Microwave Optics

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Aim

In this experiment, we aim to: (a) determine the refractive index n of a polymer slab from its constructive and destructive thin-film microwave interference; and (b) determine the lattice constant a of an array of thin copper rods from its Bragg diffraction of the incident microwave.

Introduction

Thin Film Interference

When plane electromagnetic wave of wavelength λ is incident on a dielectric surface, part of the electromagnetic wave is reflected, and part of it is transmitted. If the dielectric is thin, i.e. its thickness t is comparable to λ, the plane electromagnetic wave will be reflected again at the second dielectric surface, as shown in Figure 1.

[pic]

Figure 1. Electromagnetic waves incident at angle θ1 reflected from the top and bottom surfaces of a thin dielectric film of thickness t, and refractive index n.

After emerging from the top surface of the dielectric, the ray B which propagated through the thin film would incur an optical path difference of

|[pic] |(1) |

compared to ray A. With the help of the law of refraction

|[pic] |(2) |

the path difference between rays A and B can be simplified to

|[pic] |(3) |

Because ray A suffers a 180° phase shift when it reflects off the top dielectric surface, the two rays interference destructively if their path difference is an integer multiple of λ,

|[pic] |(4) |

and destructively if their path difference

References: [Instructions: List any book, webpage, or article that you have referred to while writing up this guided report.]