Feld, M. S.
Fink, M.
Fischer, B.
Grzegorczyk, T. M.
Habashy, T. M.
He, S.
Henty, B. E.
Jiang, Q.
Jin, Y.
Keller, O.
Kong, J. A.
Kroll, N.
Kuang, J.
Lerosey, G.
Lu, W. B.
Mathey, P.
Mittra, R.
Nieto-V., M.
Odoulov, S.
Pacheco, J.
Pendry, J. B.
Psaltis, D.
Ruan, Z.
Rytz, D.
Smith, D. R.
Smolyaninov, I. I.
Stancil, D. D.
Tikhonchuk, V. T.
White, J. O.
Wolf, E.
Wu, B. I.
Yang, C.
Yaqoob, Z.
Yariv, A.
Zhang, Y.
Zozulya, A. A.

IEEE Antennas Wireless Propag. Lett.

N. Engheta, "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Antennas Wireless Propag. Lett. 1, 10-13 (2002). [CrossRef]

IEEE J. Quantum Electron.

M. Cronin-Golomb, J. O. White, A. Yariv, B. Fischer, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. 20, 12-30 (1984). [CrossRef]

J. Opt. Soc. Am. A

Nature Photonic.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, "Optical phase conjugation for turbidity suppression in biological samples," submitted toNature Photonic.

New J. Phys.

S. He, Y. Jin, Z. Ruan and J. Kuang, "On subwavelength and open resonators involving metamaterials of negative refraction index," New J. Phys. 7, 210 (2005). [CrossRef]

Opt. Commun.

S. I. Bozhevolnyi, O. Keller, and I. I. Smolyaninov, "Scattered light enhancement near a phase conjugating mirror," Opt. Commun. 115, 115-120 (1995). [CrossRef]

Phys. Lett. A

A. A. Zozulya, and V. T. Tikhonchuk, "Investigation of stability of four-wave mixing in photorefractive media," Phys. Lett. A 135, 447-452 (1989). [CrossRef]

Phys. Rev. B

T. J. Cui, Q. Cheng, W. B. Lu, Q. Jiang and J. A. Kong, "Localization of electromagnetic energy using a left-handed-medium slab," Phys. Rev. B 71, 045114 (2005). [CrossRef]

Phys. Rev. Lett.

P. Mathey, S. Odoulov, and D. Rytz, "Instability of single-frequency operation in semilinear photorefractive coherent oscillators," Phys. Rev. Lett. 89, 053901 (2002). [CrossRef] [PubMed]
J. de Rosny and M. Fink, "Overcoming the diffraction limit in wave physics using a time-reversal mirror and a novel acoustic sink," Phys. Rev. Lett. 89, 124301 (2002). [CrossRef] [PubMed]
B. E. Henty and D. D. Stancil, "Multipath-enabled super-resolution for rf and microwave communication using phase-conjugate arrays," Phys. Rev. Lett. 93, 243904 (2004). [CrossRef]
D. R. Smith and N. Kroll, "Negative Refractive Index in Left-Handed Materials," Phys. Rev. Lett. 84, 4184 (2000). [CrossRef] [PubMed]
J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966 (2000). [CrossRef] [PubMed]
J. Pacheco, T. M. Grzegorczyk, B. I. Wu, Y. Zhang, and J. A. Kong, "Power Propagation in Homogeneous Isotropic Frequency-Dispersive Left-Handed Media," Phys. Rev. Lett. 89, 257401 (2002). [CrossRef] [PubMed]

Science

G. Lerosey, J.de Rosny, A. Tourin, M. Fink, "Focusing Beyond the Diffraction Limit with Far-Field Time Reversal," Science 315, 1120-1122 (2007). [CrossRef] [PubMed]

Other

P. C. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
B. Ya. Zel’dovich, R. F. Pilipetskii, and V. V. Shkunov, Principles of Phase Conjugation (Springer, Berlin, 1985).
R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).
J. A. Kong, Electromagnetic Wave Theory, (EMW Publishing, 2005) Chaps. 3, 5.
Y. Li, L. Ran, H. Chen, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Experimental realization of a one dimensional LHM-RHM Resonator," IEEE Trans. Microwave Theory and Tech. special issue on Metamaterials 53, 1522-1526 (2005).
COMSOL Multiphysics 3.3 (2007), COMSOL INC. (http://www.comsol.com/)

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