Anti-reflection implementations for terahertz waves

doi:10.1007/s12200-013-0377-z

Front. Optoelectron.

2014, Vol. 7

Issue (2) : 243-262 https://doi.org/10.1007/s12200-013-0377-z

REVIEW ARTICLE

Anti-reflection implementations for terahertz waves

Yuting W. CHEN^1,^*(

),Xi-Cheng ZHANG^2,^*(

)

1. IBM Corporations, Poughkeepsie, NY 12538, USA
2. The Institute of Optics, University of Rochester, Rochester, NY 14627-0186, USA

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Abstract

Undesired reflection caused by impedance mismatch can lead to significant power loss and other unwanted effects. In the terahertz regime, anti-reflection method has evolved from simple quarter-wave anti-reflection coating to sophisticated metamaterial device and photonic structures. In this paper, we examined and compared the theories and techniques of several anti-reflection implementations for terahertz waves, with emphasis on gradient index photonic structures. A comprehensive study is presented on the design, fabrication and evaluation of this new approach.

Keywords terahertz anti-reflection gradient index photonic structure

Corresponding Author(s): Yuting W. CHEN

Issue Date: 25 June 2014

Cite this article:

Yuting W. CHEN,Xi-Cheng ZHANG. Anti-reflection implementations for terahertz waves[J]. Front. Optoelectron., 2014, 7(2): 243-262.

URL:

https://academic.hep.com.cn/foe/EN/10.1007/s12200-013-0377-z
https://academic.hep.com.cn/foe/EN/Y2014/V7/I2/243

Fig.1 Transmittance measurement using THOMAS on quarter-wave anti-reflection coated silicon window with wedge angles of 0°, 0.05°, 0.10° and 0.15°, edited for clarity [1]

Fig.2 Simulated transmissions of model plane-parallel anti-reflection coated silicon window and anti-reflection coated wedge silicon window are plotted in short dash and long dash, respectively. FTS-measurement of small silicon window sample is represented by solid line and THOMAS-measurement of aircraft-window is represented by diamond symbol, edited for clarity [1]

Fig.3 Reflection and absorption loss versus sheet conductance at 1.5 THz with index mismatch ratio of 1.42, 2.42 and 3.42 [4]

Fig.4 Simulated reflection at the GaAs and air interface with (a) quarter-wave dielectric coatings with constant refractive index and frequency dependent refractive index; (b) 16.3 nm thick metallic impedance matching layer [4]

Fig.5 THz-TDS transmitted measurements: time-domain waveforms and spectral ratio of uncoated sample versus coated sample of (a, b) high resistivity silicon, 8.3 nm chromium coating and (c, d) high resistivity GaAs, 44 nm ITO coating [4]

Fig.6 SEM image showing cross-section of the germanium substrate with four layers of silicon oxide deposited as anti-reflection coating, edited for clarity [7]

Fig.7 Transmittance of multi-layer silicon oxide coating on germanium substrate: solid circle is designed value, triangle is calculated value from SEM measurement, solid square is calculated value base on SEM measurement and EDS analysis, and solid curve is measured value under FTIR, edited for clarity [7]

Fig.8 (a) A unit cell of the metamaterial device; (b) reflectance and transmittance of the device measured under THz-TDS comparing with that of GaAs substrate [8]

Fig.9 Measured reflectance of (a) TM polarization and (b) TE polarization for incident angles from 20° to 60° [8]

Fig.10 SEM image of a micro-pyramid array with a 45-μm period [11]

Fig.11 Measured reflectivity of micro-pyramid arrays with period of 30, 45, 60, 70 and 110 μm [11]

Fig.12 3-D prototype of three-layer pyramid structure

Tab.1 Design parameters of three-layer structure from gradient index anti-reflection theory

Fig.13 Reflectance of designed three-layer structure and blank silicon versus unit wavelength

Fig.14 Transformation of three-layer photonic design

Fig.15 (a) Schematic of a unit cell inside a periodic etched layer; (b) circuit model used to describe the unit cell; (c) SEM image of such periodic etched layer [14]

Fig.16 Transformation of unit cell from periodic pillars to periodic holes

Fig.17 Relative refractive index of an etched periodic square hole layer versus etch dimension

Fig.18 Cross-section SEM image of an etched layer

Fig.19 THz-TDS measured waveforms of unetched area and etch area on silicon substrate

Fig.20 Three-layer dielectric system between air and silicon

Fig.21 Simulated reflectance versus frequency of three-layer gradient index structure with total thickness of 20, 28 and 36 μm in (a) linear scale and (b) log scale

Tab.2 Complete fabrication parameters of the three-layer structures

Fig.22 Fabrication process cycle of three-layer gradient index anti-reflection structure

Fig.23 SEM image of three-layer gradient index anti-reflection structure with a period of 20 μm

Fig.24 THz-ABCD system used for structure evaluation (Si: silicon, BS: beam splitter, P: parabolic mirror, BBO: barium borate crystal, PMT: photomultiplier tube) [17]

Tab.3 THz-ABCD system specification

Fig.25 (a) Waveform and (b) spectrum of reference signal of THz-ABCD system

Fig.26 (a) Reflected waveform and (b) reflectance spectrum of high resistivity silicon

Fig.27 Experimental setup of structure evaluation

Fig.28 Reflection measurement of a 20-μm period and a 15-μm period inverted photonic structure using THz-ABCD- (a) reflected terahertz waveforms and (b) Fourier transform reflectance spectra

Fig.29 Transmission measurement of silicon reference, a 20-μm period and a 15-μm period structure using THz-ABCD- (a) transmitted THz waveforms and (b) relative transmission spectra

Fig.30 (a) Transmitted terahertz waveforms of 15-μm period structure at azimuthal angle from 0° to 315° in 45° steps; (b) relative terahertz transmission amplitude of 15-μm period structure at 3.7 THz

Fig.31 Reflectance of p-polarized wave at normal incident on an air to silicon interface

Fig.32 Simulated reflectance spectra of three-layer gradient index structure at different incident angle

Fig.33 Simulated reflectance spectra of planar silicon at different incident angle at 3.7 THz

Fig.34 Transmitted terahertz waveforms of (a) 15-μm period structure and (b) silicon reference at incident angles from 0° to 50°

Fig.35 Simulated (solid curve in black) and measured (dash curve in red) relative transmission spectra of three-layer gradient index structure at various incident angles: (a) 0°, (b) 10°, (c) 20°, (d) 30°, (e) 40°, (f) 50°

Tab.4 Summary of parameters with their corresponding relative refractive indices

Fig.36 Combinations of parameter variation for design sensitivity analysis

Fig.37 Simulated reflectance of inverted photonic structure with variations on hole dimension in each layer

Fig.38 Simulated reflectance of three-layer, five-layer and seven-layer inverted photonic designs

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