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3/17/2016
1
ECE 5322 21st Century Electromagnetics
Instructor:Office:Phone:E‐Mail:
Dr. Raymond C. RumpfA‐337(915) 747‐[email protected]
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