# Search results

1. ### Mathematical Reformulation of Polarization Equation

Hello, I hope I got the section right ;). I orginally posted this in the physics section, but as the problem is more mathematical. It would be nice if someone knows the right direction. I've stumbled upon a math problem while going through some physics and got stuck with some mathematical...
2. ### Linear Component of Polarization - Mathematical transformation

Hello, I'm currently going through Agrawal's book 'Nonlinear Fiber Optics' and got stuck with some mathematical cosmetics (pp. 40). It is the substition of: \vec{P_L}(\vec{r},t) = \frac{1}{2} \hat{x} \left(P_L \exp{(-i \omega_0 t)} + c.c.\right) into \vec{P_L}(\vec{r},t) = \epsilon_0...
3. ### Prooving pseudo-periodicity of diffracted field for gratings

I wanted to prove the periodicity in x. All the resources I've found so far always used these handwaving arguments. But I wanted to see it coherently on paper why the proof works like that. Starting with that I stumbled on some problems. w + u^{inc} = 0 was a mere try to somehow get...
4. ### Prooving pseudo-periodicity of diffracted field for gratings

True that solves it. Thank you alot. I was wondering though: in general it holds that n \times (H_1 - H_2) Why does this not work here and just leads to the Dirichlet boundary conditions once again? Is the following logic sound to finally prove pseudo-periodicity: due to uniqueness...
5. ### Prooving pseudo-periodicity of diffracted field for gratings

Thank you andy. For the first part I agree: (n1, n2, 0) x (0,0,u) = (n2 u, -n1 u, 0) = 0. This directly implies that u = 0. But to get the boundary condition for TM, I don't see it. Without applying any other equation you directly get the same boundary condition as before, as now H =...
6. ### Prooving pseudo-periodicity of diffracted field for gratings

any hints someone can give to tackle this problem?
7. ### Prooving pseudo-periodicity of diffracted field for gratings

Thanks for looking into the pdf. Yes..thats exactly the step. To me it seems that he put n=(0,1,0). If you could shed some light...
8. ### Prooving pseudo-periodicity of diffracted field for gratings

Hi for my thesis I wanted to show the complete derivation for the grating equation - case: perfectly conducting. The later steps are all no problem, but I am struggling with the proof of pseudo-periodicity. I found in my opinion a nice summary here...
9. ### Observables, Measurements and all that

Ah..perfect. So the loop is closed :). Thanks once again!
10. ### Observables, Measurements and all that

Stevendaryl and tom.stoer! Thank you very much for your replies. I think I got it finally, one question that directly follows: is it then right to say that: <M> = \Sigma p(m|i)m and hence M = \Sigma P_m m
11. ### Density matrix for bell states

Shouldn't the density matrix be 4x4? The first one should be something like \begin{pmatrix} 1 & 0 & 0 & 1\\ 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0\\ 1 & 0 & 0 & 1 \end{pmatrix} The others then analogously, but a 100% I am not certain, because looking at the Schmidt-coefficients, they are...
12. ### Observables, Measurements and all that

Hi Folks, I somehow cannot get the difference and have to admit that I am left confused. For a probability of measuring m with the operator M on state \Psi_i p(m|i) = <\Psi_i| M^{+}_m M_m |\Psi_i> = <\Psi_i| M_m |\Psi_i>. The average of an observable is defined as <O> = <\Psi_i| O...
13. ### Measure Phase velocity/group velocity of EM-wave

Sorry for this very late reply. First of all: thank you very much for your answer. Yes, I was talking about EM-waves. More about a pulse in the visible region though. I wondered how one would then discriminate and measure phase and group velocity. Using a phase detector sounds reasonable, but...
14. ### Requirements for SVD to work

Thank you very much. I think I spotted the problem with the matrix, as for square-matrices the Moore-Penrose inverse needs independent vectors, but unfortunately there is two dependent column vectors. At first sight I just spotted degenerate row vectors, but of course there has to be dependent...
15. ### Requirements for SVD to work

hmm..what do you mean by that least square approach? I just wanted to check a solution, I just don't understand the mathematical reason why the last system cannot be solved for A00, B00 and C00. How would you go about the least square approach though?
16. ### Requirements for SVD to work

Hi chiro, thank you very much for your reply. Yes I am using the Moore-Penrose pseudo-inverse. Actually the original problem can be seen in the attached picture. After using the pseudo-inverses it is stated that only the first three systems have a solution, but that there is too little...
17. ### Requirements for SVD to work

Dear fellows, during my internship I've stumbled over a problem of analysis. To cut things short some pseudoinverses have to be calculated. For one of them it does not work, s.t. A'*A \neq I. I just wondered about the requirements to find a pseudoinverse. One of the eigenvalues is zero...
18. ### Measure Phase velocity/group velocity of EM-wave

Hey folks, some weeks ago we had an trial-exam and one of the questions there was: "How do you measure phase and group velocity." That question really got me. Having a fastly oscillating wave as carrier and then the envelope. Can someone help me? Is it impossible for the phase, as it is...
19. ### Transform Maxwell Equations into k-space

ah. that makes perfect sense. Thank you very much :).
20. ### Transform Maxwell Equations into k-space

Dear fellow physicists, looking at the derivation for the maxwell equations into k-space, I've stumbled upon something that seems not so logical to me. It is concerning the two parts where they transform \nabla \times E and \nabla \bullet E on page 27 (on the sheets 14)...
21. ### Boundary conditions - Fresnel equations

Sorry for not replying earlier. Thank you very much for your reply :)! It is clear now. Have a good one, spookyfw
22. ### Boundary conditions - Fresnel equations

Hello, whenever I come to the derivation of the Fresnel equations I get stuck on the boundary condition for the component of the E-Field that is parallel to the surface. I know for the parallel components Maxwell dictates that: E_{1t} = E_{2t}. For the parallel incoming light field...
23. ### Solving Poisson's equation with the help of Greens function

Excellent. Now I a understand. Thank you very much and thanks for your time :)!!!
24. ### Solving Poisson's equation with the help of Greens function

Thank you very much Born2bwire! Now I also get: ∫(∇2G)e−ikxdV=∫(∇G)e−ikxdS−∫∇G∇e−ikxV. That makes sense now, but when I apply the 'integration-by-parts' again on the last term, I have a slight problem because the divergence theorem..well is working with divergences, but here we have a grad...
25. ### Solving Poisson's equation with the help of Greens function

Hey all, some weeks ago in a tutorial our TA solved Poissons equation with Greens functions..would be very short, but he also derived the Greens function using a Fourier transform. Two points I really don't get and he could also not explain it. Maybe you can help me? There might be even a short...