Intraband divergences in third order optical response of 2D systems
The existence of large nonlinear optical coefficients is one of the preconditions for using nonlinear optical materials in nonlinear optical devices. For a crystal, such large coefficients can be achieved by matching photon energies with resonant energies between differ...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2019-03-01
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| Series: | APL Photonics |
| Online Access: | http://dx.doi.org/10.1063/1.5053715 |
| _version_ | 1818009401259196416 |
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| author | J. L. Cheng J. E. Sipe S. W. Wu Chunlei Guo |
| author_facet | J. L. Cheng J. E. Sipe S. W. Wu Chunlei Guo |
| author_sort | J. L. Cheng |
| collection | DOAJ |
| description | The existence of large nonlinear optical coefficients is one of the preconditions for
using nonlinear optical materials in nonlinear optical devices. For a crystal, such large
coefficients can be achieved by matching photon energies with resonant energies between
different bands, and so the details of the crystal band structure play an important role.
Here we demonstrate that large third-order nonlinearities can also be generally obtained
by a different strategy. As any of the incident frequencies or the sum of any two or three
frequencies approaches zero, the doped or excited populations of electronic states lead to
divergent contributions in the induced current density. We refer to these as intraband
divergences, by analogy with the behavior of Drude conductivity in linear response.
Physically, such resonant processes can be associated with a combination of intraband and
interband optical transitions. Current-induced second order nonlinearity, coherent current
injection, and jerk currents are all related to such divergences, and we find similar
divergences in degenerate four wave mixing and cross-phase modulation under certain
conditions. These divergences are limited by intraband relaxation parameters and lead to a
large optical response from a high quality sample; we find that they are very robust with
respect to variations in the details of the band structure. To clearly track all of these
effects, we analyze gapped graphene, describing the electrons as massive Dirac fermions;
under the relaxation time approximation, we derive analytic expressions for the third
order conductivities and identify the divergences that arise in describing the associated
nonlinear phenomena. |
| first_indexed | 2024-04-14T05:42:23Z |
| format | Article |
| id | doaj.art-b5e740d22f3146468f6fbc08b6415385 |
| institution | Directory Open Access Journal |
| issn | 2378-0967 |
| language | English |
| last_indexed | 2024-04-14T05:42:23Z |
| publishDate | 2019-03-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | APL Photonics |
| spelling | doaj.art-b5e740d22f3146468f6fbc08b64153852022-12-22T02:09:24ZengAIP Publishing LLCAPL Photonics2378-09672019-03-0143034201034201-1710.1063/1.5053715008895APPIntraband divergences in third order optical response of 2D systemsJ. L. Cheng0J. E. Sipe1S. W. Wu2Chunlei Guo3The Guo China-US Photonics Laboratory, Changchun Institute of Optics, fine Mechanics and Physics, Chinese Academy of Sciences, 3888 Eastern South Lake Road, Changchun, Jilin 130033, ChinaDepartment of Physics and Institute for Optical Sciences, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7, CanadaState Key Laboratory of Surface Physics, Key Laboratory of Micro and Nano Photonic Structures (MOE), and Department of Physics, Fudan University, Shanghai 200433, ChinaThe Guo China-US Photonics Laboratory, Changchun Institute of Optics, fine Mechanics and Physics, Chinese Academy of Sciences, 3888 Eastern South Lake Road, Changchun, Jilin 130033, ChinaThe existence of large nonlinear optical coefficients is one of the preconditions for using nonlinear optical materials in nonlinear optical devices. For a crystal, such large coefficients can be achieved by matching photon energies with resonant energies between different bands, and so the details of the crystal band structure play an important role. Here we demonstrate that large third-order nonlinearities can also be generally obtained by a different strategy. As any of the incident frequencies or the sum of any two or three frequencies approaches zero, the doped or excited populations of electronic states lead to divergent contributions in the induced current density. We refer to these as intraband divergences, by analogy with the behavior of Drude conductivity in linear response. Physically, such resonant processes can be associated with a combination of intraband and interband optical transitions. Current-induced second order nonlinearity, coherent current injection, and jerk currents are all related to such divergences, and we find similar divergences in degenerate four wave mixing and cross-phase modulation under certain conditions. These divergences are limited by intraband relaxation parameters and lead to a large optical response from a high quality sample; we find that they are very robust with respect to variations in the details of the band structure. To clearly track all of these effects, we analyze gapped graphene, describing the electrons as massive Dirac fermions; under the relaxation time approximation, we derive analytic expressions for the third order conductivities and identify the divergences that arise in describing the associated nonlinear phenomena.http://dx.doi.org/10.1063/1.5053715 |
| spellingShingle | J. L. Cheng J. E. Sipe S. W. Wu Chunlei Guo Intraband divergences in third order optical response of 2D systems APL Photonics |
| title | Intraband divergences in third order optical response of 2D
systems |
| title_full | Intraband divergences in third order optical response of 2D
systems |
| title_fullStr | Intraband divergences in third order optical response of 2D
systems |
| title_full_unstemmed | Intraband divergences in third order optical response of 2D
systems |
| title_short | Intraband divergences in third order optical response of 2D
systems |
| title_sort | intraband divergences in third order optical response of 2d systems |
| url | http://dx.doi.org/10.1063/1.5053715 |
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