- #1
Ornit
- 15
- 0
Hi all,
We are measuring our custom-made Half-Wave-Plates (HWPs) for controlling retardation error as part of incoming QC. We don't have a device for measuring retardation nor do we have access to X-ray analyzer.
We have experimental result with no model supporting it; the actual question is in bold below. Background in italics. I apologize for the long story but think it is needed for the helpful answer.
Years ago, the method was simply a setup with a laser and two parallel polarizes. Measure the power without the HWP and measure the power when the HWP is dropped on a mechanical reference between the polarizers. By calculating the ratio (extinction) and rejecting HWPs with too high values, we thought we maintain retardation error.
The extinction is T||=1- sin22θ*sin2Φ/2 with θ being the angle between the optical axis and the mechanical reference, Φ is the retardation; this formula can be proved by Jones matrix of rotated retarder in between parallel polarizers.
I now think this can keep the combined retardation error (thickness error and optical axis to mechanical axis angle error) at bay, but it is not practical when trying to tighten the tolerances.
It was noted that sometimes the measured extinction vary significantly if the HWP is flipped.
My theory was that the angle between the optical axis and the mechanical reference was not exactly 45° so when flipping, the system is not symmetric therefore the extinction vary between the two orientations. It can be shown that the difference in retardation between orientations will be 180°+4ε, ε being the error in the optical-to-mechanical axis, regardless of jig misalignment.
The solution was to improve the stage holding the HWP so we can adjust θz for minimum extinction, compensating for any error in θ and measuring the effect of Φ only, directly correlated to the retardation error.
And here comes the question: Some of the HWPs (but not all) have significantly different minimum extinctions when flipped. I cannot find a theoretical explanation nor can I vary the Zemax models I have to explain the experiment but it is repeatable. Have you encountered such an odd behavior? Any ideas what can cause it?
Thanks
Ornit
We are measuring our custom-made Half-Wave-Plates (HWPs) for controlling retardation error as part of incoming QC. We don't have a device for measuring retardation nor do we have access to X-ray analyzer.
We have experimental result with no model supporting it; the actual question is in bold below. Background in italics. I apologize for the long story but think it is needed for the helpful answer.
As a practical guideline, we know that a Half Wave Plate (=HWP) rotates the polarization by twice the angle to the optical axis, so HWP at 45° between optical axis and mechanical reference will rotate the polarization by 90°. Our HWP is "Zero Order Waveplate" which means the HWP is composed of two Birefringent plates with their optical axis rotated 90°, and their thickness differ by a precise amount for which the light phase changes (retards) by 180°. But a real HWP will not be perfect and its retardation will not be exactly 180°. The difference is the retardation error.
Years ago, the method was simply a setup with a laser and two parallel polarizes. Measure the power without the HWP and measure the power when the HWP is dropped on a mechanical reference between the polarizers. By calculating the ratio (extinction) and rejecting HWPs with too high values, we thought we maintain retardation error.
The extinction is T||=1- sin22θ*sin2Φ/2 with θ being the angle between the optical axis and the mechanical reference, Φ is the retardation; this formula can be proved by Jones matrix of rotated retarder in between parallel polarizers.
I now think this can keep the combined retardation error (thickness error and optical axis to mechanical axis angle error) at bay, but it is not practical when trying to tighten the tolerances.
Defining the axis & terminology: Z is the optical axis (laser propagates along Z). Y is the up/down and X the left/right. "Flipped" means rotation around Y, θy=180°, so the HWP front surface, that was facing the laser now becomes the back surface and faces the detector. θy=0° and θy=180° are called "orientations".
Define minimum extinction as the minimum extinction when minimizing over θz.
Define minimum extinction as the minimum extinction when minimizing over θz.
It was noted that sometimes the measured extinction vary significantly if the HWP is flipped.
My theory was that the angle between the optical axis and the mechanical reference was not exactly 45° so when flipping, the system is not symmetric therefore the extinction vary between the two orientations. It can be shown that the difference in retardation between orientations will be 180°+4ε, ε being the error in the optical-to-mechanical axis, regardless of jig misalignment.
The solution was to improve the stage holding the HWP so we can adjust θz for minimum extinction, compensating for any error in θ and measuring the effect of Φ only, directly correlated to the retardation error.
And here comes the question: Some of the HWPs (but not all) have significantly different minimum extinctions when flipped. I cannot find a theoretical explanation nor can I vary the Zemax models I have to explain the experiment but it is repeatable. Have you encountered such an odd behavior? Any ideas what can cause it?
Thanks
Ornit