In Chapter 1, we introduced some of the concepts of geometrical optics.
However, geometrical optics cannot account for wave effects such as
diffraction. In this Chapter, we introduce wave optics by starting from
Maxwell's equations and deriving the wave equation. We thereafter
discuss solutions of the wave equation and review power flow and
polarization. We then discuss boundary conditions for electromagnetic
fields and subsequently derive Fresnel's equations. We also discuss
Fourier transform and convolution and then develope diffraction theory
through the use of the Fresnel diffraction formula, which is derived in a
unique manner using Fourier transforms. In the process, we define the
spatial frequency transfer function and the spatial impulse response in
Fourier optics. We also describe the distinguishing features of Fresnel
and Fraunhofer diffraction and provide several illustrative examples. In
the context of diffraction, we also develope wavefront transformation by
a lens and show the Fourier transforming properties of the lens. We also
analyze resonators and the diffraction of a Gaussian beam. Finally, in the
last Section of this chapter, we discuss Gaussian beam optics and
introduce the ^-transformation of Gaussian beams. In all cases, we
restrict ourselves to wave propagation in a medium with a constant
refractive index (homogeneous medium). Beam propagation in
inhomogeneous media is covered in Chapter 4.
\
However, geometrical optics cannot account for wave effects such as
diffraction. In this Chapter, we introduce wave optics by starting from
Maxwell's equations and deriving the wave equation. We thereafter
discuss solutions of the wave equation and review power flow and
polarization. We then discuss boundary conditions for electromagnetic
fields and subsequently derive Fresnel's equations. We also discuss
Fourier transform and convolution and then develope diffraction theory
through the use of the Fresnel diffraction formula, which is derived in a
unique manner using Fourier transforms. In the process, we define the
spatial frequency transfer function and the spatial impulse response in
Fourier optics. We also describe the distinguishing features of Fresnel
and Fraunhofer diffraction and provide several illustrative examples. In
the context of diffraction, we also develope wavefront transformation by
a lens and show the Fourier transforming properties of the lens. We also
analyze resonators and the diffraction of a Gaussian beam. Finally, in the
last Section of this chapter, we discuss Gaussian beam optics and
introduce the ^-transformation of Gaussian beams. In all cases, we
restrict ourselves to wave propagation in a medium with a constant
refractive index (homogeneous medium). Beam propagation in
inhomogeneous media is covered in Chapter 4.
\
EmoticonEmoticon