Physics Asked by javierhersan on December 22, 2020

I am having trouble understanding the Guided Fields derivation process. Firstly, We derive the Helmholtz equation easily:

$Δ⋅vec{E}+ frac{∂^2vec{E}}{∂z^2} – gamma$

_{0}$⋅vec{E}= 0$

Then we decompose the Helmholtz equation into two new equations thanks to decomposing the field in tangential and transversal components ($vec{E}=vec{E_t}+vec{E_z}$):

$Δ_t⋅vec{E_t}+ frac{∂^2vec{E_t}}{∂z^2} – gamma$

_{0}$⋅vec{E_t}= 0$

$Δ_t⋅vec{E_z}+ frac{∂^2vec{E_z}}{∂z^2} – gamma$

_{0}$⋅vec{E_z}= 0$

The first thing I do not undestand is why we can apply variable separation to solve this differential equation, are not we leaving some solutions applying this method?

$E_z(x,y,z) = F_E(x,y)⋅e^{-gamma⋅z}$

$H_z(x,y,z) = F_H(x,y)⋅e^{-gamma⋅z}$

Secondly, the boundary conditions, which are derived from Maxwell’s equation and the boundary with a perfect conductor, are the following:

TE Mode: $frac{∂F_H}{∂n} = 0$

TM Mode: $F_E = 0$

How do we get the boundary conditions of the TE Mode?

And lastly having all this conditions and the Helmholtz equation, how we can assure that $k_c^2$ is real and greater than $0$

$Δ_t⋅F_{E/H}+ k_c^2⋅F_{E/H}= 0$ , $frac{∂F_H}{∂n} = 0$, $F_E = 0$

Thank you very much, any help is appreciated.

2 Asked on October 29, 2021 by user40003

0 Asked on October 29, 2021 by kai-li

condensed matter ground state phonons quantum mechanics symmetry breaking

1 Asked on October 29, 2021

classical mechanics constrained dynamics degrees of freedom lagrangian formalism spacetime dimensions

2 Asked on October 28, 2021

2 Asked on October 28, 2021

3 Asked on October 28, 2021

1 Asked on October 28, 2021

1 Asked on October 28, 2021

analyticity anharmonic oscillators asymptotics schroedinger equation

3 Asked on October 28, 2021

discrete eigenvalue hilbert space operators quantum mechanics

1 Asked on October 28, 2021

angular momentum linear algebra operators quantum mechanics symmetry

1 Asked on October 28, 2021

energy conservation moon newtonian gravity newtonian mechanics tidal effect

2 Asked on October 28, 2021

1 Asked on October 28, 2021 by scrrr

2 Asked on October 28, 2021

cavity qed condensed matter quantum electrodynamics quantum mechanics quantum optics

1 Asked on October 28, 2021

feynman diagrams lagrangian formalism path integral quantum field theory renormalization

2 Asked on October 28, 2021

crystals physical chemistry solid state physics thermodynamics

1 Asked on October 28, 2021 by sciencepiofficial

0 Asked on October 28, 2021

Get help from others!

Recent Answers

- haakon.io on Why fry rice before boiling?
- Jon Church on Why fry rice before boiling?
- Joshua Engel on Why fry rice before boiling?
- Peter Machado on Why fry rice before boiling?
- Lex on Does Google Analytics track 404 page responses as valid page views?

Recent Questions

- Iv’e designed a space elevator using a series of lasers. do you know anybody i could submit the designs too that could manufacture the concept and put it to use
- Need help finding a book. Female OP protagonist, magic
- Why is the WWF pending games (“Your turn”) area replaced w/ a column of “Bonus & Reward”gift boxes?
- Does Google Analytics track 404 page responses as valid page views?
- Why fry rice before boiling?

© 2022 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, MenuIva, UKBizDB, Menu Kuliner, Sharing RPP