13 Spinoptics in Plasmonics
477
1
−
=
2 μm
(b)
(c)
(d)
1 μm
(a)
1
=
σ
σ
Fig. 13.10 Measured near-field intensity. a for λ = 1 polarization and b for λ = −1 polarization,
at ε = 800 nm. The observed fringe maxima are presented in c for λ = 1 and in d for λ = −1
states. The black circle in c and d represents the location of the annular nanoslit. The inset in b with
a dark spot in the center (marked with an arrow) is the measured intensity distribution inside the
circular slit. Reprinted with permission from Ref. [46]. Copyright 2008 American Physical Society
The coupling of light to non-radiative surface modes is achieved via momentum
modification by a surface defect, such as a nanoaperture [50, 51]. In particular, a
nanoslit introduces a momentum modification (matching) in perpendicular direction,
exciting a surface wave with a phase front parallel to the slit. Moreover, only TM
polarized incident waves (with an electric field perpendicular to the slit) can be
efficiently coupled by the slit to surface plasmons. This polarization selectivity in
SPP excitation implies highly anisotropic interaction. Due to the circular shape of the
annular slit, it is convenient to analyze the wave propagation in a rotating reference
frame attached to a local anisotropy axis [46, 52, 53]. For the observer moving
along a path with radius r the local structure (slit) orientation appears to be rotated
with the rate ∂ = dτ/dϕ = 1/r where τ (ϕ ) is the slit orientation, and ϕ is the path
parameter (see Fig. 13.10b). The Helmholtz equation in a non-inertial reference frame
rotating with ∂ (ϕ ), is (∇ 2 + k 2 − 2λ ∂k)E λ = 0, where E λ = 2 −1/2
E x + iλ E y
are the eigenvectors of circular polarizations. Note that a spin-dependent Coriolis
term appears in the corrected Helmholtz equation. This equation can be written as
∇ 2 + K 2
E λ = 0, where K (Θ) ≈ k(Θ) − λ ∂ is the generalized momentum [47,
48, 53]. A similar term also appears in the time-independent Schrödinger equation
in the presence of a vector potential. This spin-dependent wavevector modification
477
1
−
=
2 μm
(b)
(c)
(d)
1 μm
(a)
1
=
σ
σ
Fig. 13.10 Measured near-field intensity. a for λ = 1 polarization and b for λ = −1 polarization,
at ε = 800 nm. The observed fringe maxima are presented in c for λ = 1 and in d for λ = −1
states. The black circle in c and d represents the location of the annular nanoslit. The inset in b with
a dark spot in the center (marked with an arrow) is the measured intensity distribution inside the
circular slit. Reprinted with permission from Ref. [46]. Copyright 2008 American Physical Society
The coupling of light to non-radiative surface modes is achieved via momentum
modification by a surface defect, such as a nanoaperture [50, 51]. In particular, a
nanoslit introduces a momentum modification (matching) in perpendicular direction,
exciting a surface wave with a phase front parallel to the slit. Moreover, only TM
polarized incident waves (with an electric field perpendicular to the slit) can be
efficiently coupled by the slit to surface plasmons. This polarization selectivity in
SPP excitation implies highly anisotropic interaction. Due to the circular shape of the
annular slit, it is convenient to analyze the wave propagation in a rotating reference
frame attached to a local anisotropy axis [46, 52, 53]. For the observer moving
along a path with radius r the local structure (slit) orientation appears to be rotated
with the rate ∂ = dτ/dϕ = 1/r where τ (ϕ ) is the slit orientation, and ϕ is the path
parameter (see Fig. 13.10b). The Helmholtz equation in a non-inertial reference frame
rotating with ∂ (ϕ ), is (∇ 2 + k 2 − 2λ ∂k)E λ = 0, where E λ = 2 −1/2
E x + iλ E y
are the eigenvectors of circular polarizations. Note that a spin-dependent Coriolis
term appears in the corrected Helmholtz equation. This equation can be written as
∇ 2 + K 2
E λ = 0, where K (Θ) ≈ k(Θ) − λ ∂ is the generalized momentum [47,
48, 53]. A similar term also appears in the time-independent Schrödinger equation
in the presence of a vector potential. This spin-dependent wavevector modification