# Modified Gamma and the Subwavelength

July 26, 2009 Leave a comment

I have partially completed my work on the photon probability distribution being a modified Gamma distribution and not a Gaussian distribution. To this end I have been testing microwave, light & subwavelength models using this modified Gamma distribution.

The subwavelength modified Gamma model provides a reasonably close fit with R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile and X. Zhang paper *A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation*. The fit is close but note that there are areas where the models disagree.

Source: Nature Photonics

Figure 1: GaAs nano wire in SiO2 on a metallic plane (100nm<d<500nm, 2nm<h<100nm)

The Oulton *et al* paper shows the energy distribution for d=200nm & h=100nm, Figure 2.

Source: Nature Photonics

Figure 2: Energy distribution (d=200nm, h=100nm)

My model shows a similar result, Figure 3.

Figure 3: Modified Gamma model (d=200nm, h=100nm)

The Oulton *et al* paper shows the energy distribution for d=200nm & h=100nm, Figure 4.

Source: Nature Photonics

Figure 4: Energy distribution (d=200nm, h=2nm)

My model shows a similar result, Figure 5.

Figure 5: Modified Gamma model (d=200nm, h=2nm)

The energy in the gap area for Oulton *et al* model is 15% for h=2nm & up to 20% for h-100nm. The modified Gamma model’s energy in the gap area is about 10% and 15% respectively, about 5% consistently less than Outlon *et al*. However, the modified Gamma model is sensitive to the dimensions of the SiO2 layer, and I have assumed this to be 800nm across and 400 nm high.

I think this is a great fit for subwavelength, coming out of nowhere, while at the same time giving good assurances at the microwave and optical frequencies.

If you know what the internal dimensions of the WR 430 microwave waveguide are, do contact me and let me know.

Ben Solomon