Waveguide Losses and Input-output Coupling

1

Lih Y. LinEE 539B 2-

EE 539BIntegrated Optics and Nanophotonics

2 Waveguide Losses and Input/Output Coupling

2.1 Losses in optical waveguides2.2 Waveguide input and output coupling

Integrated Optics Theory and Technology, by R. G. Hunsperger, 5th ed., Ch. 6-7, Springer Verlag.

2


Loss Mechanisms

Scattering loss Predominates in glass or dielectric (such as

oxide) waveguides. Absorption loss

Most important in semiconductor and other crystalline materials.

Radiation loss Significant when waveguides are bent.

3


Scattering Losses

Volume scattering loss Caused by imperfections Loss/unit length proportional to number of

scattering centers per length Depends strongly on the relative size of the

imperfections compared to in the material Volume scattering negligible compared to

surface scattering loss Surface scattering loss

4


Surface Scattering Loss (I)More significant for higher-order modes.

mgR t

LN

=cot2

Number of reflections from each surface:

Exercise:A waveguide has tg = 3 m and n2 = 2.0. An optical wave with m = 0.8kn2 and = 900 nm propagates in the waveguide. How many reflections from each surface will the light experience for each cm traveled?

Convert loss coefficient to dB:

)cm( 3.4)cmdB(

)(

1-

0

=

=

L

zeIzI

5


Surface Scattering Loss (II)

roughness surface of Variances :

)(4 ,

111

sincos

21

2

2/1223

212

223

23

221

21

31

'

'32

+

=

==

++

=

A

knkn

tA

gm

ms

s increases as increases. Higher order mode (smaller m) has higher surface scattering loss.In dielectric film waveguide, such as glasses and oxides, surface variation ~ 0.1 m s ~ 0.5-5 dB/cm.In semiconductor waveguides, thickness variation ~ 0.01 m. Surface scattering loss is negligible compared to absorption loss.

Ref: P.K. Tien, Appl. Opt. V. 10, 2395 (1971)

6


Interband Absorption

Design wavguide material compositions so that the operating wavelength lies beyond the tail of the absorption curve to minimize interband absorption.

7


Free-Carrier Absorption

8


Loss Coefficient for Free-Carrier Absorption (I)

Motion of the free electrons under an applied electric field E0exp(jt)

)exp(*20

tjgj

meE

x

=

Nexp =1The displacement causes polarization

220

2

222

02

20

20

220

)*/()(

)*/()(

)*/()(

gmgNeK

ngmNenK

gjmNenK

i

r

+

=

=+

=

=And complex dielectric constant

n0: Index of refraction without the free carriers

mobilityElectron : *

9


Loss Coefficient for Free-Carrier Absorption (II)

30

22

20

3

*)(4

cnmNe

nkK

KKk ir

ifc

=

=

Example: n-type GaAs at = 1.15 m

)cmin ( 10)(cm -318-1 NNfc

Complex dielectric constant Loss

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Radiation Loss (I)Main loss mechanism for curved waveguide.To preserve the phase front, the tangential phase velocity must be proportional to the distance from the center of curvature.

RX

dtdR

dtdXR

zr

z

r

0

0

0)(

=

=

=

+

Phase velocity > speed of light when X > Xr.

How far must the photons travel before they can be considered as having been removed from the guided mode?Coherent length:

1

2

2

=

aaZc

11


Radiation Loss (II)

ct ZP

PdzzdP

zP11)(

)(1

=

P1: Power in the tail of the mode beyond Xr (i.e., the power to be lost by radiation within a length Zc)Pt: Total power

0

0

( ) cos( ) for 2 2

( ) cos( )exp ( ( / 2)) for | |2 2

a aE x E hx x

a aE x E h x a x

=

=

( )2 0 10

1 22 2

1 cos ( )exp 2 exp2

exp( )1 1sin( ) cos ( )

2 2 2

zha R aC C R

a haha ah

= =

+ +

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Lets pack 16 stages of modulatorsd

456

6810

Constraints: Spacing between waveguides at

least d Input and output cannot be on the

same side Waveguides cannot cross each other

3d

Scattering and absorption loss: 1 unit per d

Radiation loss (in units):

Whats the loss you obtain?

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16 x 16 Thermo-Optic Switch

Use Mach-Zehnder interferometer configuration for 2x2 switch unit Insertion loss = 6.6dB

Thin-film heater3-dB directional

couplerI0 I1

I2

( ) ( ) ( )( ) ( )

coupler ldirectiona in the ratio couplingpower :2cos14

2sin2cos212

02

22201

kkkIIkII

=

+=

Apply heat to change refractive index: n/T(K) ~ 10-5

T. Goh, M. Yasu, K. Hattori, A. Himeno, M. Okuno, and Y. Ohmori, IEEE Photonics Technol. Lett.,June, 1998.

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Measurement of Waveguide Losses End-Fire Coupling to Waveguides of Different Lengths

12

21 )/ln(ZZPP

=

Q: Disadvantages?

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Measurement of Waveguide Losses Prism-Coupled Loss Measurement

Advantages: Non-destructive. Light can be selectively coupled into each mode by properly choosing the

angle of incidence.

16


Coupling light into the waveguide and out of the waveguide incurs losses too.

Efficient coupling design is important.

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General Definitions for Coupling Loss

PmPin z

x

Coupling efficiency to the m-th mode

in

mm P

P=

Q: A single mode optical beam is coupled into a waveguide with guiding core dimension a few times larger than the wavelength. What kind of modes will be generated in the waveguide?

Coupling loss (dB)

m

in

PPlog10=L

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Direct Focusing

modeth -m theofon distributi Field :),(beamincident theofon distributi Field :),(

),(),(

),(),(22

2*

yxByxA

dxdyyxBdxdyyxA

dxdyyxByxA

m

mm

=

In most cases, A(x,y) can be represented by Gaussian beams.

19


TEM0,0 Gaussian BeamWavefront changeBeam spreading

2

00 1)(

+=zzWzW

phase Radial )(2

)(exp

phase alLongitudin tanexp

factor Amplitude )(

exp)(

)(

22

0

1

2

220

0

+

+=

zRyxkj

zzkzj

zWyx

zWWArA Beam radius

+=

201)(zzzzR Radius of curvature

of the wavefront

20

0Wz Rayleigh range

Q: Which factor affects the coupling most?

Ref: Verdeyen, Laser Electronics, 3rd ed., Prentice Hall.

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Gaussian Beam Through a Thin Lens

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End-Butt CouplingExact coupling efficiency can be obtained by overlap integrals.

Approximation: (assuming all waveguide modes are well confined, and )Lg tt

+

+

+=

2cos

)1(1

12

cos)()1(

64 222

2222

mtt

tmtt

tnnnn

m Lg

L

gL

g

gL

gLm

22


Misalignment EffectLongitudinal misalignmentLateral misalignment

2 ,for cos2

0

gLLg

L

ttXtt

tX

PP

23


Tapered Mode Size Converters

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Prism CouplersAir-waveguide coupling

Phase-matching condition

mm kn = sin1cannot be satisfied.

Prism-waveguide coupling

Phase-matching condition

mpm kn = sin

can be satisfied.(Assuming normal incidence to the prism.)

25


Example: Output Prism CouplerA prism coupler with index np = 2.2 is used to observe the modes of a waveguide. The light source is a He-Ne laser with 0 = 632.8 nm. If the light from a particular mode is seen at an angle of 26.43 with the normal to the prism surface, what is the propagation constant m for that mode?

Q: What is the interaction length required to obtain complete coupling?

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Coupled-Mode Theory

L

2: Coupling coefficient (depending on overlap integral

between the prism mode and the waveguide mode)

L =

=

=2cos m

WL

For a given L, the coupling coefficient required for complete coupling:

Wm

2cos

= Q1: What defines W?Q2: What will happen if L > /2?

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Notes on Prism Coupling In order to get 100% coupling with a uniform beam, the trailing edge

of the beam must exactly intersect the right-angle corner of the prism.

Disadvantages For most semiconductor waveguides, m ~ kn2 Difficult to find

prism materials

Incident beam must be highly collimated Coupling efficiency sensitive to the separation between the prism

and the waveguide

28


Grating Coupler

0

Periodic structure of the grating perturbs the waveguide modes in the region underneath the grating.

0

0

0 m

2 , 0, 1, 2, ...

: Propagation constant of the m-th mode covered by the grating

~

= + =

mkn = sin11m kn >

Phase-matching condition:can be satisfied even though

29


Example of Grating CouplerGrating: = 0.4 m on a GaAs planar waveguide0 = 1.15 mPropagation constant for the lowest-order mode in the waveguide: 0 = 3.6k

Assume 1st-order coupling, || = 1, what incident angle should the light make in order to couple to the lowest-order mode?At what 0 do we start to need higher-order coupling?
EE 539BIntegrated Optics and NanophotonicsLoss MechanismsScattering LossesSurface Scattering Loss (I)Surface Scattering Loss (II)Interband AbsorptionFree-Carrier AbsorptionLoss Coefficient for Free-Carrier Absorption (I)Loss Coefficient for Free-Carrier Absorption (II)Radiation Loss (I)Radiation Loss (II)Lets pack 16 stages of modulators16 x 16 Thermo-Optic SwitchMeasurement of Waveguide Losses? End-Fire Coupling to Waveguides of Different LengthsMeasurement of Waveguide Losses? Prism-Coupled Loss MeasurementGeneral Definitions for Coupling LossDirect FocusingTEM0,0 Gaussian BeamGaussian Beam Through a Thin LensEnd-Butt CouplingMisalignment EffectTapered Mode Size ConvertersPrism CouplersExample: Output Prism CouplerCoupled-Mode TheoryNotes on Prism CouplingGrating CouplerExample of Grating Coupler

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Waveguide Losses and Input-output Coupling