Dr. Vadym Zayets

Goal: To study and understand the features and properties of surface plasmons near cutoff condition.

Reason: The cutoff conditions in a double-dielectric plasmonic waveguide have never been studied before.

Note: The properties of plasmons near cutoff in the case of thinner oxide thickness (5nm -12 nm) and in the case of thicker oxide thickness (200 nm -900 nm) are significantly different.

need to know: To understand cutoff condition in dielectric waveguide click here

 

MO enhancement in the case plasmons (general fact are here)

Below the data are calculated for a slab single-surface double-dielectric plasmonic waveguide.

Metal should be thicker than 3 skin depths (~ 100 nm)

 

Si substrate (wavelength: 1550 nm)

 

 

 

 

Optical confinement near cutoff

example: Co:SiO2:Si (lambda=1550 nm)

In double-dielectric plasmonic case (In studied case it is semiconductor-oxide-metal plasmonic waveguide. See the numerical examples above) there always there is two cutoff thicknesses of the oxides. The surface plasmons can propagate only in the case when the oxide thickness is thinner than the thinner cutoff thickness(~ 5-12 nm) or thicker than the thicker cutoff thickness.

	thinner cutoff thickness	thicker cutoff thickness
plasmon's effective refractive index	~ refractive index of semiconductors (~3.39)	~ refractive index of oxide (~1.446)
1/e penetration depth into dielectric	medium (~ 5 um)	very deep (~ 200- 300um)
optical field near metal	medium	high
MO FoM	high (~100 %)	high (~100 %)
optical loss	medium (2-4 dB/um) - average	low( 0.1-0.2 dB/um)
required precision for oxide thickness	high (~0.2-0.4 nm)	medium (~10 nm-15 nm)
non-reciprocal phase shift	medium (0.5-8 deg/um)	medium (0.7 deg/um)
FoM for non-reciprocal phase shift	low (0.2 deg/dB)	medium (2 deg/dB)
1/e penetration depth into metal (skin depth)	31.8 nm	34 nm

Examples below is for Co:SiO2:Si (lambda=1550 nm) plasmonic waveguide.

 

cutoff: thinner SiO2

Optical field across plasmonic waveguide (normal scale) Optical field across plasmonic waveguide (logarithmic scale)

cutoff: thicker SiO2

Optical field across plasmonic waveguide (normal scale) Optical field across plasmonic waveguide (logarithmic scale)

Fig.1 Animated figure. Field distribution along thickness of plasmonic waveguide. Both linear and logarithmic y-axis scale are used. Animation parameter is thickness of SiO2 layer. The distance=0 corresponds to a metal-SiO2 interface. The blue and green lines correspond to opposite magnetization of Co.

The important difference between distributions of optical field of plasmons near two cutoff thicknesses is that in the case of thick SiO2 a significant amount of optical field is confined inside this layer. It is reason of lower optical loss in this case. The more optical field is inside dielectric and the less optical field is inside metal, the smaller optical loss of plasmons will be.

 

 

 

 

 

 

 

 

 

 

 

 

example: Fe:SiO2:Si (lambda=1550 nm)

 

 

 

 

 

 

 

 

 

skin depth: 41.3 nm/ 45.8 nm

 

example: Co:MgO:Si (lambda=1550 nm)

 

 

 

 

 

 

 

 

skin depth: 31.8 nm/ 33.8 nm

 

 

 

 

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Examples of calculation of field distribution of a surface plasmon

 

Tip

The calculation of the surface of a surface plasmon is more difficult that the calculation of the field of a waveguide mode, because for the plasmon geometry there are many unrealistic parastic solutions. In the case when such parasitic can not be filtered out, a simpler geometry should be used. The solution for this

 

Fiiles to download

 

comsol only:

geom3a.mph

 

Matlab+ Comsol:

main calculation file

plasmons.m

within each different geometry of a plasmonic waveguidecan be used: PlasmonGeometry3a.m,

files used: SetMaterial.m, ferro.m, nSiO2.m, nGaAlAs.m, nSi.m, nAlO.m, MgO.m, FeMy.mat, CoMy.mat, NiMy.mat