Beam Propagation Method - Principles

Principles

BPM is generally formulated as a solution to Helmholtz equation in a time-harmonic case,

(\nabla^2 + k_0^2n^2)\psi = 0

with the field written as,

.

Now the spatial dependence of this field is written according to any one TE or TM polarizations

\psi(x,y) = A(x,y)exp(+jk_o\nu y) ,

with the envelope

A(x,y) following a slowly varying approximation,
\frac{\partial^2( A(x,y) )}{\partial y^2} = 0

Now the solution when replaced into the Helmholtz equation follows,

\leftA(x,y) = \pm 2 jk_0 \nu \frac{\partial A_k(x,z)}{\partial z}

With the aim to calculate the field at all points of space for all times, we only need to compute the function for all space, and then we are able to reconstruct . Since the solution is for the time-harmonic Helmholtz equation, we only need to calculate it over one time period. We can visualize the fields along the propagation direction, or the cross section waveguide modes.

Read more about this topic:  Beam Propagation Method

Famous quotes containing the word principles:

    “Every political system is an accumulation of habits, customs, prejudices, and principles that have survived a long process of trial and error and of ceaseless response to changing circumstances. If the system works well on the whole, it is a lucky accident—the luckiest, indeed, that can befall a society.”
    —Edward C. Banfield (b. 1916)

    “It is always easier to fight for one’s principles than to live up to them.”
    —Alfred Adler (1870–1937)

    “His principles are like the bristles of a domesticated pig, they don’t pierce through the pork.”
    —Franz Grillparzer (1791–1872)