Optical electric field

When light is incident on a material, the optical electric field E results in a polarization P of the material. The polarization can be expressed as the sum of the linear polarization and a nonlinear polarization P ... 

This chapter provides an overview of the basic principles and designs of such sensors. A chemical sensor to detect trace explosives and a broadband fiber optic electric-field sensor are presented as practical examples. The polymers used for the trace explosive sensor are unpoled and have chromophores randomly orientated in the polymer hosts. The electric field sensor uses a poled polymer with chromophores preferentially aligned through electrical poling, and the microring resonator is directly coupled to the core of optical fiber. 

Light-matter interactions can be described via an induced polarization, i.e., the induced dipole moment per unit volume. Ultrafast laser pulses, which are used in laser scanning microscopes, have high enough intensity to induce a nonlinear polarization in various materials. For intense optical electric field E, the polarization vector P can be expanded in the power series (Boyd 1992)... 

Since externally applied optical electric fields are typically small in comparison with characteristic interatomic or crystalline fields, even when focused laser light is used, the nonlinear-... 

Fig. 6.2. A general multilayer structure with m layers between a semi-finite transparent ambient and a semi-infinite substrate. Each layer j (j = 1,2,..., m) has thickness dj and its optical properties are described by its complex index of refraction. The optical electric field at any point in layer j is n represented by two components one propagating in the positive x direction and one propagating in the negative x direction...

The generation of photoexcited species at a particular position in the film structure has been shown in (6.19) and (6.20) to be proportional to the product of the modulus squared of the electric field, the refractive index, and the absorption coefficient. The optical electric field is strongly influenced by the mirror electrode. In order to illustrate the difference between single (ITO/polymer/Al) and bilayer (ITO/polymer/Ceo/Al) devices, hypothetical distributions of the optical field inside the device are indicated by the gray dashed line in Fig. 6.1. Simulation of a bilayer diode (Fig. 6.1b) clearly demonstrates that geometries may now be chosen to optimize the device, by moving the dissociation region from the node at the metal contact to the heterojunction. Since the exciton dissociation in bilayer devices occurs near the interface of the photoactive materials with distinct electroaffinity values, the boundary condition imposed by the mirror electrode can be used to maximize the optical electric field E 2 at this interface [17]. 

Fig. 6.4. Calculated value of the square of the normalized optical electric field E 2 at the Ceo/PEOPT interface for PEOPT thicknesses of 30 nm (solid line) and 40 nm (dashed line) versus thickness of the C60 layer at a wavelength of 460 nm. The inset shows the calculated distribution of the square of the normalized optical electric field E 2 inside an ITO (120 nm)/PEDOT-PSS (110 nm)/PEOPT (30 nm)/C6o (34 nm) device at the same wavelength...

It is now possible to reach intensities of 10 ° W/cm at the focus of a laser beam, producing an optical electric field of 2x 10 V/cm [1]. This field is almost a factor of one hundred times larger than the atomic unit of field, 5.14 X 10 V/cm, the field experienced by the electron in the ground state of hydrogen. Furthermore, it is far larger than the field required, classically, to ionize the hydrogen atom, E = 1/16 a.u., 3.2 x 10 V/cm, which corresponds to an intensity of 2.5 x 10 W/cm. ... 

A classical treatment of Raman scattering (3,4) is based on the effects of molecular vibrations on the polarizability, a, in Eq. (2.1). Consider the incident optical electric field to be governed by Eq. (2.2) ... 

Figure 2.1. Polarization (P) induced in a molecule s electron cloud by an incident optical electric field E. Scattering may be in various directions, but 90° and 180° are shown.

A detailed theoretical treatment based on both electrostatic and electrodynamic effects of an optical electric field on a metal particle is beyond the scope of this chapter, but such approaches have been discussed extensively (1,5-7). Several of the main theoretical points are of value to analytical applications and will be summarized here. 

In equations (5)-(8), i is the molecule s moment of Inertia, v the flow velocity, K is the appropriate elastic constant, e the dielectric anisotropy, 8 is the angle between the optical field and the nematic liquid crystal director axis y the viscosity coefficient, the tensorial order parameter (for isotropic phase), the optical electric field, T the nematic-isotropic phase transition temperature, S the order parameter (for liquid-crystal phase), the thermal conductivity, a the absorption constant, pj the density, C the specific heat, B the bulk modulus, v, the velocity of sound, y the electrostrictive coefficient. Table 1 summarizes these optical nonlinearities, their magnitudes and typical relaxation time constants. Also included in Table 1 is the extraordinary large optical nonlinearity we recently observed in excited dye-molecules doped liquid... 

A mechanism involving spatial variation of the permittivity, e, has been suggested by Baldus and Zilker (2001). This model assumes that a spatial modulation of the refractive index, hence permittivity, is induced in the film. This is certainly reasonable, given the well-known photoorientation and birefringence gratings in azo systems. A force is then exerted between the optical electric field and the gradient in permittivity. Specifically, the force is proportional to the intensity of the electric field in the mass transport direction and to the gradient of the permittivity ... 

Respond to light by generating eleetrons and positively eharged vacaneies. Nonlinear optics effects are generally deseribed by a polarization equation for the optieal response (P) of a material to an optical electric field (Ef ... 

Fig. 1 is a stylized depiction of a near-field probe tip and the optical electric field merging from the aperture. A probe is fabricated by first heating and pulling a length... 

Mathematically, integral Kramers-Kronig relations have very general character. They represent the Hilbert transform of any complex function s(co) = s (co) + s"(co) satisfying the condition s (co) = s(—co)(here the star means complex conjugate). In our particular example, this condition is applied to function n(co) related to dielectric permittivity s(co). The latter is Fourier transform of the time dependent dielectric function s(f), which takes into account a time lag (and never advance) in the response of a substance to the external, e.g. optical, electric field. Therefore the Kramers-Kronig relations follow directly from the causality principle. 

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