Guided-mode resonance (GMR) effect Guided-mode resonance (GMR) effect for filtering devices in LCD display panels

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(Second Lecture) Techno Forum on Micro-optics and Nano-optics Technologies

Guided-mode resonance (GMR) effect Guided-mode resonance (GMR) effect for filtering devices in LCD display panels

송 석 호, 한양대학교 물리학과, http://optics.anyang.ac.kr/~shsong

1. What is the GMR effect of waveguide gratings?

2 What is the photonic band structure (or dispersion relation)?

Key 2. What is the photonic band structure (or, dispersion relation)?

3. What can we play with GMR filters for display?

4. What is the practical difficulties to be solved in GMR applications?

Key notes

(2)

GMR color filter

(3)

GMR color filter

(4)

GMR color filter

(5)

GMR polarizer

(6)

GMR polarizer

DBEF와 편광필름의 투과도(532 )

Reflective polarizer display, US 5828488 (1995.03.10), 3M (St. Paul, MN)

DBEF와 편광필름의 투과도(532nm)

( 투과단위 :uW )

(7)

GMR bandpass filter

(8)

Narrow-line bandpass filters

GMR bandpass filter

p

R. Magnusson and S. S. Wang, Appl. Optics 34, 8106-8109 (1995).

S. Tibuleac and R. Magnusson, Opt. Lett. 26, 584-586 (2001).

0 42

Λ=6.91μm nc=1.0

0 58

d=3.7μm n =4 R

0.42

ns=1.4

0.58 nh=4

T ⁿ^l^=2.65

0.8 1

Periodic waveguide

0 .8 0 .9 1

G r a t in g

H o m o g e n e o u s

0 4 0.6

η R

Homogeneous layer

with the same 0 .5 0 .6 0 .7

g

0.2

0.4 effective index

0 1 0 .2 0 .3 0 .4

8.5 9 9.5 10 10.5 11 11.5 12 12.5

0

λ(μm)

( μ m ) 0

0 .1

8 .5 9 9 .5 1 0 1 0 .5 1 1 1 1 .5 1 2 1 2 .5

W A V E L E N G T H

(9)

DIFFRACTIVE OPTICAL ELEMENTS (DOEs) ?

GMR effect

DOE/PhC : Fine spatial patterns arranged to control propagation of light

Transmission type

ff ^x

Region C

fΛ

θ_in 0

-1 +1

Incident wave Backward diffracted waves

n_C θ_C,i

Grating Diffraction Region G Region S

d x

Λ

-1 +2

F d diff t d 0

n_S

n_H n_L

θ_S,i

Operating Regimes

Region S

z

+1 0 Forward diffracted waves

..

-10

-2 0 R₀ T₀

(

^θ ⁺ ^θ

)

⁼ ^λ

Λ sin sin m 2Λ sinθ =λ

..

²¹⁰ ₁

m

Multiwave regime (Λ>>λ)^Λ

(

^sin^θ_in ⁺^sin^θ_m

)

⁼ ^m^λ Two-wave regime (Λ∼λ)²^Λ^sin^θ_in ⁼^λ Zero-order regime (Λ<<λ)

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Basic resonance interactions

GMR effect

Basic resonance interactions

Excitation of a leaky guided mode

Consider simplest 1D WGG case for clarity

Higher-order diffraction regime Zero-order diffraction regime

Incident light

0

Incident light

0 Higher-order diffraction regime Zero-order diffraction regime

0 +1 −1

0 Higher-order diffraction

≥+2 ≤−2

≥+1 ≤−1

lights

+1 −1

0

0 2 1 0 1 2 i , 2, 1,0, 1, 2, i = " − − + + "

Diffraction order

(11)

GMR effect

Guided mode resonance (GMR)

Incident light

0 1

Incident light 0 +1 −1

≥+2 ≤−2 ≥+1 ≤−1

Higher-order diffraction lights

ε

₁

ε

_g

+1 −1

0 0

ε

₂

the higher-order diffraction lights can be guided on a thin layer of grating.

If ε

_g (average dielectric constant )

> ε

₁

, ε

₂

Î “

Guided mode resonance (GMR)” of waveguide gratings

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Basic Concepts of GMR

GMR effect

Theory and applications of guided-mode resonance filters

APPLIED OPTICS / Vol. 32, No. 14 / 10 May 1993, 2606 S. S. Wang and R. Magnusson

ε_gis the average relative permittivity,

A guided wave can be excited Δε is the modulation amplitude, g

K = 2π/Λ, where Λ is the grating period.

θ A guided wave can be excited

if the effective waveguide index of refraction, N, is in the range

x θ

z 2

k π

= λ

N k

≡ β k^x =β

kx ≡ β

λ0

k

2 2

z g x

k = k ε −k k εi

kz

(13)

Propagation constant of waveguide grating

x θ

z

x

Coupled-wave equations governing wave propagation in the waveguide grating can be expressed as

the wave equation associated with an unmodulated dielectric waveguide is given by the wave equation associated with an unmodulated dielectric waveguide is given by

( )

2 2

z g x x

k = k ε −k k =β

kx =β

we obtain the effective propagation constant of the waveguide grating:

with Eq. (2),

x β

Propagation constant

k εi

kz

(14)

θ’

Diffraction equation of waveguide grating

θ

Diffraction equation Diffraction equation

{

¹ ³

}

¹

max ε , ε = ε sin ' iθ − λ Λ

i = -1

i = +2

i = +1

1 sin ' i λ _g ε θ − < ε

Λ

i = -2 i +2

(15)

How to intuitively understand the GMR effect, for example, in mirrors?

GMR filters

C t ti /d t ti

direct path indirect path

Constructive/destructive Interference

Photon energy Forbidden

B d Allowed

B d Allowed Forbidden

B d

Allowed Photonic band structure

Band Band Band Band Band Photonic band structure

Photonic band gap (PBG)

No transmission of light within the bandgap due to destructive interference in transmitted light.

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Photonic band structure is analogous to energy-band structure of electrons

PBG

Photons and Electrons Photons and Electrons

Nanophotonics, Paras N. Prasad, 2004, John Wiley & Sons, Inc., Hoboken, New Jersey., ISBN 0-471-64988-0

Both photons and electrons are elementary particles that are elementary particles that simultaneously exhibit particle and wave-type behavior.

Photons and electrons may Photons and electrons may appear to be quite different as described by classical physics, which defines photons as electromagnetic waves g transporting energy and electrons as the fundamental charged particle (lowest mass) of matter.

A quantum description, on the other hand, reveals that

photons and electrons can be treated analogously and

treated analogously and exhibit many similar characteristics.

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Consider free-space propagation of photons and electrons.

PBG

In a “free-space” propagation, there is no interaction potential or it is constant in space.

For photons, it simply implies that no spatial variation of refractive index n occurs.

The wavevector dependence of energy is different for photons (linear dependence) and electrons (quadratic dependence).(q p )

Photons

Photons Electrons Electrons Photons

Photons Electrons Electrons

For free space propagation all values of frequency for photons and energy for electrons are permitted For free-space propagation, all values of frequency for photons and energy for electrons are permitted.

This set of allowed continuous values of frequency (or energy) form together a band.

The band structure refers to the characteristics of dependence of frequency ω (or energy) on wavevector k, called dispersion relation.

Energy band structure = Dispersion relation ( ω -k relation)

(18)

Ph t i b d (PBG) i l t l t b d

PBG

Photonic bandgap (PBG) is analogous to electron energy bandgap

2 2

E 2 k

= = m 2m

Gap in energy spectra of electrons arises in periodic structure

(19)

Photonic band structure

Dispersion curve (photonic band diagram) (photonic band diagram)

(20)

PBG formation by periodic structures

Photonic bandgap

1. Dispersion curve for ^{free space} 3. At the band edges, standing waves form, with the energy being either in the high or the low index regions

a k

a π

λ 2 = =

2. In a periodic system, when half the wavelength corresponds to the periodicity

4. Standing waves transport no energy

the Bragg effect prohibits photon propagation. with zero group velocity

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Standing waves at band edges

Air band n

ω Standing waves with zero group velocity

n

₁

n

₂

n

₁

n

₂

n

₁

n

₂

n

₁

standing wave in n₂

Air band

Bandgap

standing wave in n₁

g p

n₁: high index material n₂: low index material

0 π/a

g ₁

Dielectric band

k

π/a

(22)

Reduced Brillouin zone

Plot the dispersion curves for both the positive and the negative sides, and then shift the curve segments with |k|>π/a upward or downward and then shift the curve segments with |k|>π/a upward or downward one reciprocal lattice vectors.

This reduced range of wave vectors is called the “Brillouin zone”

This reduced range of wave vectors is called the Brillouin zone

(23)

Photonic Band Gaps (PBG)

p ( )

B d #2

Bandgap #2

S di

Bandgap (no transmission) Standing wave v

_group

=0

Long wavelength

limit: effective index

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2D Photonic band structure

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2-D Photonic Crystals

1. In 2-D PBG, different layer spacing, a, can be met along different direction. Strong interaction occurs when λ/2 = a.

2. PBG (Photonic band gap) = stop bands overlap in all directions

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B d Di

Band Diagram

Air band

Stop band

Dielectric band

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(28)

(29)

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Photonic bandgaps (stop bands) in GMR gratings

GMR PBGs

Outside stopband

Photonic bandgaps (stop bands) in GMR gratings

0.9

1 TE₀

0.9 Five leaky waves 1

At stopband

0.6 0.7 0.8

k₀n_c/K

0.6 0.7 0.8

Three leaky waves Four leaky waves

3^rd stopband

0 3 0.4

0.5 ^k⁰ⁿ^s^/K

k 0/K

0 3 0.4 0.5

One leaky wave

Two leaky waves ₂^nd_stopband 2^ndorder

stopband

0.1 0.2 0.3

k0n

f/K

0.1 0.2 0.3

Non-leaky regime ₁st stopband

0 0.5

0 0 -4 -3 -2

β_I/K β_R/K

C l ti t t f l k d β β j β

Complex propagation constant of leaky mode β=β

_R

+j β

_I

(31)

Symmetry in grating profile of GMR elements

T y p e I z

(a) Grating with symmetric profile

z

x

Λ

FΛ

(b) G ti ith t i fil (b) Grating with asymmetric profile

T y p e I I

Λ n

F₁Λ

n_c

n_s F₂Λ

n_h d n_l

M Λ

Details: Y. Ding and R. Magnusson, “Use of nondegenerate resonant leaky modes to g g g y fashion diverse optical spectra,” Optics Express, May 3, 2004

(32)

Symmetric profile band diagram

Complex propagation constant of leaky mode β=β

_R

+j β

_I

0 585 0 585

0.58 0.585

F=0.33 0.58

0.585

F=0.33

F<0.5

^β_leakage^I^{=0, no}

0.57 0.575 k 0/K

resonance

0.57 0.575 k 0/K

Reduced BZ notation

-0.02 -0.01 0 0.01 0.02 0.03

0.565

βR/K 0 1 2 3

x 10^-4 0.565

β_I/K

Vincent/Neviere 1979: Asymmetry “defeats selection rule”

notation

P. Vincent and M. Neviere, “Corrugated dielectric waveguides: A numerical study of the second- order stop bands,” Appl. Phys. 20, 345-351 (1979).

Vincent/Neviere 1979: Asymmetry defeats selection rule

Perturbation model: 0 π phase differences of radiated fields (symmetric profile)

R. F. Kazarinov and C. H. Henry, “Second-order distributed feedback lasers with mode selection provided by first-order radiation loss,” IEEE J. Quant. Elect. QE-21, 144-150 (1985).

Perturbation model: 0,π phase differences of radiated fields (symmetric profile)

Numerical calculations of resonance at edges (symmetric profile) Numerical calculations of resonance at edges (symmetric profile)

D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, and J. M. Bendickson, “Effects of modulation strength in guided-mode resonant subwavelength gratings at normal incidence,” J. Opt. Soc.

Am. A. 17, 1221-1230 (2000).

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Design of multi-resonance elements

R l ti ti t d ith th i f ti f

• Resonance locations are estimated with the eigenfunction of homogeneous waveguide (modulation~0)

• Numerical RCWA computations p

2.2 2.4

2.2

2.4 TE_1,0

x x nc=1

n_s=1.48 n =2 45

GMR#1 GMR#2

Notation:

1.6 1.8 2

λ/Λ

1.6 1.8

2 ^TE_1,1

TE_1,2

x x

n_avg=2.45 ^GMR#2

GMR#3 GMR#4

TE

_m,ν

m represents the

Reflectance map

1.2 1.4 1.6

TE_2,0

TE

evanescent

diffraction order exciting the ν-th mode

0 0.2 0.4 0.6 0.8 1

1

d/Λ

0 0.2 0.4 0.6 0.8 1

1

TE_2,1 TE_2,2 mode

(34)

Band diagram of asymmetric profile g y p

Weak modulation

0 58 0.585

resonance at upper edge

0.585

0.575 0.58

k 0/K

0.575 0.58

k 0/K _0.2

Λ=0.3μm nc=1.0

ns=1.52 0.3 0.13

d=0.14 μ m nh=2.05 nl

0.37 R

T ⁿ^avg⁼²

-0.02 -0.01 0 0.01 0.02 0.03

0.565 0.57

β_R/K

resonance at lower edge

6 5 4 3 2

0.565 0.57

T ^avg

• Both edges are lossy

GMR t b th d

R 10^-6 10^-5 10β_I/K^-4 10^-3 10^-2

• GMRs appear at both edges

• Resonance separation depends on size of bandgap

• Resonance degeneracy of symmetric case removed

(35)

Resonant SOI leaky-mode reflector y

1

Periodic

1

Single layer, TE polarization, 2 resonance peaks

0.6 0.8

R

Periodic waveguide

0.6 0.8

λ=1.8(μm) Δθ_FWHM>40^°

η

R

0.2 0.4

η

Homogeneous layer with the same

ff ti i d

0.2 0.4

T ^0.075

Λ=1μm nc=1.0

ns=1.48 0.275 0.375

d=0.49μm nh=3.48 nl=1.0

0.275

R

T

1 1.5 2 2.5

0

λ(μm)

effective index

10⁰ 1

3 48

TE_1,1 TE_1,0

-200 -10 0 10 20

θ(°) T

10^-4 10^-2

T

0.6 0.8

n_h=3.48

n_h=3.2

η R

10^-6

η T10

TE_1,1 TE_1,0

0.2 0.4

n_h=2.8

η

1.4 1.6 1.8 2 2.2

10^-8

λ(μm)

1.4 1.6 1.8 2 2.2

0

λ(μm)

(36)

Resonant leaky-mode reflector: E-fields

l l l k

Single layer, TE polarization, 2 resonance peaks TE

_1,1

TE

_1,0

3 8

0.8 1

nh=3.48

TE1,1 TE

1,0

n

_h

=2.8

-3 8

0 4 0.6

nh=3.2

η R

n

_h

=3.2

-8

2 4

0.2 0.4

nh=2.8

n

_h

3.2

-2 -4

2 2

1.4 1.6 1.8 2 2.2

0

λ(μm)

n

_h

=3.48

2 2

-2 -2

(37)

GMR reflectors vs Bragg stacks gg

Λ 1 n 1 0

R

R I

0.075

Λ=1μm nc=1.0

0.275 0.375

d=0.49μm nh=3.48 nl=1.0

0.275

R

ns=1.48 T

21-layer SiO₂/TiO₂ Bragg stack Single-layer SOI resonance device

0.8 1

Periodic waveguide

nc=1.00_SiO2+TiO2_10.5pairs_TE

0.8 1

0.4 0.6

η R

0 2 0.4 0.6

Reflectance

1 1.5 2 2.5

0

0.2 Homogeneous layer

with the same effective index

0 0.2

1400 1600 1800 2000 2200 2400

Wavelength (nm)

1 1.5 2 2.5

λ(μm)

~600 nm wide reflection band in each case

(38)

Wideband SOI reflector

Single resonance, TE polz

n_inc= 1.0

1 0 d=0 33 μm F=0.545 n= 3.48 Si 1-F

10 ⁰

1.0 d 0.33 μm 1-F

t_c=0.65 μm n_Sub= 3.48 Si

F 0.545 n 3.48 Si

n_Layer= 1.47 Λ= 0.84μm

10^-4 10 ^-2

R &

T

0

10^-6 0 10

T

1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 10 ^-8

R ₀ T 0

Single-resonance TM-polz wideband reflector experiment reported in:

1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5

Wavelength (μm)

Mateus et al, IEEE PTL, July 2004.

(39)

Resonant SOI leaky-mode transmission element y

Single layer, TE polarization, ~100 nm flattop

Λ=1μm nc=1.0

d=0.728μm nl=1.0

R

0.444

ns=1.0

0.296 0.13 ^0.13 nh=3.48

T

0.8 1

0.4 0.6

η T

0.4 0.6

η T

λ=1.52μm

0 0.2

1.2 1.3 1.4 1.5 1.6 1.7 1.8

0

λ(μm) 0 -40 -20 0 20 40

θ(°)

(40)

R t SOI l k d l i

Resonant SOI leaky mode polarizers

0.025

Λ=0.84μm nc=1.0

0.025 0.675

d=0.504μm nh=3.48 nl=1.0

0.275

R _n=1.0

d=0.92 μm n =3 48 0.28

R

0.28

0.12 0.32

1

ns=1.48 T

1

Λ=1μm

n=1.48

nh=3.48

T

0.6

0.8 TM

0.6

0.8 TE

0.2

η R 0.4

TE 0 2

0.4

η R

TM

1.5 1.52 1.54 1.56 1.58 1.6

0

λ(μm)

TE

1.450 1.5 1.55 1.6 1.65

0.2

λ (μm) TM

Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Optics Express, vol. 12, 5661-5674 (2004).

(41)

Fabricated SOI single-layer ~100 nm polarizer

n_H= 3.48 1.0

n_L= d 500 nm

I R

n_c= 1.00

0.6

0.8 TM

ance

n_L 1.00

0.71 0.29

d = 500 nm

T

n_s= 1.48

0.2 0.4

TE

Reflecta

Λ = 820 nm

1450 1500 1550 1600 1650

0.0

Wavelength (nm)

Goal: Simple fab; higher quality via more complex distribution within period

(42)

AFM image and preliminary polarizer data

l b h h

Electron-beam writing with reactive ion etching

0.8 1.0

THE 0.8 EXP

1.0

e

0.4 0.6

TM-pol.

Transmittance

0 2 0.4 0.6

TE-pol.

Transmittance

1520 1540 1560 1580

0.0

T 0.2

W l th ( )

1520 1540 1560 1580

0.0

0.2 _THE

EXP

Wavelength (nm)

(43)

Leaky-mode resonance technology:

Application summary

• Narrow-band reflection (bandstop)/transmission (bandpass) filters (Δλ~sub nm)

• Wide-band reflection (bandstop)/transmission (bandpass) filters (Δλ~100’s nm)

• Tunable filters EO modulators and switches

• Tunable filters, EO modulators, and switches

• Mirrors for vertical cavity lasers

• Wavelength division multiplexing (WDM)

• Polzarization independent elements Polzarization independent elements

• Reflectors

• Polarizers

• Security devices y

• Laser resonator frequency selective mirrors

• Non-Brewster polarizing mirrors

• Laser cavity tuning elements y g

• Spectroscopic biosensors

• Tunable display pixels

(44)

Leaky-mode resonance photonics: y p An enabling technology platform

• Interesting physics

• Complex, interacting resonant leaky modes

• Remaining challenges in analysis

• Remaining challenges in fabrication

• Many potential application fields

• Applications emerging

• Favorable area for R&D&A

(45)

In summary

1. What is the GMR effect of waveguide gratings?

2. What is the photonic band structure (or, dispersion relation)?

3. What can we play with GMR filters for display?

Key notes

4. What is the practical difficulties to be solved in GMR applications?

RED GREEN BLUE RED GREEN BLUE

Diffuser

LCD panel

Polarized Light Emission

Light guide film LED

GMR grating

Reflector LED

Unpolarized light beam

N t l t t 07/07 Next lecture at 07/07

(06/23) Introduction: Micro- and nano-optics based on diffraction effect for next generation technologies (06/30) Guided-mode resonance (GMR) effect for filtering devices in LCD display panels

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