Perfect focusing of scalar wave fields in three dimensions

doi:10.1364/OE.18.007650

Optics Express

Editor: C. Martijn de Sterke
Vol. 18, Iss. 8 — Apr. 12, 2010
pp: 7650–7663

Perfect focusing of scalar wave fields in three dimensions

Pablo Benítez, Juan C. Miñano, and Juan C. González »View Author Affiliations

Optics Express, Vol. 18, Issue 8, pp. 7650-7663 (2010)
http://dx.doi.org/10.1364/OE.18.007650

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Abstract

A method to design isotropic inhomogeneous refractive index distribution is presented, in which the scalar wave field solutions propagate exactly on an eikonal function (i.e., remaining constant on the Geometrical Optics wavefronts). This method is applied to the design of “dipole lenses”, which perfectly focus a scalar wave field emitted from a point source onto a point absorber, in both two and three dimensions. Also, the Maxwell fish-eye lens in two and three dimensions is analysed.

OCIS Codes
(110.2760) Imaging systems : Gradient-index lenses
(260.2710) Physical optics : Inhomogeneous optical media

ToC Category:
Physical Optics

History
Original Manuscript: January 11, 2010
Revised Manuscript: March 16, 2010
Manuscript Accepted: March 19, 2010
Published: March 29, 2010

Citation
Pablo Benítez, Juan C. Miñano, and Juan C. González, "Perfect focusing of scalar wave fields in three dimensions," Opt. Express 18, 7650-7663 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-8-7650

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References

M. Born, and E. Wolf, Principles of Optics, (Pergamon, Oxford, 1975, 5th ed)
S. Cornbleet, Microwave and Geometrical Optics, (Academic, London, 1994)
J. C. Miñano, “Perfect imaging in a homogeneous threedimensional region,” Opt. Express 14(21), 9627–9635 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-21-9627 . [CrossRef] [PubMed]
J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]
U. Leonhardt, “Perfect imaging without negative refraction,” N. J. Phys. 11(9), 093040 (2009). [CrossRef]
U. Leonhardt and T. G. Philbin, “Perfect imaging with positive refraction in three dimensions,” Phys. Rev. A 81(1), 011804 (2010). [CrossRef]
M. A. Alonso and G. Forbes, “Stable aggregates of flexible elements give a stronger link between rays and waves,” Opt. Express 10(16), 728–739 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-16-728 . [PubMed]
O. N. Stavroudis, The Mathematics of Geometrical and Physical Optics, (Willey-VCH, Weinheim, 2006)
Yu. A. Kratsov, and Yu. I. Orlov, Geometrical Optics of Inhomogeneous Media, p.23, Springer Verlag, Berlin Heidelberg, 1990.
R. K. Luneburg, Mathematical Theory of Optics, (University of California Press, Los Angeles 1964)
P. M. Morse, and H. Feshbach, Methods of Theoretical Physics (New York, McGraw-Hill, 1953)
A. D. Polyanin, and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, 2nd Edition, Chapman & Hall/CRC, Boca Raton, 2003. It also coincides with the change of variables S’ = S/L + π/2 in the equation described in http://eqworld.ipmnet.ru/en/solutions/ode/ode0235.pdf .
http://www.youtube.com/watch?v=bG9XSY8i_q8
http://www.mathcurve.com/courbes2d/cayleyovale/cayleyovale.shtml
Yu. I. Bobrovnitskiĭ, “Impedance theory of sound absorption: The best absorber and the black body,” Acoust. Phys. 52(6), 638–647 (2006). [CrossRef]

Acoust. Phys.

Yu. I. Bobrovnitskiĭ, “Impedance theory of sound absorption: The best absorber and the black body,” Acoust. Phys. 52(6), 638–647 (2006). [CrossRef]

N. J. Phys.

U. Leonhardt, “Perfect imaging without negative refraction,” N. J. Phys. 11(9), 093040 (2009). [CrossRef]

Opt. Express

Phys. Rev. A

U. Leonhardt and T. G. Philbin, “Perfect imaging with positive refraction in three dimensions,” Phys. Rev. A 81(1), 011804 (2010). [CrossRef]

Phys. Rev. Lett.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

Other

M. Born, and E. Wolf, Principles of Optics, (Pergamon, Oxford, 1975, 5th ed)
S. Cornbleet, Microwave and Geometrical Optics, (Academic, London, 1994)
O. N. Stavroudis, The Mathematics of Geometrical and Physical Optics, (Willey-VCH, Weinheim, 2006)
Yu. A. Kratsov, and Yu. I. Orlov, Geometrical Optics of Inhomogeneous Media, p.23, Springer Verlag, Berlin Heidelberg, 1990.
R. K. Luneburg, Mathematical Theory of Optics, (University of California Press, Los Angeles 1964)
P. M. Morse, and H. Feshbach, Methods of Theoretical Physics (New York, McGraw-Hill, 1953)
A. D. Polyanin, and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, 2nd Edition, Chapman & Hall/CRC, Boca Raton, 2003. It also coincides with the change of variables S’ = S/L + π/2 in the equation described in http://eqworld.ipmnet.ru/en/solutions/ode/ode0235.pdf .
http://www.youtube.com/watch?v=bG9XSY8i_q8
http://www.mathcurve.com/courbes2d/cayleyovale/cayleyovale.shtml

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[1] M. Born, and E. Wolf, Principles of Optics, (Pergamon, Oxford, 1975, 5th ed)

[2] S. Cornbleet, Microwave and Geometrical Optics, (Academic, London, 1994)

[3] J. C. Miñano, “Perfect imaging in a homogeneous threedimensional region,” Opt. Express 14(21), 9627–9635 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-21-9627 . [CrossRef] [PubMed]

[4] J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

[5] U. Leonhardt, “Perfect imaging without negative refraction,” N. J. Phys. 11(9), 093040 (2009). [CrossRef]

[6] U. Leonhardt and T. G. Philbin, “Perfect imaging with positive refraction in three dimensions,” Phys. Rev. A 81(1), 011804 (2010). [CrossRef]

[7] M. A. Alonso and G. Forbes, “Stable aggregates of flexible elements give a stronger link between rays and waves,” Opt. Express 10(16), 728–739 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-16-728 . [PubMed]

[8] O. N. Stavroudis, The Mathematics of Geometrical and Physical Optics, (Willey-VCH, Weinheim, 2006)

[9] Yu. A. Kratsov, and Yu. I. Orlov, Geometrical Optics of Inhomogeneous Media, p.23, Springer Verlag, Berlin Heidelberg, 1990.

[10] R. K. Luneburg, Mathematical Theory of Optics, (University of California Press, Los Angeles 1964)

[11] P. M. Morse, and H. Feshbach, Methods of Theoretical Physics (New York, McGraw-Hill, 1953)

[12] A. D. Polyanin, and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, 2nd Edition, Chapman & Hall/CRC, Boca Raton, 2003. It also coincides with the change of variables S’ = S/L + π/2 in the equation described in http://eqworld.ipmnet.ru/en/solutions/ode/ode0235.pdf .

[13] http://www.youtube.com/watch?v=bG9XSY8i_q8

[14] http://www.mathcurve.com/courbes2d/cayleyovale/cayleyovale.shtml

[15] Yu. I. Bobrovnitskiĭ, “Impedance theory of sound absorption: The best absorber and the black body,” Acoust. Phys. 52(6), 638–647 (2006). [CrossRef]

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Perfect focusing of scalar wave fields in three dimensions

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