Fabry Perot cavity based microspectrometer

Aamer MahmoodDonald P. Butler Ph.D.

Department of Electrical EngineeringUniversity of Texas at Arlington, TX 76019

Sponsored by the National Science Foundation

Electromagnetic interference

• Electromagnetic energy from different sources will interfere when sharing the same space

101

jeEE

202

jeEE

)21(021

jtot eEEEE

Electromagnetic interference

• Interference depends on the phase of each component

0 2 4 6 8 102

1

0

1

21.938

1.936

sin x( )

sin x .5( )

sin x( ) sin x 0.5( )

100 x

101

jeEE

202

jeEE

21 EEEtot

Constructive

interference

A Fabry Perot cavity creates multiple sources with different phase from a single

source

)3(33

xxjeEE

x

jxeEE 0

Incident radiation

Transmitted radiation)( xnxj

nn eEE

Reflecting surface

Reflecting surface

Interference due to a Fabry Perot cavity

• The inter-reflector spacing determines the phase of the transmitted energy

• For maximum constructive interference

• For maximum destructive interference

2)12(

nx...3,2,1,0n

nx ...3,2,1n

wavelength

Fabry Perot cavity based spectrometer

• For an inter reflector spacing of , the transmitted radiation will add constructively at

Broadband incident radiation

Narrowband transmitted radiation

x

x

)12(

2

n

x ...3,2,1,0n

Broadband incident radiation

Narrowband transmitted radiation wavelength

amplitude

λ0

Tunable Fabry Perot cavity based spectrometer

Practical tunable Fabry Perot cavity

Support layer

Reflecting mirrorsMetal electrodes

•Provides mechanical support

•Transparent to incident radiation

•Effect electrostatic actuation•Form Fabry Perot cavity

Design Considerations

• Optical transmission through support layer– Investigated by measurements

• Mechanical displacement of support layer– Investigated by multiphysics FEM simulations

• Mechanical strength of support layer– Investigated by multiphysics FEM simulations

• Flatness of reflecting mirror during deflection– Investigated by multiphysics FEM simulations

Optical transmission through support layer

• Optical transmission through the support layer is to be measured

• The complex permittivity of the support material has been extracted using Variable angle spectrometery

0

1

2

3

4

5

6

-1

0

1

2

3

4

5

0 5 10 15 20 25 30 35 40

'

"

Wavelength(m)

Different designs

Corrugated support structure to improve flatness

Flat support structure

Mechanical displacement of support layer

FEM multiphysics simulations

Mechanical displacement of corrugated support layer

FEM multiphysics simulations

Top view of deflected top mirror

Top view of deflected support layer

Flatness of displaced reflecting mirror

(corrugated structure)

-1.3

-1.28

-1.26

-1.24

-1.22

-1.2

-1.18

-1.16

0 50 100 150 200

radial distance from center (um)

def

lect

ion

(u

m)

bottom left-top right

bottom right_top left

-10123456789

0 50 100 150 200radial distance (um)

% d

efle

ctio

n

bottom left-top right

bottom right-top left

FEM multiphysics simulations

Mechanical displacement of flat support layer

Top view of deflected top mirror

Top view of deflected support layer

FEM multiphysics simulations

Flatness of displaced reflecting mirror

(flat structure)

-1.43-1.42-1.41-1.4

-1.39-1.38-1.37-1.36-1.35-1.34-1.33-1.32

0 50 100 150 200

radial distance from center (um)

def

lect

ion

(u

m)

bottom left-top right

bottom right_top left

-1

0

1

2

3

4

5

6

7

0 50 100 150 200

radial distancefrom center (um)%

de

fle

cti

on

bottom left-top right

bottom right-top left

FEM multiphysics simulations

Tunable Fabry Perot cavity based microspectrometer

(computer generated model showing support layer)

Mechanical displacement Mises stresses due to displacement

Tunable Fabry Perot cavity based microspectrometer

(computer generated model showing metal surfaces)