Diploma thesis

In this solution, there are four selection rules that restrict the mode coupling:
n + m + o �= 0
−n + m − o �= 0
n − m − o �= 0
−n − m + o �= 0
n, m, o ∈ N\{0}. (3.37)
We evaluated these up to n = m = o = 3 and obtained 18 different possibilities with
subsequently normalised three-wave coupling factors (see Table 3.1). In the table,
pump mode → signal mode + idler mode coupling constant
n-1 → m-1 + o-1
0 → 0 + 0 1.00
1 → 1 + 1 0.50
2 → 2 + 2 0.33
0 → 1 + 1 0.80
1 → 0 + 1 0.80
1 → 1 + 0 0.80
2 → 0 + 0 0.20
0 → 2 + 0 0.20
0 → 0 + 2 0.20
0 → 2 + 2 0.77
2 → 0 + 2 0.77
2 → 2 + 0 0.77
2 → 1 + 1 0.57
1 → 2 + 1 0.57
1 → 1 + 2 0.57
1 → 2 + 2 0.42
2 → 1 + 2 0.42
2 → 2 + 1 0.42
Table 3.1: Some mode coupling possibilities in 1D waveguides
we switched into the standard notation for fiber and waveguide modes starting with
(0,0). This is a more common notation in the field of optics and is usually used to
label guided modes in fibres.
We expand our findings to two dimensional waveguides and predict 324 different
mode couplings, some of which are depicted in Table 3.2. All of these possibilities
corresponds to a different set of Sellmeier equations that have to be applied. They
only differ slightly, but all produce distinguishable phasematching contours (see
Figure 3.18).
We already observed higher order spatial mode waveguided parametric downconversion.
We measured signal and idler spectral distributions from several simultane-
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