Iterative approach to arbitrary nonlinear optical response functions of graphene

Fábio Hipólito, Darko Dimitrovski, Thomas Garm Pedersen

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Abstract

Two-dimensional materials constitute an exciting platform for nonlinear optics with large nonlinearities that are tunable by gating. Hence, gate-tunable harmonic generation and intensity-dependent refraction have been observed in, e.g., graphene and transition-metal dichalcogenides, whose electronic structures are accurately modeled by the (massive) Dirac equation. We exploit on the simplicity of this model and demonstrate here that arbitrary nonlinear response functions follow from a simple iterative approach. The power of this approach is illustrated by analytical expressions for harmonic generation and intensity-dependent refraction, both computed up to ninth order in the pump field. Moreover, the results allow for arbitrary band gaps and gating potentials. As illustrative applications, we consider (i) the gate dependence of third- and fifth-harmonic generation in gapped and gapless graphene, (ii) the intensity-dependent refractive index of graphene up to ninth order, and (iii) the intensity dependence of high-harmonic generation.

Original languageEnglish
Article number195407
JournalPhysical Review B
Volume99
Issue number19
Pages (from-to)195407
Number of pages12
ISSN2469-9950
DOIs
Publication statusPublished - 6 May 2019

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Harmonic generation
Graphene
harmonic generations
graphene
Refraction
refraction
Nonlinear optics
nonlinear optics
Dirac equation
Electronic structure
Transition metals
Refractive index
Energy gap
platforms
transition metals
nonlinearity
Pumps
refractivity
pumps

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Hipólito, Fábio ; Dimitrovski, Darko ; Pedersen, Thomas Garm. / Iterative approach to arbitrary nonlinear optical response functions of graphene. In: Physical Review B. 2019 ; Vol. 99, No. 19. pp. 195407.
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Iterative approach to arbitrary nonlinear optical response functions of graphene. / Hipólito, Fábio; Dimitrovski, Darko; Pedersen, Thomas Garm.

In: Physical Review B, Vol. 99, No. 19, 195407, 06.05.2019, p. 195407.

Research output: Contribution to journalJournal articleResearchpeer-review

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AU - Dimitrovski, Darko

AU - Pedersen, Thomas Garm

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