# Questions tagged [plane-wave]

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### How to derive the Electric field from the magnetic field?

Given a linearly polarized, monochromatic plane wave with $H = H_0y^{cos(kz − ωt)}$ traveling in the $+\hat{z}$ direction that is incident on a dielectric sphere with permittivity $e$ and radius $a$, ...
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### For unpolarized plane wave traveling normal incident from air to dielectric what are the reflection and transmission coefficients?

Given an unpolarized plane wave traveling in air and hitting a dielectric at normal incident what equations can be used to calculate the reflection and transmission coefficient? I know for a polarized ...
201 views

### Why don't plane waves always expand according to Huygens' principle?

I have seen a few videos about Huygens' principle and I don't understand why a plane wavefront doesn't expand both vertically and horisontally. According to my understanding of Huygens' principle, ...
31 views

### Magnitude of an Electric field as superposition of plane waves

I need to show the magnitude $u(x,y,z)$ of an arbitrary electric field can be written as a superposition of infinite number of plane waves travelling along different directions. Can someone provide ...
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### Diffraction of a plane wave

Let's consider a plane wave hitting a surface with an aperture of width e in the following fashion: The amplitude of the plane wave is given by: $a({\bf r})=a_0\exp(i{\mathbf k}\cdot{\mathbf r})$ ...
1 vote
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### Single gravitational plane wave or their interference can carry spin angular momentum?

I would be grateful if anybody could tell me if I had one gravitational wave in the form of a plane wave, it still would carry spin angular momentum? We know that gravitational waves are mostly the ...
1 vote
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### Why do most of the book represent Plane waves by considering a single sine or cosine wave? There should be many, right? Isn't it misrepresentation?

This Image is from Electrodynamics by Griffiths. Here also a monochromatic electromagnetic wave is considered.
1 vote
44 views

### confused by explanation of electromagnetic wave in physics textbook

I'm kind of confused by the proof used in my physics textbook to explain an electromagnetic field using Faraday's law. The text book uses Faraday's law to try to explain why a uniform electric field ...
14 views

### Non-physical plane wave states in infinite domain

My question regards Appendix A in Rubin H. Landau's A Second Course in Quantum Theory. I do not see what he means when he says $\Delta i\equiv 1$ (below). In fact, I think the infinite domain is ...
1 vote
58 views

### Do we need Killing vectors to have wave vectors in a plane wave solution?

It is well known, and there are other questions in this website that answer this, that one needs a stationary Killing vector field to judge if a plane wave has positive or negative frequency. If our ...
1 vote
33 views

### Recovering planar wave from Huygens principle

I am trying to get a basic understanding of the Huygens principle, by checking whether a planar wave is the same as what is calculated from the principle when the wave reaches a screen. ...
1 vote
37 views

### What is Raleigh expansion?

I am currently reading the paper The dielectric lamellar diffraction grating, in which the electric field above and bellow a 1D grating (grooves) is expressed as a "series of outward-going plane ...
52 views

### Confusion in the plane wave solution for the EM wave equation

When talking about the solution of the Wave Equation for the Electric Field: \begin{equation} \ddot{E}=c^2\nabla^2E \end{equation} One usually assumes a sinusoidal waveform and writes: \begin{equation}...
1 vote
85 views

### Complex form for the Plane wave

It's a very well-known fact that plane waves can be represented in the complex form: \begin{equation} \mathbf{F}(\mathbf{x},t)=\mathbf{F}_0e^{i(kx-\omega t)} \end{equation} However, I've been ...
67 views

### How to show momentum operator are plane waves using translation operator

Using the momentum operator $\hat{p}\rightarrow-i\hbar\frac{d}{dx}$ and the translation operator $e^{-i\hat{p}a/\hbar}\psi(x)=\psi(x-a)$, how to I go about showing that the eigenfunctions of the ...
77 views

### Jefimenko's equations contradiction between free space solutions

In Jefimenko's equations, which are a solution to Maxwells equations. Each term has either $\rho$ or $J$ in it. Setting $\rho$ and J to be zero, Should reduce to the electromagnetic plane wave ...
22 views

### Magnetic field of a standing monochromatic plane wave

I am given the magnetic field of a standing monochromatic plane wave $$\vec{H}(y,t)=H_0\sin(\beta y+\theta_0)\sin(\omega t+\phi_0)\,\hat e_x$$ and i am asked to determine in what type of medium its ...
49 views

### How can the particle in plane progressive harmonic wave have minimum potential energy at one of the extreme position?

consider this image context: These are fill in the blanks sort of questions, the above image contains solution. My reasoning A and B should be in SHM and we know that in SHM Kinetic Energy is max at ...
20 views

### Optical path difference between the first and p-th transmitted wave for a plane wave incident on a Fizeau interferential wedge

In this paper: Ayerden, N. P., Graaf, G. D., & Wolffenbuttel, R. F. (2016). Compact gas cell integrated with a linear variable optical filter. Optics Express, 24(3), 2981-3002. https://doi.org/10....
42 views

### Plane waves vs continuous sine waves

I've started learning QFT from Sean Carroll's lectures, but I had to postpone it until I'll manage my notes)) Meanwhile, 1 question is bugging me: it's about 3D plane waves, which in QFT are analogous ...
47 views

### What are the stokes parameters of a linear wave added to a circular one?

So consider the following thing: Let's suppose that we have a situation with two monochromatic waves propagating through the z-axis. Both waves have the same frequency and intensity. How can I find ...
28 views

### How can I prove this property about linearly polarized waves?

So I'm studying electromagnetic waves. The current topic is polarization. My professor material says in one part that the electric field of a monochromatic linearly polarized wave propagating through ...
46 views

### A couple of apparent inconsistencies on free-particle stationary states

In order to introduce my question we consider first the free electron, in a box width L, with eigenfunctions and eingenvalues given by $$\psi_k(x)=\frac1{\sqrt{L}}e^{ikx}$$ and $$E_k=\hbar^2k^2/2m$$ ...
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### Accounts on the solutions of the Dirac equation

Consider the Dirac equation $(i\gamma^{\mu}\partial_{\mu}-m)\psi = 0$. As it is well known, there are different representations for the matrices $\gamma^{\mu}$, $\mu = 0,1,2,3$, the most famous ones ...
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### Modelling sky noise using a 2D array with plane waves

I have a question about modeling sky noise which should be filtered by a spatial filter 4f system. My approach for this task is to use a 2D array with random amplitude values and another 2D array that ...
1 vote
57 views

### Why spacetime translations don't affect the physics of de Broglie plane waves?

I'm studying Merzbacher's Quantum Mechanics. In Chapter 2 Section 1, he "derives" the expression $\psi(x, t)=Ae^{i(kx-\omega t)}$ for the de Broglie plane waves for free particles. Basically ...
81 views

### Why is zero conductivity media called lossless?

Doesn't zero conductivity mean infinite resistance which would lead to infinite loss.
1 vote
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### Acoustics: Construction of the pressure field with transmitted and reflected plane waves

So I have been reading one of the papers about wave manipulation, which takes advantage of the phase shifted reflection by tailoring the design of the system. The design has two domains: air and foam (...
Two plane waves having the same frequency and different intensities: $$E_0=Ae^{i(\omega t-kr_0)}$$ and $$E_1=Be^{i(\omega t-kr_1)}$$ arrive at point $P=(x,y)$ from two point sources located at a ...