EE 231 Introduction to Optics Scalar theory of

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

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

$The Scalar theory of diffraction General solution to the propagation problem Plane wave Spatial$

$The Scalar theory of diffraction General solution to the propagation problem Decompose with Fourier$

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

$The Scalar theory of diffraction Sum up Decompose Propagate 9/29/2020 Andrea Fratalocchi (www. primalight.$

$The Scalar theory of diffraction Does not explicitly contains the input scalar field q$

$The Scalar theory of diffraction By substituting Into We finally obtain: 9/29/2020 Andrea Fratalocchi$

$The Scalar theory of diffraction We therefore have: 9/29/2020 Andrea Fratalocchi (www. primalight. org)$

$The Scalar theory of diffraction We therefore have: According to the value of the$

$The Scalar theory of diffraction According to the value of the spatial harmonics p$

$The Scalar theory of diffraction q Homework 1: consider the following scalar field 1)$

$The Scalar theory of diffraction q Homework 2: According to visual experience, light sources$

$The Scalar theory of diffraction Ø References 1) M. Born and E. Wolf, Principle$

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

EE 231 Introduction to Optics Scalar theory of diffraction Lesson 7 Andrea Fratalocchi www. primalight. org 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 1 1

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

The Scalar theory of diffraction General solution to the propagation problem Sum up Decompose 9/29/2020 Andrea Fratalocchi (www. primalight. org) Propagate EE 231 Introduction to Optics: Bessel beams slide 2 2

$The Scalar theory of diffraction General solution to the propagation problem Plane wave Spatial$

The Scalar theory of diffraction General solution to the propagation problem Plane wave Spatial frequencies Decompose with inverse Fourier Transform 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 3 3

$The Scalar theory of diffraction General solution to the propagation problem Decompose with Fourier$

The Scalar theory of diffraction General solution to the propagation problem Decompose with Fourier Transform Propagate the single plane wave 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 4 4

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

The Scalar theory of diffraction General solution to the propagation problem Propagate the single plane wave 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 5 5

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

The Scalar theory of diffraction General solution to the propagation problem Propagate the single plane wave Sum up all the contributions 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 7 7

$The Scalar theory of diffraction Sum up Decompose Propagate 9/29/2020 Andrea Fratalocchi (www. primalight.$

The Scalar theory of diffraction Sum up Decompose Propagate 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 8 8

$The Scalar theory of diffraction Does not explicitly contains the input scalar field q$

The Scalar theory of diffraction Does not explicitly contains the input scalar field q How can we express the output field as a function of the input? 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 9 9

$The Scalar theory of diffraction Does not explicitly contains the input scalar field q$

The Scalar theory of diffraction Does not explicitly contains the input scalar field q How can we express the output field as a function of the input? Fourier transform of 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 10 10

$The Scalar theory of diffraction By substituting Into We finally obtain: 9/29/2020 Andrea Fratalocchi$

The Scalar theory of diffraction By substituting Into We finally obtain: 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 11 11

$The Scalar theory of diffraction We therefore have: 9/29/2020 Andrea Fratalocchi (www. primalight. org)$

The Scalar theory of diffraction We therefore have: 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 12 12

$The Scalar theory of diffraction We therefore have: According to the value of the$

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: 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 13 13

$The Scalar theory of diffraction According to the value of the spatial harmonics p$

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 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 14 14

$The Scalar theory of diffraction According to the value of the spatial harmonics p$

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 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 15 15

$The Scalar theory of diffraction q Homework 1: consider the following scalar field 1)$

The Scalar theory of diffraction q Homework 1: consider the following scalar field 1) Evolve the field up to the distance z 2) Calculate the intensity. When evanescent waves start to appear? What are the physical consequences of this? 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 16 16

$The Scalar theory of diffraction q Homework 2: According to visual experience, light sources$

The Scalar theory of diffraction q 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 theory of diffraction 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 17 17

$The Scalar theory of diffraction Ø References 1) M. Born and E. Wolf, Principle$

The Scalar theory of diffraction Ø References 1) M. Born and E. Wolf, Principle of Optics, Chapter 8. 9/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231 Introduction to Optics: Bessel beams slide 18 18