MadSci Network: Physics

Re: how can we calculate the optical confinement factor of a laser diode?

Date: Thu Oct 14 11:47:13 2004
Posted By: Kenneth Beck, Senior Research Scientist, Chemistry and Physics of Complex Systems, Pacific Northwest National Laboratory
Area of science: Physics
ID: 1097762981.Ph

Dear Vipul,

I've included two figures to describe the integral ratio which I cannot 
describe as easily in text format (figure 1.jpg and Figure 2.jpg).

Figure 1

Figure 2

In Figure 1, Ex is the electrical field intensity of the first transverse 
mode (TE) propagating in the active region. In other words, this formula 
defines the fraction of the mode energy which is confined to the active 
layer and thus “sees” optical gain.

In practice, only the fundamental transverse mode lases. It is also found 
experimentally that its polarization is almost invariably TE. For these 
reasons, one is mostly concerned with the propagating characteristics of 
the TE mode in a symmetrical slab guide. A more general approximate 
solution for that is valid is found by Botez*. Botez’s* analytical 
techniques yield accurate results in calculating for 3-region guides. The 
approximation given by Botez* for calculating the optical confinement 
factor in a symmetrical waveguide for the TE mode is found in Figure 2

Here, lambda is the vacuum wavelength at the lasing photon energy, D is 
the normalized thickness of the active region, n(r,w) and n(r,c) are the 
indices of refraction of the active and cladding layers, respectively, 
and w is the thickness of the active layer.

Hope this helps!

---* Dr. Ken Beck

* D. Botez, “Analytical approximation of the radiation confinement factor 
for the TE0 mode of a double heterojunction laser,” IEEE   J. Quantum 
Electron., vol. QE-14, pp. 230–232, 1978.
   D. Botez, “Near and far-field analytical approximations for the 
fundamental mode in symmetrical waveguide DH lasers,” RCA Rev., vol. 39, 
pp. 577–603, 1978.

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