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ECE 5322 21st Century Electromagnetics

Instructor:Office:Phone:E‐Mail:

Dr. Raymond C. RumpfA‐337(915) 747‐6958rcrumpf@utep.edu

Guided-Mode Resonance

Lecture #11

Lecture 11 1

Lecture Outline

• Physics of Guided-Mode Resonance (GMR)

• GMR Filters

• Design of GMR Filters

• Applications

Lecture 11 Slide 2

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Physics of Guided-Mode Resonance

The Critical Angle and Total Internal Reflection

Lecture 11 Slide 4

When an electromagnetic wave is incident on a material with a lower refractive index, it is totally reflected when the angle of incidence is greater than the critical angle.

cinc

1 2

1

sinc

n

n

ExampleWhat is the critical angle for fused silica (glass).

The refractive index at optical waveguides is around 1.5.

1 1.0sin 41.81

1.5c

cinc

1n

2n

1n

2n

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The Slab Waveguide

Lecture 11 Slide 5

If we “sandwich” a slab of material between two materials with lower refractive index, we form a slab waveguide.

2n

1n

TIR

TIR

3n

Conditions

2 1

2 3

and

n n

n n

Ray Tracing Analysis

Lecture 11 Slide 6

The round trip phase of a ray must be an integer multiple of 2.Only certain angles are allowed to propagate in the waveguide.

2m

0 eff 0 sink n k n

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Rigorous Analysis

Lecture 11 Slide 7

E j H

H j E

A rigorous analysis of slab waveguides involves Maxwell’s equations.

The geometry and mode solutions for a typical slab waveguide are

x

y

z

Diffraction from Gratings

Lecture 11 Slide 8

The angles of the diffracted modes are related to the wavelength and grating through the grating equation.

The grating equation only predicts the directions of the modes, not how muchpower is in them.

Reflection Region

0trn inc incsin sin

x

n m n m

0ref inc incsin sin

x

n m n m

Transmission Region

ref incn n

trnn

x

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GMR = Diffraction + Waveguide

Lecture 11 9

QuestionWhat happens when a diffraction grating and slab waveguide are brought into proximity and the angle of a diffracted mode matches the angle of a guided mode?

Guided-Mode Resonance

Lecture 11 Slide 10

Away From Resonance At Resonance

Away from resonance, the structure exhibits the “background” response of a multilayer device. 

At resonance, part of the applied wave is coupled into a guided mode.  The guided mode slowly “leaks” out from the waveguide.  The “leaked” wave interferes with the applied wave to produce a filtering response.

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Regions of Guided-Mode Resonance (Derivation)

Lecture 11 Slide 11

Recall the grating equation

02 1 incsin sin sinn m n m

Conditions for neff to represent a guided mode

1 3 eff 2max ,n n n n

Recall from the ray tracing picture that

0 eff 0 2 sinm k n k n m

Combining the above two equations leads to an equation describing the regions of resonance for guided‐mode resonance.

01 3 1 inc 2max , sin sinn n n m n

Therefore

0eff 1 incsin sinn n m

Regions of Guided-Mode Resonance (Plot)

Lecture 11 Slide 12

01 3 1 inc 2max , sin sinn n n m n

• Estimates ranges for resonant frequencies• Predicts sensitivity to angle of incidence• Shows how higher order resonances overlap

• Zero‐order modes produces no resonance effects.

Center wavelength at normal incidence:

Bounds:

+1‐1

+2‐2

‐3

+3

2 1 3max ,

2 sincn n n

m

0 maxmin

1 inc 1 3

min

1 inc 1 3

1 inc 2

max

1 inc 2

sin max , 0

sin

sin max , 0

sin

sin 0

sin

sin 0

sin

n n nm

m

n n nm

m

n nm

m

n nm

m

n1 = 1.0

n3 = 1.52

n2 = 2.05 = 90°

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Benefits and Drawbacks

• Benefits– All-dielectric for very low loss– Extremely strong response from dielectrics– Can be made monolithic– Potentially better for high power than using metals

• Drawbacks– Larger and bulkier than equivalent metallic structures– Limited field-of-view and bandwidth compared to

metallic devices– Response is very sensitive to material properties and

structural deformations

Lecture 11 13

Guided-Mode Resonance

Filters

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Various GMR Filters

Lecture 11 Slide 15

A guided‐mode resonance (GMR) filter is both a diffraction grating and slab waveguide.

A resonance occurs when a diffracted mode exactly matches a guided mode.

Away from resonance, the device behaves like an ordinary multilayer structure.

On resonance, the device reverses the background response (roughly speaking).

Effect of Index Contrast

Lecture 11 Slide 16

2 1.52n

1 2.0n

dLn Hn

1

2

1

1

2.0

1.52

275 nm

358.9 nm

50%

2

2L

H

n

n

d

f

n n n

n n n

Width of the resonance becomes more narrow as index contrast is lowered.Position of the resonance can change slightly.

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Sensitivity to Angle of Incidence (1 of 2)

Lecture 11 Slide 17

Grating Equation

01 inc incsin sin sinmn n m

Sensitivity to Angle of Incidence

0

inc

?

We make the small angle approximation: inc incsin

0 inc inc

inc sinxn n

m m

Example 

res inc nmrad

inc

nm nmrad deg

358.9 nm 1.0358.9

1

rad 358.9 6.3

180

xn

m

res inc

inc

xn

m

Sensitivity to Angle of Incidence (2 of 2)

Lecture 11 Slide 18

2 1.52n

1 2.0n

dLn Hn

1

2

2.0

1.52

275 nm

358.9 nm

50%

1.95

2.05L

H

n

n

d

f

n

n

res 5.35 nm

Deviating from normal incidence splits the resonance.  Increasing angle of incidence shifts the position of the resonance and alters background response.

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Sensitivity to Polarization

Lecture 11 Slide 19

2 1.52n

1 2.0n

dLn Hn

1

2

2.0

1.52

275 nm

358.9 nm

50%

1.95

2.05L

H

n

n

d

f

n

n

Polarization can have a dramatic effect on the response of a GMR.See Lecture on subwavelength gratings.

Effect of Having a Finite Number of Periods

Lecture 11 Slide 20

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Design ofGMR Filters

A Simple Design Procedure

Lecture 11 Slide 22

Step 1:  Design a multilayer structure that provides the desired background response.

• For low background reflection, think anti‐reflection coatings.

• For low background transmission, think Bragg gratings.• This part of the design can also be performed using any number of optimization algorithms.  There may be other constraints which you need to consider when choosing layer thicknesses.

ar 1 2 0 ar 4n n n L n

Step 2:  Incorporate a grating (or gratings).Set duty cycle to realize effective material properties.Set grating period to place resonance at desired frequency.

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Design Example #1:Monolithic GMR Filter (1 of 2)

Lecture 11 Slide 23

Step 1:  Design a multilayer structure with minimal background reflection at 1.5 GHz.

2 2.35 1

1

1

2

1.1

2.35

0.787"

2.20"

d

d

Given

Design Constraints

1 21.0

1 2 3.0"d d

Design After Optimization

Used lsqnonlin()

Step 2:  Incorporate a grating to place resonance at 1.5 GHz.

6.04"

For E mode,

32.6%f

For 1.5 GHz,

Design Example #1: Monolithic GMR Filter (2 of 2)

Lecture 11 Slide 24

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Design Example #2:GMR Filter on a Substrate

Lecture 11 Slide 25

Step 1:  Design a multilayer structure with minimal background reflection at 0=550 nm.

1

2

2.0

1.52

n

n

00.5d

Given

Design Constraints

0 00.1 d

Design After Optimization

2 1.52n

1 2.0n d

Step 2:  Incorporate a grating to place resonance at 1.5 GHz.

358.9 nm

Let,

1

1

50%

2

2L

H

f

n n n

n n n

For 0=550 nm.

2 1.52n

1 2.0n

dLn Hn

Scalability

Lecture 11 Slide 26

Maxwell’s equations have no fundamental length scale so designs can be made to operate at different frequencies just by scaling the dimensions.

a

1 1 or f 2a

1 12 or 2f

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Example of Scaling a Design

Lecture 11 Slide 27

Scaling Factor for 25 GHz Operation

1.5 GHz

25 GHz0.06s

1

2

0.362"

0.047"

0.132"

32.6%

2.35

d

d

f

To scale the design, multiply all physical dimensions by this number.

Broadband by Combining Multiple Resonances

Lecture 11 28

M. Shokooh-Saremi, R. Magnusson, “Design and Analysis of Resonant Leaky-mode Broadband Reflectors,” PIERS Proceedings, pp. 846-851, 2008.

Multiple resonances can be combined to produce a “single” broadband response.

Literature claims asymmetry in the grating contributes to broadband nature.

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Lecture 11 29

Broadband Microwave GMRFs

J. H. Barton, C. R. Garcia, E. A. Berry, R. G. May, D. T. Gray, R. C. Rumpf, "All‐Dielectric Frequency Selective Surface for High Power Microwaves," IEEE Transactions on Antennas and Propagation, 2014.

J. H. Barton, C. R. Garcia, E. A. Berry, R. Salas, R. C. Rumpf, "3D Printed All–Dielectric Frequency Selective Surface with Large Bandwidth and Field‐of‐View," IEEE Trans. Antennas and Propagation, Vol. 63, No. 3, pp. 1032‐1039, 2015.

3D Printed GMRFCNC Machined GMRF

Polarization Independent GMR Devices

Lecture 11 30

GMR devices can be made polarization‐independent in several ways.

1. Special cases can be found where both polarizations exhibit a resonance at the same frequency.

2. Crossed gratings with rotational symmetry are polarization independent at normal incidence.

3. Anisotropy can be incorporated to compensate for the birefringence produced by gratings.

4. More?

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Lecture 11 31

Anisotropy for Polarization Independence

R. C. Rumpf, C. R. Garcia, E. A. Berry, J. H. Barton, "Finite‐Difference Frequency‐Domain Algorithm for Modeling Electromagnetic Scattering from General Anisotropic Objects," PIERS B, Vol. 61, pp. 55‐67, 2014.

GMR Devices with Few Periods

Lecture 11 32

Jay H. Barton, R. C. Rumpf, R. W. Smith, "All‐Dielectric Frequency Selective Surfaces with Few Periods," PIERS B, Vol. 41, pp. 269‐283, 2012.

GMR device is made “effectively” infinite length by incorporating reflectors at the ends of the device.

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Applications

High Power Microwave Frequency Selective Surfaces

Lecture 11 34

J. H. Barton, C. R. Garcia, E. A. Berry, R. G. May, D. T. Gray, R. C. Rumpf, "All‐Dielectric Frequency Selective Surface for High Power Microwaves," IEEE Transactions on Antennas and Propagation, 2014.

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Narrow-Line Feedback Elements for Lasers

Lecture 11 35

Alok Mehta, Raymond C. Rumpf, Zachary A. Roth, and Eric G. Johnson, "Guided Mode Resonance Filter as an External Feedback Element in a Double-Cladding Optical Fiber Laser," IEEE Photonics Tech Letters, VOL. 19, NO. 24, pp. 2030-2032 (2007).

GMRs as Biosensors

Lecture 11 36

The extreme sensitivity of GMRs make them ideally suited for detecting small changes in dimensions and refractive index.

They are becoming more popular in biosensing for this reason.

Simon Kaja, Jill D. Hilgenberg, Julie L. Clark, Anna A. Shah, Debra Wawro, Shelby Zimmerman, Robert Magnusson, and Peter Koulen, Detection of novel biomarkers for ovarian cancer with an optical nanotechnology detection system enabling label-free diagnostics, Journal of Biomedical Optics, vol. 17, no. 8, pp. 081412-1-081412-8, August 2012.

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Tunable Optical Filters

Lecture 11 37

Mohammad J. Uddin and Robert Magnusson, Guided-Mode Resonant Thermo- Optic Tunable Filters, IEEE Photonics Technology Letters, vol. 25, no. 15, pp. 1412-1415, August 1, 2013.

High sensitivity of GMR devices is exploited to make a tunable filter.

Dispersion Engineering and Pulse Shaping

Lecture 11 38

Response of a Typical GMR

Xin Wang, “Dispersion Engineering with Leaky-Mode Resonance Structures,” MS Thesis, University of Texas at Arlington, 2010.

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Polarization Beam Splitter

Lecture 11 39

O. Kilic, et al, “Analysis of guided-resonance-based polarization beam splitting in photonic crystal slabs,” J. Opt. Soc. Am. A, Vol. 25, No. 11, pp. 2680-2692, 2008.

Incident polarization

Reflected andtransmitted polarizations