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:

    “To abandon oneself to principles is really to die—and to die for an impossible love which is the contrary of love.”
    —Albert Camus (1913–1960)

    “Government ... thought [it] could transform the country through massive national programs, but often the programs did not work. Too often they only made things worse. In our rush to accomplish great deeds quickly, we trampled on sound principles of restraint and endangered the rights of individuals.”
    —Gerald R. Ford (b. 1913)

    “The honor my country shall never be stained by an apology from me for the statement of truth and the performance of duty; nor can I give any explanation of my official acts except such as is due to integrity and justice and consistent with the principles on which our institutions have been framed.”
    —Andrew Jackson (1767–1845)