# 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

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...
4. ### 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...
5. ### 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...
6. ### 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...
7. ### 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)...
8. ### 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...
9. ### 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...