tailieunhanh - Electromagnetic Waves and Antennas combined - Chapter 3

Pulse Propagation in Dispersive Media Các hình thức nhân giống của Eq. () cho phép chúng ta nghĩ về lĩnh vực tuyên truyền như đầu ra của một hệ thống tuyến tính, tuyên truyền, các bộ lọc có đáp ứng tần số H (z, ω) = e-jk (ω) z () Thật vậy, đối với một hệ thống tuyến tính bất biến với thời gian đáp ứng xung h (t) và đáp ứng tần số tương ứng với H (ω), mối quan hệ đầu vào / đầu ra có thể được thể hiện multiplicatively trong lĩnh vực tần số hoặc convolutionally trong lĩnh vực. | Pulse Propagation in Dispersive Media In this chapter we examine some aspects of pulse propagation in dispersive media and the role played by various wave velocity definitions such as phase group and front velocities. We discuss group velocity dispersion pulse spreading chirping and dispersion compensation and look at some slow fast and negative group velocity examples. We also present a short introduction to chirp radar and pulse compression elaborating on the similarities to dispersion compensation. The similarities to Fresnel diffraction and Fourier optics are discussed in Sec. . The chapter ends with a guide to the literature in these diverse topics. Propagation Filter As we saw in the previous chapter a monochromatic plane wave moving forward along the z-direction has an electric field E z E O e ikz where E z stands for either the X or the y component. We assume a homogeneous isotropic non-magnetic medium jU Po with an effective permittivity therefore k is the frequency-dependent and possibly complex-valued wavenumber defined by k co coVe co Po- To emphasize the dependence on the frequency co we rewrite the propagated held as Ê z co e jkzÊ O co Its complete space-time dependence will be eJíotÊ z co eJ mt-kz Ê 0 co A wave packet or pulse can be made up by adding different frequency components that is by the inverse Fourier transform E z t -M eJI mt-kz lÊ 0 w dw 2tt J-00 where the hat denotes Fourier transformation. . Propagation Filter 83 Setting z 0 we recognize 0 co to be the Fourier transform of the initial waveform 0 t that is 1 r 0 ejmrÊ 0 w dw TT J 0 co e JiotE 0 t dt The multiplicative form of Eq. allows US to think of the propagated held as the output of a linear system the propagation filter whose frequency response is Indeed for a linear time-invariant system with impulse response 1 f and corresponding frequency response Ef co the input output relationship can be expressed multiplicatively in the .