Dual-frequency Characterization of Bending Loss in Hollow Flexible Terahertz Waveguides

Pallavi Doradlaa,b, and Robert H. Gilesa,b

aSubmillimeter Wave Technology Laboratory, University of Massachusetts Lowell

bDepartment of Physics & Applied Physics, University of Massachusetts Lowell, USA

Feb-06-2014

Outline

Introduction

Theory

Selection of Material

Optimal Thickness

Fabrication

Liquid Flow Coating (LFC) Process

Dynamic Liquid Phase Coating Process

Experimental Method

Experimental Setup

Mode Cleaning

Experimental Method

Propagation Loss Measurement

Bending Loss Measurement

Modal Characteristics

Summary

Introduction

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1Wai Lam Chan, Jason Daibel, and Daniel M. Mittleman, “Imaging with terahertz radiation,” Rep.Prog. Phys. 70, 1325-1379 (2007)2Figure copied from: Coherent Infrared Center Advance Light Source: http://circe.lbl.gov/THzGap.html

Basic Design

Schematic cross section of metal and dielectric coated

Hollow-core THz waveguide

Theory

Theoretical Loss as a function of Wavelength for lower order TE & TM modes

𝛂 𝐓𝐌𝐩𝐪 = 𝟏𝟎 ∗𝟏

𝐫

𝐧

𝐧𝟐 + 𝐤𝟐& 𝛂 𝐓𝐄𝐩𝐪 = 𝟏𝟎 ∗

𝐮𝟒

𝐮𝟐 − 𝐩𝟐𝐧

𝐧𝟐 + 𝐤𝟐𝟏

𝐤𝟎𝟐𝐫𝟑

+𝐩𝟐

𝐮𝟒𝐫

𝛂𝐭𝐨𝐭 = 𝛂𝐩𝐫𝐨𝐩𝐚𝐠𝐚𝐭𝐢𝐨𝐧 + 𝛂𝐛𝐞𝐧𝐝𝐢𝐧𝐠

Lines of current flow Magnetic Lines

3T. Ito, M. Miyagi, H. Minamide, H. Ito and Y. Matsuura, "Flexible terahertz fiber optics with low bend-induced

losses," J. Opt. Soc. Am. B 24, 1230–1235 (2007).

Skin Depth:

ρ - Resistivity (Ωm)

f - Frequency = 1.4THz

µ0 - 4πx10-7 (Henries/meter)

δAg=0.05µm at 1.4 THz and 0.08 µm at 584 GHz;

δAu=0.07µm at 1.4 THz and 0.1 µm at 584 GHz.

When λ = 215μm

FAg = 0.684 , FAu = 0.878, FAl = 0.994

FCu = 1.159, FW = 1.965, FPb = 2.945

Selection of Metal

4Ordal, M., A., et. al., “Optical properties of the metals Al, Co, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in IR & FIR”,

Applied Optics, 22(7), 1099-1119 (1983)

0

22

Rf

Selection of Dielectric

Attenuation coefficient of as a function of bore diameter for lower order HE

modes, for TE11 and HE11 modes of Silver coated waveguide

5M. Miyagi and S. Kawakami, “Design Theory of Dielectric-Coated Circular Metallic Waveguides for Infrared

Transmission,” J. Light. Wave Technol. 2(2), 116–126 (1984).

Base Material: Polycarbonate Metal: Silver, Gold Dielectric Material: Polystyrene

Fabrication: Liquid Flow Coating Process

Fabrication: dynamic liquid phase coating process ………

Fabrication

Y Connector

Waste Collector

Peristaltic Pump

Silver

Solution

Reducing

Agent

Channel 1 Channel 2

Polycarbonate

or Glass tube

6P. Doradla, C. S. Joseph, J. Kumar, and R. H. Giles, “Propagation Loss Optimization in Metal/Dielectric Coated

Hollow Flexible Terahertz Waveguides,” Proc. of SPIE 8261, 82601P1–82610P10 (2012).

Experimental Setup

Experimental setup for the measurement of attenuation coefficient for

metal, metal/dielectric coated Terahertz waveguides

The attenuation constant for EHnm modes in dB/m is given by ,

Mode Cleaning

Two-dimensional mode profiles of the propagated terahertz beam acquired using silicon

bolometer a) 20 cm after OAP, b) after 5 cm, and c) 15 cm Polycarbonate tube.

2 2

38.686 Re

2nm

nm nu

r

2

n2

1 ν

2 1&

N

N

A polycarbonate tube with CIR 1.64 – ix0.05, 5 cm length: 1.25 dB, 6.6 dB, 16.2 dB and

15 cm length: 3.76 dB, 19.79 dB, 48.7 dB for EH11, EH12, and EH13 modes

7P. Doradla, C. S. Joseph, J. Kumar, and R. H. Giles, “Characterization of bending loss in hollow flexible

terahertz waveguides,” Opt. Express 20 (17), 19176 – 19184 (2012).

Propagation Loss

Theoretical and Experimental attenuation coefficients as a function of inner bore diameter

for silver and gold coated waveguides at 1.4 THz and 584 GHz freq.

Bore

Diamete

r

1.4 THz 584 GHz

Loss (dB/m) in Ag Loss (dB/m) in Au Loss (dB/m) in Ag Loss (dB/m) in Au

Theo. Exp. Theo. Exp. Theo. Exp. Theo. Exp.

4mm 1.44 1.77 1.85 1.98 1.03 1.62 1.29 1.89

3mm 1.8 2.64 2.31 2.93 1.4 2.3 1.63 2.6

2mm 2.9 3.5 3.73 4.02 2.19 3.0 2.73 3.65

Bending Loss

Total attenuation coefficient per bore diameter cube as a function of

bending angle and bore diameters for Ag coated waveguides at 584 GHz

(inset: 1.4 THz) with 6.5 cm bend radius.

3

3 3 3113 6

/ / /tot pq R

C r Lr L L r L C R r C C

Rr r

According to Beer-Lambert’s Law,

Modal Characteristics

Spatial output profile from Ag coated waveguides at (I) 1.4 THz, (II) 584 GHz as a function of bore diameter (rows) (2) 2 mm, (3) 3 mm, (4) 4mm; and

bending angle (columns) (1) 00, (2) 600, (3) 1200.

Summary

Attenuation Characteristics of flexible Terahertz waveguides were studied

at both 1.4 THz and 584 GHz frequencies .

Propagation loss as small as 1.7 dB/m was achieved in silver coated

waveguides by coupling the lowest loss TE11 mode.

The 2 mm ID metal coated waveguide showed least variation in

transmission loss (<1 dB/m) with 00 – 1500 bending angle.

The 1 µm thick silver coated 2 mm inner diameter waveguides can be used

at both the frequencies, to obtain low transmission losses and mode

preservation.

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