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CRC Press eBooks

Phase Response of Nonlinear Medium Induced by Transitions Between Excited Energy Levels

C Arcoumanis, K.T.V Grattan

Published Jul 10, 2014• 0 citations
Publisher

Abstract

The light-induced change in the refractive index (phase response) of nonlinear medium and other nonlinear processes are studied by using two, three, four and five-level schemes [2, 4, 5] . The thermal nonlinearly for all channels (principal and excited) are taken into consideration along with a resonance nonlinearly at a frequency of waves involved in the nonlinear process due to week spectral selectivity of thermal nonlinearity [4, 5, 7] .

DOI
10.1201/b16835-29

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The light-induced change in the refractive index (phase response) of nonlinear medium and other nonlinear processes are studied by using two, three, four and five-level schemes [2, 4, 5] . The thermal nonlinearly for all channels (principal and excited) are taken into consideration along with a resonance nonlinearly at a frequency of waves involved in the nonlinear process due to week spectral selectivity of thermal nonlinearity [4, 5, 7] .
Accurate modeling of optical nonlinearities is crucial to describe macroscopic laser propagation in a medium, including sum frequency generation, spectral broadening due to self-phase modulation, various ionization processes and soliton formation. For incident laser light the response of the medium is given by the induced polarization of the microscopic system. The polarization is usually expanded in a Taylor series for the electric field amplitude, which is truncated after the first non-linear term being of third order for isotropic media. A third-order nonlinearity leads to the well-known optical Kerr effect, where the refractive index of the medium becomes intensity dependent via n = n0+ n2I. This leads to an inherent problem when modeling laser propagation in two or more spatial dimensions, linked to the formal divergence (n2> 0) of the refractive index for increasing intensity.
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].
There is an interest in consideration of the propagation of the Gaussian monochromatic light beams through a cell filled with the medium of two-level atoms (in our case, the atomic potassium vapor), which has (at small detuning from resonant transition to low or high frequencies) the refractive index other than unity (n > 1 for v < v01 and n < 1 for v > v01, where v is the light frequency and v01 is the resonant-transition frequency). In this case, the properties of the radiation passed through the cell are changed. In the very close proximity of the resonance, the nonlinear processes (the three-photon electronic stimulated Raman scattering (SRS) and the six-photon parametric scattering (SPS)) play a crucial role. It is precisely these processes in the two-level medium that determine the irreversibly transformed spectral and angular structure of the light beams at the output of the cell.
The spectral perturbation is considered in a semiconductor active medium in the vicinity of the frequency of a strong electromagnetic wave. The nonlinear interaction of waves via the dynamic interference grating, or nonlinear scattering by population waves leads to the shift of resonance frequencies, which is manifested, in particular, in a change of the mode-beating spectrum of the laser. The spectral profile of this perturbation depends on the amplitude—phase coupling factor α. For large α, the profile becomes symmetrical in detuning from the strong-mode frequency. A change in the group refractive index corresponding to the 'slowing' of light is also calculated.