Abstract-Optimized nonlinear terahertz response of graphene in a parallel-plate waveguide

APL Photonics

Parvin Navaeipour and Marc M. Dignam

The metallic parallel-plate waveguide with monolayer graphene inside forms the system being modelled. The inner material of the waveguide is polyolefin, and the graphene is placed at the center of the waveguide at y = b/2. The pump field propagates in the +z-direction and is polarized in the x-direction.

https://aip.scitation.org/doi/10.1063/1.5045652

Third harmonic generation of terahertz radiation is expected to occur in monolayer graphene due to the nonlinear relationship between the crystal momentum and the current density. In this work, we calculate the terahertz nonlinear response of monolayer graphene inside a parallel-plate waveguide including pump depletion, self-phase, and cross-phase modulation. To overcome the phase mismatching between the pump field and third-harmonic field at high input fields due to self-phase and cross-phase modulation, we design a waveguide with two dielectric layers with different indices of refraction. We find that, by tuning the relative thicknesses of the two layers, we are able to improve phase matching and thereby increase the power efficiency of the system by more than a factor of two at high powers. With this approach, we find that despite the loss in this system, for an incident frequency of 2 THz, we are able to achieve power efficiencies of 75% for graphene with low Fermi energies of 20 meV and up to 35% when the Fermi energy is 100 meV.

Abstract-Third-harmonic terahertz generation from graphene in a parallel-plate waveguide

Parvin Navaeipour, Ibraheem Al-Naib, and Marc M. Dignam

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.013847

Graphene as a zero-band-gap two-dimensional semiconductor with a linear electron band dispersion near the Dirac points has the potential to exhibit very interesting nonlinear optical properties. In particular, third-harmonic generation of terahertz radiation should occur due to the nonlinear relationship between the crystal momentum and the current density. In this work, we investigate the terahertz nonlinear response of graphene inside a parallel-plate waveguide. We optimize the plate separation and Fermi energy of the graphene to maximize third-harmonic generation, by maximizing the nonlinear interaction while minimizing the loss and phase mismatch. The results obtained show an increase by more than a factor of 100 in the power efficiency relative to a normal-incidence configuration for a 2.0-THz incident field.

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Abstract-Third harmonic terahertz generation from graphene in a parallel-plate waveguide

Parvin Navaeipour, Ibraheem Al-Naib, and Marc M. Dignam

https://journals.aps.org/pra/accepted/9d079Na9Xb5E1f14a01c97532b94dc5b4ed24535c

Graphene as a zero-bandgap two-dimensional semiconductor with a linear electron band dispersion near the Dirac points has the potential to exhibit very interesting nonlinear optical properties. In particular, third harmonic generation of terahertz radiation should occur due to the nonlinear relationship between the crystal momentum and the current density. In this work, we investigate the terahertz nonlinear response of graphene inside a parallel-plate waveguide. We optimize the plate separation and Fermi energy of the graphene to maximize third harmonic generation, by maximizing the nonlinear interaction while minimizing the loss and phase mismatch. The results obtained show an increase by more than a factor of 100 in the power efficiency relative to a normal-incidence configuration for a 2.0 terahertz incident field.

Abstract-Nonlinear response of biased bilayer graphene at terahertz frequencies

Riley McGouran and Marc M. Dignam

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.045439

A density-matrix formalism within the length gauge is developed to calculate the nonlinear response of both doped and undoped biased bilayer graphene at terahertz frequencies. Employing a tight-binding model, we derive an effective two-band Hamiltonian with which we calculate the conduction and valence band dispersion, as well as their respective Bloch states. We then solve for the dynamic equations of the density-matrix elements, allowing for the calculation of the intraband and interband current densities and the transmitted and reflected terahertz fields. We find that the third harmonic amplitude generated for undoped biased bilayer graphene with a gap size of 4 meV is larger than that for monolayer graphene or unbiased bilayer graphene for an incident 1 THz single-cycle pulse with a field amplitude of 2.0 kV/cm. We also find for doped biased bilayer graphene that, although the dispersion becomes highly nonparabolic as a bias is applied, the third harmonic is a maximum when there is no bias and diminishes with an increase in bias.

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2 More

• Received 30 December 2016

DOI:https://doi.org/10.1103/PhysRevB.96.045439

©2017 American Physical Society

Physics Subject Headings (PhySH)

1. Research Areas

Band gapConductivityElectronic structureNonlinear opticsSemiconductors

1. Physical Systems

Graphene

1. Techniques

Tight-binding model

Nonlinear DynamicsCondensed Matter & Materials Physics

Abstract-Nonlinear response of biased bilayer graphene at terahertz frequencies

Riley McGouran, Marc M. Dignam

(Submitted on 30 Dec 2016)

https://arxiv.org/abs/1701.00028

A density-matrix formalism within the length gauge is developed to calculate the nonlinear response of both doped and undoped biased bilayer graphene (BBLG) at terahertz frequencies. Employing a tight-binding model, we derive an effective two-band Hamiltonian with which we calculate the conduction and valence band dispersion, as well as their respective Bloch states. We then solve for the dynamic equations of the density matrix elements, allowing for the calculation of the intraband and interband current densities and the transmitted and reflected terahertz fields. We find that for undoped BBLG with a gap size of 4 meV, the reflected field exhibits a third harmonic amplitude that is 45% of the fundamental in the reflected field (0.07% of the incident field fundamental) for an incident 1 THz single-cycle pulse with a field amplitude of 2.0 kV/cm. We find for doped BBLG, although the dispersion becomes highly nonparabolic as a bias is applied, the third harmonic is a maximum of 8% of the fundamental in the reflected field (0.56% of the incident field fundamental) when there is no bias and diminishes with an increase in bias.

Abstract-Nonlinear response of bilayer graphene at terahertz frequencies

Riley McGouran, Ibraheem Al-Naib, and Marc M. Dignam
https://journals.aps.org/prb/accepted/0d078O10Id513b2c787342507d9d80ab1aa30752c

A density-matrix formalism within the length gauge is developed for the purpose of calculating the nonlinear response of intrinsic bilayer graphene at terahertz frequencies. Employing a tight-binding model, we find that interplay between the interband and intraband dynamics leads to strong harmonic generation at moderate field amplitudes. Specifically, we find that at low temperature (10 K), the reflected field of undoped suspended bilayer graphene exhibits a third harmonic amplitude that is 0.06\% of the fundamental of the incident field, which corresponds to 30\% of the fundamental in the reflected field for an incident 1 THz single-cycle pulse with a field amplitude of 1.5 kV/cm. More interestingly, we find that as the central frequency of the incident field is increased, the third harmonic amplitude also increases; reaching a maximum of 53\% of the fundamental in the reflected field (0.11\% of the fundamental in the incident field) for an incident frequency of 2 THz and amplitude of 2.5 kV/cm.

Abstract-Nonlinear Response of Bilayer Graphene at Terahertz Frequencies

Riley McGouran, Ibraheem Al-Naib, Marc M. Dignam

(Submitted on 15 Aug 2016)

http://arxiv.org/abs/1608.04343

A density-matrix formalism within the length gauge is developed for the purpose of calculating the nonlinear response of intrinsic bilayer graphene at terahertz frequencies. Employing a tight-binding model, we find that interplay between the interband and intraband dynamics leads to strong harmonic generation at moderate field amplitudes. Specfically, we find that at low temperature (10 K), the reflected field of undoped suspended bilayer graphene exhibits a third harmonic amplitude that is 30\% of the fundamental in the reflected field for an incident 1 THz single-cycle pulse with a field amplitude of 1.5 kV/cm. More interestingly, we find that as the central frequency of the incident radition is increased, the third harmonic amplitude also increases; reaching a maximum of 53\% for an incident frequency of 2 THz and amplitude of 2.5 kV/cm.

Abstract-Intense terahertz field effects on photoexcited carrier dynamics in gated graphene

Hassan A. Hafez¹, Pierre L. Lévesque², Ibraheem Al-Naib^3,4, Marc M. Dignam³, Xin Chai¹, Saman Choubak⁵, Patrick Desjardins⁵, Richard Martel² and Tsuneyuki Ozaki^1,a)


a) Author to whom correspondence should be addressed. Electronic mail: ozaki@emt.inrs.ca
Appl. Phys. Lett. 107, 251903 (2015); http://dx.doi.org/10.1063/1.4938081

We study nonlinear effects of intense terahertz (THz) field on photoexcited carrier dynamics in gated monolayer graphene. By employing optical-pump/intense-THz-probe spectroscopy on lightly doped graphene, we observe a crossover from negative to positive photo-induced THz differential transmission as the THz probe field is increased. We attribute this qualitative change in the response to a crossover from a regime where the photo-induced increase in the carrier density dominates the differential response to one where a THz-field-induced increase in the scattering rate dominates.

Abstract-Optimizing third-harmonic generation at terahertz frequencies in graphene

Ibraheem Al-Naib, Max Poschmann, and Marc M. Dignam

Phys. Rev. B 91, 205407 – Published 11 May 2015

http://journals.aps.org/prb/abstract/10.1103/PhysRevB.91.205407

We model third-harmonic generation in doped monolayer graphene at terahertz frequencies by employing a nearest-neighbor tight-binding model in the length gauge. We show that for a given incident-field amplitude there is an optimum Fermi level that maximizes the emitted third-harmonic field. The optimum Fermi level depends very strongly on the incident-field amplitude as well as on the scattering time and increasing either enhances the third-harmonic response. We consider the general case of Fermi-level-independent scattering as well as three different scattering mechanisms that are Fermi-level dependent: phonon, long-range impurity, and short-range impurity scattering. For each case, we determine the optimal Fermi level as well as the amplitude of the optimized third-harmonic response for single-cycle incident fields with central frequencies of 1 THz and amplitudes in the range of 25–75 kV/cm. We find that although nonlinear processes beyond third order suppress third-harmonic generation, we still obtain third-harmonic amplitudes as large as 1.6% of the fundamental of the transmitted field.

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