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

Guided-mode resonance (GMR) effectGuided-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

GMR color filter

GMR color filter

GMR color filter

GMR polarizer

GMR polarizer

DBEF와편광필름의투과도(532 )

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

DBEF와편광필름의투과도(532nm) ( 투과단위 :uW )

GMR bandpass filter

Narrow-line bandpass filters

GMR bandpass filter

pR. 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 nl=2.65

0.8

1

Periodic waveguide

0 .8

0 .9

1

G ra t in g

H o m o g e n e o u s

0 4

0.6

η R

Homogeneous layerwith 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 12.50

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 .5W A V E L E N G T H

DIFFRACTIVE OPTICAL ELEMENTS (DOEs) ?GMR effect

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

Transmission type

ff x

Region C

fΛ

θin 0

-1

+1Incident wave Backward diffracted

wavesnC θC,i

Grating Diffraction Region G

Region S

xd

Λ

-1+2

F d diff t d

0

nS

nHnL

θS,i

Operating Regimes

Region S

z0+1 Forward diffracted

waves

..0-1

-20 R0 T0

( ) λ=θ+θΛ msinsin λ=θΛ sin2

..01

21m

Multiwave regime (Λ>>λ) Two-wave regime (Λ∼λ)Zero-order regime (Λ<<λ)( ) λ=θ+θΛ msinsin min λ=θΛ insin2

Basic resonance interactionsGMR effect

Basic resonance interactionsExcitation of a leaky guided mode

Consider simplest 1D WGG case for clarity

Higher-order diffraction regime Zero-order diffraction regime

Incident light 0

Incident light0

Higher-order diffraction regime Zero-order diffraction regime

0

−1+1

0

Higher-orderdiffraction

≥+2 ≤−2 ≥+1 ≤−1 lights

−1+1

0 0

2 1 0 1 2i , 2, 1,0, 1, 2,i = − − + +Diffraction order

GMR effect

Guided mode resonance (GMR)

Incident light 0

1

Incident light0

−1+1

≥+2 ≤−2 ≥+1 ≤−1

Higher-orderdiffractionlights

ε1

εg

−1+1

0 0 ε2

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

If εg (average dielectric constant ) > ε1 , ε2

“Guided mode resonance (GMR)” of waveguide gratings

Basic Concepts of GMR

GMR effect

Theory and applications of guided-mode resonance filtersAPPLIED OPTICS / Vol. 32, No. 14 / 10 May 1993, 2606S. S. Wang and R. Magnusson

εg is the average relative permittivity,

A guided wave can be excited

gΔε is the modulation amplitude, 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 rangex

θ

z 2k πλ

=Nkβ

≡ xk β=

xk β≡

0λk

2 2z g xk k kε= − ik ε

zk

Propagation constant of waveguide grating

xθ

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

( )2 2 z g x xk k k kε β= − =

xk β=

we obtain the effective propagation constant of the waveguide grating:with Eq. (2),

x β

Propagation constantik ε

zk

θ’

Diffraction equation of waveguide grating

θ

Diffraction equationDiffraction equation

{ }1 3 1max , sin ' i λε ε ε θ= −Λ

i = -1

i = +2

i = +1

1 sin ' gi λε θ ε− <Λ

i = -2i +2

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

GMR filters

C t ti /d t ti

direct path indirect path

Constructive/destructiveInterference

Photon energy

Forbidden B d

Allowed B d

Allowed Forbidden B d

Allowed Photonic band structureBandBand Band Band Band

Photonic band structure

Photonic band gap (PBG)

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

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

PBG

Photons and ElectronsPhotons and ElectronsNanophotonics, Paras N. Prasad, 2004, John Wiley & Sons, Inc., Hoboken, New Jersey., ISBN 0-471-64988-0

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

Photons and electrons mayPhotons and electrons may appear to be quite different as described by classical physics, which defines photons as electromagnetic waves gtransporting 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 andtreated analogously and exhibit many similar characteristics.

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 )

PhotonsPhotons ElectronsElectronsPhotonsPhotons ElectronsElectrons

For free space propagation all values of frequency for photons and energy for electrons are permittedFor 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)

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

PBG

Photonic bandgap (PBG) is analogous to electron energy bandgap

22

2E k

m=

2m

Gap in energy spectra of electrons arises in periodic structure

Photonic band structure

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

PBG formation by periodic structuresPhotonic 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

aka πλ ==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

Photonic band structure

Standing waves at band edges

nAir bandω Standing waves with zero group velocity

n1 n2 n1 n1 n1n2 n2

standing wave in n2

Air band

Bandgap

standing wave in n1

g p

n1: high index materialn2: low index material0 π/a

g 1

Dielectric bandk

π/a

Reduced Brillouin zone

Photonic band structure

Reduced Brillouin zonePlot the dispersion curves for both the positive and the negative sides, and then shift the curve segments with |k|>π/a upward or downwardand 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

Photonic Band Gaps (PBG)

Photonic band structure

p ( )

B d #2Bandgap #2

S diBandgap (no transmission) Standing wavevgroup=0

Long wavelengthlimit: effective indexlimit: effective index

2D Photonic band structure

2-D Photonic Crystals2D Photonic band structure

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

B d Di

2D Photonic band structure

Band Diagram

Air band

Stop band

Dielectric band

2D Photonic band structure

2D Photonic band structure

2D Photonic band structure

Photonic bandgaps (stop bands) in GMR gratings

GMR PBGs

Outside stopband

Photonic bandgaps (stop bands) in GMR gratings

0.9

1 TE0

0.9

1Five leaky waves

At stopband

0.6

0.7

0.8

k0nc/K

0.6

0.7

0.8

Three leaky waves

Four leaky waves

3rd stopband

0 3

0.4

0.5k0ns/K

k 0/K

0 3

0.4

0.5

One leaky wave

Two leaky waves 2nd stopband2nd order stopband

0.1

0.2

0.3

k0nf/K

0.1

0.2

0.3Non-leaky regime 1st stopband

0 0.50

-4 -3 -20

βI/KβR/K

C l ti t t f l k d β β j βComplex propagation constant of leaky mode β=βR+j βI

Symmetry in grating profile of GMR elements

zT y p e I (a) Grating with symmetric profile

z

x Λ

F Λ

(b) G ti ith t i fil(b) Grating with asymmetric profile T y p e II

Λ n

F 1 Λ

n c

n s F 2 Λ

dn h n l

M Λ

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

Symmetric profile band diagramComplex propagation constant of leaky mode β=βR+j βI

0 585 0 585

0.58

0.585

F=0.33 0.58

0.585

F=0.33

F<0.5 βI=0, no leakage

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 0.030.565

βR/K 0 1 2 3x 10-4

0.565βI/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).

Design of multi-resonance elementsR 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 computationsp

2.2

2.4

2.2

2.4TE1,0x

x

nc=1 ns=1.48 n =2 45

GMR#1

GMR#2

Notation:

1.6

1.8

2

λ/Λ

1.6

1.8

2 TE1,1

TE1,2

x

x

navg=2.45 GMR#2

GMR#3

GMR#4

TEm,νm represents the

Reflectance map

1.2

1.4

1.6

1.2

1.4

1.6

TE2,0 TE

evanescent diffraction order exciting the ν-thmode

0 0.2 0.4 0.6 0.8 11

d/Λ0 0.2 0.4 0.6 0.8 1

1TE2,1 TE2,2

mode

Band diagram of asymmetric profileg y pWeak 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=0.3μmn c =1.0

n s=1.520.3 0.13

d=0.14 μ m

n h =2.05

n l

0.37

R

T navg=2

-0.02 -0.01 0 0.01 0.02 0.030.565

0.57

βR/K

resonance at lower edge

6 5 4 3 20.565

0.57

T avg

• Both edges are lossy GMR t b th d

R10-6 10-5 10-4 10-3 10-2

βI/K

• GMRs appear at both edges• Resonance separation depends on size of bandgap• Resonance degeneracy of symmetric case removed• Resonance degeneracy of symmetric case removed

Resonant SOI leaky-mode reflectory

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)ΔθFWHM>40°

η

R

0.2

0.4

η

Homogeneous layerwith 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 2.50

λ(μm)

effective index

1001

3 48

TE1,1 TE1,0

-20 -10 0 10 200

θ(°)

T

10-4

10-2

T

0.6

0.8nh=3.48

nh=3.2

η R

10-6

10η T

TE1,1 TE1,0 0.2

0.4nh=2.8

η

1.4 1.6 1.8 2 2.210-8

λ(μm)1.4 1.6 1.8 2 2.20

λ(μm)

Resonant leaky-mode reflector: E-fields l l l kSingle layer, TE polarization, 2 resonance peaks

TE1,1 TE1,03

8

0.8

1

nh=3.48

TE1,1 TE1,0 nh=2.8

-3 8

0 4

0.6

nh=3.2

η R

nh=3.2

-82 4

0.2

0.4nh=2.8

nh 3.2

-2 -42 2

1.4 1.6 1.8 2 2.20

λ(μm)

nh=3.48

2 2

-2 -2

GMR reflectors vs Bragg stacksgg

Λ 1n 1 0RRI

0.075

Λ=1μmnc=1.0

0.275 0.375

d=0.49μm

nh=3.48

nl=1.0

0.275

R

ns=1.48T

21-layer SiO2/TiO2 Bragg stackSingle-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

Ref

lect

ance

1 1.5 2 2.50

0.2 Homogeneous layerwith 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

Wideband SOI reflectorSingle resonance, TE polz

ninc = 1.0

1 0 d=0 33 μm1-FF=0.545 n= 3.48 Si

10 0

1.0 d 0.33 μm1-F

tc=0.65 μm

nSub = 3.48 Si

F 0.545 n 3.48 Si

nLayer = 1.47 Λ= 0.84μm

10-4

10 -2

R & T

0

10-6

100T

1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.510

-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 ( μ m) Mateus et al, IEEE PTL, July 2004.

Resonant SOI leaky-mode transmission elementySingle layer, TE polarization, ~100 nm flattop

Λ=1μm nc=1.0

d=0.728μmnl=1.0

R

0.444

ns=1.0 0.296 0.13 nh=3.48 0.13

T

0.8

1

0.8

1

0.4

0.6

η T

0.4

0.6

η T λ=1.52μm

0

0.2

0

0.2

1.2 1.3 1.4 1.5 1.6 1.7 1.80

λ(μm)-40 -20 0 20 40

0

θ(°)

R t SOI l k d l iResonant SOI leaky mode polarizers

0.025

Λ=0.84μmnc=1.0

0.025 0.675

d=0.504μm

nh=3.48

nl=1.0

0.275

R n=1.0

d=0.92μm

n =3 48

0.28

R

0.280.12 0.32

1

ns=1.48 T

1

Λ=1μmn=1.48

n h=3.48

T

0.6

0.8 TM

0.6

0.8TE

0.2

0.4

ηR

TE 0 2

0.4

η R

TM

1.5 1.52 1.54 1.56 1.58 1.60

λ(μm)

TE

1.45 1.5 1.55 1.6 1.650

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).

Fabricated SOI single-layer ~100 nm polarizer

nH = 3.48 1.0

nL = d 500 nm

I Rnc = 1.00

0.6

0.8 TM

ance

nL1.00

0.71 0.29

d = 500 nm

T

ns = 1.480.2

0.4

TE

Ref

lect

a

Λ = 820 nm

1450 1500 1550 1600 16500.0

Wavelength (nm)

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

AFM image and preliminary polarizer datal b h hElectron-beam writing with reactive ion etching

0.8

1.0 THE EXP0.8

1.0

e

0.4

0.6TM-pol.

Tran

smitt

ance

0 2

0.4

0.6

TE-pol.

Tran

smitt

ance

1520 1540 1560 15800.0

0.2T

W l th ( )

1520 1540 1560 15800.0

0.2 THE EXP

Wavelength (nm)Wavelength (nm)

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 elementsPolzarization independent elements• Reflectors• Polarizers• Security devicesy• Laser resonator frequency selective mirrors• Non-Brewster polarizing mirrors• Laser cavity tuning elementsy g• Spectroscopic biosensors• Tunable display pixels

Leaky-mode resonance photonics:y pAn enabling technology platform

• Interesting physics• Interesting physics

• Complex, interacting resonant leaky modes

• Remaining challenges in analysis• Remaining challenges in analysis

• Remaining challenges in fabrication

• Many potential application fields• Many potential application fields

• Applications emerging

• Favorable area for R&D&A• Favorable area for R&D&A

In summary1. 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 REDGREEN GREENBLUE BLUE

Diffuser

LCD panel

PolarizedLight

Emission

Light guide filmLED

GMR grating

ReflectorLED

Unpolarizedlight beam

N t l t t 07/07Next 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(07/07) Surface-plasmons: A basic(07/14) Surface-plasmon waveguides for biosensor applications(07/21) Efficient light emission from LED, OLED, and nanolasers by surface-plasmon resonance