Intensity-dependent refractive index

Especially at high excitation densities, the refractive index of the material depends on the intensity of the light. Materials with large nonlinear refraction may potentially be used in applications such as optical switching, amplification, and limiting. As we have already described the interaction of an optical beam with the nonlinear optical medium in terms of the nonlinear polarization, we can express the polarization that influences the propagation of the optical beam of frequency (o as 

Notice that the second-order nonlinear term does not appear in Equation 3.150 as the second-order nonlinearity cannot result in an optical beam of frequency co as 

Noting that the linear refractive index is no = (1 + and C Wo Equation 

The nonlinear refractive index is expressed in terms of either the field (U2) or the intensity (H2) coefficient forms of the second-order nonlinear refractive index as [180] 

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The existence of the nonlinear polarization field does not ensure the generation of significant signal fields. With the exception of phenomena based on an intensity-dependent refractive index, the generation of the nonlinearly produced signal waves at frequency cos can be treated in the slowly varying amplitude approximation with well-known guided wave coupled mode theory (1). As already explicitly assumed in Equation 1, the amplitudes of the waves are allowed to vary slowly with... 

This approach is based on the introduction of molecular effective polarizabilities, i.e. molecular properties which have been modified by the combination of the two different environment effects represented in terms of cavity and reaction fields. In terms of these properties the outcome of quantum mechanical calculations can be directly compared with the outcome of the experimental measurements of the various NLO processes. The explicit expressions reported here refer to the first-order refractometric measurements and to the third-order EFISH processes, but the PCM methodology maps all the other NLO processes such as the electro-optical Kerr effect (OKE), intensity-dependent refractive index (IDRI), and others. More recently, the approach has been extended to the case of linear birefringences such as the Cotton-Mouton [21] and the Kerr effects [22] (see also the contribution to this book specifically devoted to birefringences). 

The spectral width of a pulse train emitted by a femtosecond laser can be significantly broadened in a single mode fiber [27]. This process that maintains the mode structure is described in the time domain by the optical Kerr effect or selfphase modulation. The first discussion is simplified by assuming an unchanging pulse-shape under propagation. After propagating the length l the intensity dependent refractive index n(t) = n0 + ri2/(f) leads to a self induced phase shift... 

The second and third terms of the right hand side of Eq. (25) constitute the second- and third-order nonlinear contributions to the total polarization. These corrections to the polarization are responsible for numerous nonlinear optical processes such as the generation of light beams with new frequencies or an intensity dependent refractive index. 

There is a host of other intriguing phenomena associated with the structure and dynamics of stars, which we only list here. The inhomogeneous monomer density distribution in Fig. 2 is responsible for temperature and/or solvency variation in analogy to polymer brushes attached on a flat solid surface [198]. In fact, multiarm star solutions display a reversible thermoresponsive vitrification (see also Sect. 5) which, in contrast to polymer solutions, occurs upon heating rather than on cooling [199]. Another effect is the organization of multiarm stars in filaments induced by weak laser light due to action of electrostrictive forces [200]. This effect was recently attributed [201] to local concentration fluctuations which provide localized-intensity dependent refractive index variations. Hence, the structure factor speciflc to the particular material plays a crucial role in the pattern formation. 

An extremely useful feature of the third-order nonlinear optical response is the intensity-dependent refractive index, where the refractive index of the medium changes due to the interaction with a light beam. This optically-induced change in the refractive index is essential for all-optical switching applications. 

In order to successfully substitute the role of the electron by the photon in photonic applications, it is necessary to achieve high processing speeds. For applications of the intensity-dependent refractive index, one could define the following figure of merit that evaluates the optical switching performance of a third-order nonlinear optical material [24] ... 

The photorefractive effect is a physical mechanism where the change in the intensity-dependent refractive index is dependent on the spatial variations of intensity. It is a non-local process, because unlike most processes, the change in the refractive index is not dependent on the magnitude of the intensity that produces such change. 

The Optical Kerr Gate (OKG) method allows measurement of x by studying the polarization change of a probe beam, propagating through the system where the optical birefringence is induced through an intensity-dependent refractive index. The method was described by Ho [69]. 

When there is a spatial variation of the laser intensity, tlie beam shape might change as it travels through a nonlinear material. Tills effect, which relates to the intensity-dependent refractive index, allows measurement of by two simple methods Power Limiting and Z-scan. 

The first method, Power Limiting, was proposed by Soileau et al, [70] and it is based on the idea of studying the intensity of the transmitted beam through a sample. It assumes a positive intensity-dependent refractive index. 

With the Fabry-Perot etalon method, x is obtained by measuring the intensity-dependent phase shift that results from the intensity-dependent refractive index. 

The measurement of third-order nonlinear response, characterized by is simplified because no geometrical condition in the material is required. The intensity-dependent refractive index, a unique feature of the third-order nonlinear response, allows to characterize by smdying the change in the refractive index of the nonlinear material. This effect is exploited in numerous technical applications, and results in different experimental techniques that determine x - However, the absence of a geometrical condition in the material results in an extra complication when measurements are performed, since all materials (cell walls, glass, air,...) contribute to ... 

Y(-co to, to, -to) Intensity Dependent Refractive Index IDRI Degenerate Four Wave Mixing (DFWM)... 

During the last decade, solid-state lasers captured the market and substituted the complex dye systems more and more (Fig. 1). The breakthrough for solid-state femtosecond oscillators was connected with the development of the Kerr lens mode-locking technique for the Tiisapphire laser [7]. The simple Tiisapphire cavity contains the active medium (Tiisapphire rod) and dispersive elements. Kerr lensing in a Tiisapphire rod develops due to an intensity-dependent refractive index across the spatial beam profile yielding a self-focusing of the laser beam. With an additional aperture in the beam... 

Composite materials formed by nanometer-sized metal particles embedded in dielectrics have a growing interest o wing to the large values of fast optical Ken-susceptibility, whose real part is related to the intensity-dependent refractive index 2 [ ] Ion implantation has been shown to produce a high density of metal nanoparticles (MN) in glasses [2], The high-precipitate volume fraction and small size of MN leads to giant value of the [3]. This stimulates an interest in the use of ion implantation to fabricate nonlinear optical materials. 

The tensors and 7 constitute the molecular origin of the second-and third-order nonlinear optical phenomena such as electro-optic Pock-els effect (EOPE), optical rectification (OR), third harmonic generation (THG), electric field induced second harmonic generation (EFI-SHG), intensity dependent refractive index (IDRI), optical Kerr effect (OKE), electric field induced optical rectification (EFI-OR). To save space we do not indicate the full expressions for and 7 related to the different second and third order processes but we introduce the notations —(Ajy,ui,cj2) and 7(—a , o i,W2,W3), where the frequency relations to be used for the various non-linear optical processes which can be obtained in the case of both static and oscillating monochromatic fields are reported in Table 1.7. 

P( P(-o> w,0) P(0 -fa>,w) Y( - Y(-2(i) (i>,tD,0) Y(-o) (i>,0,0) Second harmonic generation (SHG) Electrooptic Pockels effect Optical rectification Third harmonic generation DC electric-field-induced SHG Intensity-dependent refractive index Optical Kerr effect Coherent anti-Stokes Raman pSHG pEOPE pOR. yTHG. EFISH oj DC-SHG. JlDRI or. yOKE. yCARS... 

Optical bistability is a third-order effect that occurs when a material with an intensity-dependent refractive index can yield two possible states for a single input intensity. This corresponds to the optical equivalent of the transistor. Although much attention has been given to all-optical computing, it is questionable whether such a devise can economically compete with ever cost-decreasing, performance-increasing modern electronic computers, at least in the... 

Intensity dependent refractive index changes Nematic Phase ... 

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