In the far infrared, superlattice dielectric functions can be well represented by an effective-medium model. The overall symmetry of a superlattice is uniaxial, and each of the principal components of the resulting dielectric tensor typically contains a different series of resonances. Here we examine some consequences that are of importance to many of the spectroscopy experiments that are undertaken. We describe sharp Brewster modes near longitudinal frequencies in p-polarized oblique incidence reflectivity and give details of guided wave and surface modes, including interface polaritons at the superlattice–vacuum interface. After discussing the basic optical principles we examine their application to the measurement of phonon confinement parameters.
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The limit qx = ∊11/2(ω/c) is not reached in all cases. In addition, modes can change type along their dispersion curves.
A type I Brewster mode extends from an L+ frequency if ∊xx < ∊1, whereas a type II mode extends if ∊xx > ∊1.
Table 2
Surface Modes between an Isotropic Medium of Positive Dielectric Function ∊1 and a Superlattice
If a pole appears in∊zz before either of these conditions is met a virtual mode can continue as a real mode terminating at ωs.
These modes are associated with strong dispersion in ∊1 and are included only for the sake of completeness.
Table 3
Surface Modes between an Isotropic Medium of Negative Dielectric Function ∊1 and a Superlattice
∊xx
∊zz
Mode Type
Minimum qx Limit
Maximum qx Limit
+ve
+ve
Real
−ve
+ve
qx = 0
qx→ ∞
at L+ or L0 mode
where ∊xx∊zz = ∊12
+ve
+ve
Real
−ve
+ve
qx = ∊zz1/2ω/c
qx→ ∞
at ∊xx = 0
where ∊xx∊zz = ∊12
+ve
+ve
Real
−ve
+ve
qx = ∊zz1/2ω/c
qx→ ∞
at pole in ∊1
where ∊xx∊zz = ∊12
Table 4
Modes Observable in a Standard ATR Experiment (with qz1 Imaginary) for a Superlattice Deposited on an Isotropic Substrate
qz2
qz3
Modes Observed
Additional Conditions
Real
Real
Bulk-interference modes
Real
Imaginary
Guided waves
Imaginary
Real
Leaky surface polaritons Bulk polaritons
p polarization, ∊xx < 0
Imaginary
Imaginary
Perturbed surface polaritons
p polarization, ∊xx < 0 or ∊3 < 0
Tables (4)
Table 1
Brewster Modes for Light Incident from an Isotropic Medium of Positive Dielectric Constant ∊1 onto a Superlattice
The limit qx = ∊11/2(ω/c) is not reached in all cases. In addition, modes can change type along their dispersion curves.
A type I Brewster mode extends from an L+ frequency if ∊xx < ∊1, whereas a type II mode extends if ∊xx > ∊1.
Table 2
Surface Modes between an Isotropic Medium of Positive Dielectric Function ∊1 and a Superlattice
If a pole appears in∊zz before either of these conditions is met a virtual mode can continue as a real mode terminating at ωs.
These modes are associated with strong dispersion in ∊1 and are included only for the sake of completeness.
Table 3
Surface Modes between an Isotropic Medium of Negative Dielectric Function ∊1 and a Superlattice
∊xx
∊zz
Mode Type
Minimum qx Limit
Maximum qx Limit
+ve
+ve
Real
−ve
+ve
qx = 0
qx→ ∞
at L+ or L0 mode
where ∊xx∊zz = ∊12
+ve
+ve
Real
−ve
+ve
qx = ∊zz1/2ω/c
qx→ ∞
at ∊xx = 0
where ∊xx∊zz = ∊12
+ve
+ve
Real
−ve
+ve
qx = ∊zz1/2ω/c
qx→ ∞
at pole in ∊1
where ∊xx∊zz = ∊12
Table 4
Modes Observable in a Standard ATR Experiment (with qz1 Imaginary) for a Superlattice Deposited on an Isotropic Substrate