Dispersion Definition and 261 Threads

So I see them in the books labelled as accoustic and optical phonons but I don't seem to find a comprehensive treatment of the matter for a beginner who doesn't know a thing about the dispersion curves. I'd prefer not to dwell too much into the mechanical treatment if possible since I just need...

Homework Statement Here is the problem description: Develop an Excel file that given a set of data from an RTD pulse injection will determine the model parameters of the following schematics, and then predict the conversion in a CONTINUOUS reactor with a n-order reaction (where n is not equal...

What is the physical meaning of acoustic and optical branches in phonons dispersion curves ?

Hi. Is the superposition of two different monochromatic waves in a dispersive medium still a wave (i.e. a solution of a wave equation) if the phase velocity is not the same? Since the wave equation contains the phase velocity, the two individual waves are solutions of different wave equations...

Hi, I have transmission line with dispersion relation ω=sin(kx), so then means that for one value of ω I have two values of k. I apply voltage with some frequency with is allowed to move in the line. First question is, how can I influence what k will be generated inside the line. The another...

Homework Statement What would the focal length be of a diffraction grating if the set up is a laser placed 1 m from the 0 order diffraction? Would it be the distance from the grating to the laser or the distance from the grating to the image? Homework Equations 1/f = 1/o + 1/i Rd = [Df]-1...

What makes dispersion be different from scattering? What exactly is the definition of scattering? Google says it is to deflect or diffuse.how can deflection be a synonym for scattering? How are they related?

The LIGO paper https://dcc.ligo.org/LIGO-P150914/public puts limits on the dispersion of gravitational waves, which can be interpreted as an upper limit of 10^-22 eV on the mass of the graviton. We all know that low-amplitude gravitational waves are supposed to propagate at c according to the...

Hello! I still would like to thank those who participated to my previous thread about group velocity and dispersion. Now there is a (maybe) simpler question. A sinusoidal, electro-magnetic plane wave in the vacuum propagates in a certain direction with the following wavenumber, which is supposed...

OK I'm about to grow (more) gray hairs... Could some friendly soul smarter than myself kindly help me solve for both f and theta respectively in the following equation, please: x = sin[ (pi*f*W)/c * sin(theta) ] / [ (pi*f*W)/c * sin(theta) ] Getting stuck at "arcsin of arcsin" sort of...

One of the most accurate formulas for dispersion is the Sellmeier equation: n^2(\lambda) = 1 + \sum_i \frac{B_i \lambda^2}{\lambda^2 - C_i} Dispersion does not arise with Huygen's Principle. Is there a theoretical model that describes dispersion and explains why Sellmeier's equation takes the...

I have some qualitative questions about the relation between band structure, density of states, and Fermi energy (or Fermi level). 1) Say you have a given electronic band structure (energy as a function of k) obtained by any method. How do you relate this to the Fermi energy (or Fermi level) ...

I am a beginner in quantum mechanics and I am confused about the operator ΔA defined to be ΔA Ξ A - <A>. Can someone please tell me how to interpret <A>? From what I can understand, <A> is the expectation value and is defined to be <Ψ|A|Ψ>. But that is just a scalar correct? How do subtract a...

Hey all, I am trying to recreate the phonon dispersion plot of the paper below http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-730-physics-for-solid-state-applications-spring-2003/projects/ProjP21.pdf The problem is I do not know what the Tau, L, and X on the x-axis...

can anyone tell me what is the dispersion energy in semi conductors

Today I was presented with dispersion in my introductory physics class. Before this topic was presented we were told of two important rules for waves: 1) The speed of a wave is dependent on the medium in which it travels and 2) the frequency of wave does not change when going from one medium to...

Could a thin sheet of glass with appropriate edge angles work as a dispersion prism? If the prism were laying flat my thoughts are the light should be contained via TIR in a plane that would remain perpendicular to the top and bottom while said plane dispersed horizontally according to...

I'm revising for a uni exam with past exam papers, and have gotten stuck on the details of dispersion. The two exam questions prompting this are a) What is the physical reason why the index of refraction for blue light is bigger than that of red light? and b) Explain how dispersion makes a...

Homework Statement I need to calculate the energy dispersion relation in the tight binding for simple cubic, base centered cubic and face centered cubic crystals. There are no values given, they just need the result depending on the lattice constant a. Homework Equations E (k) = alpha + beta *...

Hello! (Wave) I want to find the dispersion relation for the solutions in the form $u(x,t)=e^{i(kx-\omega t)}, k, \omega>0$ of the following partial differential equations: $u_t+au_x=du_{xx}$ $i u_t+u_{xx}=0$ $u_{tt}=au_{xx}$, where $a,d>0$. Which of the above equations are dispersion...

In class I learn that we can get the dispersion relation for particles by using E=hbar*w and p=hbar*k. The calculated phase velocity is w/k = hbar*k/2m, while the group velocity is dw/dk=hbar*k/m. All these make sense to me, except one thing: I always thought that E=hbar*w=hf is only applicable...

Hi. Here's the dispersion relation for a diatomic linear chain, where the distance is a/2 between each atom. My issue here is that if you set m_1=m_2=m, i.e. set both atoms equal to each other, it doesn't automatically reduce to the old acoustic dispersion relation as the ± term doesn't...

Hi I have Hamiltonian matrix and overlap matrix. How to calculate tight binding dispersion for graphene in matlab? I would be appreciated if could some one give me a hand on my problem.

I'm trying to get my head around what this means exactly. I've plotted the graph to help verse me with the functions that I've derived. From the free electron model, the wavefunctions are treated as planewaves of the form \psi_\mathbf{k}(\mathbf{r}) = e^{i\mathbf{k}\cdot\mathbf{r}} Due to...

Homework Statement Consider a propagating wave packet with initial length L0. Use the bandwidth theorem to show that the minimum range of angular frequencies present in the wave packet is approximately: \begin{equation} \Delta \omega = \frac{v_{g}}{L_{0}} \end{equation} where vg is the group...

Hi Everyone, I'm trying to understand dispersion relations in general. I know that for a simple wave like a light wave there is a 'constant phase' so the dx/dt is equal to the ratio of the angular frequency (omega) by the wave vector (k). However what does a 'constant phase' mean? How can I...

I know that in a vacuum, speed of light is constant. My question is more about the speed of light in a material like air. Dispersion of light in a prism tells us that the speed of light or the material index depends on the wavelength ( or frequency which is constant ) so I thought that air...

I'm having trouble simplyfying this, I guess there's a trick but for the life of me can't remember what it is. Here is what I have so far: ##\omega ^{2} = f\left ( \frac{1}{m}+\frac{1}{M} \right )-f(( \frac{1}{m}+\frac{1}{M} \right ))^{2} - \frac{4q^{2} a^{2}}{mM})^{\frac{1}{2}}## so I divide...

Hi. A very quick question. Why is it impossible for a wave to travel on a linear one-atomic chain if its wavelength equals the lattice constant? I.e. the lattice points vibrate with a wavelength equal to the distance between them? Here's what I mean...

1. The problem statement A diffraction grating has a slit separation of 2094.0 nm. What is the dispersion of the 2nd order lines at an angle of 30 degrees (in degrees per micrometer)? Homework Equations dsinΘ=mλ y=(mDλ)/d 3. Attempt at a solution I began by finding λ using the first...

Homework Statement Our lecturer seemed to skip over how to get from the Group Velocity Dispersion to the actual temporal stretch of a pulse sent down an optical fibre, instead we were given just the two formula. I've been trying to work out where the temporal stretch comes from but can't work...

Homework Statement Pulsars are stars that have suffered gravitational collapse. They rotate rapidly and emit a narrow beam of radiation. The pulse lengths, at the earth, are ∼1ms and the periods are ∼1s. Within a few months of the discovery of pulsars distance estimates were obtained by...

Can dispersion of light take place through lens, i.e. can lens (incl. Convex and Concave) scatter white light into its constituents?

I am learning some basic solid state physics idea, like density of state ...etc. For particle in a 1D box, E = n^2 (pi)^2 (h_bar)^2 / 2mL^2 But why it is written as E = (h_bar)^2 k^2 /2m does it means that energy eigenvalue E is related to momentum k ? I guess it is not because momentum is...

There are numerous publications about pairwise velocity dispersion ( PVD ) of galaxies in real redshift surveys. It is customary to use an exponential form for the distribution of pairwise velocities and then model the redshift space distortions in the 2PCF to retrieve the PVD. Now if i have a...

Homework Statement A red beam of light in air enters crown glass at an angle of 60.00 to the normal. Find the angleof refraction. Repeat for a violet beam oflight entering crown glass (same angle). Homework Equations Not too sure, I believe I would use Snells law here.. does that sound...

Hi there, I am trying to understand the dispersion curve(as shown below) of a 1D lattice with diatomic basic. Here are my questions 1) Can both optical and acoustic branch of phonon can simultaneously exist in crystal? 2)Why there is a band gap between optical and acoustic phonon...

There was a question in one of my study materials that asked if you increased the incident angle of white light striking the surface of a glass prism, would the colors disperse less or more. The answer was disperse more. I didn't have an answer because I saw a conflict between the two...

Homework Statement I've determined the dispersion relation for a particular traveling wave and have found that it contains both a real and an imaginary part. So, I let k=\alpha+i\beta and solved for \alpha and \beta I found that there are \pm signs in the solutions for both \alpha and \beta...

Hello, I am working on a project where I am trying to take a photo of paper that I insert into a slot of an iPhone cover that I created with a 3D printer. My goal in this stage of design is to be able to take a photo that will disperse the light evenly across so that the lighting is uniform...

how the dispersion relation(i.e. E-k relation) affects carrier mobility in metals or semi-metals?

From my understanding, normal and anomalous dispersion are because the phase velocity is a function of k so it is different for different components of a group so the group will spread out over time. So what's group velocity dispersion? Is it the same affect (dispersion/ spreading out)...

Homework Statement This is not a homework problem but I'll post it here.It's just a question that came to my mind. Why does distant objects appear dimmer? The Attempt at a Solution My answer would be the inverse square law. For a point light,it can be quite easy to explain.As the...

I have synthesized nano-hydroxyapatite particles via wet chemistry precipitation of a Ca-PO4 solution. In water and PBS, these crystals tend to clump together in aggrigates up to 20-30 microns. The only way that I can get them to disperse is to sonicate them in either Hexafluoro-2-propanol or...

In some textbooks ##\Delta \hat{x}## is called dispersion of coordinate ##\Delta \hat{x}=(\langle \hat{x^2} \rangle-\langle \hat{x} \rangle ^2)^{\frac{1}{2}}##. For me that is standard deviation. What do you think?

Hello everyone I need to know why is it so important to use anomalous dispersion in FWM which four wave mixing and is there any experiment using HNLF high nonlinear fiber ?? Any papers about that I tried. To look but nothing

Homework Statement Using the Debye dispersion approximation, calculate the heat capacity of a harmonic, monatomic, 1D lattice. Next, find the temperature dependence in the low temperature limit. (Assume that the longitudinal mode has spring constant CL = C, and the two transverse modes both...

Sorry if it's a silly question but I was trying to find such an experiment and wasn't successful. What I am thinking is, in the standard delayed choice quantum eraser, the dispersion pattern on the screen correlates to whether or not we can detect which path the electron took. What if the...

If different frequencies of light have different refractive indices for the same material and travel at different speed in the same material, isn't it inaccurate to say that the speed of light through a certain material is c/n, where n is the "standard" refractive index?

Hi, Homework Statement I have two questions, in fact, both involving 2D graphene: (1) How may I determine the number of nearest neighbours in a primitive cell of graphene? (2) Given that graphene has linear energy dispersion near the fermi level and the dispersion is given by E=(hbar)vF|k|...