Measuring the Polarization Rotation Angle of a Faraday Rotator Mirror with the Optical Vector Analyzer
Short Summary
Faraday Rotator Mirrors (FRMs) utilize the Faraday Effect to rotate the input polarization state by some set amount, often by 90°. FRMs are commonly used as a component in isolators and are especially useful in fiber optic interferometers. When using FRMs in an interferometer, however, if the FRM polarization state rotation is not exactly 90° some fringe visibility fading may still occur. This application note details how Luna’s Optical Vector Analyzer (OVA) can be used to easily deduce the error in the FRM rotation angle.
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www.lunainc.com 1 Riverside Circle, Suite 400 | Roanoke, VA 24016 solutions@lunainc.com 1.540.769.8400 Engineering Note EN-FY1401 Revision 4 h April 22, 2014 Measuring the Polarization Rotation Angle of a Faraday
Rotator Mirror with the Optical Vector Analyzer
Contents Introduction ……………………………………………………………………………………………………… 1 Measurement Set-Up ………………………………………………………………………………………… 1
Jones Matrix Calculation of PMD ………………………………………………………………………… 2
Measurement Example ……………………………………………………………………………………… 4
1 Introduction
Faraday Rotator Mirrors (FRMs) utilize the Faraday Effect to rotate the input polarization
state by some set amount, often by 90~. FRMs are commonly used as a component in
isolators and are especially useful in fiber optic interferometers. If a Michelson
interferometer is made with single mode fiber and a simple reflecting mirror (ie. a high-
reflectivity metal film), birefringence in either arm of the interferometer will cause the
polarization state to rotate. When the light reflects off of the mirror and propagates back
through the same path the optical retardance due to the fiber birefringence doubles.
When the light from each arm of the interferometer is recombined, differences in the
polarization orientation between the two arms will result in fading of the interferometer
fringe amplitude visibility. Worse yet, this polarization based fading will typically be
wavelength dependent and will be very sensitive to small changes in the input
polarization state orientation. This visibility fading problem can be overcome by
replacing the simple reflecting mirrors with FRMs set to rotate the polarization state by
90~. In this case, the retardance due to fiber birefringence on the path to and from the
FRM is of equal magnitude but opposite sign and thus cancels, and the interferometer
fringe visibility is optimized. An alternative is to construct a Michelson interferometer out
of Polarization Maintaining (PM) components and maintain a stable input polarization
state, but this alternative is typically more expensive and performs less well due to the
variety of ways that optical power can leak from one polarization state to the other in a
PM network. When using FRMs in an interferometer, however, if the FRM polarization
state rotation is not exactly 90~ some fringe visibility fading may still occur. This
application note details how Lunafs Optical Vector Analyzer (OVA) can be used to easily
deduce the error in the FRM rotation angle.
2 Measurement Set-Up
Although the OVA does not measure the absolute polarization angle of the device under
test, it does compute the full Jones Matrix of the DUT over the scan range, and this
PHOENIXTM is a trademark of Luna Innovations Incorporated. Page 2 of 7 2013 Luna Innovations Incorporated. All rights reserved. EN-FY1401 Jones Matrix can be analyzed to find the device Polarization Mode Dispersion (PMD)
and Polarization Dependent Loss (PDL). If highly birefringent fiber, such as Polarization
Maintaining fiber (PMF), is added to the path to the FRM, the magnitude of the PMD
measured will be an indication of the rotation angle of the FRM.
To measure the polarization rotation angle of the test FRM, first the PMD of the PMF
segment should be characterized, as depicted in Figure 1a. Leads on either side of the
PMF segment may be Single Mode Fiber (SMF), and the quality of alignment of the
connector keys to the stress rods of the PMF segment is inconsequential. The best way
to get an accurate measurement of the PMD of the PMF segment is to terminate the
PMF segment with a connector that will reflect strongly when unconnected. Any
connector with a flat glass to air interface, such as an FC-PC connector, will work well.
An angled connector would result in a weak reflection that may approach the OVA
sensitivity level and result in a poor signal to noise ratio. If the PMF connector must be
angled to match the FRM connector, then a short SMF patchcord to a highly reflective
mirror could be used in place of the FRM, but any rotation of the polarization vector in
the SMF to the mirror could lead to crossover from fast to slow modes of the PMF and
thus reduce the apparent PMD associated with the PMF segment. After the PMF
segment is scanned and the PMD recorded, the test FRM is connected downstream of
the PMF segment as indicated in Figure 1b, and the PMD trace for the FRM is
recorded.
a)
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2
2
PM
PM
i
i
PM
e
e
J
,1001RM. 2 a, b
The result for J
TOT is:
PM
PM
i
i
TOT
e
e
J
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eigenvalues do not evolve in the spectral domain, so the resulting PMD is zero:
121, 0,perfectFRMPMD. 8
Consider the case where instead of a 90~ rotation, the real rotation is 90~+ , where is
some small angle, 90~. The mirror Jones Matrix becomes:
sincos
cossin
FRMM. 9
The result for J
TOT is:
PMPMiiTOTeeJsincoscossin
PHOENIXTM is a trademark of Luna Innovations Incorporated. Page 5 of 7 2013 Luna Innovations Incorporated. All rights reserved. EN-FY1401 compared to either of the side peaks, the user should clean or re-polish the connector
end face. Cursors indicate the separation of the side peaks are 22.6 ps, and this is the
value for the PMD we expect to measure for the PMF segment. The side peaks of the
scan of the FRM in Figure 2b have the same separation, but are much smaller in
proportion to the center peak, and we expect the PMD for this case to be much smaller
because most of the power in the time impulse response is in the center peak. Note
that the time domain filter limits must be placed outside of these side lobe locations in
order to get an accurate PMD measurement. For both of these OVA scans, the time
domain filters were set at a width of approximately 47 ps to give Window Resolution
Bandwidth of 100 pm, and the spectral Filter Resolution Bandwidth was set to 0 so that
no additional spectral filtering was applied.
a)
b)
Figure 2. Time domain amplitude profiles of a) a FC-PC connector at the end of a 10 m PMF
segment and b) a FRM with a 10 m PMF segment in the path to the OVA.
Figure 3 shows the PMD plots for the two cases described in Figure 2. The scan of the
PMF segment alone shows high levels of PMD, with an average of about 22.5 ps, and
the scan of the FRM shows much lower average PMD, between 0 and 2.7 ps over the
scan range.
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b)
Figure 3. PMD for a) the 10 m PMF segment alone, and b) for the FRM with the 10 m PMF
segment in series.
Figure 4 shows the result for FRM rotation error angle calculated using Equation 13.
Figure 4. FRM polarization rotation angle error, as computed from the PMD curves in Figure 3.
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