Spontaneous emission noise distribution from a gain-guided multimode waveguide

The angular distribution of the spontaneous emission is discussed for a stripe-defined waveguide. The signal (defined as photons incident at the input port of the waveguide) is distinguished from the "noise" by considering only spontaneously emitted photons as "noise" and reducing the photon conservation equation to a linear differential equation under the condition that the total photon density is not so high that the local gain of the medium saturates. Simple analytical representations for the lateral distribution of population inversion
N
and local gain
g
are introduced to obtain an angular distribution of "noise" by the ray optics approach and this is applied to calculate the far-field pattern of superluminescent diodes (SLD). By comparing measured and calculated far-field patterns of SLD's, it is shown that theoretical results obtained by assuming a Gaussian lateral distribution of
N
and parabolic for
g
fit the experimental results very well. Referring to the ("noise") angular distribution, it is found that the on-axis component increases exponentially with the waveguide length Z
0
, whereas the off-axis component saturates according to
W/Z_{0}
(
W
= the waveguide width). The "noise" beam width decreases rapidly as
Z_{0}/W
increases and then saturates gradually. In considering this device as an optical amplifier, the calculations show that the shorter the Z
0
, the higher the signal-to-noise ratio. It is, however, essential to ensure that there is no spurious coupling because this type of amplifier generates very wide beam "noise."