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Frontiers of Optoelectronics

Front. Optoelectron.    2014, Vol. 7 Issue (2) : 243-262     DOI: 10.1007/s12200-013-0377-z
Anti-reflection implementations for terahertz waves
Yuting W. CHEN1,*(),Xi-Cheng ZHANG2,*()
1. IBM Corporations, Poughkeepsie, NY 12538, USA
2. The Institute of Optics, University of Rochester, Rochester, NY 14627-0186, USA
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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 Authors: 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.
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Yuting W. CHEN
Xi-Cheng ZHANG
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
layer1 (air)2345 (silicon)
effective index of refraction1.01.552.252.953.42
thickness (per unit wavelength)-0.31560.2250.172-
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
layer1 (air)2345 (silicon)
refractive index1.01.552.252.953.42
layer height-8.9 μm6.3 μm4.8 μm-
air ratio/%10077.4442.2510.890
hole dimension(Λ = 20 μm)-17.6 μm×17.6 μm13.0 μm×13.0 μm6.6 μm×6.6 μm-
holedimension(Λ = 15 μm)-13.2 μm×13.2 μm9.7 μm×9.7 μm4.9 μm×4.9 μm-
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]
laserSP Hurricane amplifier: 1 kHz repetition rate 750 mW power 100 fs pulse duration
terahertz emitternitrogen purged
biased electric field~20 kV/cm
terahertz receivernitrogen purged; fused silica lens
modulation frequency500 Hz
lock-in time constant100 ms
measurement typenormal reflection (incident angle: 0°)
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°
original design-5% discrepancy+ 5% discrepancy
layer 2a2 = 13.2 μm,n2 = 1.55a2,0 = 12.54 μm,n2,0 = 1.70a2,1 = 13.86 μm,n2,1 = 1.37
layer 3a3 = 9.7 μm,n3 = 2.25a3,0 = 9.22 μm,n3,0 = 2.33a3,1 = 10.19 μm,n3,1 = 2.17
layer 4a4 = 4.9 μm,n4 = 2.95a4,0 = 4.66 μm,n4,0 = 2.98a4,1 = 5.15 μm,n4,1 = 2.92
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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