Tutorial on Modeling of Metamaterial Structure in Ansys HFSS

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Tutorial

on

Modeling of Metamaterial Absorber Structure

in Ansys HFSS

Saptarshi Ghosh

Thesis Supervisor: Dr. Kumar Vaibhav Srivastava

Department of Electrical Engineering

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Presentation Outline

2

Introduction to Metamaterials

Overview of Metamaterial Absorbers

Modeling of Metamaterial Absorber Structure 1

PEC-PMC modes

Floquet Modes

Modeling of Other Metamaterial Absorber Structures

Conclusion

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Introduction to Metamaterials

3

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Overview of Metamaterial

4

 Artificial composite materials consisting of structural units smaller than the wavelength (λ) of the incident radiation.

Conventional material with atoms

Unit-cell driven metamaterial (size < λ/4)

 Controllable electromagnetic properties (ε, µ, n,…) at desired frequency.

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Historical Overview

 1968: Veselago [1] predicted the existence of LHM.

 1996: Realization of negative permittivity practically [2] by Pendry.

 1999: Experimental verification of negative permeability [3] by Pendry.  2000: First Experimental Demonstration of LHM [4] by Smith.

 2001: First realization of Negative Refractive Index [5] by Shelby.

5

[1] V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of µ and ε,” Sov.

Phys. Uspekhi, Vol. 10, No. 4, pp. 509-514, 1968.

[2] J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic microstructure,” Phys. Rev. Lett., Vol. 76, No. 25, pp. 4773-4776, June 1996.

[3] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Micr. Theory. Tech., Vol. 47, No. 11, pp. 2075-2084, Nov. 1999.

[4] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett., Vol. 84, No. 18, pp. 4184-4187, 2000. [5] R. A.Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,”

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Metamaterial Absorbers

6

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

[6] P.Saville, “Review of Radar Absorbing Materials,” Defense R & D Canada-Atlantic, Jan. 2005.

Salisbury Screen

Conventional Absorbers [6]

Pyramidal Absorber

~λ

Wide bandwidth above 90% absorption bandwidth

Disadvantage :

large thickness and fragile Single-band absorber

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Metamaterial Absorber [7]

8

 Structure is ultra-thin (λλλλ₀/35) compared to conventional absorbers.  Effective electromagnetic constitutive parameters (ε

eff and µeff) have

been tailored using unit cell design.

 Absorbers can be made scalable- from microwave, terahertz, infrared, optical frequency range.

 Structures can be easily fabricated _{using PCB technology.}  First experimentally realized by Landy et. al. in 2008 [12].

[7] N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,”

Phys. Rev. Lett., vol. 100, pp. 207402, May 2008.

a₁ = 4.2 mm, a₂ = 12 mm, W = 4 mm, G = 0.6 mm, t = 0.6 mm, L = 1.7 mm, H = 11.8 mm

FR4 substrate thickness = 0.72 mm Copper thickness = 0.017 mm

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Metamaterial Absorber

9

 When the reflected power (|S11|2) and transmitted power (|S21|2) have

been minimized simultaneously, absorptivity (A) will be maximum.

2 21 2 11 | | | | 1 S S A = − − |S₁₁|2 = 0.01% |S₂₁|2 _{~ 0.9%} A = 1-|S₁₁|2_-|S 21|2 = 96% At 11.65 GHz, Simulated Absorptivity

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Metamaterial Absorber [8]

10

 When the reflected power (|S

11

|

2

) and transmitted power (|S

21

|

2

)

have been

minimized simultaneously

, absorptivity (A) will be

maximum.

 The design is made such a way that the

input impedance is

matched exactly with the free space impedance

.

 Input impedance can be matched with free space impedance by

controlling the effective material parameters

.

[8] D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, pp. 036617, 2005.

2 21 2 11 | | | | 1 S S A = − − ε ε µ µ η ε µ η ε ε µ µ ω ′′ + ′ ′′ + ′ = = = j j Z eff eff eff eff 0 0 0 0 ) (

(

)

(

)

2 21 2 11 2 21 2 11 0 1 1 ) ( S S S S Z − − − + =η ω

µ

ε

′ = ′

µ

ε

′′ = ′′ at absorption frequency

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Effective Material Parameters [9]

11

[9] C. L. Holloway, E. F. Keuster, and A. Dienstfrey, “Characterizing metasurfaces /metafilms: the connection between surface susceptibilities and effective material properties,” IEEE Antennas Wireless Propag. Lett., Vol. 10, pp. 1507-1511, 2011.

µ

ε

′ ≈ ′

ε

′′ ≈

µ

′′       + + − − + = 21 11 21 11 0 1 1 2 1 S S S S d k j eff ε _      + − − + + = 21 11 21 11 0 1 1 2 1 S S S S d k j eff µ

Re(ε_eff): 1.04; Re(µ_eff): -1.12 Im(ε_eff): 11.06; Im(µ_eff): 8.86 At

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Metamaterial Absorber Structure 1

12

We are first going to design a single-band metamaterial absorber.

 Metamaterial absorber structures are periodic structures

 Since metamaterial absorber structures are resonant structures, there must be some equivalent capacitances (C) and inductances (L).

 Inductance can be realized by any metallic patch

 Capacitance can be realized by any gap between two metallic patches depending on the direction of E-field.

Points to remember: LC f 2 2 1 π ≈

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Metamaterial Absorber Structure 1

13

8 x 8 Array Front View of Unit Cell Side View

Perspective View a = 10 mm, w = 0.4 mm, l = 6.5 mm, g = 0.2 mm Copper thickness = 0.035 mm, FR4 thickness = 1 mm (ε_r =4.25 & tanδ =0.02) t

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HFSS →Insert the Design → Draw a 3-D rectangular box

Metamaterial Absorber Structure 1

3D box

Properties window Project manager

Progress window Message manager

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Project Variables

15

 Project variables are applicable to a particular project

 Prefixed with “$” sign

 Project variable is applied to all the designs inside a project

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Design Variables

16  Design variables are applicable

to a particular design

 Independent from one design to another design

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Square Metal Ground Plane

17

Positional coordinates : 0,0,0

X-size: 10 mm; Y-size: 10 mm; Z-size: 0.035 mm
Assign material: copper

FR-4 Dielectric Substrate

Positional coordinates : 0,0,0

X-size: 10 mm; Y-size: 10 mm; Z-size: 0.035 mm

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Top Metallic Patch

18

First draw a square box

Then, draw a middle line and add it to the square loop
Lastly, subtract a small gap from the middle line

Assign material: copper

Air Box

An air box needs to be provided for providing boundary condition

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

PEC/PMC Boundary condition

19 Opposite Current : PEC

PEC: Opposite Current

Same Current : PMC

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

PEC/PMC Boundary condition

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Assigning Wave ports

21

 Since back side is full metal plane, transmission (S21) is zero

 No need to put wave port 2 at the back

 Deembedding is not necessary, as we are interested in magnitude of reflection coefficient (|S₁₁|2_{) only.}

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Analysis

 Solution Frequency: 6 GHz  Maximum delta S (∆S): 0.02  Frequency range: 2 GHz – 10 GHz

 Sweep type : Fast/ Interpolating/ Discrete

Sweep type Solution time Comments

Fast 7 min 10 sec Quickest, but most inaccurate

Interpolating 10 min 12 sec Not the quickest, not the most accurate Discrete ∼∼16 hours ∼∼ Slowest, but most accurate

It is the difference in error between two consecutive passes

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

 Since only 1 port, only 1 S-parameter is available  Reflection coefficient: S(1,1) in dB or in mag

 Reflection coefficient : -24 dB at 6.07 GHz

 Absorptivity: {1- (mag(S(1,1))2_)}*100

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA 24

Surface Current Distributions

Top surface Bottom surface

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

 What if the PEC/PMC boundary conditions will be interchanged ?

Some Common Questions

PEC boundary PMC boundary

 Reflection dip will change to 7.42 GHz instead of 6.07 GHz

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

 Will this PEC/PMC boundary condition be valid if the structure is complicated ?

 Will this PEC/PMC boundary condition work when the current flow will not be as simple as this ?

 How to measure the oblique incidence measurement ?

 How to measure the reflectivity when the structure is rotated ?

Some Common Questions

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

 Used exclusively with planar periodic structures

 Example : Planar phased array, frequency selective surface (FSS)

Floquet Ports

The analysis of the infinite structure is then accomplished by analyzing a single unit cell by providing periodic boundary conditions (PBC).

PBC PBC P B C P B C

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Master/ Slave Boundary Condition

Master 1

Master 2 Slave 1

Slave 2

No change in reflection coefficient or reflection dip under normal incidence even if there is reversal of master 2 and slave 2 directions

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Assigning Floquet ports

29  No need to put floquet port 2 at the back

 Deembedding is not necessary, as we are interested in magnitude of reflection coefficient (|S₁₁|2_{) only.}

 We have to provide lattice vectors “a” and “b” to define the

periodicity in x-y plane

Periodic in x-direction

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

 Fast sweep is not available in lower versions of HFSS (upto HFSS 13)  Result remains almost same

 Absorptivity: {1- (mag(S(1,1))2_)}*100

Analysis and Results

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

 There is a phase delay between the Master and Slave boundary  The default value is zero

 Assign some variables in place of scan angles

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

 When phi scan angle is varied from 0o _{to 90}o_{, the incident wave is}

polarized keeping the incident wave propagation direction constant  Since the structure is asymmetrical, reflection dip will change

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

 Floquet port has the extra advantage of modal decomposition

 During assigning “floquet port”, the default number of modes is : 2  These number of modes and type of modes can be manually controlled

Oblique Incidence

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Variation of theta scan angle (θ) from 0o _{to 90}o

TE Polarization

TM Polarization

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Some Other Examples

C L f 2 1 2 1 × ≈ π

Resonant frequency will decrease to 4 GHz whereas the early presented structure has a reflection dip at 6 GHz

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Some Other Examples (contd.)

Structure is symmetrical w.r.t. incident field vector directions.

 The structure exhibits reflection dip at close to 6 GHz

 Small deviation in frequency from the initial proposed structure is due to difference in gap (g) value

Structure is four-fold symmetrical

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA

Conclusion

37

A brief introduction about metamaterial and metamaterial absorber has been discussed.

A single-band metamaterial absorber structure has been studied in detail.

Different boundary conditions and modes have been investigated to analyze the structure.

S a p ta rsh i G h o sh , II T K a n p u r, I N D IA 38

Thank You