MSEG 667 Nanophotonics: Materials and Devices 5: Optical Resonant Cavities Prof. Juejun (JJ) Hu...

MSEG 667Nanophotonics Materials and Devices

5 Optical Resonant Cavities

Prof Juejun (JJ) Hu

hujuejunudeledu

Optical resonance and resonant cavities

Optical resonant mode A time-invariant stable electromagnetic field pattern (complex

amplitude) an eigen-solution to the Maxwell equations Discretized resonant frequencies (eigen-values) ie these

modes appear only at particular frequencieswavelengths The modal fields are usually spatially confined in a finite domain

Optical resonant cavities (resonators) Devices that support optical resonant modes

Guided mode resonance surface plasmon (polariton) resonance and spoof surface plasmon resonance all refer to coupling to propagating modes even though the same term ldquoresonancerdquo is referenced

Resonance a mechanical analog

The resonance frequency of a string determines the pitch of sound it produces

An ldquoinfinite corridorrdquo in two mirrors

Electromagnetic waves between two perfect

conductors (perfect mirrors)

Photon

Interference between back-and-forth reflected light

Standing wave formation

A simple mathematical model

Field amplitude 1

hellip

t1 r1 t2 r2

a1

a2hellip

an

α = 2pKλ L

r

aaa

n

iitot

11

1

2

12

1 r

aaT tottot

Transmission coefficient

Ray tracing summation of field amplitude taking into account interference effect (the phase term)

when |r| lt 1

1 1 2

1exp

2a t ikL L t

2 1a a r

2 1 exp 2r r r ikL L 1

1n

na a r

A close inspection of phasor summationhellip

2

12

1 r

aaT tottot


A vector on the complex plane with a moduluslength le1

Firstly letrsquos look at a lossless cavity ie α = 0 r1 = r2 = 1 and thus |r| = 1

when |r| lt 1

When kL ne Np the vectors have different directionshellip

When kL = Np the vectors are aligned (resonant condition)

Finite non-vanishing transmitted intensity ONLY at resonance

Transmission spectra

ω

Peak FWHM = 0

Eq (1)

Ttot

Phasor

FSR = pcLFree Spectral Range

1 2 exp exp 2r r r L ikL


2

12

1 r

aaT tottot


When there is loss in the cavity |r| lt 1 and Eq (1) holds

when |r| lt 1

The transmission spectra have non-vanishing values even when the resonant condition is not met


FSR = pcLTtot

ω

Peak FWHM ne 0

Eq (1)

FSR Free Spectral Range peak separationω0 resonant (angular) frequencyΔω peak FWHM (Full Width at Half Maximum)

Quality factor Q Cavity finesse

r

rFSRF

1

50)1(

50

00

rc

rLQ

Extinction ratio 10log10(TmaxTmin)

A vector on the complex plane with a moduluslength le1Phasor

Free Spectral Range


Standing wave modes in F-P cavities

1 1

1exp

2L RE z t ikz z

hellip

t1 r1 t2 r2

α = 2pKλ L

1 1 2

1exp 2 exp

2R LE z t r ikL L ikz z

zy

x

1 1

nR L n R LE z r E z

1 1

nL R n L RE z r E z

Cavity field

1 1 2 2

1 1

1

1

tot L R R L L R R L

L R R L

E z E z E z E z E z

E z E zr


Standing wave modes in F-P cavities (contrsquod)

hellip

N = 4 N = 5

N = 3N = 2N = 1

Important concepts

Quality factor (Q-factor)

Finesse

Free spectral range (FSR frequency domain)

Reference Juejun Hu PhD thesis Appendix I

00

loss

WQ

P

W Energy stored in the cavity in JPloss Power loss in Js or WFWHM should be calculated in the linear scale

2~2 g

FSRF Q

n L

02

g

cFSR

n L

Include the factor 2 for travelling wave cavities


Optical loss in cavities

Round trip loss in an F-P cavity

Coupling loss (mirror loss) Non-unity mirror reflectance Independent of cavity length

Internal loss (distributed loss) Absorptionscattering of light in the cavity Loss proportional to cavity length L

Both Q and finesse scales inversely with cavity loss If distributed loss dominates Q is independent of cavity length If coupling loss dominates F is independent of cavity length

2 2 2 2 21 2 1 21 1 exp 2 ~ 1 2r r r L r r L

2 21 21 r r

2 L

Cavity perturbation theory

Resonant frequency shift due to perturbation Material perturbation

Sharp perturbation

The frequency shift scales with field intensity

e + eDe

e eS Johnson et al rdquoPerturbation theory for Maxwellrsquos equations with shifting material boundariesrdquo Phys Rev E 65 066611 (2002)

2

3

200 2

32

r E r d rO

r E r d r

Standing wave vs travelling wave cavities

Standing wave resonators PhC cavitiesFabry-Perot (F-

P) cavity Light forms a standing wave

inside the cavity

Traveling wave resonators Micro-ringdiskracetrack

resonators microspheres Light circulates inside the

resonant cavity

2-d PhC cavity (top-view)

F-P cavity

Micro-disk

Micro-ring

Microsphere attached to a

fiber end



inside the cavity



resonant cavity


F-P cavity


Whispering gallery mode

CW mode

Sound wave

Acoustics

Optics

Standing wave resonators Light forms a standing wave

inside the cavity

Traveling wave resonators Light circulates inside the

resonant cavity

0 expzE E ikz

0 expzE E ikz

z

z

z

z sin 02 sinE E kz

cos 02 cosE E kz

cos

sin

1 11

1 12z

z

E E

E E

Azimuthally symmetric travelling wave cavities support CW amp CCW travelling wave modes as well as standing wave modes

and they are all degenerate (ie same resonant frequency)


z z z+ =

Degeneracy lifting in travelling wave cavities

Antisymmetric mode

Symmetric mode

Breaking the cavity azimuthal symmetry leads to resonance

frequency splitting of standing wave modes

Nat Photonics 4 46 (2010)APL 97 051102 (2010)IEEE JSTQE 12 52 (2006)PNAS 107 22407 (2010)

Optical coupling to cavity modes

Coupling approaches Free space coupling F-P cavity Waveguidefiber coupling traveling wave cavities PhC cavities

Phase matching condition efficient coupling

External Q-factor Energy loss due

to coupling Qex

Extinction ratio depends on coupling

Critical couplingJ Hu et al Opt Lett 33 2500-2502 (2008)

exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)

Increase coupling strength

Critical coupling

Critical coupling Complete power transfer

Pthru = 0

Occurs when Qex = Qin

Maximum field enhancement inside the resonator

Under coupling Qex gt Qin

Over coupling Qex lt Qin

input

thru = 0

Matrix representation of directional couplers

a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at

Ch 4 Photonics Optical Electronics in Modern Communications A Yariv and P Yeh

Linear lossless uni-directional reciprocal single-mode couplers

where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t

Matrix K1 Matrix K2 Matrix Kn

Coupling matrix approach for travelling wave cavities

a2

a1

b2

b1

Losslesscoupler

α waveguide loss β propagation constant L round-trip length

5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on

A Yariv Electron Lett 36 321-322 (2000)


Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1

3rd order add-drop filters

Coupled resonator steady state solution 2 equations for each coupler 8 total 1 equation for each ring section 6 total 2 known inputs a1 a16

Compile the equation coefficients into a 14-by-14 matrix

Solve the set of linear equations The algorithm can be automated to solve coupled cavities of arbitrary topology

The versatile optical resonator

Selective spectral transmissionreflection Optical filters for WDM

Coherent optical feedback Lasers

Increased optical path (interaction) length Spectroscopy and sensing Modulators and switches Slow light coupled resonator optical waveguide (CROW) Cavity-enhanced photodetector

Enhanced field amplitude (photon LDOS) Nonlinear optics Cavity quantum-electrodynamics (QED) Cavity optomechanics

Wavelength Division Multiplexing (WDM)

Better use of existing fiber bandwidth

Little cross-talk between channels

Transparent to data format and rate

Mature technology

See what the ldquoFiOS boyrdquo says about WDM





Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip

Ring resonator add-drop filter

λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn

Add-drop filter design rulesbull Low insertion loss critical coupling low WG lossbull Low cross-talk

large extinction ratio FSR gtgt channel spacingbull Flat response in the pass band

bull B Little et al J Lightwave Technol 15 998 (1997)

bull B Little et al IEEE PTL 16 2263 (2004)

bull T Barwicz et al JLT 24 2207 (2006)

bull F Xia et al Opt Express 15 11934 (2007)

bull P Dong et al Opt Express 18 23784 (2010)

Semiconductor lasers

AlGaAs-GaAs-AlGaAs double heterojunction lasers

n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser

Vertical Cavity Surface Emitting Lasers (VCSELs)

On-wafer testing Single longitudinal

mode operation Low threshold

current Long lifetime

httpwwwrp-photonicscomvertical_cavity_surface_emitting_lasershtml

httpwwwrp-photonicscomexternal_cavity_diode_lasershtml

External Cavity Lasers and VECSELs

Rev Sci Instrum 72 4477 (2001)

Vertical External-cavity Surface-emitting Lasers

(VECSELs)

Wide wave-length tuning range single longitudinal

mode operation

The strong photon-matter interaction in integrated high-Q optical resonators make them ideal for sensing

Detection of refractive index change induced by surface binding of biological molecular species proteins nucleic acids virus particles

Specific surface bindingWGM

resonance

High Q-factor leads to superior spectral resolution and improved sensitivity

Cavity-enhanced IR spectroscopy achieves high sensitivity and small footprint simultaneously

Optical path length L

Source Receiver

Lambert-beerrsquos law

LLI )exp(1

FootprintSensitivity

Single-pass spectrophotometer Cavity-enhanced spectroscopy

Analyst 135 133-139 (2010)

Extinction ratio change due to presence of absorption

Silicon micro-ring switchmodulator

Refractive index change in silicon via free carrier dispersion effect opticalelectrical carrier injection

Low power consumption due to small footprintV Almeida et al ldquoAll-optical control of light on a silicon chiprdquo Nature 431 1081 (2004)Q Xu et al ldquoMicrometer-scale silicon electro-optic modulatorrdquo Nature 435 325 (2005)

The challenges narrow band operation amp fabricationthermal sensitivity

Si waveguide cross-section 450

nm times 200 nm

2000 GHzQ = 1000

MSEG 667 Nanophotonics Materials and Devices 5 Optical Reson






A close inspection of phasor summationhellip (2)



Important concepts




Standing wave vs travelling wave cavities (2)





Optical coupling to cavity modes (2)

Critical coupling



Coupling matrix approach for travelling wave cavities (2)



Slide 26

Wavelength Division Multiplexing (WDM) (2)





The strong photon-matter interaction in integrated high-Q optic

Cavity-enhanced IR spectroscopy achieves high sensitivity and s


The challenges narrow band operation amp fabricationthermal sen


Optical resonant mode A time-invariant stable electromagnetic field pattern (complex

amplitude) an eigen-solution to the Maxwell equations Discretized resonant frequencies (eigen-values) ie these

modes appear only at particular frequencieswavelengths The modal fields are usually spatially confined in a finite domain

Optical resonant cavities (resonators) Devices that support optical resonant modes

Guided mode resonance surface plasmon (polariton) resonance and spoof surface plasmon resonance all refer to coupling to propagating modes even though the same term ldquoresonancerdquo is referenced






Photon




Field amplitude 1

hellip

t1 r1 t2 r2

a1

a2hellip

an

α = 2pKλ L

r

aaa

n

iitot

11

1

2

12

1 r

aaT tottot



when |r| lt 1

1 1 2

1exp

2a t ikL L t

2 1a a r


1n

na a r


2

12

1 r

aaT tottot




when |r| lt 1





ω

Peak FWHM = 0

Eq (1)

Ttot

Phasor




2

12

1 r

aaT tottot



when |r| lt 1



FSR = pcLTtot

ω

Peak FWHM ne 0

Eq (1)



r

rFSRF

1

50)1(

50

00

rc

rLQ



Free Spectral Range



1 1

1exp

2L RE z t ikz z

hellip

t1 r1 t2 r2

α = 2pKλ L

1 1 2

1exp 2 exp


zy

x

1 1

nR L n R LE z r E z

1 1

nL R n L RE z r E z

Cavity field

1 1 2 2

1 1

1

1

tot L R R L L R R L

L R R L

E z E z E z E z E z

E z E zr



hellip

N = 4 N = 5

N = 3N = 2N = 1

Important concepts


Finesse



00

loss

WQ

P


2~2 g

FSRF Q

n L

02

g

cFSR

n L








2 2 2 2 21 2 1 21 1 exp 2 ~ 1 2r r r L r r L

2 21 21 r r

2 L



Sharp perturbation


e + eDe


2

3

200 2

32

r E r d rO

r E r d r




inside the cavity



resonant cavity


F-P cavity

Micro-disk

Micro-ring


fiber end



inside the cavity



resonant cavity


F-P cavity



CW mode

Sound wave

Acoustics

Optics


inside the cavity


resonant cavity

0 expzE E ikz

0 expzE E ikz

z

z

z

z sin 02 sinE E kz

cos 02 cosE E kz

cos

sin

1 11

1 12z

z

E E

E E




z z z+ =


Antisymmetric mode

Symmetric mode








to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26















Photon




Field amplitude 1

hellip

t1 r1 t2 r2

a1

a2hellip

an

α = 2pKλ L

r

aaa

n

iitot

11

1

2

12

1 r

aaT tottot



when |r| lt 1

1 1 2

1exp

2a t ikL L t

2 1a a r


1n

na a r


2

12

1 r

aaT tottot




when |r| lt 1





ω

Peak FWHM = 0

Eq (1)

Ttot

Phasor




2

12

1 r

aaT tottot



when |r| lt 1



FSR = pcLTtot

ω

Peak FWHM ne 0

Eq (1)



r

rFSRF

1

50)1(

50

00

rc

rLQ



Free Spectral Range



1 1

1exp

2L RE z t ikz z

hellip

t1 r1 t2 r2

α = 2pKλ L

1 1 2

1exp 2 exp


zy

x

1 1

nR L n R LE z r E z

1 1

nL R n L RE z r E z

Cavity field

1 1 2 2

1 1

1

1

tot L R R L L R R L

L R R L

E z E z E z E z E z

E z E zr



hellip

N = 4 N = 5

N = 3N = 2N = 1

Important concepts


Finesse



00

loss

WQ

P


2~2 g

FSRF Q

n L

02

g

cFSR

n L








2 2 2 2 21 2 1 21 1 exp 2 ~ 1 2r r r L r r L

2 21 21 r r

2 L



Sharp perturbation


e + eDe


2

3

200 2

32

r E r d rO

r E r d r




inside the cavity



resonant cavity


F-P cavity

Micro-disk

Micro-ring


fiber end



inside the cavity



resonant cavity


F-P cavity



CW mode

Sound wave

Acoustics

Optics


inside the cavity


resonant cavity

0 expzE E ikz

0 expzE E ikz

z

z

z

z sin 02 sinE E kz

cos 02 cosE E kz

cos

sin

1 11

1 12z

z

E E

E E




z z z+ =


Antisymmetric mode

Symmetric mode








to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26











Field amplitude 1

hellip

t1 r1 t2 r2

a1

a2hellip

an

α = 2pKλ L

r

aaa

n

iitot

11

1

2

12

1 r

aaT tottot



when |r| lt 1

1 1 2

1exp

2a t ikL L t

2 1a a r


1n

na a r


2

12

1 r

aaT tottot




when |r| lt 1





ω

Peak FWHM = 0

Eq (1)

Ttot

Phasor




2

12

1 r

aaT tottot



when |r| lt 1



FSR = pcLTtot

ω

Peak FWHM ne 0

Eq (1)



r

rFSRF

1

50)1(

50

00

rc

rLQ



Free Spectral Range



1 1

1exp

2L RE z t ikz z

hellip

t1 r1 t2 r2

α = 2pKλ L

1 1 2

1exp 2 exp


zy

x

1 1

nR L n R LE z r E z

1 1

nL R n L RE z r E z

Cavity field

1 1 2 2

1 1

1

1

tot L R R L L R R L

L R R L

E z E z E z E z E z

E z E zr



hellip

N = 4 N = 5

N = 3N = 2N = 1

Important concepts


Finesse



00

loss

WQ

P


2~2 g

FSRF Q

n L

02

g

cFSR

n L








2 2 2 2 21 2 1 21 1 exp 2 ~ 1 2r r r L r r L

2 21 21 r r

2 L



Sharp perturbation


e + eDe


2

3

200 2

32

r E r d rO

r E r d r




inside the cavity



resonant cavity


F-P cavity

Micro-disk

Micro-ring


fiber end



inside the cavity



resonant cavity


F-P cavity



CW mode

Sound wave

Acoustics

Optics


inside the cavity


resonant cavity

0 expzE E ikz

0 expzE E ikz

z

z

z

z sin 02 sinE E kz

cos 02 cosE E kz

cos

sin

1 11

1 12z

z

E E

E E




z z z+ =


Antisymmetric mode

Symmetric mode








to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26











2

12

1 r

aaT tottot




when |r| lt 1





ω

Peak FWHM = 0

Eq (1)

Ttot

Phasor




2

12

1 r

aaT tottot



when |r| lt 1



FSR = pcLTtot

ω

Peak FWHM ne 0

Eq (1)



r

rFSRF

1

50)1(

50

00

rc

rLQ



Free Spectral Range



1 1

1exp

2L RE z t ikz z

hellip

t1 r1 t2 r2

α = 2pKλ L

1 1 2

1exp 2 exp


zy

x

1 1

nR L n R LE z r E z

1 1

nL R n L RE z r E z

Cavity field

1 1 2 2

1 1

1

1

tot L R R L L R R L

L R R L

E z E z E z E z E z

E z E zr



hellip

N = 4 N = 5

N = 3N = 2N = 1

Important concepts


Finesse



00

loss

WQ

P


2~2 g

FSRF Q

n L

02

g

cFSR

n L








2 2 2 2 21 2 1 21 1 exp 2 ~ 1 2r r r L r r L

2 21 21 r r

2 L



Sharp perturbation


e + eDe


2

3

200 2

32

r E r d rO

r E r d r




inside the cavity



resonant cavity


F-P cavity

Micro-disk

Micro-ring


fiber end



inside the cavity



resonant cavity


F-P cavity



CW mode

Sound wave

Acoustics

Optics


inside the cavity


resonant cavity

0 expzE E ikz

0 expzE E ikz

z

z

z

z sin 02 sinE E kz

cos 02 cosE E kz

cos

sin

1 11

1 12z

z

E E

E E




z z z+ =


Antisymmetric mode

Symmetric mode








to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26











2

12

1 r

aaT tottot



when |r| lt 1



FSR = pcLTtot

ω

Peak FWHM ne 0

Eq (1)



r

rFSRF

1

50)1(

50

00

rc

rLQ



Free Spectral Range



1 1

1exp

2L RE z t ikz z

hellip

t1 r1 t2 r2

α = 2pKλ L

1 1 2

1exp 2 exp


zy

x

1 1

nR L n R LE z r E z

1 1

nL R n L RE z r E z

Cavity field

1 1 2 2

1 1

1

1

tot L R R L L R R L

L R R L

E z E z E z E z E z

E z E zr



hellip

N = 4 N = 5

N = 3N = 2N = 1

Important concepts


Finesse



00

loss

WQ

P


2~2 g

FSRF Q

n L

02

g

cFSR

n L








2 2 2 2 21 2 1 21 1 exp 2 ~ 1 2r r r L r r L

2 21 21 r r

2 L



Sharp perturbation


e + eDe


2

3

200 2

32

r E r d rO

r E r d r




inside the cavity



resonant cavity


F-P cavity

Micro-disk

Micro-ring


fiber end



inside the cavity



resonant cavity


F-P cavity



CW mode

Sound wave

Acoustics

Optics


inside the cavity


resonant cavity

0 expzE E ikz

0 expzE E ikz

z

z

z

z sin 02 sinE E kz

cos 02 cosE E kz

cos

sin

1 11

1 12z

z

E E

E E




z z z+ =


Antisymmetric mode

Symmetric mode








to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26











1 1

1exp

2L RE z t ikz z

hellip

t1 r1 t2 r2

α = 2pKλ L

1 1 2

1exp 2 exp


zy

x

1 1

nR L n R LE z r E z

1 1

nL R n L RE z r E z

Cavity field

1 1 2 2

1 1

1

1

tot L R R L L R R L

L R R L

E z E z E z E z E z

E z E zr



hellip

N = 4 N = 5

N = 3N = 2N = 1

Important concepts


Finesse



00

loss

WQ

P


2~2 g

FSRF Q

n L

02

g

cFSR

n L








2 2 2 2 21 2 1 21 1 exp 2 ~ 1 2r r r L r r L

2 21 21 r r

2 L



Sharp perturbation


e + eDe


2

3

200 2

32

r E r d rO

r E r d r




inside the cavity



resonant cavity


F-P cavity

Micro-disk

Micro-ring


fiber end



inside the cavity



resonant cavity


F-P cavity



CW mode

Sound wave

Acoustics

Optics


inside the cavity


resonant cavity

0 expzE E ikz

0 expzE E ikz

z

z

z

z sin 02 sinE E kz

cos 02 cosE E kz

cos

sin

1 11

1 12z

z

E E

E E




z z z+ =


Antisymmetric mode

Symmetric mode








to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26











hellip

N = 4 N = 5

N = 3N = 2N = 1

Important concepts


Finesse



00

loss

WQ

P


2~2 g

FSRF Q

n L

02

g

cFSR

n L








2 2 2 2 21 2 1 21 1 exp 2 ~ 1 2r r r L r r L

2 21 21 r r

2 L



Sharp perturbation


e + eDe


2

3

200 2

32

r E r d rO

r E r d r




inside the cavity



resonant cavity


F-P cavity

Micro-disk

Micro-ring


fiber end



inside the cavity



resonant cavity


F-P cavity



CW mode

Sound wave

Acoustics

Optics


inside the cavity


resonant cavity

0 expzE E ikz

0 expzE E ikz

z

z

z

z sin 02 sinE E kz

cos 02 cosE E kz

cos

sin

1 11

1 12z

z

E E

E E




z z z+ =


Antisymmetric mode

Symmetric mode








to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26










Important concepts


Finesse



00

loss

WQ

P


2~2 g

FSRF Q

n L

02

g

cFSR

n L








2 2 2 2 21 2 1 21 1 exp 2 ~ 1 2r r r L r r L

2 21 21 r r

2 L



Sharp perturbation


e + eDe


2

3

200 2

32

r E r d rO

r E r d r




inside the cavity



resonant cavity


F-P cavity

Micro-disk

Micro-ring


fiber end



inside the cavity



resonant cavity


F-P cavity



CW mode

Sound wave

Acoustics

Optics


inside the cavity


resonant cavity

0 expzE E ikz

0 expzE E ikz

z

z

z

z sin 02 sinE E kz

cos 02 cosE E kz

cos

sin

1 11

1 12z

z

E E

E E




z z z+ =


Antisymmetric mode

Symmetric mode








to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26















2 2 2 2 21 2 1 21 1 exp 2 ~ 1 2r r r L r r L

2 21 21 r r

2 L



Sharp perturbation


e + eDe


2

3

200 2

32

r E r d rO

r E r d r




inside the cavity



resonant cavity


F-P cavity

Micro-disk

Micro-ring


fiber end



inside the cavity



resonant cavity


F-P cavity



CW mode

Sound wave

Acoustics

Optics


inside the cavity


resonant cavity

0 expzE E ikz

0 expzE E ikz

z

z

z

z sin 02 sinE E kz

cos 02 cosE E kz

cos

sin

1 11

1 12z

z

E E

E E




z z z+ =


Antisymmetric mode

Symmetric mode








to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26












Sharp perturbation


e + eDe


2

3

200 2

32

r E r d rO

r E r d r




inside the cavity



resonant cavity


F-P cavity

Micro-disk

Micro-ring


fiber end



inside the cavity



resonant cavity


F-P cavity



CW mode

Sound wave

Acoustics

Optics


inside the cavity


resonant cavity

0 expzE E ikz

0 expzE E ikz

z

z

z

z sin 02 sinE E kz

cos 02 cosE E kz

cos

sin

1 11

1 12z

z

E E

E E




z z z+ =


Antisymmetric mode

Symmetric mode








to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26













inside the cavity



resonant cavity


F-P cavity

Micro-disk

Micro-ring


fiber end



inside the cavity



resonant cavity


F-P cavity



CW mode

Sound wave

Acoustics

Optics


inside the cavity


resonant cavity

0 expzE E ikz

0 expzE E ikz

z

z

z

z sin 02 sinE E kz

cos 02 cosE E kz

cos

sin

1 11

1 12z

z

E E

E E




z z z+ =


Antisymmetric mode

Symmetric mode








to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26












inside the cavity



resonant cavity


F-P cavity



CW mode

Sound wave

Acoustics

Optics


inside the cavity


resonant cavity

0 expzE E ikz

0 expzE E ikz

z

z

z

z sin 02 sinE E kz

cos 02 cosE E kz

cos

sin

1 11

1 12z

z

E E

E E




z z z+ =


Antisymmetric mode

Symmetric mode








to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26











CW mode

Sound wave

Acoustics

Optics


inside the cavity


resonant cavity

0 expzE E ikz

0 expzE E ikz

z

z

z

z sin 02 sinE E kz

cos 02 cosE E kz

cos

sin

1 11

1 12z

z

E E

E E




z z z+ =


Antisymmetric mode

Symmetric mode








to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26











inside the cavity


resonant cavity

0 expzE E ikz

0 expzE E ikz

z

z

z

z sin 02 sinE E kz

cos 02 cosE E kz

cos

sin

1 11

1 12z

z

E E

E E




z z z+ =


Antisymmetric mode

Symmetric mode








to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26











Antisymmetric mode

Symmetric mode








to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26














to coupling Qex



exintot QQQQ

1111





to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26














to coupling Qex


Critical coupling

exintot QQQQ

1111

Tra

nsm

issi

on (

dB)

Wavelength (μm)


Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26










Critical coupling


Pthru = 0





input

thru = 0


a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26











a1

a2

b1

b2 a2

a1

b2

b1

Lossless coupler

1 1

2 2

b at

b at



where

a1

a2

b1

b2

Coupler1

Coupler2

hellip Coupler n

1 2 nb K K K a

Cascadability

2 2 1t



a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26











a2

a1

b2

b1

Losslesscoupler


5 mm

1 1

2 2

b at

b at

2 2

1exp

2a b i L L

222 2

1 122

2 cos

1 2 cos

A t A t Lb a

A t A t L

1exp

2A L

where

15481546 15521550 15540

02

04

06

08

1

Wavelength (nm)

Tra

nsm

issi

on



Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26











Coupler1

a3

a1

a4

a2

Coupler2

Coupler3

a7

a5

a8

a6

a11

a9

a12

a10

Coupler4

a15

a13

a16

a14

L6 a6 L5 a5

L4 a4 L3 a3

L2 a2 L1 a1














Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26



















Mature technology






Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26















Mature technology

Multiplexing

De-multiplexing

λ1 λ2 λ3 hellip


λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26











λ1λ2

bullbullbull

λn

λ1 λ2

hellip

λn










n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26












n-type AlGaAs

GaAs

p-type AlGaAs

+

-

mirrormirror

Laser output

Edge-emitting laser










(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26



















(VECSELs)


mode operation




resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26













resonance




Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26












Source Receiver


LLI )exp(1



Analyst 135 133-139 (2010)







nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26















nm times 200 nm

2000 GHzQ = 1000










Important concepts










Critical coupling






Slide 26










MSEG 667 Nanophotonics: Materials and Devices 5: Optical Resonant Cavities Prof. Juejun (JJ) Hu...

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Transcript of MSEG 667 Nanophotonics: Materials and Devices 5: Optical Resonant Cavities Prof. Juejun (JJ) Hu...