| Author | Message | ||
     jayanta mukherjee (neo) Member Username: neo Post Number: 9 Registered: 05-2005 |
I am trying to solve the scalar Helhmoltz equation in an optical-resonator (OR) using FlexPDE. Kindly tell me how to implement a reflective boundary condition at the mirrors of (OR). Normally when solving such problems a BPM algorithm is used where the propagating wave is assumes as a summation of a forward and a backward traveling wave. In that case the Fields at the boundaries are just multiplied with the respective mirror reflectivities. I am however confused as to how to implement such a boundary condition in FlexPDE. Thanks in Advance Jayanta Mukherjee | ||
| Patricio A. Greco (pagreco) Member Username: pagreco Post Number: 4 Registered: 12-2004 |
I recomend to solve the complex Helhmoltz equation. Calculate a conductivity value to obtain the adecuate refletivity and solve like a medium transition. The results will be adjusted more to real fenomena. | ||
| jayanta mukherjee (neo) Member Username: neo Post Number: 10 Registered: 05-2005 |
hi! Can you please elaborate a little bit more on ur suggestion. I have not been able to follow. Can u write to me the form of the Neumann/ Dirichlet BC that would suggest. My Helhmoltz Eqn uses general complex fields and refractive index. thanks in advance. neo | ||
| Patricio A. Greco (pagreco) Member Username: pagreco Post Number: 5 Registered: 12-2004 |
If you define the wall of the mirror with many times the penetration deep you can set the electrical field 0 as boundary.Then you don't meed to define more than the medium caracteristics in each part of your model. I simulated a waveguide termination with this princeple and worked very good. Patricio | ||
| jayanta mukherjee (neo) Member Username: neo Post Number: 11 Registered: 05-2005 |
i have tried using this idea, This sure works, but does't give the desired results. Can you please tell me exactly the idea you used. As for me I used an an exponentially dying electric field at the resonator mirrors.it does not simulate a standing wave. neo | ||
| Patricio A. Greco (pagreco) Member Username: pagreco Post Number: 6 Registered: 12-2004 |
I don't know how you introduce the field excitation . but If you wanna study the resonance I recomend use an eigenvalue analysis.With the same dominium solve the equations to determine the lambda values. I worked in the waveguide with the Magnetic potential vector with the following equations: Azr: div(grad(Azr))+Uo*w^2*(Azr*Eo*k+(G/w)*Azi) =-Uo*Jzr Azi: div(grad(Azi))+Uo*w^2*(Azi*Eo*k-(G/w)*Azr) =-Uo*Jzi where: k -> relative dielectric constant G -> conductivity. w = 2*pi*f Then I defined a conductivity ramp : G=A*ustep(x-lm)*(x-lm) If I change the A constant appears standing waves. If you define a incident wave you know the indident power flow , then when you calculate the pointing vector in any point outside the conductive medium if the magnitude are less than incident there are standing wave. If is 0 all power are reflected. I hope this could be usefull, Patricio | ||
| Patricio A. Greco (pagreco) Member Username: pagreco Post Number: 7 Registered: 12-2004 |
When I say calculate the pointing vector at any point, this is the surface integral. This surface must to be penpendicular to wave traveling direction. | ||
| jayanta mukherjee (neo) Member Username: neo Post Number: 12 Registered: 05-2005 |
Hello R.G.N I am also waiting for your comments on this problem. PLease advice. neo | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 389 Registered: 06-2003 |
This is not an application area in which I am proficient, and I would have to do some homework before I could risk an opinion. I assume Dr. Greco knows more about it than I do. | ||
| Patricio A. Greco (pagreco) Member Username: pagreco Post Number: 8 Registered: 12-2004 |
Neo: If you send your script I can see what is happening. That is all can I do for you. Thank you , Patricio. | ||
| jayanta mukherjee (neo) Member Username: neo Post Number: 13 Registered: 05-2005 |
What would the syntax for writing the following periodic boundary condition along the sides AB and CD of a 2D Rectangular domain ABCD? E(x,0)=E(x,y=2L), where L is a constant. I have read the help but could not figrure out the syntax. Please help. JM | ||
| jayanta mukherjee (neo) Member Username: neo Post Number: 14 Registered: 05-2005 |
Forgot to mention that the Length of the rectangle is L(along the y-axix). thanks Neo |