Unit of nonlinear absorption strength?

[FlorianLindinger]

Dear Nick,

I could not find a unit for the nonlinear absorption strength and was not able to infer one from the default value. What are its units? Moreover, is there go-to literature to get the nonlinear strength, the drude relaxation rate and the reduced mass? In particular in the context of GaSe @1030nm.

Best wishes,
Flo

[NickKarpowicz]

Hi Flo,
The nonlinear absorption in LWE ($\beta$) is defined via the nonlinear current density it induces, which has this form:

$$ J^\mathrm{abs}_i(t) = \beta E^{2n-2}(t)E_i(t) $$

$n$ is the number of photons involved in the transition, $E_i$ is the field in the $i$ direction, and $E$ is the total field.

$\beta$ actually has different units depending on the number of photons (this is determined by the frequency of pulse 1 and the band gap, which is given in eV in the box after $\beta$). Unfortunately its almost impossible to find relevant numbers in literature. I've only been able to get them by matching simulations to experimental results. The clearest thing to use is the power loss once there's a nonlinear absorption active (e.g. an open-aperture z-scan type measurement). If there's such data, one can get to a reasonable number...

For effective mass (reduced mass, relative to free electron mass), one should be able to get it from the literature, although in crystals it can be complicated and direction dependent. GaSe seems to be about 0.15: https://www.sciencedirect.com/science/article/pii/S1369800121005722

Drude momentum relaxation time likely won't affect your simulations, and it's also one where you likely have to extract it from a relevant measurement, but basically start with 10 fs or so and check if it even matters...

I hope this helps!