Scalar theory of diffraction

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Presentation transcript:

Scalar theory of diffraction EE 231 Introduction to Optics Scalar theory of diffraction Lesson 7 Andrea Fratalocchi www.primalight.org

The Scalar theory of diffraction General solution to the propagation problem Sum up Decompose Propagate

The Scalar theory of diffraction General solution to the propagation problem Plane wave Spatial frequencies Decompose with inverse Fourier Transform

The Scalar theory of diffraction General solution to the propagation problem Decompose with Fourier Transform Propagate the single plane wave

The Scalar theory of diffraction General solution to the propagation problem Propagate the single plane wave

The Scalar theory of diffraction General solution to the propagation problem Propagate the single plane wave

The Scalar theory of diffraction General solution to the propagation problem Propagate the single plane wave Sum up all the contributions

The Scalar theory of diffraction Sum up Decompose Propagate

The Scalar theory of diffraction Does not explicitly contains the input scalar field How can we express the output field as a function of the input?

The Scalar theory of diffraction Does not explicitly contains the input scalar field How can we express the output field as a function of the input? Fourier transform of

The Scalar theory of diffraction By substituting Into We finally obtain:

The Scalar theory of diffraction We therefore have:

The Scalar theory of diffraction We therefore have: According to the value of the spatial harmonics p and q, we can have 2 different scenario:

The Scalar theory of diffraction According to the value of the spatial harmonics p and q, we can have 2 different scenario: Homogeneous plane wave with real propagation constant kz=2*pi*m

The Scalar theory of diffraction According to the value of the spatial harmonics p and q, we can have 2 different scenario: Evanescent plane wave with imaginary propagation constant kz=2*pi*m

The Scalar theory of diffraction Homework 1: consider the following scalar field Evolve the field up to the distance z Calculate the intensity. When evanescent waves start to appear? What are the physical consequences of this?

The Scalar theory of diffraction Homework 2: According to visual experience, light sources (monochromatic or not), spread their content of energy during propagation more strongly if the region that emits light is more localized in space. Explain this phenomenon with the theory of diffraction

The Scalar theory of diffraction References M. Born and E. Wolf, Principle of Optics, Chapter 8.