Kylan Jersey, Ian Harley-Trochimczyk, Yanqi Zhang, and Felipe Guzman, "Optical truss interferometer for the LISA telescope," Appl. Opt. 62, 5675-5682 (2023)
The Laser Interferometer Space Antenna telescopes must exhibit an
optical path length stability of ${\rm pm}/\sqrt {{\rm Hz}}$ in the mHz observation band to meet
mission requirements. The optical truss interferometer is a proposed
method to aid in the ground testing of the telescopes, as well as a
risk-mitigation plan for flight units. This consists of three
Fabry–Perot cavities mounted to the telescope, which are used to
monitor structural displacements. We have designed and developed a
fiber-based cavity injection system that integrates fiber components,
mode matching optics, and a cavity input mirror into a compact input
stage. The input stages, paired with return mirror stages, can be
mounted to the telescope to form optical truss cavities. We performed
a thorough sensitivity analysis using various simulation methods to
support the fabrication and assembly of three first-generation
prototype cavities, each of which exhibited satisfactory performance
based on our models.
Soham Kulkarni, Ada Umińska, Joseph Gleason, Simon Barke, Reid Ferguson, Jose Sanjuán, Paul Fulda, and Guido Mueller Appl. Opt. 59(23) 6999-7003 (2020)
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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Optical Design Parameters for the OTI Input Stagea
Fiber
Wavelength
Mode Field Diameter
Fiber NA
Single-mode PM cable
1064 nm
0.12
Collimator
Focal Length
AR Coating
Output Mode
Adjustable mounting
12 mm
Lens 1
Focal Length
Position
Coatings
Surface 1: plane
Incident beam waist
Both sides
Surface 2: convex
35.5 mm
4.45 mm (thickness)
Lens 2
Focal Length
Position
Coatings
Surface 1: concave
−19.3 mm
17.26 mm (from lens 1)
Surface 2: concave
−1112.1 mm
5.57 mm (thickness)
The fiber cable and collimator used here are commercially available products, and their specifications were assumed to be constant during optimization. The focal length, thickness, and position of each fused-silica lens were the variables used to optimize the mode matching system. Note that surface 2 of lens 2 is the cavity input mirror, and thus was not a variable in optimization and does not significantly contribute to the focusing power of lens 2.
Table 2.
Simulation Results Showing the Effect of Tolerances on Different Optical Parameters in the OTI Input Stagea
Parameter
Tolerance Range
Simulated Effect
Lens 1 surface 2
15.979 mm
()
Radius of curvature
()
Lens 1
4.45 mm
()
Thickness
()
Lens 1—lens 2
17.26 mm
()
Separation
()
Lens 1 decenter
()
Lens 1 tilt
()
The simulated power coupling efficiencies shown in the right column are taken at the upper and lower limits of each parameter’s tolerance range while leaving all other parameters ideal. Our investigations show that the worst offenders are the tip/tilt and decentering of the mode matching lenses.
Table 3.
Expected Thermal Expansion Due to a Temperature Variation in the Primary Components in the OTI Input and Return Stagesa
Component
Length [mm]
CTE []
Displacement [pm]
Zerodur housing
38
0.038
Invar 36 sleeve
37.5
0.488
Fused silica optics
4.5−5.6
0.026–0.033
This is looking at thermal expansion only along the optical axis, which is the primary concern for future experiments. All components displace by less than a picometer in the expected thermal environment.
Table 4.
Characterizing Optical Power Losses through the Fiber Components and OTI Input Stages Results, and Cavity 00 Mode Coupling During Preliminary Testinga
Optical Power Loss
Unit #1
Unit #2
Unit #3
PM mating sleeves
0.75 dB
1.02 dB
1.14 dB
PM fiber circulator
0.99 dB
0.99 dB
0.99 dB
OTI input stage
1.25 dB (75%)
1.49 dB (71%)
1.37 dB (73%)
Cavity Alignment
Unit #1
Unit #2
Unit #3
75.7%
73.1%
79.1%
The total power loss was measured as the ratio between the powers measured at port-2 and port-3 of the fiber circulator, and the internal loss through each OTI input stage was calculated using the measured loss through each fiber component.
Tables (4)
Table 1.
Optical Design Parameters for the OTI Input Stagea
Fiber
Wavelength
Mode Field Diameter
Fiber NA
Single-mode PM cable
1064 nm
0.12
Collimator
Focal Length
AR Coating
Output Mode
Adjustable mounting
12 mm
Lens 1
Focal Length
Position
Coatings
Surface 1: plane
Incident beam waist
Both sides
Surface 2: convex
35.5 mm
4.45 mm (thickness)
Lens 2
Focal Length
Position
Coatings
Surface 1: concave
−19.3 mm
17.26 mm (from lens 1)
Surface 2: concave
−1112.1 mm
5.57 mm (thickness)
The fiber cable and collimator used here are commercially available products, and their specifications were assumed to be constant during optimization. The focal length, thickness, and position of each fused-silica lens were the variables used to optimize the mode matching system. Note that surface 2 of lens 2 is the cavity input mirror, and thus was not a variable in optimization and does not significantly contribute to the focusing power of lens 2.
Table 2.
Simulation Results Showing the Effect of Tolerances on Different Optical Parameters in the OTI Input Stagea
Parameter
Tolerance Range
Simulated Effect
Lens 1 surface 2
15.979 mm
()
Radius of curvature
()
Lens 1
4.45 mm
()
Thickness
()
Lens 1—lens 2
17.26 mm
()
Separation
()
Lens 1 decenter
()
Lens 1 tilt
()
The simulated power coupling efficiencies shown in the right column are taken at the upper and lower limits of each parameter’s tolerance range while leaving all other parameters ideal. Our investigations show that the worst offenders are the tip/tilt and decentering of the mode matching lenses.
Table 3.
Expected Thermal Expansion Due to a Temperature Variation in the Primary Components in the OTI Input and Return Stagesa
Component
Length [mm]
CTE []
Displacement [pm]
Zerodur housing
38
0.038
Invar 36 sleeve
37.5
0.488
Fused silica optics
4.5−5.6
0.026–0.033
This is looking at thermal expansion only along the optical axis, which is the primary concern for future experiments. All components displace by less than a picometer in the expected thermal environment.
Table 4.
Characterizing Optical Power Losses through the Fiber Components and OTI Input Stages Results, and Cavity 00 Mode Coupling During Preliminary Testinga
Optical Power Loss
Unit #1
Unit #2
Unit #3
PM mating sleeves
0.75 dB
1.02 dB
1.14 dB
PM fiber circulator
0.99 dB
0.99 dB
0.99 dB
OTI input stage
1.25 dB (75%)
1.49 dB (71%)
1.37 dB (73%)
Cavity Alignment
Unit #1
Unit #2
Unit #3
75.7%
73.1%
79.1%
The total power loss was measured as the ratio between the powers measured at port-2 and port-3 of the fiber circulator, and the internal loss through each OTI input stage was calculated using the measured loss through each fiber component.