- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Reflection parity and space-time parity photonic conservation laws in parametric nonlinear optics

Gavriel Lerner1,2,*, Matan Even Tzur1,2, Ofer Neufeld1,2,3, Avner Fleischer4, and Oren Cohen1,2,5,†

  • *Contact author: gavriel@campus.technion.ac.il
  • †Contact author: oren@technion.ac.il
PDF

Phys. Rev. Research 6, L042034 – Published 4 November, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L042034

Abstract

Conservation laws are some of the most generic and useful concepts in physics. In nonlinear optical parametric processes, conservation of photonic energy, momenta and parity often lead to selection rules, restricting the allowed polarization and frequencies of the emitted radiation. Here we present a scheme to derive conservation laws in optical parametric processes in which many photons are annihilated and a single photon is emitted. We first rederive with it the known nonlinear optical conservation laws, and then utilize it to predict and explore conservations of reflection parity and space-time parity. Conservation of reflection-parity arises from a generalized reflection symmetry of the polarization in a superspace, analogous to the superspace employed in the study of quasicrystals. Conservation of space-time parity similarly arises from space-time reversal symmetry in superspace. We explore these conservation laws numerically in the context of high-harmonic generation and outline experimental setups where they can be tested.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (43)

  1. R. W. Boyd, Nonlinear Optics, 3rd ed., Vol. 5 (Academic Press, Burlington, 2003).
  2. M. D. Perry and J. K. Crane, High-order harmonic emission from mixed fields, Phys. Rev. A 48, R4051 (1993).
  3. J. B. Bertrand, H. J. Wörner, H. C. Bandulet, É. Bisson, M. Spanner, J. C. Kieffer, D. M. Villeneuve, and P. B. Corkum, Ultrahigh-order wave mixing in noncollinear high harmonic generation, Phys. Rev. Lett. 106, 023001 (2011).
  4. G. Gariepy, J. Leach, K. T. Kim, T. J. Hammond, E. Frumker, R. W. Boyd, and P. B. Corkum, Creating high-harmonic beams with controlled orbital angular momentum, Phys. Rev. Lett. 113, 153901 (2014).
  5. D. D. Hickstein, F. J. Dollar, P. Grychtol, J. L. Ellis, R. Knut, C. Hernández-García, D. Zusin, C. Gentry, J. M. Shaw, T. Fan, K. M. Dorney, A. Becker, A. Jaroń-Becker, H. C. Kapteyn, M. M. Murnane, and C. G. Durfee, Non-collinear generation of angularly isolated circularly polarized high harmonics, Nat. Photonics 9, 743 (2015).
  6. L. Rego, J. S. Román, A. Picón, L. Plaja, and C. Hernández-García, Nonperturbative twist in the generation of extreme-ultraviolet vortex beams, Phys. Rev. Lett. 117, 163202 (2016).
  7. A. Fleischer, O. Kfir, T. Diskin, P. Sidorenko, and O. Cohen, Spin angular momentum and tunable polarization in high-harmonic generation, Nat. Photonics 8, 543 (2014).
  8. K. M. Dorney, L. Rego, N. J. Brooks, J. San Román, C.-T. Liao, J. L. Ellis, D. Zusin, C. Gentry, Q. L. Nguyen, J. M. Shaw, A. Picón, L. Plaja, H. C. Kapteyn, M. M. Murnane, and C. Hernández-García, Controlling the polarization and vortex charge of attosecond high-harmonic beams via simultaneous spin–orbit momentum conservation, Nat. Photonics 13, 123 (2019).
  9. O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics, Nat. Photonics 9, 99 (2014).
  10. O. Neufeld, D. Podolsky, and O. Cohen, Floquet group theory and its application to selection rules in harmonic generation, Nat. Commun. 10, 405 (2019).
  11. C. L. Tang and H. Rabin, Selection rules for circularly polarized waves in nonlinear optics, Phys. Rev. B 3, 4025 (1971).
  12. O. E. Alon, V. Averbukh, and N. Moiseyev, Selection rules for the high harmonic generation spectra, Phys. Rev. Lett. 80, 3743 (1998).
  13. D. Baykusheva, A. Chacón, D. Kim, D. E. Kim, D. A. Reis, and S. Ghimire, Strong-field physics in three-dimensional topological insulators, Phys. Rev. A 103, 023101 (2021).
  14. K. Chinzei and T. N. Ikeda, Time crystals protected by Floquet dynamical symmetry in Hubbard models, Phys. Rev. Lett. 125, 060601 (2020).
  15. G. Lerner, O. Neufeld, L. Hareli, G. Shoulga, E. Bordo, A. Fleischer, D. Podolsky, A. Bahabad, and O. Cohen, Multiscale dynamical symmetries and selection rules in nonlinear optics, Sci. Adv. 9, ade0953 (2023).
  16. O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, A. Fleischer, E. Bordo, T. Fan, D. Popmintchev, T. Popmintchev, H. Kapteyn, M. Murnane, and O. Cohen, Helicity-selective phase-matching and quasi-phase matching of circularly polarized high-order harmonics: Towards chiral attosecond pulses, J. Phys. B: At. Mol. Opt. Phys. 49, 123501 (2016).
  17. E. Pisanty, G. J. Machado, V. Vicuña-Hernández, A. Picón, A. Celi, J. P. Torres, and M. Lewenstein, Knotting fractional-order knots with the polarization state of light, Nat. Photonics 13, 569 (2019).
  18. E. Pisanty, L. Rego, J. San Román, A. Picón, K. M. Dorney, H. C. Kapteyn, M. M. Murnane, L. Plaja, M. Lewenstein, and C. Hernández-García, Conservation of torus-knot angular momentum in high-order harmonic generation, Phys. Rev. Lett. 122, 203201 (2019).
  19. M. Luttmann, M. Vimal, M. Guer, J. F. Hergott, A. Z. Khoury, C. Hernández-García, E. Pisanty, and T. Ruchon, Nonlinear up-conversion of a polarization möbius strip with half-integer optical angular momentum, Sci. Adv. 9, eadf3486 (2023).
  20. M. E. Tzur, O. Neufeld, E. Bordo, A. Fleischer, and O. Cohen, Selection rules in symmetry-broken systems by symmetries in synthetic dimensions, Nat. Commun. 13, 1312 (2021).
  21. M. E. Tzur, O. Neufeld, A. Fleischer, and O. Cohen, Selection rules for breaking selection rules, New J. Phys. 23, 103039 (2021).
  22. C. Hernández-García, A. Turpin, J. San Román, A. Picón, R. Drevinskas, A. Cerkauskaite, P. G. Kazansky, C. G. Durfee, and Í. J. Sola, Extreme ultraviolet vector beams driven by infrared lasers, Optica 4, 520 (2017).
  23. F. Kong, C. Zhang, H. Larocque, Z. Li, F. Bouchard, D. H. Ko, G. G. Brown, A. Korobenko, T. J. Hammond, R. W. Boyd, E. Karimi, and P. B. Corkum, Vectorizing the spatial structure of high-harmonic radiation from gas, Nat. Commun. 10, 2020 (2019).
  24. A. Forbes, M. de Oliveira, and M. R. Dennis, Structured light, Nat. Photonics 15, 253 (2021).
  25. E. Frumker, N. Kajumba, J. B. Bertrand, H. J. Wörner, C. T. Hebeisen, P. Hockett, M. Spanner, S. Patchkovskii, G. G. Paulus, D. M. Villeneuve, A. Naumov, and P. B. Corkum, Probing polar molecules with high harmonic spectroscopy, Phys. Rev. Lett. 109, 233904 (2012).
  26. D. Baykusheva, M. S. Ahsan, N. Lin, and H. J. Wörner, Bicircular high-harmonic spectroscopy reveals dynamical symmetries of atoms and molecules, Phys. Rev. Lett. 116, 123001 (2016).
  27. S. Gholam-Mirzaei, J. Beetar, and M. Chini, High harmonic generation in ZnO with a high-power Mid-IR OPA, Appl. Phys. Lett. 110, 061101 (2017).
  28. O. Neufeld, D. Ayuso, P. Decleva, M. Y. Ivanov, O. Smirnova, and O. Cohen, Ultrasensitive chiral spectroscopy by dynamical symmetry breaking in high harmonic generation, Phys. Rev. X 9, 031002 (2019).
  29. D. Ayuso, O. Neufeld, A. F. Ordonez, P. Decleva, G. Lerner, O. Cohen, M. Ivanov, and O. Smirnova, Synthetic chiral light for efficient control of chiral light–matter interaction, Nat. Photonics 13, 866 (2019).
  30. D. Ayuso, A. F. Ordonez, P. Decleva, M. Ivanov, and O. Smirnova, Enantio-sensitive unidirectional light bending, Nat. Commun. 12, 3951 (2021).
  31. O. Neufeld and O. Cohen, Background-free measurement of ring currents by symmetry-breaking high-harmonic spectroscopy, Phys. Rev. Lett. 123, 103202 (2019).
  32. D. Baykusheva and H. J. Wörner, Chiral discrimination through bielliptical high-harmonic spectroscopy, Phys. Rev. X 8, 031060 (2018).
  33. G. Vampa, T. J. Hammond, M. Taucer, X. Ding, X. Ropagnol, T. Ozaki, S. Delprat, M. Chaker, N. Thiré, B. E. Schmidt, F. Légaré, D. D. Klug, A. Y. Naumov, D. M. Villeneuve, A. Staudte, and P. B. Corkum, Strong-field optoelectronics in solids, Nat. Photonics 12, 465 (2018).
  34. I. Tyulnev, Á. Jiménez-Galán, J. Poborska, L. Vamos, P. St. J. Russell, F. Tani, O. Smirnova, M. Ivanov, R. E. F. Silva, and J. Biegert, Valleytronics in bulk MoS2 with a topologic optical field, Nature 628, 746 (2024).
  35. S. Mitra, Á. Jiménez-Galán, M. Aulich, M. Neuhaus, R. E. F. Silva, V. Pervak, M. F. Kling, and S. Biswas, Light-wave-controlled Haldane model in monolayer hexagonal boron nitride, Nature 628, 752 (2024).
  36. O. Neufeld, N. Tancogne-Dejean, U. De Giovannini, H. Hübener, and A. Rubio, Light-driven extremely nonlinear bulk photogalvanic currents, Phys. Rev. Lett. 127, 126601 (2021).
  37. D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Metallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett. 53, 1951 (1984).
  38. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L042034 for technical derivation of known conservation laws, and additional discussion on conservation laws and dynamical symmetries.
  39. T. Fan et al., Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism., Proc. Natl. Acad. Sci. USA 112, 14206 (2015).
  40. D. B. Milošević, Circularly polarized high harmonics generated by a bicircular field from inert atomic gases in the p state: A tool for exploring chirality-sensitive processes, Phys. Rev. A 92, 043827 (2015).
  41. D. B. Milošević, High-order harmonic generation by a bichromatic elliptically polarized field: Conservation of angular momentum, J. Phys. B: At. Mol. Opt. Phys. 48, 171001 (2015).
  42. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L'Huillier, and P. B. Corkum, Theory of high-harmonic generation by low-frequency laser fields, Phys. Rev. A 49, 2117 (1994).
  43. H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Springer, Berlin, 2013).

Outline

Information

Phys. Rev. Research 6, L042034– Published 4 November, 2024
  • Received 28 January 2023
  • Accepted 9 July 2024
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation