Transient four-wave mixing and coherent transient optical phenomena

Ye, Peixian; Shen, Y. R.

doi:10.1103/physreva.25.2183

Cited by 70 publications

(16 citation statements)

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“…Hd(t, rj) = I j(gto, g (rj)t -[ j(go), g (rj)t &+bee&, (rj}(t 2 t, ) ]] denote-s the phase difference of the induced nonlinear polarization at the local environment specified by g; and A;(t;) is the envelope of the exciting pulsed field which has a carrier frequency at o); and peaks at t; As noted .from Eq. (16), all the molecules at the surface will generate the maximum coherent output whenever the phase difference vanishes [13,14], i.e. ,…”

Section: Transient Effectmentioning

confidence: 99%

“…A one-to-one correspondence between each wavemixing process capable of producing spectra with reduced inhomogeneous broadening and photon-echo processes was established [13]. In a recent study, Shen further pointed out that doubly resonant differencefrequency generation (DR DFG) in the time domain with properly time-ordered input pulses can yield an output in the form of a rephased echo [14].…”

Section: Introductionmentioning

confidence: 98%

“…As shown in Fig. 1, we explore surface SFG in refiection (E, ) from an interface between linear media 1 [13,16] to Fig. 2 Here oi", =(E"Eg, ) -If& is the frequency of the transition~ev )~~ga ).…”

Section: Introductionmentioning

confidence: 99%

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Theory of doubly resonant infrared-visible sum-frequency and difference-frequency generation from adsorbed molecules

Huang

Shen

1994

Phys. Rev. A

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We theoretically analyze doubly resonant infrared-visible sum-frequency (DR IVSFG) and diferencefrequency generation (DR IVDFG) from a monolayer of adsorbates at an interface. Our calculated results with a model molecule indicate that the resonant amplitude of nonlinear optical susceptibility of DR IVDFG and DR IVSFG processes conveys information about the electron-vibration coupling in adsorbates. Moreover, owing to a dephasing-rephasing procedure involved, DR IVDFG can also be developed into a sensitive probe for investigating the coherent phase relaxation process in adsorbed molecules without the complication of inhomogeneous broadening.PACS number(s): 42.50.Md, 68.35.Ja

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Section: Transient Effectmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Theory of doubly resonant infrared-visible sum-frequency and difference-frequency generation from adsorbed molecules

Huang

Shen

1994

Phys. Rev. A

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“…[9]. To investigate the nonlinear response of graphene flakes, we employ the four-wave mixing technique [10]. This involves the generation of mixed optical frequency harmonics 2!…”

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confidence: 99%

Coherent Nonlinear Optical Response of Graphene

et al. 2010

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We investigate the nonlinear optical properties of graphene flakes using four-wave mixing. The corresponding third-order optical susceptibility is found to be remarkably large and only weakly dependent on the wavelength in the near-infrared frequency range. The magnitude of the response is in good agreement with our calculations based on the nonlinear quantum response theory. DOI: 10.1103/PhysRevLett.105.097401 PACS numbers: 78.67.Wj, 42.65.Ky, 78.47.nj Graphene, a single sheet of carbon atoms in a hexagonal lattice, is the basic building block for all graphitic materials. Although it has been known as a theoretical concept for some time [1], a layer of graphene has only recently been isolated from bulk graphite and deposited on a dielectric substrate [2]. The great interest in studying graphene is driven by its linear, massless band structureand many unusual electrical, thermal, mechanical, and optical properties [3,4] [here the upper (lower) sign corresponds to the electron (hole) band, p is the quasimomentum, and V % 10 6 m=s is the Fermi velocity]. For example, the optical absorption of graphene has been shown to be wavelength independent ('2:3% per layer) in a broad range of optical frequencies [5][6][7]. Recently, it has been predicted that the linear dispersion described by Eq. (1) should lead to strongly nonlinear optical behavior at microwave and terahertz frequencies [8]. At higher, optical frequencies one can also expect an enhanced optical nonlinearity as, due to graphene's band structure, interband optical transitions occur at all photon energies. Here we report on the first observation of the coherent nonlinear optical response of graphene at visible and nearinfrared frequencies. We show that graphene has an exceptionally high nonlinear response, described by the effective nonlinear susceptibility j ð3Þ j $ 10 À7 esu (electrostatic units). This nonlinearity is shown to be essentially dispersionless over the wavelength range in our experiments (emission at e ' 760-840 nm). These results are in good agreement with predictions derived from nonlinear quantum response theory. The large optical nonlinearity of graphene can be used for exceptionally high-contrast imaging of single and multilayered graphene flakes.Single-and few-layer graphene samples are fabricated using the method of mechanical exfoliation [2] and deposited onto a 100 m thick glass cover slip. Prior to investigation in the nonlinear microscope, the layer thickness is estimated via contrast measurements under an optical microscope, using a method similar to Ref. [9]. To investigate the nonlinear response of graphene flakes, we employ the four-wave mixing technique [10]. This involves the generation of mixed optical frequency harmonics 2! 1 À ! 2 under irradiation by two monochromatic waves with the frequencies ! 1 and ! 2 .Figure 1(a) illustrates the principle of the method: two incident pump laser beams with wavelengths 1 (tunable from 670 nm to 980 nm) and 2 (1130 nm to 1450 nm) are focused collinearly onto a sample and mix together...

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“…(1) cannot be solved directly, and different perturbative methods have been developed that allow the evaluation of p under some approximations. A very flexible and powerful method has been proposed by Yee and Gustafson [1], and successfully applied to transient and stationary four-wave mixing by Ye and Shen [2]. The method, based on diagrammatic technique, provides a general procedure for calculating the perturbative terms at any order of the density operator expansion…”

Section: -Introductionmentioning

confidence: 99%

Diagrammatic representation of the third-order polarization in transient CARS

et al. 1991

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Summary. --A diagrammatic perturbative approach is adopted to derive the expression for the third-order polarization, p(8) which originates the anti-Stokes emission in a time-resolved CARS experiment. The various contributions to P(3) are calculated assuming that laser fields are off-resonance with respect to any electronic level of material system. The resonant part of the polarization consists of two terms, in which the roles of the pump and probe pulses at frequency oJ1 are exchanged. The global expression allows the direct calculation of the signal time profile in a transient CARS experiment once a model is assumed for the laser pulse shape.PACS 42.65.Dr -Stimulated Raman scattering and spectra; CARS. PACS 42.65.Re -Ultrafast optical techniques. PACS 42.50.Md -Optical transient phenomena (including quantum beats, dephasings and revivals, photon echoes, free induction decay, and optical nutation).

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Transient four-wave mixing and coherent transient optical phenomena

Cited by 70 publications

References 16 publications

Theory of doubly resonant infrared-visible sum-frequency and difference-frequency generation from adsorbed molecules

Theory of doubly resonant infrared-visible sum-frequency and difference-frequency generation from adsorbed molecules

Coherent Nonlinear Optical Response of Graphene

Diagrammatic representation of the third-order polarization in transient CARS

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