Recent content by spookyfw

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    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...
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    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...
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    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...
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    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...
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    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 =...
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    Prooving pseudo-periodicity of diffracted field for gratings

    any hints someone can give to tackle this problem?
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    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...
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    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...
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    Observables, Measurements and all that

    Ah..perfect. So the loop is closed :). Thanks once again!
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    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
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    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...
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    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...
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    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...
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    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...
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    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?
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