Tutorial on Modeling of Metamaterial Structure in Ansys HFSS

Tutorial on

Saptarshi Ghosh, IIT Kanpur, INDIA

Modeling of Metamaterial Absorber Structure in Ansys HFSS

Saptarshi Ghosh

Thesis Supervisor: Dr. Kumar Vaibhav Srivastava Department of Electrical Engineering Indian Institute of Technology, Kanpur, India

Presentation Outline 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 2


Introduction to Metamaterials

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Overview of Metamaterial Artificial composite materials consisting of structural units smaller than the wavelength (λ) of the incident radiation. Controllable electromagnetic properties (ε, µ, n,…) at desired frequency.


Conventional material with atoms

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

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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.

[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,” Science, Vol. 292, pp. 77-79, April 2001. 5


Metamaterial Absorbers

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Conventional Absorbers [6]

~λ

Salisbury Screen Saptarshi Ghosh, IIT Kanpur, INDIA

Pyramidal Absorber Single-band absorber

Wide bandwidth above 90% absorption bandwidth Disadvantage : large thickness and fragile

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

Metamaterial Absorber [7]


Structure is ultra-thin (λ λ0/35) compared to conventional absorbers. Effective electromagnetic constitutive parameters (εeff 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]. 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 [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.

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Metamaterial Absorber When the reflected power (|S11|2) and transmitted power (|S21|2) have been minimized simultaneously, absorptivity (A) will be maximum.

A = 1− | S11 |2 − | S 21 |2 At 11.65 GHz,


|S11|2 = 0.01% |S21|2 ~ 0.9% A = 1-|S11|2-|S21|2 = 96% Simulated Absorptivity

What is the reason behind the absorptivity?

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Metamaterial Absorber [8] When the reflected power (|S11|2) and transmitted power (|S21|2) have been minimized simultaneously, absorptivity (A) will be maximum. A = 1− | S11 |2 − | S 21 |2 The design is made such a way that the input impedance is matched exactly with the free space impedance.


2 2 ( 1 + S11 ) − S 21 Z (ω ) = η 0 (1 − S11 )2 − S 21 2

Input impedance can be matched with free space impedance by controlling the effective material parameters. µ0 µ eff µ eff µ ′ + jµ ′′ Z (ω ) = = η0 = η0 ε 0ε eff ε eff ε ′ + jε ′′

at absorption frequency

ε ′ = µ′ ε ′′ = µ ′′

[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. 10

Effective Material Parameters [9] ε eff

2j = 1+ k0d

 1 − S 11 − S 21   1 + S 11 + S 21

  

µ eff

2j = 1+ k0d

 1 + S 11 − S 21   1 − S 11 + S 21

  


At 11.65 GHz

Re(εeff): 1.04; Re(µeff): -1.12

Im(εeff): 11.06; Im(µeff): 8.86

ε ′ ≈ µ ′ ε ′′ ≈ µ ′′ [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.

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Metamaterial Absorber Structure 1 We are first going to design a single-band metamaterial absorber. Points to remember:


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.

f ≈

1 2π

2 LC

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Metamaterial Absorber Structure 1 t


8 x 8 Array a = 10 mm, w = 0.4 mm, l = 6.5 mm, g = 0.2 mm Copper thickness = 0.035 mm, FR4 thickness = 1 mm (εr =4.25 & tanδ =0.02)

Front View of Unit Cell

Side View

Perspective View

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Metamaterial Absorber Structure 1 HFSS →Insert the Design → Draw a 3-D rectangular box

3D box


Project manager

Properties window

Message manager

Progress window 14

Project Variables Project variables are applicable to a particular project Prefixed with “$” sign Project variable is applied to all


the designs inside a project

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Design Variables Design variables are applicable to a particular design Independent from one design to


another design

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Square Metal Ground Plane 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 Assign material: copper

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Top Metallic Patch 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 Assign material: vacuum

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PEC/PMC Boundary condition

Opposite Current : PEC

Same Current : PMC

Same Current : PMC

PEC: Opposite Current

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PEC/PMC Boundary condition

PEC boundary

PMC boundary

Assigning Wave ports


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.

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Analysis


Solution Frequency: 6 GHz Maximum delta S (∆S): 0.02 Frequency range: 2 GHz – 10 GHz Sweep type : Fast/ Interpolating/ Discrete

It is the difference in error between two consecutive passes

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

Results


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


Surface Current Distributions

Top surface

Bottom surface

Current is flowing in circulating loop around the incident magnetic field 24

Some Common Questions


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

PEC boundary

PMC boundary

Reflection dip will change to 7.42 GHz instead of 6.07 GHz Reflection coefficient (S11) will decrease to -9.03 dB instead of -24 dB

Some Common Questions


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 ?

Solution

Use Floquet Ports

Floquet Ports Used exclusively with planar periodic structures Example : Planar phased array, frequency selective surface (FSS) The analysis of the infinite structure is then accomplished by analyzing a single unit cell by providing periodic boundary conditions (PBC).

PBC

PBC


PBC

PBC

Periodic in x-y plane

Master/ Slave Boundary Condition

Master 2


Slave 1

Master 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

Assigning Floquet ports 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

Periodic in y-direction

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Analysis and Results


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

Any Other advantage ?

Angle variation


There is a phase delay between the Master and Slave boundary The default value is zero Assign some variables in place of scan angles

Polarization Angle variation


When phi scan angle is varied from 0o to 90o, the incident wave is polarized keeping the incident wave propagation direction constant Since the structure is asymmetrical, reflection dip will change

Oblique Incidence


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

TE mode

TM mode

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


TE Polarization

When mode is TE (0,0)

TM Polarization

When mode is TM (0,0)


Some Other Examples

f ≈

1 2π

1 L × 2C

Resonant frequency will decrease to 4 GHz whereas the early presented structure has a reflection dip at 6 GHz However, the structure is still asymmetrical w.r.t. field vector directions

Some Other Examples (contd.) Structure is symmetrical w.r.t. incident field vector directions. Structure is four-fold symmetrical


Structure is polarization-insensitive

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

Conclusion 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.


Some other examples have also been discussed.

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Thank You

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Tutorial on Modeling of Metamaterial Structure in Ansys HFSS

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