Abstract

Density matrix theory is presented to explain recent experimental observations of intense optically induced magnetism due to a “mixed” type of nonlinearity proportional to the product of the electric- and magnetic-field strengths of light. Two previously unknown quadratic optical effects are predicted—namely, transverse optical magnetization and magnetic charge separation—and quantitative agreement is obtained with experimental results regarding the former of these. The mechanistic origin of a third quadratic nonlinearity, namely, magneto-electric second-harmonic generation, which is familiar on a phenomenological basis in classical nonlinear optics, is also examined. Transverse optical magnetism is shown to enable large permeability changes at optical frequencies accompanied by magnetic dispersion near resonances. This phenomenon provides for all-optical generation of magnetic moments, large transverse magnetic fields, static electric dipoles, and terahertz radiation in (unbiased) transparent homogeneous dielectrics or semiconductors. Intriguing possibilities for applications are considered, including magneto-electric refractive index modification, optical electric power generation, and spin control.

© 2009 Optical Society of America

Full Article  |  PDF Article

Errata

Stephen C. Rand, "Quantum theory of coherent transverse optical magnetism: erratum," J. Opt. Soc. Am. B 27, 1983-1984 (2010)
https://www.osapublishing.org/josab/abstract.cfm?uri=josab-27-10-1983

References

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  1. S. L. Oliveira and S. C. Rand, “Intense nonlinear magnetic dipole radiation at optical frequencies: molecular scattering in a dielectric liquid,” Phys. Rev. Lett. 98, 093901 (2007).
    [CrossRef] [PubMed]
  2. S. C. Rand, W. M. Fisher, and S. L. Oliveira, “Optically-induced magnetization in homogeneous, undoped dielectric media,” J. Opt. Soc. Am. B 25, 1106-1117 (2008).
    [CrossRef]
  3. W. M. Fisher and S. C. Rand, “Dependence of optically-induced magnetism on molecular electronic structure,” J. Lumin. (2009), doi:10.1016/j.jlumin.2009.02.036.
  4. J. C. Maxwell, “A dynamical theory of electromagnetic fields,” The Scientific Papers of James Clerk Maxwell (Cambridge Univ. Press, 1890), pp. 526-597.
  5. L. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon Press, 1984), pp. 268-270.
  6. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  7. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
  8. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780-1782 (2006).
    [CrossRef] [PubMed]
  9. A. V. Kimel, A. Kirilyuk, F. Hansteen, R. V. Pisarev, and T. Rasing, “Non-thermal optical control of magnetism and ultrafast laser-induced spin dynamics in solids,” J. Phys.: Condens. Matter 19, 043201 (2007).
    [CrossRef]
  10. S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294, 1488-1495 (2001).
    [CrossRef] [PubMed]
  11. U. A. Khawaja and H. Stoof, “Skyrmions in a ferromagnetic Bose-Einstein condensate,” Nature 411, 918-920 (2001).
    [CrossRef] [PubMed]
  12. J. Baudon, M. Hamamda, J. Grucker, M. Boustimi, F. Perales, G. Dutier, and M. Ducloy, “Negative index media for matter-wave optics,” Phys. Rev. Lett. 102, 140403 (2009).
    [CrossRef] [PubMed]
  13. See, for example, spin-based techniques in M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).
  14. J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190-193 (1965).
    [CrossRef]
  15. W. M. Fisher and S. C. Rand, Parametric Optical Magnetism and the Complex Mathieu Equation, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference (IQEC'09) OSA Technical Digest (CD) (Optical Society of America, 2009), paper ITuF3, http://www.opticsinfobase.org/abstract.cfm?URI=IQEC-2009-ITuF3.
    [PubMed]
  16. W. M. Fisher and S. C. Rand, “Light-induced dynamics in an oscillator model with Lorentz forces,” Phys. Rev. A (submitted).
  17. B. Y. Zel'dovich, “Impedance and parametric excitation of oscillators,” Phys. Usp. 51, 465-484 (2008).
    [CrossRef]
  18. See, for example, I. I. Sobelman, Atomic Spectra and Radiative Transitions (Springer-Verlag, 1979).
  19. Other applications of optical magnetism do not require operation near electronic resonances. The experiments of indicate that by programming the intensity of irradiation, large spatial variations of magnetic susceptibility could be induced over wide spectral ranges of transparency, limited only by the bandwidth of available light sources. Hence transformation optics applications with low losses may be feasible at optical frequencies in unstructured, transparent materials. For spintronics, mid-gap irradiation of semiconductor hosts is capable of generating large internal magnetic fields to lock the spin orientation of conduction electrons and lengthen their decoherence times. Although the induced magnetic field reverses with each optical half-cycle, spin precession proceeds without spin flips if the optical magnetic field greatly exceeds the dephasing fields and is prealigned with the quantization axis. In this way, spin coherence can be extended over long (illuminated) paths.
  20. See the review by M. Kauranen and S. Cattaneo, “Polarization techniques for surface nonlinear optics,” in Progress in Optics, Vol. 51, E.Wolf, ed. (Elsevier, 2008), Chapter 2. No radiation is generated at the fundamental frequency or its second harmonic via a quadratic E2 or B2 nonlinearity in effectively centro-symmetric media like liquids. Only susceptibility elements for nonlinearities driven by an EB field combination are allowed. The susceptibility tensor for second-harmonic generation (SHG) in a bulk centro-symmetric medium does have a nonzero element χzyx for the field combination ByEx, which emits radiation perpendicular to the pump beam. However, the radiation is at 2ω, unlike the MD radiation reported at the fundamental frequency ω in liquid samples in . In the present theory, the quantum mechanical symmetry requirement in a 2-level system is not inversion, but rather that R(y) and x transform identically. The ED and MD transition moments must simultaneously be nonzero between states 1 and 2, which dictates that the initial and final states have opposite parity. In multilevel systems this rule may be relaxed by virtual transitions to other states, rendering the process partly allowed in the presence of complete inversion symmetry.
    [CrossRef]
  21. G. A. Mourou, C. P. J. Barty, and M. D. Perry, “Ultrahigh-intensity lasers: physics of the extreme on a tabletop,” Physics Today 51(1), 22-28 (1998).
  22. Y. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Coherent spin manipulation without magnetic fields in strained semiconductors,” Nature 427, 50-53 (2003).
    [CrossRef]
  23. C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
    [CrossRef] [PubMed]
  24. V. A. Stoica, Y.-M. Sheu, D. A. Reis, and R. Clarke, “Wideband detection of transient solid-state dynamics using ultrafast fiber lasers and asynchronous optical sampling,” Opt. Express 16, 2322-2335 (2008).
    [CrossRef] [PubMed]

2009

J. Baudon, M. Hamamda, J. Grucker, M. Boustimi, F. Perales, G. Dutier, and M. Ducloy, “Negative index media for matter-wave optics,” Phys. Rev. Lett. 102, 140403 (2009).
[CrossRef] [PubMed]

2008

2007

S. L. Oliveira and S. C. Rand, “Intense nonlinear magnetic dipole radiation at optical frequencies: molecular scattering in a dielectric liquid,” Phys. Rev. Lett. 98, 093901 (2007).
[CrossRef] [PubMed]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

A. V. Kimel, A. Kirilyuk, F. Hansteen, R. V. Pisarev, and T. Rasing, “Non-thermal optical control of magnetism and ultrafast laser-induced spin dynamics in solids,” J. Phys.: Condens. Matter 19, 043201 (2007).
[CrossRef]

2006

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

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

2003

Y. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Coherent spin manipulation without magnetic fields in strained semiconductors,” Nature 427, 50-53 (2003).
[CrossRef]

2001

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294, 1488-1495 (2001).
[CrossRef] [PubMed]

U. A. Khawaja and H. Stoof, “Skyrmions in a ferromagnetic Bose-Einstein condensate,” Nature 411, 918-920 (2001).
[CrossRef] [PubMed]

1999

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1965

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190-193 (1965).
[CrossRef]

Awschalom, D. D.

Y. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Coherent spin manipulation without magnetic fields in strained semiconductors,” Nature 427, 50-53 (2003).
[CrossRef]

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294, 1488-1495 (2001).
[CrossRef] [PubMed]

Barty, C. P. J.

G. A. Mourou, C. P. J. Barty, and M. D. Perry, “Ultrahigh-intensity lasers: physics of the extreme on a tabletop,” Physics Today 51(1), 22-28 (1998).

Baudon, J.

J. Baudon, M. Hamamda, J. Grucker, M. Boustimi, F. Perales, G. Dutier, and M. Ducloy, “Negative index media for matter-wave optics,” Phys. Rev. Lett. 102, 140403 (2009).
[CrossRef] [PubMed]

Boustimi, M.

J. Baudon, M. Hamamda, J. Grucker, M. Boustimi, F. Perales, G. Dutier, and M. Ducloy, “Negative index media for matter-wave optics,” Phys. Rev. Lett. 102, 140403 (2009).
[CrossRef] [PubMed]

Buhrman, R. A.

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294, 1488-1495 (2001).
[CrossRef] [PubMed]

Cattaneo, S.

See the review by M. Kauranen and S. Cattaneo, “Polarization techniques for surface nonlinear optics,” in Progress in Optics, Vol. 51, E.Wolf, ed. (Elsevier, 2008), Chapter 2. No radiation is generated at the fundamental frequency or its second harmonic via a quadratic E2 or B2 nonlinearity in effectively centro-symmetric media like liquids. Only susceptibility elements for nonlinearities driven by an EB field combination are allowed. The susceptibility tensor for second-harmonic generation (SHG) in a bulk centro-symmetric medium does have a nonzero element χzyx for the field combination ByEx, which emits radiation perpendicular to the pump beam. However, the radiation is at 2ω, unlike the MD radiation reported at the fundamental frequency ω in liquid samples in . In the present theory, the quantum mechanical symmetry requirement in a 2-level system is not inversion, but rather that R(y) and x transform identically. The ED and MD transition moments must simultaneously be nonzero between states 1 and 2, which dictates that the initial and final states have opposite parity. In multilevel systems this rule may be relaxed by virtual transitions to other states, rendering the process partly allowed in the presence of complete inversion symmetry.
[CrossRef]

Chtchelkanova, A. Y.

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294, 1488-1495 (2001).
[CrossRef] [PubMed]

Chuang, I. L.

See, for example, spin-based techniques in M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).

Clarke, R.

Daughton, J. M.

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294, 1488-1495 (2001).
[CrossRef] [PubMed]

Ducloy, M.

J. Baudon, M. Hamamda, J. Grucker, M. Boustimi, F. Perales, G. Dutier, and M. Ducloy, “Negative index media for matter-wave optics,” Phys. Rev. Lett. 102, 140403 (2009).
[CrossRef] [PubMed]

Dutier, G.

J. Baudon, M. Hamamda, J. Grucker, M. Boustimi, F. Perales, G. Dutier, and M. Ducloy, “Negative index media for matter-wave optics,” Phys. Rev. Lett. 102, 140403 (2009).
[CrossRef] [PubMed]

Fisher, W. M.

S. C. Rand, W. M. Fisher, and S. L. Oliveira, “Optically-induced magnetization in homogeneous, undoped dielectric media,” J. Opt. Soc. Am. B 25, 1106-1117 (2008).
[CrossRef]

W. M. Fisher and S. C. Rand, “Dependence of optically-induced magnetism on molecular electronic structure,” J. Lumin. (2009), doi:10.1016/j.jlumin.2009.02.036.

W. M. Fisher and S. C. Rand, Parametric Optical Magnetism and the Complex Mathieu Equation, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference (IQEC'09) OSA Technical Digest (CD) (Optical Society of America, 2009), paper ITuF3, http://www.opticsinfobase.org/abstract.cfm?URI=IQEC-2009-ITuF3.
[PubMed]

W. M. Fisher and S. C. Rand, “Light-induced dynamics in an oscillator model with Lorentz forces,” Phys. Rev. A (submitted).

Gossard, A. C.

Y. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Coherent spin manipulation without magnetic fields in strained semiconductors,” Nature 427, 50-53 (2003).
[CrossRef]

Grucker, J.

J. Baudon, M. Hamamda, J. Grucker, M. Boustimi, F. Perales, G. Dutier, and M. Ducloy, “Negative index media for matter-wave optics,” Phys. Rev. Lett. 102, 140403 (2009).
[CrossRef] [PubMed]

Hamamda, M.

J. Baudon, M. Hamamda, J. Grucker, M. Boustimi, F. Perales, G. Dutier, and M. Ducloy, “Negative index media for matter-wave optics,” Phys. Rev. Lett. 102, 140403 (2009).
[CrossRef] [PubMed]

Hansteen, F.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

A. V. Kimel, A. Kirilyuk, F. Hansteen, R. V. Pisarev, and T. Rasing, “Non-thermal optical control of magnetism and ultrafast laser-induced spin dynamics in solids,” J. Phys.: Condens. Matter 19, 043201 (2007).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Itoh, A.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

Kato, Y.

Y. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Coherent spin manipulation without magnetic fields in strained semiconductors,” Nature 427, 50-53 (2003).
[CrossRef]

Kauranen, M.

See the review by M. Kauranen and S. Cattaneo, “Polarization techniques for surface nonlinear optics,” in Progress in Optics, Vol. 51, E.Wolf, ed. (Elsevier, 2008), Chapter 2. No radiation is generated at the fundamental frequency or its second harmonic via a quadratic E2 or B2 nonlinearity in effectively centro-symmetric media like liquids. Only susceptibility elements for nonlinearities driven by an EB field combination are allowed. The susceptibility tensor for second-harmonic generation (SHG) in a bulk centro-symmetric medium does have a nonzero element χzyx for the field combination ByEx, which emits radiation perpendicular to the pump beam. However, the radiation is at 2ω, unlike the MD radiation reported at the fundamental frequency ω in liquid samples in . In the present theory, the quantum mechanical symmetry requirement in a 2-level system is not inversion, but rather that R(y) and x transform identically. The ED and MD transition moments must simultaneously be nonzero between states 1 and 2, which dictates that the initial and final states have opposite parity. In multilevel systems this rule may be relaxed by virtual transitions to other states, rendering the process partly allowed in the presence of complete inversion symmetry.
[CrossRef]

Khawaja, U. A.

U. A. Khawaja and H. Stoof, “Skyrmions in a ferromagnetic Bose-Einstein condensate,” Nature 411, 918-920 (2001).
[CrossRef] [PubMed]

Kimel, A. V.

A. V. Kimel, A. Kirilyuk, F. Hansteen, R. V. Pisarev, and T. Rasing, “Non-thermal optical control of magnetism and ultrafast laser-induced spin dynamics in solids,” J. Phys.: Condens. Matter 19, 043201 (2007).
[CrossRef]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

Kirilyuk, A.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

A. V. Kimel, A. Kirilyuk, F. Hansteen, R. V. Pisarev, and T. Rasing, “Non-thermal optical control of magnetism and ultrafast laser-induced spin dynamics in solids,” J. Phys.: Condens. Matter 19, 043201 (2007).
[CrossRef]

Landau, L.

L. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon Press, 1984), pp. 268-270.

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

Lifshitz, E. M.

L. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon Press, 1984), pp. 268-270.

Malmstrom, L. D.

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190-193 (1965).
[CrossRef]

Maxwell, J. C.

J. C. Maxwell, “A dynamical theory of electromagnetic fields,” The Scientific Papers of James Clerk Maxwell (Cambridge Univ. Press, 1890), pp. 526-597.

Mourou, G. A.

G. A. Mourou, C. P. J. Barty, and M. D. Perry, “Ultrahigh-intensity lasers: physics of the extreme on a tabletop,” Physics Today 51(1), 22-28 (1998).

Myers, R. C.

Y. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Coherent spin manipulation without magnetic fields in strained semiconductors,” Nature 427, 50-53 (2003).
[CrossRef]

Nielsen, M. A.

See, for example, spin-based techniques in M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).

Oliveira, S. L.

S. C. Rand, W. M. Fisher, and S. L. Oliveira, “Optically-induced magnetization in homogeneous, undoped dielectric media,” J. Opt. Soc. Am. B 25, 1106-1117 (2008).
[CrossRef]

S. L. Oliveira and S. C. Rand, “Intense nonlinear magnetic dipole radiation at optical frequencies: molecular scattering in a dielectric liquid,” Phys. Rev. Lett. 98, 093901 (2007).
[CrossRef] [PubMed]

Pendry, J. B.

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

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Perales, F.

J. Baudon, M. Hamamda, J. Grucker, M. Boustimi, F. Perales, G. Dutier, and M. Ducloy, “Negative index media for matter-wave optics,” Phys. Rev. Lett. 102, 140403 (2009).
[CrossRef] [PubMed]

Perry, M. D.

G. A. Mourou, C. P. J. Barty, and M. D. Perry, “Ultrahigh-intensity lasers: physics of the extreme on a tabletop,” Physics Today 51(1), 22-28 (1998).

Pershan, P. S.

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190-193 (1965).
[CrossRef]

Pisarev, R. V.

A. V. Kimel, A. Kirilyuk, F. Hansteen, R. V. Pisarev, and T. Rasing, “Non-thermal optical control of magnetism and ultrafast laser-induced spin dynamics in solids,” J. Phys.: Condens. Matter 19, 043201 (2007).
[CrossRef]

Pitaevskii, L. P.

L. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon Press, 1984), pp. 268-270.

Rand, S. C.

S. C. Rand, W. M. Fisher, and S. L. Oliveira, “Optically-induced magnetization in homogeneous, undoped dielectric media,” J. Opt. Soc. Am. B 25, 1106-1117 (2008).
[CrossRef]

S. L. Oliveira and S. C. Rand, “Intense nonlinear magnetic dipole radiation at optical frequencies: molecular scattering in a dielectric liquid,” Phys. Rev. Lett. 98, 093901 (2007).
[CrossRef] [PubMed]

W. M. Fisher and S. C. Rand, “Dependence of optically-induced magnetism on molecular electronic structure,” J. Lumin. (2009), doi:10.1016/j.jlumin.2009.02.036.

W. M. Fisher and S. C. Rand, “Light-induced dynamics in an oscillator model with Lorentz forces,” Phys. Rev. A (submitted).

W. M. Fisher and S. C. Rand, Parametric Optical Magnetism and the Complex Mathieu Equation, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference (IQEC'09) OSA Technical Digest (CD) (Optical Society of America, 2009), paper ITuF3, http://www.opticsinfobase.org/abstract.cfm?URI=IQEC-2009-ITuF3.
[PubMed]

Rasing, T.

A. V. Kimel, A. Kirilyuk, F. Hansteen, R. V. Pisarev, and T. Rasing, “Non-thermal optical control of magnetism and ultrafast laser-induced spin dynamics in solids,” J. Phys.: Condens. Matter 19, 043201 (2007).
[CrossRef]

Rasing, Th.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

Reis, D. A.

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Roukes, M. L.

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294, 1488-1495 (2001).
[CrossRef] [PubMed]

Schurig, D.

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

Sheu, Y.-M.

Smith, D. R.

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

Sobelman, I. I.

See, for example, I. I. Sobelman, Atomic Spectra and Radiative Transitions (Springer-Verlag, 1979).

Stanciu, C. D.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Stoica, V. A.

Stoof, H.

U. A. Khawaja and H. Stoof, “Skyrmions in a ferromagnetic Bose-Einstein condensate,” Nature 411, 918-920 (2001).
[CrossRef] [PubMed]

Treger, D. M.

S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294, 1488-1495 (2001).
[CrossRef] [PubMed]

Tsukamoto, A.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef] [PubMed]

van der Ziel, J. P.

J. P. van der Ziel, P. S. Pershan, and L. D. Malmstrom, “Optically-induced magnetization resulting from the inverse Faraday effect,” Phys. Rev. Lett. 15, 190-193 (1965).
[CrossRef]

von Molnar, S.

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S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294, 1488-1495 (2001).
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Opt. Express

Phys. Rev. Lett.

S. L. Oliveira and S. C. Rand, “Intense nonlinear magnetic dipole radiation at optical frequencies: molecular scattering in a dielectric liquid,” Phys. Rev. Lett. 98, 093901 (2007).
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C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
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Phys. Usp.

B. Y. Zel'dovich, “Impedance and parametric excitation of oscillators,” Phys. Usp. 51, 465-484 (2008).
[CrossRef]

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S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294, 1488-1495 (2001).
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J. C. Maxwell, “A dynamical theory of electromagnetic fields,” The Scientific Papers of James Clerk Maxwell (Cambridge Univ. Press, 1890), pp. 526-597.

L. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon Press, 1984), pp. 268-270.

See, for example, I. I. Sobelman, Atomic Spectra and Radiative Transitions (Springer-Verlag, 1979).

Other applications of optical magnetism do not require operation near electronic resonances. The experiments of indicate that by programming the intensity of irradiation, large spatial variations of magnetic susceptibility could be induced over wide spectral ranges of transparency, limited only by the bandwidth of available light sources. Hence transformation optics applications with low losses may be feasible at optical frequencies in unstructured, transparent materials. For spintronics, mid-gap irradiation of semiconductor hosts is capable of generating large internal magnetic fields to lock the spin orientation of conduction electrons and lengthen their decoherence times. Although the induced magnetic field reverses with each optical half-cycle, spin precession proceeds without spin flips if the optical magnetic field greatly exceeds the dephasing fields and is prealigned with the quantization axis. In this way, spin coherence can be extended over long (illuminated) paths.

See the review by M. Kauranen and S. Cattaneo, “Polarization techniques for surface nonlinear optics,” in Progress in Optics, Vol. 51, E.Wolf, ed. (Elsevier, 2008), Chapter 2. No radiation is generated at the fundamental frequency or its second harmonic via a quadratic E2 or B2 nonlinearity in effectively centro-symmetric media like liquids. Only susceptibility elements for nonlinearities driven by an EB field combination are allowed. The susceptibility tensor for second-harmonic generation (SHG) in a bulk centro-symmetric medium does have a nonzero element χzyx for the field combination ByEx, which emits radiation perpendicular to the pump beam. However, the radiation is at 2ω, unlike the MD radiation reported at the fundamental frequency ω in liquid samples in . In the present theory, the quantum mechanical symmetry requirement in a 2-level system is not inversion, but rather that R(y) and x transform identically. The ED and MD transition moments must simultaneously be nonzero between states 1 and 2, which dictates that the initial and final states have opposite parity. In multilevel systems this rule may be relaxed by virtual transitions to other states, rendering the process partly allowed in the presence of complete inversion symmetry.
[CrossRef]

G. A. Mourou, C. P. J. Barty, and M. D. Perry, “Ultrahigh-intensity lasers: physics of the extreme on a tabletop,” Physics Today 51(1), 22-28 (1998).

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[PubMed]

W. M. Fisher and S. C. Rand, “Light-induced dynamics in an oscillator model with Lorentz forces,” Phys. Rev. A (submitted).

See, for example, spin-based techniques in M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).

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Figures (1)

Fig. 1
Fig. 1

Plot of the electric (solid curve) and magnetic (dashed curve) susceptibilities of a 2-level system with various proportions of optically induced magnetic dipole response. The horizontal axis corresponds to χ ( m ) ( ω ) = 0 , and the dashed curves correspond to χ ( m ) = χ ( e ) ( ω ) 4 (upper curve at left), and χ ( m ) = χ ( e ) ( ω ) 2 (lower left). The linewidth-to-resonant-frequency ratio is Γ ω 0 = 0.1 . All curves assume resonance at λ 0 = 500 nm and a plasma frequency of ω p = 2 × 10 15 rad s 1 .

Equations (52)

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i ρ ̇ = [ H , ρ ] i ρ ̇ relax .
H o = ω 1 | 1 1 | + ω 2 | 2 2 | ,
V = μ ¯ e E ¯ μ ¯ m B ¯ .
E ¯ ( t ) = 1 2 [ E + ε ̂ + E ε ̂ + ] e i φ + h.c. ,
B ¯ ( t ) = i 2 [ B + ε ̂ B ε ̂ + ] e i φ + h.c. .
E + = E = E 0 2
μ ¯ ( e ) = ( μ ( e ) ε ̂ + + μ + ( e ) ε ̂ ) ,
μ ¯ ( m ) = i ( μ + ( m ) ε ̂ μ ( m ) ε ̂ + ) ,
μ ¯ ( e ) ( t ) 12 = r ̂ μ ( e ) ( t ) 12 = r ̂ d V ψ 1 * ( r , t ) e r ψ 2 ( r , t ) + h.c. = r ̂ d V c 1 * ( t ) ψ 1 * ( r ) e r c 2 ( t ) ψ 2 ( r ) + h.c. = r ̂ 1 | μ ( e ) | 2 ρ 21 ( t ) + h.c.
μ ¯ ( e ) = Tr { μ ¯ ( e ) , ρ } = x ̂ ( μ 12 ρ 21 + μ 21 ρ 12 ) ,
μ ¯ ( m ) ( t ) 12 = ( e 2 m ) d V ψ 1 * ( r , θ , φ , t ) r ¯ × p ¯ ψ 2 ( r , θ , φ , t ) + h.c. = ( e 2 m ) d V c 1 * ( t ) ψ 1 * ( r , θ , φ ) L ¯ c 2 ( t ) ψ 2 ( r , θ , φ ) + h.c.
μ ¯ ( m ) = 1 | μ ¯ ( m ) | 2 ρ 21 ( t ) + h.c. = Tr { μ ¯ ( m ) , ρ } .
μ ¯ ( m ) ( t ) 12 = ( e 2 m ) d V ψ 1 * ( r , θ , φ , t ) r ¯ [ p ¯ r + p ¯ θ + p ¯ φ ] ψ 2 ( r , θ , φ , t ) + h.c. = e 2 m y ̂ d V ψ 1 * ( r , θ , φ , t ) r ̃ p φ ψ 2 ( r , θ , φ , t ) + h.c. ,
ρ ( e ) ( t ) = ρ ̃ ( e ) e i ω t
ρ ( m ) ( t ) = ρ ̃ ( m ) e ± i ω t ,
μ ¯ ( m ) ( t ) = y ̂ 1 | μ ( m ) | 2 ρ 21 ( m ) ( t ) ρ ̃ 21 ( e ) + h.c. ,
μ ¯ ( m ) ( t ) = y ̂ Tr { μ ( m ) , ρ ( m ) ( t ) ρ ̃ ( e ) } .
ρ = | ψ ψ | = | ψ ( r , t ) | ψ ( θ , φ , t ) ψ ( θ , φ , t ) | ψ ( r , t ) | = ρ ( m ) ( t ) ρ ( e ) ( t ) .
V ( t ) = 1 2 [ ( Ω + * ( m ) + Ω * ( m ) ) + ( Ω + ( e ) + Ω + ( m ) e i φ ) e i φ + ( Ω ( e ) + Ω ( m ) e i φ ) e i φ ] + h.c.
V 12 ( e ) 1 | V ( e ) | 2 = 1 2 1 | [ Ω + ( e ) + Ω * ( e ) ] e i φ + h.c. | 2
V 12 ( m ) 1 | V ( m ) | 2 = 1 2 1 | [ Ω + * ( m ) + Ω * ( m ) ] + h.c. | 2 1 2 1 | [ Ω + ( m ) + Ω * ( m ) ] e 2 i φ + h.c. | 2 .
E ( t ) B ( t ) = { 1 2 [ E 0 x ̂ ] e i φ + h.c. } { 1 2 [ B 0 y ̂ ] e i φ + h.c. } = 1 4 { E 0 B 0 e 2 i φ + E 0 * B 0 * e 2 i φ + E 0 B 0 * + E 0 * B 0 } .
ρ 12 ( t ) = ρ ̃ 12 ( m ) * ( ω ) ρ ̃ 12 ( e ) ( ω ) + ρ ̃ 12 ( m ) ( ω ) ρ ̃ 12 ( e ) ( ω ) e 2 i φ = ρ ̃ 12 ( ω = 0 ) + ρ ̃ 12 ( 2 ω ) e 2 i φ
ρ 12 ( e ) = 1 2 { [ Ω + ( e ) + Ω * ( e ) ] 12 ( Δ 1 + i Γ 12 ) e i ω t } ( ρ 11 ρ 22 ) ,
ρ 12 ( m ) = 1 2 { [ Ω + ( m ) + Ω ( m ) ] 12 ( ω 0 + i Γ 12 ( m ) ) e i ω t + [ Ω + ( m ) + Ω * ( m ) ] 12 ( Δ 2 + i Γ 12 ( m ) ) e i ω t } ( ρ 11 ( 0 ) ρ 22 ( 0 ) ) ,
ρ 11 ρ 22 = [ 1 + Γ 12 ( e ) | Ω + ( e ) + Ω * ( e ) | 2 γ 22 ( Δ 1 2 + Γ 12 ( e ) 2 ) ] 1 .
M ¯ = N Tr { μ ¯ ( m ) ( t ) , ρ ( t ) } = N Tr { μ ¯ ( m ) ( t ) , ρ ( m ) ( t ) ρ ( e ) ( t ) } = N y ̂ [ 2 | μ ( m ) ( t ) | 1 ρ 12 ( m ) ( t ) ρ 12 ( e ) ( t ) + h.c ] .
M ¯ ( t ) = y ̂ ( N e 2 m ) { 1 2 [ 2 | L y | 1 [ Ω 0 ( e ) ] 12 [ Ω 0 ( m ) ] 12 ( Δ 1 + i Γ 12 ( e ) ) ( Δ 2 + i Γ 12 ( m ) ) e i ω t + 2 | L y | 1 [ Ω 0 ( e ) ] 12 [ Ω 0 ( m ) ] 12 ( ω 0 + i Γ 12 ( e ) ) ( Δ 2 + i Γ 12 ( m ) ) e i ω t ] + h.c. } ( ρ 11 ρ 22 ) .
M ¯ = 1 2 M ̃ e i φ + h.c. ,
M ̃ = y ̂ ( N e m ) 1 2 [ 2 | L y | 1 [ Ω 0 ( e ) ] 12 [ Ω 0 ( m ) ] 12 ( Δ 1 + i Γ 12 ( e ) ) ( Δ 2 + i Γ 12 ( m ) ) + 2 | L y | 1 * [ Ω 0 * ( e ) ] 12 [ Ω 0 ( m ) * ] 12 ( ω 0 i Γ 12 ( e ) ) ( Δ 2 i Γ 12 ( m ) ) ] ( ρ 11 ρ 22 ) .
M ̃ = y ̂ N ( e m ) 2 | L y | 1 Ω 0 ( e ) Ω 0 ( m ) ( Δ 1 + i Γ 12 ( e ) ) ( Δ 2 + i Γ 12 ( m ) ) ( ρ 11 ρ 22 ) .
R = | M ̃ c P ̃ | = | ( e m c ) 2 | L y | 1 ρ ̃ 12 ( e ) ρ ̃ 12 ( m ) 2 | e x | 1 ρ ̃ 12 ( e ) | = | ( 2 | x ( p φ m c ) | 1 2 | x | 1 ) ρ ̃ 12 ( m ) | .
R max = 1 2 .
χ ( m ) = M ̃ H 0 = ( N e m H 0 ) [ 2 | L y | 1 Ω 0 ( e ) Ω 0 ( m ) 2 ( Δ 1 + i Γ 12 ( e ) ) ( Δ 2 + i Γ 12 ( m ) ) ] ( ρ 11 ρ 22 ) = ( N μ 0 e 3 2 m 2 2 ) [ | 2 | L y | 1 | 2 1 | x | 2 ( Δ 1 + i Γ 12 ( e ) ) ( Δ 2 + i Γ 12 ( m ) ) ] ( ρ 11 ρ 22 ) E 0 .
P ( t ) = 1 2 P ̃ e i ω t + h.c. = 1 2 ε 0 χ ( e ) ( ω ) E 0 e i ω t + h.c. ,
P ̃ = 2 N μ 21 ρ ̃ 12 ( e ) = ( N e 2 ) [ | 1 | x | 2 | 2 E 0 ( Δ 1 + i Γ 12 ( e ) ) ] ( ρ 11 ρ 22 )
χ ( e ) = ( N e 2 ε 0 ) | 2 | x | 1 | 2 ( Δ 1 + i Γ 12 ( e ) ) .
χ ( m ) ( ω ) χ ( e ) ( ω ) = ( μ 0 ε 0 e 2 m 2 ) | 2 | L y | 1 | 2 E 0 2 | x | 1 ( Δ 2 + i Γ 12 ( m ) ) = 2 c 2 | 2 | μ ( m ) | 1 | 2 E 0 e i φ p 2 | μ ( e ) | 1 Δ 2 2 + Γ 12 2 ( m ) ,
2 | V ± ( m ) | 1 = ( ) l 2 m 2 1 2 { B ± α 2 l 2 m 2 μ ( m ) α 1 l 1 m 1 + c.c. } ( l 2 1 l 1 m 2 q m 1 ) .
P ¯ = N Tr { μ ¯ ( e ) , ρ ( t ) } ,
μ ¯ ( e ) = μ 0 ( e ) z ̂ .
P ¯ ( t ) = N z ̂ ( μ 21 ( e ) ρ 12 ( m ) ( t ) ρ 12 ( e ) + h.c. ) = N z ̂ { ( 1 2 μ 21 ( e ) [ Ω 0 ( m ) ] 12 [ Ω 0 ( e ) ] 12 ( Δ 1 + i Γ 12 ( e ) ) ( ω 0 + i Γ 12 ( m ) ) e 2 i ω t + h.c. ) + ( 1 2 μ 21 ( e ) [ Ω 0 ( m ) ] 12 [ Ω 0 ( e ) ] 12 ( Δ 1 + i Γ 12 ( e ) ) ( Δ 2 + i Γ 12 ( m ) ) + h.c. ) }
| ψ = i c i | i = cos θ | 1 + sin θ | 2 .
Tr { ρ } = i ρ i i = Tr { ρ } = 1.
| i c i c i | 2 j | c j | 2 k | c k | 2 ,
i , j ρ i j ρ j i j ρ j j k ρ k k = Tr { ρ } Tr { ρ } = 1 .
( ρ 11 2 + ρ 22 2 ) + 2 | ρ 12 | 2 1 ,
2 | ρ 12 | 2 1 ( ρ 11 2 + ρ 22 2 ) .
θ ( ρ 11 2 ( θ ) + ρ 22 2 ( θ ) ) = 4 cos 3 θ sin θ + 4 sin 3 θ cos θ = 0.
θ = ± ( 2 n + 1 ) π 4 , n = 0 , 1 , 2 .
( ρ 11 2 + ρ 22 2 ) min = 1 2 .
| ρ 12 | max 1 2 .

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