tailieunhanh - Nonlinear Optics - Chapter 2

Wave-Equation Description of Nonlinear Optical Interactions Các phương trình sóng cho truyền thông quang học phi tuyến Chúng ta đã thấy trong chương cuối cùng như thế nào phi tuyến trong phản ứng của một hệ thống vật chất vào một lĩnh vực laser cường độ cao có thể gây ra sự phân cực của môi trường để phát triển các thành phần tần số mới không có mặt trong lĩnh vực bức xạ nhiệt. Những tần số thành phần mới của hành vi phân cực như là nguồn của các thành phần tần số mới của trường điện từ | Chapter 2 Wave-Equation Description of Nonlinear Optical Interactions . The Wave Equation for Nonlinear Optical Media We have seen in the last chapter how nonlinearity in the response of a material system to an intense laser field can cause the polarization of the medium to develop new frequency components not present in the incident radiation field. These new frequency components of the polarization act as sources of new frequency components of the electromagnetic field. In the present chapter we examine how Maxwell s equations describe the generation of these new components of the field and more generally we see how the various frequency components of the field become coupled by the nonlinear interaction. Before developing the mathematical theory of these effects we shall give a simple physical picture of how these frequency components are generated. For definiteness we consider the case of sum-frequency generation as shown in part a of Fig. where the input fields are at frequencies m1 and m2. Because of nonlinearities in the atomic response each atom develops an oscillating dipole moment which contains a component at frequency m1 m2. An isolated atom would radiate at this frequency in the form of a dipole radiation pattern as shown symbolically in part b of the figure. However any material sample contains an enormous number N of atomic dipoles each oscillating with a phase that is determined by the phases of the incident fields. If the relative phasing of these dipoles is correct the field radiated by each dipole will add constructively in the forward direction leading to radiation in the form of a well-defined beam as illustrated in part c of the figure. The system will act as a phased array of dipoles when a certain condition known as the phase-matching condition see Eq. in the next section is satis- 69 70 2 Wave-Equation Description of Nonlinear Optical Interactions Figure Sum-frequency generation. fied. Under these conditions the .