Plane Wave Optical Field

A good understanding of the reorientation dynamics can be obtained if we separate it into two regimes (1) optical torque elastic torque 

For case (1) we may ignore the elastic term in Equation (8.57) and get an equation for 6 of the form 

From Equation (8.61) we can see that 0(Xp) is appreciable only if is appreciable. In other words, if the laser pulse duration is short (e.g., nanosecond), it has to be very intense in order to induce an appreciable reorientation effect. In this respect and because the surface elastic torque is not involved, the dynamical response of a nematic liquid crystal is quite similar to its isotropic phase counterpart. However, the dependence on the geometric factor sin 2p is a reminder that the nematic phase is, nevertheless, an (ordered) aligned phase, and its overall response is dependent on the direction of incidence and the polarization of the laser. 

The effective optical nonlinearity in the transient case, compared to the steady-state value, can be estimated from Equation (8.61). 

For case (2), which naturally occurs when the laser pulse is over, we have 

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Any field amphtude distribution and associated propagation effects can be described equivalendy by a superposition of plane waves of appropriate amphtude and direction provided that every component plane wave satisfies equation 16. If, for example, an optical field amphtude given by the function... 

How must this theory be modified to describe the effect of the optical excitation The incident electric and magnetic X-ray fields are now pulses Ex(r, t) = Exo(t) exp[j(q r - Oxt)] and Hx(r, t) = Hxo(t) exp[/(q/r - Oxt)]. They still are plane waves with a carrier frequency Ctx, but their amphtudes Exo(t) and Hxo(t) vary with time. The same statement applies to the electron density n r, t), which also is time dependent. However, these variations are all slow with time scales on the order of 1/Ox, and one can neglect 5Exo(0/ 8Hxo(t)/8t as compared to iOxExo(t) and iTlxHxo(0- Detailed calculations then show that [17]... 

Fig. 21 Spiral structiu-e formed by seven beam interference central beam is right-handed circularly polarized, and the side beams linearly [32,33]. Simulated by interference of plane waves according to Eq. 2 with side beams comprising an 80° angle with the optical axis (the -field of the central beam is Eo = o/V2(l, i,0), where + corresponds to the right-handedness i = V )...

Were it not for the particle, of course, A would just be a unit vector parallel to the direction of propagation of the incident plane wave, and the field lines would be parallel lines. At sufficiently large distances from the particle the field lines are nearly parallel, but close to it they are distorted. It is the nature of this distortion in the neighborhood of a small sphere and its relation to the optical properties of the sphere that we now wish to investigate. 

A general form of the electromagnetic field can be obtained from a superposition of various EM, S, and EMS modes. Thereby it should be observed that the EMS modes can have different velocity field vectors C. These wave concepts provide new possibilities in the study of problems in optics and photon physics, both when considering plane waves and axisymetric modes with associated wavepackets. 

The optical absorption is defined as follows133 it is the decay rate, per unit time, of the density of the pure electromagnetic energy of a plane wave inside the matter medium, and it is equal to a>e"(a>) [we assume the field directed along an eigendirection of e(K, a>), so that e" will be considered as a scalar quantity]. Actually, this definition is that of the conductivity hence the name optical conductivity given to coe(a>). Therefore, we may calculate e(K, oj), and hence the optical conductivity, from the relations (1.68) in Section I. 

A Gaussian beam is a modified plane wave whose amplitude decreases, not necessarily monotonically, as one moves radially away from the optical axis. The simplest, or fundamental, Gaussian beam has an exp(—p /w ) radial dependence, where p is the radial distance from the optical axis and w is the 1/e radius of the electromagnetic field. The phase of a Gaussian beam also differs from that of a plane wave due to diffraction effects, as we will show subsequently. 

The paraxial approximation is essentially a Taylor series expansion of an exact solution of the wave equation in powers of p/w, terminated at ( p/tv), that allows us to exploit the rapid decay of a Gaussian beam away from the optical axis. We will develop a more precise criterion in the sequel. We will also show that the phase and amplitude modulation of the underlying plane wave structure of the electromagnetic field is a slowly varying function of distance from the point where the beam is launched. 

In the application to the optical field, the vector potential (or the electric field in the lowest order) corresponding to carrier plane waves of given frequencies at,... 

Figure 4. Two configurations for evanescent wave optics, (a) Top total internal reflection of a plane wave at the base of a glass prism. Bottom the reflectivity R recorded by a detector as a function of the angle of incidence shows the increase to unity at 6, the critical angle for total reflection, (b) ATR setup for the excitation of surface plasmons (PSPs) in Kretschmann geometry. Top a thin metal film (thickness 50 nm) is evaporated onto the base of the prism and acts as resonator driven by the photon field. Bottom the resonant excitation of the PSP wave is seen in the reflectivity curve as a sharp dip at coupling angle 6g.

X and x are the second and third-order nonlinear optical susceptibilities. Two important manifestations of optical nonlinearities are harmonic generation and refractive fndex modulation by electric and optical fields. Their origin can conveniently be explained by considering a plane wave propagation through the nonlinear medium. The polarization is then given by... 

Fig. la. Schematic showing the optical field (magnetic component) at an interface which supports surface plasmons. The dielectric function in the dielectric medium is the diectric function in the metal can be approximated hy the Drude-Lorentz expression given in the upper right hand corner. Notice that the field extends much farther into the dielectric than the metal, b. The reflectivity in an ATR configuration. The 0 is the critical angle and 0gp is the angle at which the surface plasmon is excited. Reflectivity extends from zero to one. Notice that the reflectivity from s waves, i.e., those waves with their electric vector perpendicular to the plane of incidence do not excite a surface mode.. 

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