Diffraction in Optics with Andrea Fratalocchi
Delve into the world of diffraction in optics as explained by Andrea Fratalocchi. Explore the concepts, examples, and the study methods of diffraction using Maxwell Equations and numerical computations. Gain insights into how diffraction differs from refraction and the complexities involved in analyzing light-matter interactions.
Uploaded on | 0 Views
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
EE 231 Introduction to Optics Scalar theory of diffraction Lesson 2 Andrea Fratalocchi www.primalight.org 3/19/2025 1 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 1
What is diffraction? 3/19/2025 2 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 2
What is diffraction? Slit experiment Light focusing through a lens 3/19/2025 3 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 3
What is diffraction? Sommerfeld definition of diffraction: Diffraction encompasses optical phenomena that cannot be interpreted by the propagation of rays following the laws of reflection and refraction in homogenous/in-homogenous media. Slit experiment Light focusing through a lens 3/19/2025 4 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 4
Question: are these examples of diffraction? 3/19/2025 5 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 5
Question: are these examples of diffraction? No All these are effects of refraction of light rays. Our brain can only interpret light rays propagating along straight lines and creates false images when light is bent around curved trajectories 3/19/2025 6 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 6
How to study diffraction? By using Maxwell Equations, which are the fundamental set of equations to study all forms of light-matter interactions The solution of the vectorial set of Maxwell equation is a quite challenging task in general, and in many cases cannot be done analytically. Numerical computations can be carried out, but: Require large simulation times and/or supercomputers Give only numbers, making physical interpretations not simple Depend on many degrees of freedoms, which makes it difficult to isolate governing physical quantities 3/19/2025 7 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 7
How to study diffraction? Powerful tools to address this problem are approximate theories, whose equations are easily solved even in the case of complex geometries. One of the most important approaches the scalar theory of diffraction. The advantages of this method are: Simple and easy to use Gives analytic functions, which make it easy to understand the physics of diffraction phenomena Gives very good approximate results, which are in very good agreement with numerical computations 3/19/2025 8 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 8
The Scalar theory of diffraction The scalar theory of diffraction is based on some assumptions, which have to be clearly known in order to use this approach consistently and get reliable results From Maxwell equations: Wave equation 2 3/19/2025 9 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 9
The Scalar theory of diffraction The same equation is obtained for the magnetic field in a uniform medium: If the electric field is linearly polarized and does not change polarization during the dynamics, we can model the evolution of the electromagnetic wave from a single scalar quantity U, following a scalar wave equation: 1st assumption The field U(x,y,z;t) is often called disturbance field, or scalar field. The scalar field can equally represent the electric of magnetic field, as they both follow the same wave equation. 3/19/2025 10 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 10
The Scalar theory of diffraction In our study we will consider monochromatic waves: 2nd assumption After substitution in the scalar wave equation, we obtain: Helmholtz equation This is the fundamental equation that describes scalar diffraction problems of light matter interactions. 3/19/2025 11 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 11
The Scalar theory of diffraction What is the intensity I(x,y,z) observable for the scalar field U? 3/19/2025 12 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 12
The Scalar theory of diffraction What is the intensity I(x,y,z) observable for the scalar field U? In the scalar theory, the scalar field U can represents equally the electric or the magnetic field, and therefore all proportionality constants become unimportant. As we saw in the previous lesson, the intensity of an electromagnetic wave is proportional to the absolute square of the electric or magnetic field. In the scalar theory the intensity I(x,y,z) is therefore calculated as follows: 3/19/2025 13 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 13
The Scalar theory of diffraction The general diffraction problem: Propagation problem Propagation problem Observation screen Input field Diffracting element The problem is decomposed into 2 problems 3/19/2025 14 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 14
The Scalar theory of diffraction 1. Propagation problem: Given the spatial distribution of a scalar field V at a specific plane (x,y), propagate it to a specific z Propagation problem Input field Diffracting element This problem can be completely solved for arbitrary fields V 3/19/2025 15 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 15
The Scalar theory of diffraction 1. Propagation problem: Given the spatial distribution of a scalar field impinging on a diffractive object at z=0, calculate the emerging field at z=0 This problem is very hard and general solutions do not exist, however, approximate methods are available 3/19/2025 16 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 16
The Scalar theory of diffraction Homework 2.1 Propagation problem: interference of plane waves At z=0, we have the following scalar field Propagate the field at a generic z and calculate the correspondent Intensity (Hint: use the plane wave solution derived in the previous lesson) 3/19/2025 17 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 17
The Scalar theory of diffraction Homework 2.2 Is this diffraction? Motivate your answer 3/19/2025 18 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 18
The Scalar theory of diffraction References 1) M. Born and E. Wolf, Principle of Optics, 6th Edition, Chapter 1.1-1.3. 3/19/2025 19 Andrea Fratalocchi (www.primalight.org) EE231 Introduction to Optics: Diffraction slide 19
