Two-Photon Absorption in Graphene Enhanced by the Excitonic Fano Resonance

Abstract

We report our observation of two-photon absorption (2PA) in graphene enhanced by the excitonic Fano resonance at the saddle point with femtosecond laser pulses in the spectral range from 1.8 to 2.9 eV (or, from 435 to 700 nm). On the basis of the second-order, time-dependent perturbation theory on interband transitions among three states near the saddle point of two-dimensional systems (used in the Bassani−Hassan theoretical model), we develop a semiempirical model to take excitons in graphene into consideration. We find that the model is in agreement with the photon-energy dependence of the observed 2PA spectrum with a scaling factor of B = (1−5) × 10 2 cm/MW/eV 5 . ■ INTRODUCTIONThe interaction between graphene and femtosecond laser pulses is of relevance to many practical applications in photonics and optoelectronics. One of the successful applications is that saturation in interband transitions induced by one-photon absorption (1PA) in graphene has been utilized for mode-locking technology. 1−3 1PA saturation results from band-filling effects when graphene is exposed to intense laser pulses. These reports, however, have ignored the presence of two-photon absorption (2PA), which has been experimentally confirmed in saturable absorber mirrors made of InGaAs quantum wells. 4 Theoretical simulations show that the presence of 2PA has a significant impact onto the stability of continuouswave, mode-locking operation. 4 Interestingly, apart from 1PA saturation, two-photon-induced interband transitions in graphene also have potential for photonic applications. In ref 5, coherent control and noncontact generation of ballistic photocurrents in multilayer epitaxial graphene at wavelengths of 3.2 μm/1.6 μm and 4.8 μm/2.4 μm have been demonstrated by utilizing the quantum interference between one-photon-induced and two-photoninduced interband transitions. Utilizing such noncontact method for generating electrical currents can overcome the difficulty of making reliable contacts for future graphene-based electronic devices, which have drawn intensive research interest 6−8 because of the superior electron transport properties of graphene. 9−11 Moreover, such a method eliminates the parasitic effects due to electrical contacts on graphene in potential applications. Therefore, two-photon absorption is of importance to graphene photonics and optoelectronics.From the fundamental point of material properties, 2PA of graphene has not been systematically investigated in the visible spectral region. We have previously demonstrated, both theoretically and experimentally, that 2PA is as important as 1PA saturation in AB-stacking bilayer epitaxial graphene in the near-infrared (NIR) spectral range. 12 In the report, we considered only the optical transitions near the Dirac point (K-point) in the theoretical calculation, and no significant contributions from the optical transitions around the saddle point (M-point) of graphene was experimentally observed in this NIR spectral range. Strong optical transitions around the saddle point due t...

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Two-photon absorption and saturable absorption of mid-IR in graphene

“…The measured saturation intensities, I s , and saturation fluences, F s , are presented in Figure 6 as functions of photon energy, E ph (See Supporting Information for the listed values), and compared with measurements published in literature. 2,5,9,[17][18][19]38,39 In each case, graphene sheets were produced by either mechanical exfoliation, epitaxy, or CVD and the direction of incident radiation was perpendicular to the graphene plane. Cases for graphene flakes suspended in a solution or polymer were excluded from the analysis because the angle of incidence is not uniform and the incident beam is more likely to interact with flake edges where disorder is high.…”

“…Two-photon absorption (2PA) has been observed in the spectral region between 435 nm and 1100 nm (1.1 eV to 2.9 eV). 18,19 The strength of 2PA is greater in stacked layers than single layer graphene due to the increased number of energy bands caused by interlayer coupling and thus a greater number of possible electronic transitions. 18 The effective modulation depth of graphene is limited by 2PA which can be detrimental to passive mode-locking.…”