Kevin K. Lehmann, Paul S. Johnston, and Paul Rabinowitz, "Brewster angle prism retroreflectors for cavity enhanced spectroscopy," Appl. Opt. 48, 2966-2978 (2009)
The design of a high finesse optical cavity made from two prism retroreflectors is fully described. Optical beam propagation calculations to determine the specification of prism angles and relative dimensions, the size of the astigmatic beam as it propagates in the cavity, and the sensitivity of the optic axis to changes in prism alignment and fabrication errors are presented. The effects of material dispersion are also quantified for three different materials: fused silica, calcium fluoride, and barium fluoride. The predictions made are found to be in good agreement with experimental results obtained from prisms we had made from fused silica. Prisms made of and are predicted to be useful for applications in the UV and mid-IR spectral regions, respectively.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
Coordinates and Beam Radii of Cavity Axis Points (in mm)a
x
476.4
483.1
475.1
462.9
6.759
0.000
8.000
20.28
y
217.1
223.9
231.9
219.6
14.76
8.000
0.000
12.28
beam radii
0.730
0.730
0.730
0.730
0.765
0.765
0.764
0.763
with
0.814
0.948
0.948
0.814
1.024
1.193
1.189
1.017
Points labeled as per Fig. 1. Optic axis is in x, y plane.
Table 2
Displacements of Optic Axis Points due to Misalignmentsa
Prism ABCD
pitch
z
roll
z
yaw
x
0.000
0.000
0.000
0.000
0.000
y
0.002
0.002
0.002
0.000
0.000
0.000
0.000
trans
x
0.399
0.410
0.395
0.378
0.006
0.000
0.015
0.032
y
0.000
0.000
Prism EFGH
pitch
z
0.965
0.964
0.963
0.970
0.966
0.965
0.962
0.964
roll
z
1.398
1.397
1.396
1.403
1.398
1.398
1.399
1.399
yaw
x
0.000
0.002
0.001
0.002
0.002
0.006
0.005
y
0.000
0.002
0.000
0.000
0.001
Angular rotations pitch, roll, and yaw and the translation are defined in the text. Changes are in mm per minute of arc for rotations and mm/mm for translation.
Table 3
Displacements of the Optic Axis Points due to Errors in the Prism Fabricationa
Rotate EF
In-plane
x
1.475
0.000
0.000
1.745
1.474
y
0.000
0.271
0.873
1.745
0.000
Out-of -plane
z
Rotate FG
In-plane
x
0.000
1.741
1.471
0.873
0.000
y
0.270
1.741
0.000
0.270
Out-of-plane
z
1.743
1.742
1.741
1.747
1.745
1.745
1.741
1.741
Rotate EH
In-plane
x
0.000
0.004
0.003
0.000
y
0.001
0.004
0.000
0.001
0.000
0.000
0.003
Out-of-plane
z
1.063
1.062
1.061
1.067
1.064
1.065
1.064
1.062
Rotate AB
In-plane
x
0.935
0.000
0.000
1.740
1.464
y
0.000
0.173
0.871
1.745
0.000
Out-of-plane
z
1.590
1.587
1.589
1.599
1.743
1.745
1.743
1.739
Rotate BC
In-plane
x
0.000
1.103
0.937
0.871
0.000
y
0.172
1.107
0.000
0.000
0.269
Out-of-plane
z
Rotate AD
In-plane
x
0.007
0.000
0.000
0.000
0.000
0.000
0.000
y
0.001
0.000
0.000
0.000
0.000
0.000
Out-of-plane
z
0.972
0.971
0.970
0.977
1.064
1.065
1.064
1.062
x
0.052
0.000
0.073
0.157
0.000
y
0.000
0.000
0.010
0.000
0.000
0.029
For each surface, we give the effect of rotation around the center of the surface for both the z axis (in-plane rotation) and the perpendicular to the surface normal and z axes (out-of-plane rotation). Response is given in mm per minute of arc.
Tables (3)
Table 1
Coordinates and Beam Radii of Cavity Axis Points (in mm)a
x
476.4
483.1
475.1
462.9
6.759
0.000
8.000
20.28
y
217.1
223.9
231.9
219.6
14.76
8.000
0.000
12.28
beam radii
0.730
0.730
0.730
0.730
0.765
0.765
0.764
0.763
with
0.814
0.948
0.948
0.814
1.024
1.193
1.189
1.017
Points labeled as per Fig. 1. Optic axis is in x, y plane.
Table 2
Displacements of Optic Axis Points due to Misalignmentsa
Prism ABCD
pitch
z
roll
z
yaw
x
0.000
0.000
0.000
0.000
0.000
y
0.002
0.002
0.002
0.000
0.000
0.000
0.000
trans
x
0.399
0.410
0.395
0.378
0.006
0.000
0.015
0.032
y
0.000
0.000
Prism EFGH
pitch
z
0.965
0.964
0.963
0.970
0.966
0.965
0.962
0.964
roll
z
1.398
1.397
1.396
1.403
1.398
1.398
1.399
1.399
yaw
x
0.000
0.002
0.001
0.002
0.002
0.006
0.005
y
0.000
0.002
0.000
0.000
0.001
Angular rotations pitch, roll, and yaw and the translation are defined in the text. Changes are in mm per minute of arc for rotations and mm/mm for translation.
Table 3
Displacements of the Optic Axis Points due to Errors in the Prism Fabricationa
Rotate EF
In-plane
x
1.475
0.000
0.000
1.745
1.474
y
0.000
0.271
0.873
1.745
0.000
Out-of -plane
z
Rotate FG
In-plane
x
0.000
1.741
1.471
0.873
0.000
y
0.270
1.741
0.000
0.270
Out-of-plane
z
1.743
1.742
1.741
1.747
1.745
1.745
1.741
1.741
Rotate EH
In-plane
x
0.000
0.004
0.003
0.000
y
0.001
0.004
0.000
0.001
0.000
0.000
0.003
Out-of-plane
z
1.063
1.062
1.061
1.067
1.064
1.065
1.064
1.062
Rotate AB
In-plane
x
0.935
0.000
0.000
1.740
1.464
y
0.000
0.173
0.871
1.745
0.000
Out-of-plane
z
1.590
1.587
1.589
1.599
1.743
1.745
1.743
1.739
Rotate BC
In-plane
x
0.000
1.103
0.937
0.871
0.000
y
0.172
1.107
0.000
0.000
0.269
Out-of-plane
z
Rotate AD
In-plane
x
0.007
0.000
0.000
0.000
0.000
0.000
0.000
y
0.001
0.000
0.000
0.000
0.000
0.000
Out-of-plane
z
0.972
0.971
0.970
0.977
1.064
1.065
1.064
1.062
x
0.052
0.000
0.073
0.157
0.000
y
0.000
0.000
0.010
0.000
0.000
0.029
For each surface, we give the effect of rotation around the center of the surface for both the z axis (in-plane rotation) and the perpendicular to the surface normal and z axes (out-of-plane rotation). Response is given in mm per minute of arc.