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Surface Plasmons

Plasmonic waveguides on GaAs substrate (wavelength: 1550 nm)

Numerical examples. Enhancement of MO effect in the case of double-dielectric single-surface slab plasmonic waveguide.


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)
Experimental confirmation of low optical loss in Fe:SiO2:AlGaAs waveguide is 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)


GaAs substrate (lambda=1550 nm)

GaAs is transparent at this wavelength





Optical confinement near cutoff

example: Co:SiO2:AlGaAs(3 um):GaAs (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 (~2.96) ~ refractive index of oxide (~1.44)
1/e penetration depth into GaAs deep (~ 20 um) extremely deep (~ 200 um)
optical field near metal medium high
MO FoM high (~100 %) high (~100 %)
optical loss low( less than 0.5 dB/um) - average low( less than 0.5 dB/um) (experiment: 0.38 dB/um)
required precision for oxide thickness high (~0.2-0.4 nm) medium (~10 nm-15 nm)
non-reciprocal phase shift high (2.5 deg/um) low (0.22 deg/um)
FoM for non-reciprocal phase shift high (2deg/dB) high (2 deg/dB)
1/e penetration depth into metal (skin depth) 32 nm 34 nm

Examples below is for Co:SiO2:AlGaAs(3 um): GaAs (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.


Fig.3 1/e penetration depth of optical field into dielectric and optical loss in Co:SiO2:AlGaAs(3um):GaAs plasmonic waveguide

Fig.4 Non-reciprocal phase shift and Phase-Shift FoM (ratio of the phase shift to optical loss) for Co:SiO2:AlGaAs(3um):GaAs plasmonic waveguide Fig.5 MO Figure-of-Merit (Ratio of non-reciprocal optical loss to average optical loss) and 1/e plasmon propagation distance for Co:SiO2:AlGaAs(3um):GaAs plasmonic waveguide














































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