Polarization independent ultra-sharp filtering at oblique incidence with resonant gratings Anne-Laure Fehrembach, Fabien Lemarchand, Anne Sentenac,

Institut Fresnel, Marseille, France

Olga Boyko, Anne Talneau

Laboratoire de Photonique et de Nanostructures, Marcoussis, France

LPN

0

1

R

Goal : =0.2nm ~100% efficiency

with standard collimated incident beam (=0.2°)

polarization independence oblique incidence

Resonant grating

Resonant grating filters: basic principles

2sin( )

inck x

kx- K

2/

0 K=2/d

kinc

(-1)

kp

2/p

kx

kp, 2/p)2/

0

light conekinc

kinc

(-1)

kpkx

ky

~ p

kp , p)x

z

y

kinc

Advantages and limitations:• ultra-narrow bandwidth: < 0.1nm achievable• weak angular tolerance: < 0.05°• strong polarization sensitivity

kinc(-1)

ps

kp , p)

d

Angular tolerant configuration

Perturbative model:

2/

0 kx

kx

x

y

z

kinc(-1) (+1)

0

2/

kinc

(-1) (+1)

kinc

(-1) (+1)

TE2

TE1 0 kx

2/

kinc

(-1) (+1)

2 counter propagative modes, small large

kx

2/

0

kinc

(-1)

kx0

(-1)

kinc

2/

Polarization independent configuration

Symmetry plane, small

symmetric TEp

anti - symmetric TEs

p

s

symmetry plane

2/

k

s

p

1,-1

kinc

(0,1)

(1,0)

symmetry plane

kx

2/

1,-1

ps

Angular tolerant and polarization independent oblique incidence configuration

• Symmetry plane, 2 counter propagative modes

k

2/

1,-1

ps

kinc

(0,1)

(-1,0)

(0,-1)

TE2

(1,0)

TE1

symmetry plane

Fehrembach, Sentenac, Appl. Phys. Lett., 86, 121105 (2005)

2,0

1,0

small , small large

Design and fabrication

• design  "Doubly periodic patern"

• fabrication• layers deposition:

glass substrate / Ta2O5 / SiO2/ Ta2O5 / SiO2 (220nm

etched)

• electronic lithography etching (component size 1mm2)

Scanning electron microscopy

picture of the grating

Diameters dB = 347nm dA= 257nmdC= 170nm

d/4 d/4

d = 890nm

A

B

C

Asmall , small large

5.4 5.6 5.8 6 6.21.535

1.54

1.545

1.55

(°)

(

m)

ps

theory

Results: resonant grating dispersion relationMinimum of transmittivity versus incident angle and wavelength

• experimental and theoretical dispersion relations are similar

(same gap width ~ 5nm, opening around 5.8°)

• Points A and A’: polarization independent, angular tolerant resonance

• Points B et B’: weak angular tolerance, polarization sensitivity

5.4 5.6 5.8 6.0 6.21.545

1.550

1.555

1.560 p s

(m

)

experience

A

B’A’B

Results: resonant grating spectra

Points B and B’: s and p resonances split up, wide bandwidth, low efficiency (=0.02°)

Points A and A’: polarization independence, narrow bandwidth, quite good efficiency

Theory

=5.5°

=5.8°Experience

=5.5°

=5.8°

diameter at waist 580µm,

full angle divergence 0.2°

R=28% T=52% R+T=80%

• Grating finite size effects (1mm²) ?

Results: experience vs theory

Plane waveTheory, Gaussian beam

divergence 0.2° Experience

divergence 0.2°

=0.1nm =0.17°

R=100% T=0% R+T=100%

=0.2nm

R=65% T=35% R+T=100%

• Performances deterioration:

• Etching imperfections (write fields stitching errors) ?

little diffusion at resonance but 20% energy is

lost

=0.4nm

• Experimental demonstration of a resonant grating filter with

• 0.4nm bandwidth

• polarization independence

• under 5.8° of incidence

• Performances deterioration: weak angular tolerance and finite size effect

Etching in high index, over a wide area

New component: =0.2nm, =0.6°, etched over 3mm²

Conclusion

Transmittivity versus collecting angle, at and outside resonance

0.001

0.01

0.1

1

-15.0 -10.0 -5.0 0.0 5.0 10.0 15.0

Collecting angle (mrad)

tran

smit

tivi

ty

Rnorm

Hrnorm

Collecting angle of the detector:

2.7mrad (1mm located at 36cm)

diffusion ?

diffusion ?

Transmittivity and reflectivity with a collecting lens

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1541 1541.5 1542 1542.5 1543

longueur d'onde

R e

t T

20% of energy at resonance remains lost

pour info: angle de collection 200 mrad en T (lentille)et 60 mrad en R (cube)

Polarisation s+p

Incident Réfléchi