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Engineering the Reststrahlen band with hybrid plasmon/phonon excitations

Published online by Cambridge University Press:  28 December 2015

W. Streyer
Affiliation:
Micro and Nanotechnology Laboratory, University of Illinois at Urbana Champaign, Electrical and Computer Engineering, 208 North Wright St, Urbana, Illinois, USA
K. Feng
Affiliation:
University of Notre Dame, Electrical Engineering, Notre Dame, Indiana, USA
Y. Zhong
Affiliation:
Micro and Nanotechnology Laboratory, University of Illinois at Urbana Champaign, Electrical and Computer Engineering, 208 North Wright St, Urbana, Illinois, USA
A.J. Hoffman
Affiliation:
University of Notre Dame, Electrical Engineering, Notre Dame, Indiana, USA
D. Wasserman*
Affiliation:
Micro and Nanotechnology Laboratory, University of Illinois at Urbana Champaign, Electrical and Computer Engineering, 208 North Wright St, Urbana, Illinois, USA
*
Address all correspondence to D. Wasserman at dwass@illinois.edu

Abstract

There has been increasing interest in so-called phononic materials, which can support surface modes known as surface phonon polaritons, consisting of electromagnetic waves coupled to lattice vibrations at the surface of a polar material. While such excitations have a variety of desirable features, they are limited to the spectral range between a material's longitudinal and transverse optical phonon frequencies. In this work, we demonstrate that for materials whose free-carrier concentrations can be controlled, hybrid plasmonic/phononic modes can be supported across a range of frequencies including those generally forbidden by purely phononic materials.

Information

Type
Plasmonics, Photonics, and Metamaterials Research Letters
Copyright
Copyright © Materials Research Society 2015 
Figure 0

Table I. Parameters for each sample used in the permittivity model as described in Eq. (1).

Figure 1

Figure 1. (a) Reflection spectra of unpatterned samples A (gray, SI GaAs wafer), B (red, 2 µm Si:GaAs nB = 6 × 1017cm−3), and C (blue, 2 µm Si:GaAs nC = 3.8 × 1018 cm−3). (b) Extracted real (solid) and imaginary (dashed) components of the permittivity of samples A (gray), B (red), and C (blue). Inset in (a) shows the structure of unpatterned samples studied. Stacked area plots show the contributions to the real and imaginary permittivity in (c) sample B and (d) sample C from free carriers and lattice vibrations. (e) Calculated FOM for LSP(h)'s (dotted) and SP(h)P's (solid) as a function of wavelength for each of the three samples (A-gray, B-red, and C-blue).

Figure 2

Figure 2. Schematic representation of the experimental setup for determination of surface mode dispersion. In (a), the incident photon has no momentum in the grating direction, while in (b) the incident photon has a momentum component given by kph.x = ko sin θ sin φ, where θ = 10°, fixed by our experimental apparatus, and φ varies from 0° to 50°. (c) Calculated dispersion of semi-infinite phononic/air (gray) and hybrid (phononic/plasmonic)/air (red) interfaces. The black line shows the dispersion of the free-space photon, while the dashed blue lines show the sum of the grating momentum and incident photon momentum in the grating direction (kph.x + 2π/Λ), where Λ is the grating period. Coupling to the grating, as calculated by RCWA, is shown for the undoped sample A (black squares), the doped epilayer of sample B (red squares), and a hypothetical sample of infinite thickness, doped to the same concentrations as sample B (red circles).

Figure 3

Figure 3. Magnetic field |Hy| plots at λ ~ 36 µm and λ = 35.9 µm, corresponding to the normal incidence coupling wavelengths for the (a) undoped and (b) doped samples A and B, respectively. TE-polarized (c, d) RCWA-simulated and (e, f) experimental reflection from (c, e) undoped SI GaAs (sample A) and (d, f) 2 µm Si:GaAs ND = 6 × 1017 cm−3 (sample B). Each sample is patterned with a 1D grating with period Λ = 35 µm, ridge width w = 18 µm, and ridge depth d = 1.4 µm.

Figure 4

Figure 4. Magnetic field |Hy| at λ ~ 34.8 µm and λ ~ 34.2 µm, for the (a) undoped and (b) doped sample, respectively, with light incident at 50° from normal. TM-polarized (c, d) RCWA-simulated and (e, f) experimental reflection from (c, e) undoped SI GaAs wafer and (d, f) 2 µm Si:GaAs ND = 6 × 1017cm−3 sample. Each sample is patterned with a 1D grating with period Λ = 35 µm and ridge width w = 18 µm and deep-etched ridge depth d = 1.8 µm. Insets in (c) and (d) show the experimental configuration.