Guido Niederer,
Hans Peter Herzig,
Joseph Shamir,
Hans Thiele,
Marc Schnieper,
and Christian Zschokke
G. Niederer (guido.niederer@unine.ch), H. P. Herzig, and J. Shamir are with the Institute of Microtechnology, Rue A.-L. Breguet 2, 2000 Neuchâtel, Switzerland.
H. Thiele, M. Schnieper, and C. Zschokke are with the Centre Suisse d’Electromagnetique et de Microtechnique SA, Badenstrasse 569, 8048 Zürich, Switzerland.
J. Shamir is also with the Department of Electrical Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel.
Guido Niederer, Hans Peter Herzig, Joseph Shamir, Hans Thiele, Marc Schnieper, and Christian Zschokke, "Tunable, oblique incidence resonant grating filter for telecommunications," Appl. Opt. 43, 1683-1694 (2004)
We have designed a tunable, oblique-incidence resonant grating filter that covers the C band as an add-drop device for incident TE-polarized light. We tune the filter by tilting a microelectromechanical systems platform onto which the filter is attached. The fabrication tolerances as well as the role of finite incident-beam size and limited device size were addressed. The maximum achievable efficiency of a finite-area device as well as a scaling law that relates the resonance peak width and the minimum device size is derived. In good agreement with simulations, measurements indicate a negligible change in shape of the resonance peak from 1526 nm at a 45° angle of incidence to 1573 nm at a 53° angle with a full width at half-maximum of 0.4 nm. In this range the shift of the peak wavelength is linear with respect to changes in the angle of incidence.
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Percentage Change of λres as a Result of +3% Increase of the Design Parameter
Percentage Change of FWHM as a Result of +3% Increase of the Design Parameter
Period (nm)
592
2.62
7.81
nTiO2
2.298
1.96
5.86
AOI (deg)
45°
0.55
3.28
dwg (nm)
287
0.36
-6.86
nsubstrate
1.51
0.22
-4.73
nSiO2
1.444
0.13
2.35
Fill factor
0.513
0.01
-0.51
dgrating (nm)
38
0.00
5.87
dSiO2 (nm)
146
0.00
-4.09
Amount of incomplete etching (nm)
3
-0.01
-14.83
Amount of overetching into SiO2 (nm)
3
0.00
0.20
The percentage changes of resonance wavelength λres and of resonance width FWHM (full width at half-maximum) that result from increasing the design parameter in column 2 by 3% are listed in columns 3 and 4, respectively. Values below 3% indicate an attenuation of the relative error in the optical response, whereas values above 3% indicate an amplification of the error. The device with the rounded design parameter shows a FWHM of 0.517 nm at 1544.6 nm at an AOI of 45°.
Table 2
Peak Reflection Efficiency of an Infinite Device as a Function of Absorption Loss Coefficient α of the Waveguide Material
Im (n)
αabs dB/cm
FWHM (nm)
Rmax (%)
0
0
0.517
100
1 × 10-6
0.35
0.518
99.7
2 × 10-6
0.71
0.519
99.4
5 × 10-6
1.77
0.521
98.4
1 × 10-5
3.53
0.526
96.8
2 × 10-5
7.06
0.535
93.7
5 × 10-5
17.66
0.561
85.3
1 × 10-4
35.32
0.604
73.7
Table 3
Simulations for a Device with Coupling Coefficient α = 1.70 mm-1a
Efficiency (%)
Grating Length
Gaussian Waist
Δz
30
0.765
0.234
0.194
40
1.024
0.296
0.268
50
1.360
0.380
0.380
60
1.724
0.471
0.515
70
2.228
0.596
0.719
80
3.012
0.788
1.064
90
4.720
1.173
1.871
95
7.133
1.693
3.061
98
12.067
2.682
5.534
99
17.900
3.784
8.464
99.5
26.500
5.328
12.778
For a given efficiency in column 1 the minimum device length Lg is given in column 2. The corresponding Gaussian beam widths w and their positions at Δz are given in columns 3 and 4, respectively. All lengths are millimeters.
Table 4
Results of a Lorentzian Curve Fit of the Measured Reflection and Transmission Spectra at Several Angles of Incidencea
Angle (°)
Reflection Spectra
Transmission Spectra
λc (nm)
w (nm)
Rmax (a.u.)
λc (nm)
w (nm)
ΔTmax (a.u.)
45
1526.80
0.40
3.71
1526.80
0.39
0.94
46
1533.04
0.43
3.74
1533.01
0.41
0.94
47
1538.92
0.44
3.59
1538.90
0.43
0.92
48
1545.01
0.45
3.72
1544.99
0.42
0.93
49
1550.80
0.46
3.71
1550.78
0.43
0.93
50
1556.77
0.47
3.64
1556.74
0.44
0.93
51
1562.10
0.47
3.68
1562.09
0.43
0.91
52
1567.63
0.48
3.79
1567.61
0.45
0.94
53
1572.93
0.49
3.88
1572.89
0.43
0.97
Rmax is the peak reflection and ΔTmax is the drop in transmission relative to the offset. The average slope between 45° and 53° AOI is 5.8 nm/°.
Percentage Change of λres as a Result of +3% Increase of the Design Parameter
Percentage Change of FWHM as a Result of +3% Increase of the Design Parameter
Period (nm)
592
2.62
7.81
nTiO2
2.298
1.96
5.86
AOI (deg)
45°
0.55
3.28
dwg (nm)
287
0.36
-6.86
nsubstrate
1.51
0.22
-4.73
nSiO2
1.444
0.13
2.35
Fill factor
0.513
0.01
-0.51
dgrating (nm)
38
0.00
5.87
dSiO2 (nm)
146
0.00
-4.09
Amount of incomplete etching (nm)
3
-0.01
-14.83
Amount of overetching into SiO2 (nm)
3
0.00
0.20
The percentage changes of resonance wavelength λres and of resonance width FWHM (full width at half-maximum) that result from increasing the design parameter in column 2 by 3% are listed in columns 3 and 4, respectively. Values below 3% indicate an attenuation of the relative error in the optical response, whereas values above 3% indicate an amplification of the error. The device with the rounded design parameter shows a FWHM of 0.517 nm at 1544.6 nm at an AOI of 45°.
Table 2
Peak Reflection Efficiency of an Infinite Device as a Function of Absorption Loss Coefficient α of the Waveguide Material
Im (n)
αabs dB/cm
FWHM (nm)
Rmax (%)
0
0
0.517
100
1 × 10-6
0.35
0.518
99.7
2 × 10-6
0.71
0.519
99.4
5 × 10-6
1.77
0.521
98.4
1 × 10-5
3.53
0.526
96.8
2 × 10-5
7.06
0.535
93.7
5 × 10-5
17.66
0.561
85.3
1 × 10-4
35.32
0.604
73.7
Table 3
Simulations for a Device with Coupling Coefficient α = 1.70 mm-1a
Efficiency (%)
Grating Length
Gaussian Waist
Δz
30
0.765
0.234
0.194
40
1.024
0.296
0.268
50
1.360
0.380
0.380
60
1.724
0.471
0.515
70
2.228
0.596
0.719
80
3.012
0.788
1.064
90
4.720
1.173
1.871
95
7.133
1.693
3.061
98
12.067
2.682
5.534
99
17.900
3.784
8.464
99.5
26.500
5.328
12.778
For a given efficiency in column 1 the minimum device length Lg is given in column 2. The corresponding Gaussian beam widths w and their positions at Δz are given in columns 3 and 4, respectively. All lengths are millimeters.
Table 4
Results of a Lorentzian Curve Fit of the Measured Reflection and Transmission Spectra at Several Angles of Incidencea
Angle (°)
Reflection Spectra
Transmission Spectra
λc (nm)
w (nm)
Rmax (a.u.)
λc (nm)
w (nm)
ΔTmax (a.u.)
45
1526.80
0.40
3.71
1526.80
0.39
0.94
46
1533.04
0.43
3.74
1533.01
0.41
0.94
47
1538.92
0.44
3.59
1538.90
0.43
0.92
48
1545.01
0.45
3.72
1544.99
0.42
0.93
49
1550.80
0.46
3.71
1550.78
0.43
0.93
50
1556.77
0.47
3.64
1556.74
0.44
0.93
51
1562.10
0.47
3.68
1562.09
0.43
0.91
52
1567.63
0.48
3.79
1567.61
0.45
0.94
53
1572.93
0.49
3.88
1572.89
0.43
0.97
Rmax is the peak reflection and ΔTmax is the drop in transmission relative to the offset. The average slope between 45° and 53° AOI is 5.8 nm/°.