Wave Equation, Beam Envelopes
The Wave Equation, Beam Envelopes node is the main node for the Electromagnetic Waves, Beam Envelopes interface. The electric field is factorized into the product
,
for Wave Vectors set to unidirectional. Inserting this electric field formulation into the Maxwell’s equations results in the following wave equation for the envelope function
,
where
.
The wave number k is defined by
,
where n is the refractive index and the wave number of free space k0 is defined as
.
Here c0 is the speed of light in vacuum.
When Wave Vectors are set to bidirectional, the electric field is defined as the sum of two fields
The second field adds an additional wave equation to solve
,
where
.
When solving the equations as an eigenfrequency problem the eigenvalue is the complex-valued eigenfrequency λ = −jω + δ, where δ is the damping of the solution. The Q factor is given from the eigenvalue by the formula
.
The settings for the Wave Equation, Beam Envelopes feature node are the same as Wave Equation, Electric.