Nonperturbative model of harmonic generation in undoped graphene in the terahertz regime
We present a formalism to calculate the nonlinear terahertz response of monolayer graphene using a two-band tight-binding model of graphene. We develop the dynamic equations for the electron density matrix in the length gauge to calculate the interband and intraband carrier dynamics at terahertz fre...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2015-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/17/11/113018 |
| _version_ | 1797751026342690816 |
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| author | Ibraheem Al-Naib J E Sipe Marc M Dignam |
| author_facet | Ibraheem Al-Naib J E Sipe Marc M Dignam |
| author_sort | Ibraheem Al-Naib |
| collection | DOAJ |
| description | We present a formalism to calculate the nonlinear terahertz response of monolayer graphene using a two-band tight-binding model of graphene. We develop the dynamic equations for the electron density matrix in the length gauge to calculate the interband and intraband carrier dynamics at terahertz frequencies. Using the calculated nonlinear interband and intraband current densities, we obtain the nonlinear transmitted and reflected terahertz fields. We find that when the conditions are such that the interband and intraband current densities are comparable, strong generation of odd harmonics is observed. We examine the response of undoped graphene as a function of a wide variety of system parameters, including operating temperature, Fermi velocity, pulse duration, and terahertz central frequency. We find that the response is generally most sensitive to the operating temperature and the terahertz central frequency. In particular, changing the ambient temperature from 10 to 100 K reduces the third harmonic field by a factor of 20, while increasing the terahertz central frequency from 0.5 to 5 THz results in an increase in the ratio of the generated third harmonic field to the fundamental of the reflected field from 19% to 49%. The very strong dependence on the temperature and central frequency is found to be due to the strong dependence of the nonlinear generation on the strength of the interplay between the intraband and interband dynamics. Our work demonstrates that, under the right conditions of low temperature and moderate THz field central frequency, third harmonic generation should be experimentally observable in undoped monolayer graphene at moderate THz field amplitudes of only 1 kV cm ^−1 . |
| first_indexed | 2024-03-12T16:42:23Z |
| format | Article |
| id | doaj.art-553782160d7c4df2a48528623f6d2b1f |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:42:23Z |
| publishDate | 2015-01-01 |
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| series | New Journal of Physics |
| spelling | doaj.art-553782160d7c4df2a48528623f6d2b1f2023-08-08T14:23:48ZengIOP PublishingNew Journal of Physics1367-26302015-01-01171111301810.1088/1367-2630/17/11/113018Nonperturbative model of harmonic generation in undoped graphene in the terahertz regimeIbraheem Al-Naib0J E Sipe1Marc M Dignam2Department of Physics, Engineering Physics and Astronomy, Queen’s University , Kingston, Ontario K7L 3N6, CanadaDepartment of Physics and Institute for Optical Sciences, University of Toronto , Toronto, Ontario M5S 1A7, CanadaDepartment of Physics, Engineering Physics and Astronomy, Queen’s University , Kingston, Ontario K7L 3N6, CanadaWe present a formalism to calculate the nonlinear terahertz response of monolayer graphene using a two-band tight-binding model of graphene. We develop the dynamic equations for the electron density matrix in the length gauge to calculate the interband and intraband carrier dynamics at terahertz frequencies. Using the calculated nonlinear interband and intraband current densities, we obtain the nonlinear transmitted and reflected terahertz fields. We find that when the conditions are such that the interband and intraband current densities are comparable, strong generation of odd harmonics is observed. We examine the response of undoped graphene as a function of a wide variety of system parameters, including operating temperature, Fermi velocity, pulse duration, and terahertz central frequency. We find that the response is generally most sensitive to the operating temperature and the terahertz central frequency. In particular, changing the ambient temperature from 10 to 100 K reduces the third harmonic field by a factor of 20, while increasing the terahertz central frequency from 0.5 to 5 THz results in an increase in the ratio of the generated third harmonic field to the fundamental of the reflected field from 19% to 49%. The very strong dependence on the temperature and central frequency is found to be due to the strong dependence of the nonlinear generation on the strength of the interplay between the intraband and interband dynamics. Our work demonstrates that, under the right conditions of low temperature and moderate THz field central frequency, third harmonic generation should be experimentally observable in undoped monolayer graphene at moderate THz field amplitudes of only 1 kV cm ^−1 .https://doi.org/10.1088/1367-2630/17/11/113018grapheneterahertzhigh-harmonic generation |
| spellingShingle | Ibraheem Al-Naib J E Sipe Marc M Dignam Nonperturbative model of harmonic generation in undoped graphene in the terahertz regime New Journal of Physics graphene terahertz high-harmonic generation |
| title | Nonperturbative model of harmonic generation in undoped graphene in the terahertz regime |
| title_full | Nonperturbative model of harmonic generation in undoped graphene in the terahertz regime |
| title_fullStr | Nonperturbative model of harmonic generation in undoped graphene in the terahertz regime |
| title_full_unstemmed | Nonperturbative model of harmonic generation in undoped graphene in the terahertz regime |
| title_short | Nonperturbative model of harmonic generation in undoped graphene in the terahertz regime |
| title_sort | nonperturbative model of harmonic generation in undoped graphene in the terahertz regime |
| topic | graphene terahertz high-harmonic generation |
| url | https://doi.org/10.1088/1367-2630/17/11/113018 |
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