Coupled-cavity structures in photonic crystals

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COUPLED

-

CAVITY STRUCTURES IN

PHOTONIC CRYSTALS

MEHMET BAY

INDIR

EKMEL O

ZBAY

Department of Physics, Bilkent University, Turkey

MRS Meeting, April 1

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¾

Motivations

¾

Underlying Physics

¾

Investigation of coupled

-

cavity structures: FDTD, TMM,

experiment, and tight

-

binding approximation

¾

¾Localized cavity modesLocalized cavity modes ¾

¾EigenmoseEigenmose splittingsplitting ¾

¾Photonic moleculesPhotonic molecules

¾

Observation of a new type of waveguiding mechanism:

Coupled

Coupled-

-cavity waveguides (CCWs)

cavity waveguides (CCWs)

¾

Possible Applications

¾

Waveguides, waveguide bends, splitters, switches

¾

WDM: adding or dropping a selective wavelength or band

¾

Strong enhancement of the spontaneous emission

¾

Increasing efficiency of nonlinear processes

¾

Dispersion compensators

¾

¾Summary

Summary

OUTLINE

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MOTIVATIONS

PHOTONIC INTEGRATED CIRCUIT

[from Krauss’ paper]

TO CONSTRUCT ALL OPTICAL COMPONENTS ON A SINGLE CHIP

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0.7 0.8 0.9 1.0 1.1 1.2 -50 -40 -30 -20 -10 0 Measurement FDTD T ransm is si on ( d B ) Frequency (ω/ω₀)

( )

[

∇

×

E

_Ω

r

]

=

(

Ω

) ( ) ( )

r

E

_Ω

r

×

∇

2 ₀ 0

c

ε

2D PHOTONIC CRYSTALS: LOCALIZED CAVITY MODE

Observation of strongly localized cavity modes within the photon

Observation of strongly localized cavity modes within the photonic band gap ic band gap analogous to acceptor impurity state in semiconductors

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EIGENMODE SPLITTING

Formation of bonding and

Formation of bonding and antibondingantibonding photonic modesphotonic modes

0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 -50 -40 -30 -20 -10 0 ω₂ ω₁ Measurement FDTD Tr an sm is si o n ( d B) Frequency (ω/ω₀)

Linear combination of the individual evanescent cavity modes

( )

=

_Ω

( )

+

_Ω

(

Λ

)

ω

r

E

r

E

r

-E

A

B

( )

[

∇

×

E

_ω

r

]

=

( ) ( ) ( )

ω

c

2

ε

₀

r

E

_ω

r

×

∇

α 1 β 1 Ω ω_1,2 ± ± =

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0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 -50 -40 -30 -20 -10 0 Γ₂ Γ₃ Γ₁ Experiment FDTD T ransm is si on ( d B) Frequency (ω/ω₀)

PHOTONIC MOLECULES

Benzene-like molecule + + +

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-THE TIGHT

THE TIGHT--BINDING PICTURE IN PHOTONIC STRUCTURESBINDING PICTURE IN PHOTONIC STRUCTURES

Dispersion relation, group velocity, and photon lifetime depend

Dispersion relation, group velocity, and photon lifetime depend only a single only a single tight

tight--binding parameter binding parameter κκ that that can be directly determined from experimentscan be directly determined from experiments

( )

[

∇

×

E

r

]

=

( ) ( ) ( )

ω

c

2

ε

₀

r

E

r

×

∇

( )

_E

_e

Λ _Ω

(

_n

Λ

)

n ink

₋

=

∑

−

_E

_r

r

E

₀

(

1 cos(

)

(

k

Ω

κ

k

Λ

ω

=

+

)

sin(

)

(

)

(

k

ΩΛ

k

Λ

v

_g

=

∇

_k

ω

=

−

κ

c

L

)

k

(

v

L

)

k

(

_g p

=

−

π

τ

2

9

9 highly localized_{highly localized}

9

9 weakly interacting cavity modes_{weakly interacting cavity modes}

Tight

Tight--binding approximationbinding approximation

Cavity Regions Λ Photonic Crsytal Overlapping Localized Cavity Modes

Stefanou and Modinos, Phys. Rev. B 57, 12127 (1998); Yariv et al., Opt. Lett. 24, 711 (1999) Bayindir, et al., Phys. Rev. Lett. 82, 2140 (2000)

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Straight Waveguide

¾

¾Formation of a cavity band (waveguiding band)Formation of a cavity band (waveguiding band) due to interaction between the localized modes

due to interaction between the localized modes

¾

¾Demonstration of a new type of waveguidingDemonstration of a new type of waveguiding

mechanism in photonic crystals.

¾

¾Full transmission is measured throughoutFull transmission is measured throughout

the CCW band

the CCW band ¾

¾Very sharp band edges can be used forVery sharp band edges can be used for

switching applications switching applications 0.6 0.7 0.8 0.9 1.0 1.1 1.2 -60 -50 -40 -30 -20 -10 0 Experiment FDTD T ransm is si on ( d B) Frequency (ω/ω₀)

PROPAGATION OF PHOTONS BY HOPPING

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0.90 0.95 1.00 1.05 1.10

ω

k

/

Ω

Experiment Theory 0.0 0.2 0.4 0.6 0.8 1.0

k

Λ/π

0.00 0.02 0.04

v

g

/c

DISPERSION RELATION, GROUP VELOCITY, PHOTON LIFETIME:

MEASUREMENTS AND CALCULATIONS

0.85 0.90 0.95

Frequency (

ω/ω

₀

)

0 50 100 τ p (ns) Experiment Theory

(

1 cos(

)

(

k

Ω

κ

k

Λ

ω

=

+

) k sin( ) k ( v_g = −ΩΛ

κ

Λ

c

L

)

k

(

v

L

)

k

(

_g p

π

τ

=

−

2 at the CCW band edges

at the CCW band edges

_“

_{heavy photon”}

Bayindir and Ozbay, Phys. Rev. B 62, R2247 (2000)

0 →

g

v

∞

→

p

τ

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Zig

--

zag

Waveguide

0.6 0.7 0.8 0.9 1.0 1.1 1.2 -60 -50 -40 -30 -20 -10 0 Experiment FDTD T ransm is si on ( d B) Frequency (ω/ω₀)

Problem of guiding light

around very sharp corners

in conventional waveguides

BENDING OF EM WAVES ALONG ARBITRARY PATH

¾

¾Possibility of constructing lossless and Possibility of constructing lossless and reflectionlessreflectionless bends in optical circuitsbends in optical circuits

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0.6 0.7 0.8 0.9 1.0 1.1 1.2 -60 -50 -40 -30 -20 -10 0

Left Port Experiment FDTD Tran sm is si o n ( d B) Frequency (ω/ω₀) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 -60 -50 -40 -30 -20 -10 0

Right Port Experiment FDTD T ransm issi on ( d B) Frequency (ω/ω₀)

Bayindir, et al., Appl. Phys. Lett. 77, 3902 (2000), JQE (in press)

POWER SPLITTERS

¾

¾The electromagnetic power in the input port splits equally The electromagnetic power in the input port splits equally into the two output ports throughout the waveguiding band

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0.6 0.7 0.8 0.9 1.0 1.1 1.2 -60 -50 -40 -30 -20 -10 0 Left Port Experiment FDTD Transm issi o n ( d B) Frequency (ω/ω₀) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 -60 -50 -40 -30 -20 -10 0 Right Port Experiment FDTD T ran sm is si on ( d B) Frequency (ω/ω₀)

COUPLED CAVITY SWITCHES

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λ_i λ₁,λ₂… λ_N cavity λ₁λ₂… λ_i λ_j λ_k… λ_N

WAVEGUIDES

λ_j cavity λ_k cavity λ₁,λ₂… λ_N λ₁λ₂… λ_i ... λ_n… λ_N

WAVEGUIDES

coupled-cavity waveguide _λ_i_{− λ}_k coupled-cavity waveguide _λ_l_{− λ}_n

WDM APPLICATIONS

Single wavelength dropping

Single wavelength dropping Band droppingBand dropping

Bayindir and Ozbay, APL [

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0.25 0.30 0.35 0.40 0.45 0.50 -50 -40 -30 -20 -10 0 T_1-2 T_1-3 T_1-4 T_1-5 Measurement T ransm is si on (dB ) Frequency (a/λ) 0.25 0.30 0.35 0.40 0.45 0.50 -50 -40 -30 -20 -10 0 T_1-2 T_1-3 T_1-4 T_1-5 FDTD Simulation Tr ansm issi on ( d B) Frequency (a/λ) f_k 2 2 1 1 5 5 4 4 3 3

DROPPING OF A SELECTIVE FREQUENCY FROM PW

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f_k 2 2 1 1 5 5 4 4 3 3 0.25 0.30 0.35 0.40 0.45 0.50 -50 -40 -30 -20 -10 0 T_1-2 T_1-3 T_1-4 T_1-5 FDTD Simulation T ransm is si on ( d B) Frequency (a/λ)

DROPPING OF A SELECTIVE FREQUENCY FROM CCW

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BAND DROPPING FROM PW

2 2 1 1 3 3 0.25 0.30 0.35 0.40 0.45 0.50 -50 -40 -30 -20 -10 0 T_1-2 T_1-3 T_1-4 FDTD Simulation T ransm is si on ( d B) Frequency (a/λ) 4 4

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2 2 1 1 3 3 4 4 0.25 0.30 0.35 0.40 0.45 0.50 -50 -40 -30 -20 -10 0 T_1-2 T_1-3 T_1-4 FDTD Simulation T ransm issi on ( d B) Frequency (a/λ)

BAND DROPPING FROM CCW

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0.25 0.30 0.35 0.40 0.45 0.50 -40 -30 -20 -10 0 FDTD Simulations T_1-2 T_1-3 T ransm issi on ( d B) Frequency (a/λ) 0.25 0.30 0.35 0.40 0.45 0.50 -40 -30 -20 -10 Measurement T_1-2 T_1-3 T ransm issi on ( d B) Frequency (a/λ)

COUPLED WAVEGUIDES: DIRECTIONAL COUPLERS

f₁ f₂ f₁ f₂ 1 1 2 2 33

Bayindir and Ozbay, Optics Express [

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0.25 0.30 0.35 0.40 0.45 0.50 -40 -30 -20 -10 Measurement T_1-2 T_1-3 T ransm issi on ( d B) Frequency (a/λ) 0.25 0.30 0.35 0.40 0.45 0.50 -50 -40 -30 -20 -10 0 T_1-2 T_1-3 FDTD Simulation T ran sm issi on ( d B) Frequency (a/λ)

DIRECTIONAL COUPLERS: COUPLED

DIRECTIONAL COUPLERS: COUPLED--CAVITY WAVEGUIDESCAVITY WAVEGUIDES

f₁ 1 1 2 2 33 f₂ 1 t 1 t 1 t 1 t 2 t 2 t 1 2 t t << (1) (2) TIGHT

TIGHT--BINDING MODEL:BINDING MODEL: INTERACTING CHAINS INTERACTING CHAINS

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APPLICATIONS APPLICATIONS g

v

/

1 ∝

η

v

_g

→

0

Large gain

INCREASING EFFICIENCY OF NONLINEAR PROCESESS INCREASING EFFICIENCY OF NONLINEAR PROCESESS

1480 1500 1520 1540 1560 1580 1600 1620 -1000 -800 -600 -400 -200 0 200 400 600 800 1000 D ispersion Coef ficient(ps /nm/mm) Wavelength (nm) 2 2 2

2 ω

λ

π

d

k

d

c

D

=

−

DISPERSION COMPENSATORS DISPERSION COMPENSATORS

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7 8 9 10 11 12 13 14 -60 -50 -40 -30 -20 -10 0 Defect Band T ransm is si on ( d B) Frequency (GHz) 9 10 11 12 0.0 0.2 0.4 0.6 0.8 1.0 Measurement Calculation k Λ / π Frequency (GHz)

QUASIPERIODIC [ PENROSE ] PHOTONIC CRYSTALS

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ϕ

i i i

z

re

z

→

periodic photonic crystal

disordered photonic crystal

r

: randomness parameter

ϕ

: random variable between

[

0 ,

π

]

COUPLED

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3D LAYER

-

BY

-

LAYER PHOTONIC CRYSTALS

network analyzer

Receiver

Removed Rod

Transmitter

Symmetry:

Symmetry: Face Face centeredcentered tetragonal (tetragonal (fctfct))

Material:

Material: Alumina of refractive index Alumina of refractive index εε

=3.1 =3.1 at microwave frequencies at microwave frequencies Dimensions: Dimensions: 0.32 cm 0.32 cm ×× 0.32 cm 0.32 cm ×× 15.25 15.25 cm cm Three

Three--dimensional stop band: dimensional stop band: from 10.6 from 10.6

GHz to 12.8

GHz

Bayindir, et al., Phys. Rev. Lett. 82, 2140 (2000); Bayindir, et al., Phys. Rev. B 61, R11855 (2000)

All phenomenon were observed in 3D layer

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COUPLED

COUPLED--CAVITIES IN 1D STRUCTURESCAVITIES IN 1D STRUCTURES

SiO SiO₂₂1.47 971.47 97 Si Si₃₃NN₄₄2.10 702.10 70 n d [nm] Glass Glass

Experimental results agree well with TMM and TB predictions for

Experimental results agree well with TMM and TB predictions for the three coupledthe three coupled--cavitiescavities

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(1 cos( )) ) (k Ω κ kΛ ω = + ) sin( ) ( ) (k k ΩΛ kΛ v_g =∇_kω =− κ c L k v L k _g p π τ ( )= ( )+2 heavy photon at the CMC band edges

0 →

g

v

∞

→

p

τ

Efficiency of the second harmonic generation process can be incEfficiency of the second harmonic generation process can be increasedreased as a result of large optical field amplitude and low group v

as a result of large optical field amplitude and low group velocity at theelocity at the

waveguiding band edges

Nearly full transmission was measured throughout the CMC bandNearly full transmission was measured throughout the CMC band

The transfer matrix method results agree well with the experimThe transfer matrix method results agree well with the experimental ental

observations

The position and bandwidth of waveguiding band can be adjusted bThe position and bandwidth of waveguiding band can be adjusted by y changing the thicknesses of the layers and the distance bet

changing the thicknesses of the layers and the distance between theween the cavity layers

cavity layers

COUPLED

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PHOTOLUMINESCENCE FROM THE COUPLED

PHOTOLUMINESCENCE FROM THE COUPLED--MICROCAVITY STRUCTUREMICROCAVITY STRUCTURE

Spectrometer Ar+ _laser (488 nm) SiO SiO₂₂ Si Si₃₃NN₄₄ _Spontaneous Emis sion

The photoluminescence spectrum was strongly modified in the preThe photoluminescence spectrum was strongly modified in the presence of sence of FabryFabry--Perot Perot microcavitymicrocavity

A strong spontaneous emission was achieved for a wide range of A strong spontaneous emission was achieved for a wide range of wavelengthswavelengths

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HIGHLY CONFINED WAVEGUIDES

Full confinement of electromagnetic waves in 3D layer

Full confinement of electromagnetic waves in 3D layer--byby--layer photonic crystalslayer photonic crystals

Noda

Noda et alet al, APL 75, 3739 1999; , APL 75, 3739 1999;

Bayindir

Bayindir et al., et al., PRB 63, 081107(R) (2001)PRB 63, 081107(R) (2001)

Straight Waveguide

_{Bended Waveguide}

Power Splitter

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Receiver

Photonic Crystal E H

Transmitter

network analyzer

EXPERIMENTAL SETUP

Symmetry: Face

Symmetry: Face centeredcentered tetragonal (tetragonal (fctfct)) Material: Alumina of refractive index

Material: Alumina of refractive index

ε

ε =3.1 at microwave frequencies=3.1 at microwave frequencies Dimensions: 0.32 cm

Dimensions: 0.32 cm ×× 0.32 cm 0.32 cm ×× 15.25 cm15.25 cm Photonic band gap: 10.6 GHz

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10 11 12 13 14 15 -50 -40 -30 -20 -10 0 Perfect Waveguide Guiding Band

T

ransm

issi

on (

d

B)

Frequency (GHz)

STRAIGHT WAVEGUIDE

G

G NeNearly full transmission was achieved for certain frequenciesarly full transmission was achieved for certain frequencies

G

G The full transmission within the waveguiding band was a proof ofThe full transmission within the waveguiding band was a proof of how well how well the wave was confined and guided without

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WAVEGUIDE BENT

10 11 12 13 14 15 -50 -40 -30 -20 -10 0

T

ransm

issi

on (

d

B)

Frequency (GHz)

G

G The full transmission through a 90The full transmission through a 90oo _{bent was achieved}_{bent was achieved}_{for certain frequencies}_{for certain frequencies} throughout the waveguiding band

throughout the waveguiding band

Comparison with simulation

[Noda’s Group, APL (1999)]:

The bending band covers 68%

of the stop band which is very

close to the simulation results

value of 67%.

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POWER SPLITTER

10 11 12 13 14 15 -50 -40 -30 -20 -10 0 Leftport Rightport

T

ransm

issi

on (

d

B)

Frequency (GHz)

G

G The electromagnetic power in the input port splits into the twoThe electromagnetic power in the input port splits into the two output portsoutput ports throughout the guiding band

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THEORETICAL MODEL: TIGHT BINDING APPROXIMATION

G

G The coupling between these localized cavity modes allows propagThe coupling between these localized cavity modes allows propagation ofation of photons

photons by hopping through the vacancy of the missing rodby hopping through the vacancy of the missing rod

Each vacancy just below the removed

rod behaves as a boxlike cavity

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DISPERSION RELATION & PHOTON LIFETIME

10 11 12 13 14 0.0 0.2 0.4 0.6 0.8 1.0 Experiment Theory k Λ / π Frequency (GHz)

(

1 cos(

)

(

k

Ω

κ

k

Λ

ω

=

+

10 11 12 13 14 0 10 20 30 40 50 60 Experiment Theory τ p (n s) Frequency (GHz)

c

L

k

v

L

k

_g p

π

τ

(

)

=

(

)

+

2

G

G Experimental results were in good agreement with the tightExperimental results were in good agreement with the tight--bindingbinding approximation predictions

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λ₁,λ₂… λ_k… λ_N λ_k λ₁,λ₂… λ_N cavity 10 11 12 13 14 15 -60 -50 -40 -30 -20 -10 0 Measurements Waveguide Cavity T ran smi ssi on ( d B) Frequency (GHz)

WDM APPLICATIONS: DROPPING A SELECTIVE WAVELENGTH

Electromagnetic wave with a specific frequency can dropped from Electromagnetic wave with a specific frequency can dropped from the guided mode inside the waveguide.the guided mode inside the waveguide.

Tunability can achieved by changing properties of the cavity.Tunability can achieved by changing properties of the cavity.

Bayindir and Ozbay [

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3D LAYER

3D LAYER--BYBY--LAYER STRUCTURES AT OPTICAL WAVELENGTHSLAYER STRUCTURES AT OPTICAL WAVELENGTHS

Lin et al, Nature 394, 251 (1998) _{Noda et al, Science 289, 604}

(2000)

Highly confined waveguides, waveguide bends, power splitter, addHighly confined waveguides, waveguide bends, power splitter, add--drop filters, switchesdrop filters, switches can be used in future

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SUMMARY

Various applications of 1D, 2D, and 3D coupledVarious applications of 1D, 2D, and 3D coupled-cavity structures were demonstrated -cavity structures were demonstrated

The tight-The tight-binding approximation was successfully applied to the photonic sbinding approximation was successfully applied to the photonic structurestructures

The finiteThe finite-difference-difference--timetime--domain (FDTD) and the transfer matrix method (TMM) resultsdomain (FDTD) and the transfer matrix method (TMM) results agree well with our measurements

agree well with our measurements

ACKNOWLEDGEMENTS

These works were supported by

These works were supported by ¾

¾ Turkish Department of Defense Grant No. KOBRATurkish Department of Defense Grant No. KOBRA--01, Thales JP8.0401, Thales JP8.04 ¾

¾ NATO Grant No. SfP971970NATO Grant No. SfP971970 ¾

¾ National Science Foundation Grant No. INTNational Science Foundation Grant No. INT--98206469820646