![]() ![]() There are some optical elements which can not be described with ABCD matrices, and which convert a Gaussian beam into a non-Gaussian beam an example are axicons. Note that with physicists' sign convention, all matrix components need to be turned into their complex conjugates however, in many cases of interest, the matrix components are purely real. In textbooks, ABCD matrices for many kinds of optical elements are available. Where, , and are the components of the ABCD matrix. When a Gaussian beam passes an optical element such as a curved mirror or a lens, this can be described by transforming its parameters with an ABCD matrix according to Propagation over some distance then simply increases the parameter by that distance. Effectively, is turned into its complex conjugate.) (With electrical engineer's sign convention, the sign of the term with in the definition of would be opposite. The transverse profile of the optical intensity of the beam with an optical power can be described with a Gaussian function: The name “Gaussian beams” results from the use of the Gaussian amplitude and intensity profile functions it is not a concept in Gaussian optics. The definition of Gaussian beams concerns both the intensity and phase profile, as explained in the following: Intensity Profile The same type of analysis with Equation 16.25 and Equation 16.24 would also show that the speed of an electromagnetic wave is c 1/ 00 c 1 / 0 0. In optics and particularly in laser physics, laser beams often occur in the form of Gaussian beams, which are named after the mathematician and physicist Johann Carl Friedrich Gauß. We could just as easily have assumed an electromagnetic wave with field components Ez (x, t) E z ( x, t) and By (x, t) B y ( x, t). Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. The wave energy is determined by the wave amplitude. In electromagnetic waves, the amplitude is the maximum field strength of the electric and magnetic fields ( Figure 16.10). The charge alters that space, causing any other charged object that enters the space to be affected by this field. All charged objects create an electric field that extends outward into the space that surrounds it. If some energy is later absorbed, the field strengths are diminished and anything left travels on.Ĭlearly, the larger the strength of the electric and magnetic fields, the more work they can do and the greater the energy the electromagnetic wave carries. The electric field concept arose in an effort to explain action-at-a-distance forces. Once created, the fields carry energy away from a source. However, there is energy in an electromagnetic wave itself, whether it is absorbed or not. These fields can exert forces and move charges in the system and, thus, do work on them. Other times, it is subtle, such as the unfelt energy of gamma rays, which can destroy living cells.Įlectromagnetic waves bring energy into a system by virtue of their electric and magnetic fields. Sometimes this energy is obvious, such as in the warmth of the summer Sun. Explain how the energy of an electromagnetic wave depends on its amplitude, whereas the energy of a photon is proportional to its frequencyĪnyone who has used a microwave oven knows there is energy in electromagnetic waves.Calculate the Poynting vector and the energy intensity of electromagnetic waves.Express the time-averaged energy density of electromagnetic waves in terms of their electric and magnetic field amplitudes.By the end of this section, you will be able to: ![]()
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