Presentation is loading. Please wait.

Presentation is loading. Please wait.

Gaussian Beams and the Paraxial Wave Equation.

Published byScott Charles Modified over 7 years ago

Similar presentations

Presentation on theme: "Gaussian Beams and the Paraxial Wave Equation."— Presentation transcript:

1 Gaussian Beams and the Paraxial Wave Equation

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16 Hermite-Gaussian beam modes Taken from J. Strohaber’s dissertation Solutions to the paraxial wave equation in Cartesian coordinates by separation of variables

17 Laguerre-Gaussian beam modes Taken from J. Strohaber’s dissertation Solutions to the paraxial wave equation in polar coordinates by separation of variables

18 Laguerre-Gaussian beam modes Taken from J. Strohaber’s dissertation Solutions to the paraxial wave equation in polar coordinates by separation of variables

19 Laguerre-Gaussian beam modes Taken from J. Strohaber’s dissertation Solutions to the paraxial wave equation in polar coordinates by separation of variables

20 Ince-Gaussian beam modes Taken from J. Strohaber’s dissertation Solutions to the paraxial wave equation in elliptical coordinates by separation of variables

21

22

Download ppt "Gaussian Beams and the Paraxial Wave Equation."

Similar presentations

Chapter 2 Propagation of Laser Beams

Chapter 2 Propagation of Laser Beams
The Hydrogen Atom. Model The “orbitals” we know from general chemistry are wave functions of “hydrogen-like” atoms Hydrogen-like: any atom, but it has.

The Hydrogen Atom. Model The “orbitals” we know from general chemistry are wave functions of “hydrogen-like” atoms Hydrogen-like: any atom, but it has.
Radiation forces on a dielectric sphere in the Rayleigh and Mie scattering regime Yong-Gu Lee Reference: Yasuhiro Harada et al. Radiation forces on a dielectric.

Radiation forces on a dielectric sphere in the Rayleigh and Mie scattering regime Yong-Gu Lee Reference: Yasuhiro Harada et al. Radiation forces on a dielectric.
Lecture 2eee3401 Chapter 2 Coordinate Systems 1)Cartesian (rectangular) 2)Circular cylindrical 3)Spherical 4)Others (elliptic cylindrical, conical,…) A.

Lecture 2eee3401 Chapter 2 Coordinate Systems 1)Cartesian (rectangular) 2)Circular cylindrical 3)Spherical 4)Others (elliptic cylindrical, conical,…) A.
Higher Order Gaussian Beams Jennifer L. Nielsen B.S. In progress – University of Missouri-KC Modern Optics and Optical Materials REU Department of Physics.

Higher Order Gaussian Beams Jennifer L. Nielsen B.S. In progress – University of Missouri-KC Modern Optics and Optical Materials REU Department of Physics.
Polar Coordinates (MAT 170) Sections 6.3

Polar Coordinates (MAT 170) Sections 6.3
1 6.3 Separation of Variables and the Logistic Equation Objective: Solve differential equations that can be solved by separation of variables.

1 6.3 Separation of Variables and the Logistic Equation Objective: Solve differential equations that can be solved by separation of variables.
Continuous String Take limit of h→0 and m/h→ r Wave Equation.

Continuous String Take limit of h→0 and m/h→ r Wave Equation.
1Chapter 2. 2 Example 3Chapter 2 4 EXAMPLE 5Chapter 2.

1Chapter 2. 2 Example 3Chapter 2 4 EXAMPLE 5Chapter 2.
EXAMPLE 4 Graph a linear inequality in one variables Graph the inequality y  –3. SOLUTION Graph the equation y = –3. The inequality is , so use a solid.

EXAMPLE 4 Graph a linear inequality in one variables Graph the inequality y  –3. SOLUTION Graph the equation y = –3. The inequality is , so use a solid.
Polar Coordinates. Common Coordinate Systems There are two common coordinate systems: Cartesian Rectangular Coordinate SystemPolar Coordinate System.

Polar Coordinates. Common Coordinate Systems There are two common coordinate systems: Cartesian Rectangular Coordinate SystemPolar Coordinate System.
§3.3. 2 Separation of spherical variables: zonal harmonics Christopher Crawford PHY 416 2014-10-29.

§ Separation of spherical variables: zonal harmonics Christopher Crawford PHY
3x – 5y = 11 x = 3y + 1 Do Now. Homework Solutions 2)2x – 2y = – 6 y = – 2x 2x – 2(– 2x) = – 6 2x + 4x = – 6 6x = – 6 x = – 1y = – 2x y = – 2(– 1) y =

3x – 5y = 11 x = 3y + 1 Do Now. Homework Solutions 2)2x – 2y = – 6 y = – 2x 2x – 2(– 2x) = – 6 2x + 4x = – 6 6x = – 6 x = – 1y = – 2x y = – 2(– 1) y =
Matrix Solutions to Linear Systems. 1. Write the augmented matrix for each system of linear equations.

Matrix Solutions to Linear Systems. 1. Write the augmented matrix for each system of linear equations.
3.5 – Solving Systems of Equations in Three Variables.

3.5 – Solving Systems of Equations in Three Variables.
Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.1 Graphing and Functions.

Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.1 Graphing and Functions.
The Cartesian Coordinate System and Linear Equations in Two Variables

The Cartesian Coordinate System and Linear Equations in Two Variables
1Lesson 2 Introduction to Optical Electronics Quantum (Photon) Optics (Ch 12) Resonators (Ch 10) Electromagnetic Optics (Ch 5) Wave Optics (Ch 2 & 3) Ray.

1Lesson 2 Introduction to Optical Electronics Quantum (Photon) Optics (Ch 12) Resonators (Ch 10) Electromagnetic Optics (Ch 5) Wave Optics (Ch 2 & 3) Ray.
10.4 Rotation and Systems of Quadratic Equations.

10.4 Rotation and Systems of Quadratic Equations.
Copyright © 2011 Pearson, Inc. 8.4 Translation and Rotation of Axes.

Copyright © 2011 Pearson, Inc. 8.4 Translation and Rotation of Axes.

Similar presentations

Ads by Google