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Second-harmonic generation

Not to be confused with two-photon absorption.
Energy level scheme of SHG process

Second-harmonic generation (SHG), also known as frequency doubling, is the lowest-order wave-wave nonlinear interaction that occurs in various systems, including optical, radio, atmospheric, and magnetohydrodynamic systems.[1] As a prototype behavior of waves, SHG is widely used, for example, in doubling laser frequencies. SHG was initially discovered as a nonlinear optical process[2] in which two photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with twice the energy of the initial photons (equivalently, twice the frequency and half the wavelength), that conserves the coherence of the excitation. It is a special case of sum-frequency generation (2 photons), and more generally of harmonic generation.

The second-order nonlinear susceptibility of a medium characterizes its tendency to cause SHG. Second-harmonic generation, like other even-order nonlinear optical phenomena, is not allowed in media with inversion symmetry (in the leading electric dipole contribution).[3] However, effects such as the Bloch–Siegert shift (oscillation), found when two-level systems are driven at Rabi frequencies comparable to their transition frequencies, will give rise to second-harmonic generation in centro-symmetric systems.[4][5] In addition, in non-centrosymmetric crystals belonging to crystallographic point group 432, SHG is not possible [6] and under Kleinman's conditions SHG in 422 and 622 point groups should vanish,[7] although some exceptions exist.[8]

In some cases, almost 100% of the light energy can be converted to the second-harmonic frequency. These cases typically involve intense pulsed laser beams passing through large crystals and careful alignment to obtain phase matching. In other cases, like second-harmonic imaging microscopy, only a tiny fraction of the light energy is converted to the second harmonic, but this light can nevertheless be detected with the help of optical filters.

Schematic view of the SHG conversion of an exciting wave in a non-linear medium with a non-zero second-order non-linear susceptibility

Generating the second harmonic, often called frequency doubling, is also a process in radio communication; it was developed early in the 20th century and has been used with frequencies in the megahertz range. It is a special case of frequency multiplication.

  1. ^ He, Maosheng; Forbes, Jeffrey M. (2022-12-07). "Rossby wave second harmonic generation observed in the middle atmosphere". Nature Communications. 13 (1): 7544. Bibcode:2022NatCo..13.7544H. doi:10.1038/s41467-022-35142-3. ISSN 2041-1723. PMC 9729661. PMID 36476614.
  2. ^ Franken, P. A.; Hill, A. E.; Peters, C. W.; Weinreich, G. (1961-08-15). "Generation of Optical Harmonics". Physical Review Letters. 7 (4): 118–119. Bibcode:1961PhRvL...7..118F. doi:10.1103/PhysRevLett.7.118.
  3. ^ Boyd, R. (2007). "The Nonlinear Optical Susceptibility". Nonlinear optics (third ed.). pp. 1–67. doi:10.1016/B978-0-12-369470-6.00001-0. ISBN 9780123694706. S2CID 15660817.
  4. ^ Cardoso, G. C.; Pradhan, P.; Morzinski, J.; Shahriar, M. S. (2005). "In situ detection of the temporal and initial phase of the second harmonic of a microwave field via incoherent fluorescence". Physical Review A. 71 (6): 063408. arXiv:quant-ph/0410219. Bibcode:2005PhRvA..71f3408C. doi:10.1103/PhysRevA.71.063408.
  5. ^ Pradhan, P.; Cardoso, G. C.; Shahriar, M. S. (2009). "Suppression of error in qubit rotations due to Bloch–Siegert oscillation via the use of off-resonant Raman excitation". Journal of Physics B: Atomic, Molecular and Optical Physics. 42 (6): 065501. Bibcode:2009JPhB...42f5501P. doi:10.1088/0953-4075/42/6/065501. S2CID 15051122.
  6. ^ Nye, J. F. (1985). Physical properties of crystals: their representation by tensors and matrices (1st published in pbk. with corrections, 1985 ed.). Oxford [Oxfordshire]: Clarendon Press. ISBN 0-19-851165-5. OCLC 11114089.
  7. ^ Kleinman, D. A. (1962-11-15). "Theory of Second Harmonic Generation of Light". Physical Review. 128 (4): 1761–1775. Bibcode:1962PhRv..128.1761K. doi:10.1103/PhysRev.128.1761. ISSN 0031-899X.
  8. ^ Dailey, Christopher A.; Burke, Brian J.; Simpson, Garth J. (May 2004). "The general failure of Kleinman symmetry in practical nonlinear optical applications". Chemical Physics Letters. 390 (1–3): 8–13. Bibcode:2004CPL...390....8D. doi:10.1016/j.cplett.2004.03.109.

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