tailieunhanh - Nonlinear Optics - Chapter 6

Nonlinear Optics in the Two-Level Approximation Chúng tôi xử lý quang học phi tuyến trong các chương trước đó đã cho hầu hết các phần đã sử dụng mở rộng dòng điện liên quan đến phản ứng của một hệ thống vật chất để sức mạnh của lĩnh vực quang học được áp dụng. | Chapter 6 Nonlinear Optics in the Two-Level Approximation . Introduction Our treatment of nonlinear optics in the previous chapters has for the most part made use of power series expansions to relate the response of a material system to the strength of the applied optical field. In simple cases this relation can be taken to be of the form P t Ẽ0X 1 Ẽ t Ễ0X 2 È t 2 Ễ0X 3 Ẽ t 3 . However there are circumstances under which such a power series expansion does not converge and under such circumstances different methods must be employed to describe nonlinear optical effects. One example is that of a saturable absorber where the absorption coefficient a is related to the intensity I 2ne0c E 2 of the applied optical field by the relation a0 a . T 1 I Is where a0 is the weak-field absorption coefficient and Is is an optical constant called the saturation intensity. We can expand this equation in a power series to obtain a a0 1 I Is I Is I Is . However this series converges only for I Is and thus only in this limit can saturable absorption be described by means of a power series of the sort given by Eq. . It is primarily under conditions such that a transition of the material system is resonantly excited that perturbation techniques fail to provide an adequate 277 278 6 Nonlinear Optics in the Two-Level Approximation description of the response of the system to an applied optical field. However under such conditions it is usually adequate to deal only with the two atomic levels that are resonantly connected by the optical field. The increased complexity entailed in describing the atomic system in a nonperturbative manner is thus compensated in part by the ability to make the two-level approximation. When only two levels are included in the theoretical analysis there is no need to perform the sums over all atomic states that appear in the general quantum-mechanical expressions for x 3 given in Chapter 3. In the present chapter we shall for the most