Re: "selecting synchronous terms" in wave equations

Andrew wrote:
On 25 Lip, 16:05, Phil Hobbs <p...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:
Andrew wrote:
Hello,
I try to learn some topics from optical wave propagation.
I have read recently some papers and books that concerns such
subject
matter and I found that in many papers Helmholtz equation is
separated
into two equations by "selecting synchronous terms". I guess that
"synchronous terms" are terms that change with the same frequency
(terms multiplied by exp(a), where a is the same for such terms).
The first quaestion is - Am I right ?
and the second one -
Is it allowed to do such separation from mathematical point of view ?
Thanx in advance,
Andrew :)
The wave equation is linear, so you can add and subtract different
contributions any way you like. For instance, laser beams that cross
don't affect each other. (That doesn't mean you can just ignore terms
in the integral that are hard to deal with!)

Terms that aren't synchronous form interference patterns that move, so
the interference terms go away if you time-average them. Most of the
things we measure are time-averaged, at least a bit--for instance by the
limited bandwidth of an oscilloscope or the frame time of a camera.

Cheers,

Phil Hobbs- Ukryj cytowany tekst -

- Poka cytowany tekst -

Thanx for your answer,
However the papers that I've read regards to nonlinear wave equation.


Then it isn't the Helmholtz equation. Maybe you could cite a couple of references.

Cheers,

Phil Hobbs
.

Relevant Pages

  • Re: "selecting synchronous terms" in wave equations
    ... Andrew wrote: ... I try to learn some topics from optical wave propagation. ... I have read recently some papers and books that concerns such ... into two equations by "selecting synchronous terms". ...
    (sci.optics)
  • Re: "selecting synchronous terms" in wave equations
    ... Andrew wrote: ... I try to learn some topics from optical wave propagation. ... I have read recently some papers and books that concerns such ... Phil Hobbs- Ukryj cytowany tekst - ...
    (sci.optics)
  • Re: Hypergeometrical Universe - Theory of Everything
    ... The papers are in the site (there are links to them under a Header ... hyperspherical shock wave shell, which we know as our 3-D Universe. ... Motions along the Circular Hyperspherical Lightspeed Expansive Universe ... equivalent of nonlinear optical interactions, ...
    (sci.physics.relativity)
  • Re: Here be dragons...
    ... Nowhere do they say specifically how the prototype is performing, but the nearest we get to a performance figure is obtained by lookong at 2 of their papers. ... One states that the average wave power for the prototype is 0.4kW.m, and yet their predictions for a "full size model" is based on a wave energy density of 36kW/m. ...
    (uk.rec.sailing)
  • Re: "selecting synchronous terms" in wave equations
    ... I try to learn some topics from optical wave propagation. ... I have read recently some papers and books that concerns such ... Then it isn't the Helmholtz equation. ... Lett. ...
    (sci.optics)