- #1
DanSandberg
- 31
- 0
From a textbook - The reason why the polarization plays a key role in the description of nonlinear optical phenomena is that a time-varying polarization can act as the source of new components of the electromagnetic field... the wave equation in nonlinear optical media often has the form:
[tex]\nabla[/tex] 2 E - [tex]\frac{n2}{c2}[/tex] [tex]\frac{d2E}{dt2}[/tex] = [tex]\frac{1}{\epsilon c2}[/tex][tex]\frac{d2PNL}{dt2}[/tex]
This equation is given with no derivation or justification. Can someone explain where this comes from?
EDIT: I'm having a really hard time getting the equation to come out correctly on the website. Its nabla to the second power operating on the electric field E minus the second time derivative of E times n squared over c squared (where n is the linear refractive index and c is the speed of light) equal to 1 over epsilon c squared times the second time derivative of the polarization. I'll try to uplaod a photo of the equation.
[tex]\nabla[/tex] 2 E - [tex]\frac{n2}{c2}[/tex] [tex]\frac{d2E}{dt2}[/tex] = [tex]\frac{1}{\epsilon c2}[/tex][tex]\frac{d2PNL}{dt2}[/tex]
This equation is given with no derivation or justification. Can someone explain where this comes from?
EDIT: I'm having a really hard time getting the equation to come out correctly on the website. Its nabla to the second power operating on the electric field E minus the second time derivative of E times n squared over c squared (where n is the linear refractive index and c is the speed of light) equal to 1 over epsilon c squared times the second time derivative of the polarization. I'll try to uplaod a photo of the equation.