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Abstract
A compact forward-directed transmissive beam scanner operating at a wavelength of 1550 nm was constructed and characterized. The scanner consists of two wire-grid polarizers (WGPs) surrounding a 45° Faraday rotator, causing incident light to reflect once from each WGP before transmitting through the second polarizer. Scanning is achieved by tilting one of the WGPs. Measured efficiency remained above 73% over a 90° forward scan range (${-}{45}^\circ$ to ${+}{45}^\circ$) for vertically polarized incident light. Additionally, we measured the efficiency versus beam deflection for four different incident linear polarization configurations, three of which maintained ${\gt}{70}\%$ efficiency for deflection angles up to ${-}{60}^\circ$.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. INTRODUCTION
Compact beam scanners are needed for laser-based sensing where the size and/or weight of the optical system are tightly constrained, such as endoscopic [1,2], airborne [3], vehicle-mounted [4], wearable [5] or other portable applications [6]. Reflective scanners are appealing for their high optical efficiency and potentially large scan angles. For imaging applications, two-dimensional scan patterns can be created by using two reflective one-dimensional scanners, or an integrated microelectromechanical system (MEMS) 2D or 3D scan mirror [7–9]. However, a reflective scanner requires a folded optical path, which usually results in a larger instrument footprint.
Transmissive scanners, constructed with cascaded in-line optical components, may enable more compact laser-scanning systems. For example, lateral translation of one or more lenses can be used for scanning, but a large scan range requires a short focal length lens and significant off-axis aberration must be managed [10,11]. Risley prism scanners are able to achieve moderate scan angles, but produce complex non-linear scan patterns [12–14]. Electro-optic (EO) and acousto-optic (AO) beam scanners can achieve higher scan rates than inertia-limited mechanical scanners, but the scan range is lower [15]. Electrowetting on dielectric (EWOD) scanners provide another transparent alternative to mechanical beam scanning, but these liquid prisms are capable of only moderate scanning angles, and may not scale well to macro sizes [16,17]. Depending on the needs of a specific application, these trade-offs can be understood and a best-matched technology selected. In forward scanning applications requiring a small footprint, it is desirable to have the wide angles and high optical efficiency of a reflective scanner and the compact straight-through path of a transmissive scanner, but such a scanner has not been previously demonstrated.
In this paper, we introduce a novel large-angle forward beam scanner based on polarization-selective reflective beam deflectors where the optical elements can be placed in-line with a straight-through optical path, with the potential to significantly reduce the footprint of the scanner. This double-reflection transmissive beam scanner consists of a thin-film 45° Faraday rotator interposed between two wire-grid polarizing beamsplitters. The wire grids on the polarizers face inwards towards the Faraday rotator (to maximize the reflection efficiency of the polarizers) and the transmission axes of the wire-grid polarizers are offset from each other by 45° [18]. As illustrated in Fig. 1, the polarizers are aligned such that incoming linearly polarized light incident on the first polarizer is fully transmitted. Once transmitted by the first polarizer, the light passes through the Faraday rotator and the polarization is rotated ${-}{45}^\circ$, so that it is 90° offset from the transmission axis of the second polarizer. The light is reflected from the second wire-grid polarizer, and passes through the Faraday rotator again. The Faraday rotator is a nonreciprocal device, so the polarization is rotated an additional ${-}{45}^\circ$, and it is now ${-}{90}^\circ$ offset from the transmission axis of the first polarizer, so again the light is reflected. Once more it passes through the Faraday rotator, accumulating another ${-}{45}^\circ$ rotation. This final rotation aligns the orientation of the light’s polarization with the transmission axis of the second polarizer, and the light is transmitted on the side opposite to the incoming light. Fundamentally this is a reflective beam scanner, and just as in traditional reflective scanners, tip/tilt control over one or both of the wire-grid polarizers controls the angle at which the transmitted beam leaves the system, as shown in Fig. 1.
Fig. 1. Conceptual diagram depicting the beam path through the double-reflection transmissive beam scanner, and the orientation of the electric field as the beam passes through the system. Reprinted by permission from SPIE: Baker et al., Proc. SPIE 12428, 98 (2023) [18]. © 2023.
In our demonstration system, we have chosen to control the tilt angle ($\theta$) of the front polarizer, which induces a beam deflection angle of $2\theta$. Scanning could also be achieved by tilting the rear polarizer, and two-dimensional scanning could be realized by tilting either polarizer about orthogonal axes or by tilting the two polarizers each about a single axis. As a proof of concept of this scanner design, we built a tabletop version using commercial off-the-shelf components. The behavior of each component was first characterized individually for a range of incidence angles and incident linear polarization orientations, and these measurements were used to predict the scanner efficiency over a range of beam scan angles. Then, the transmission efficiency of the assembled scanner was measured as a function of the tilt angle $\theta$ of the front polarizer. We built scanner assemblies to accommodate four different linear polarization states of the incident light, defined by the angle $\delta$. In this paper, $\delta = {90^ \circ}$ corresponds to vertically polarized light, $\delta = {0^ \circ}$ to horizontally polarized light, and $\delta = \pm {45^ \circ}$ to the linear polarization states with equal horizontal and vertical components, which we call the diagonal states. This initial demonstration validates this new design concept, which could be further optimized, miniaturized, and integrated with a MEMS-based tip/tilt system.
2. MEASUREMENTS OF DOUBLE-REFLECTION TRANSMISSIVE BEAM SCANNER
A. Method
A prototype of the double-reflection transmissive beam scanner was constructed and optically characterized as shown in Fig. 2. The illumination originated with a tunable diode laser with a fiber coupled output. A collimator at the end of a single-mode fiber collimated the output from the fiber. Since all of the optical elements in the characterization setup and the scanner are flat optics (and have no optical power), the degree of collimation of the scanned beam is dependent only on the illumination source. The $1/{e^2}$ diameter of the beam incident on the scanner was approximately 2 mm for the following measurements. Therefore, for this beam size and a 90° scan range, the resolution of the scanner is ${N_\theta} \approx 2{,}000$.
Fig. 2. System setup used to measure the transmission efficiency of the scanner system for various incident polarization states ($\delta$) and front polarizer tilt angles ($\theta$).
We measured the output power of the laser to vary by less than 0.1% over the typical measurement time period, so we assumed constant input laser power for the duration of our measurements. An absorptive polarizer (Newport 10LP-NIR) was placed after the collimator to ensure the polarization orientation of the laser light was known and the beam had a high degree of linear polarization (DoLP). A half-wave plate (ThorLabs WPH10M-1550) was placed after this so the devices under test could be characterized with different incident polarization orientations. We used a Corning Polarcor 25 mm diameter glass polarizer (Edmund Optics stock #13-621) after the half-wave plate to maintain a constant DoLP in the illumination beam regardless of half-wave plate’s fast axis rotation angle.
The collimating lens, initial polarizer, half-wave plate, and clean up polarizer were all antireflection coated for the 1550 nm wavelength range. Because this characterization system used coherent illumination and many elements had nearly parallel faces, several elements in the system had etalon effects, which caused larger measurement uncertainties [19]. The dominant etalon in our system was due to the glass substrate of the WGPs. To reduce this uncertainty, we performed a wavelength sweep (1546–1554 nm in 0.2 nm steps) for each measurement and calculated the arithmetic mean of the measured power over this sweep. This wavelength averaging reduced measurement variation due to coherent etalon effects to less than 0.2%. All three components of the scanner were at normal incidence to the input beam for the tilt angle $\theta = { 0^ \circ}$.
The Corning polarizer was mounted in a Thorlabs PRM1Z8 high-precision motorized rotation stage with its rotational axis parallel to the optical axis, such that the pass axis orientation of the polarizer could be rotated with 0.1° bidirectional repeatability [20]. The input polarization state $\delta$ was set by first rotating the Corning polarizer so that its pass axis was parallel to $\delta \in \{- {45^ \circ},{0^ \circ}, + {45^ \circ},{90^ \circ}\}$. The half-wave plate was then rotated to generate the linear polarization state aligned to the pass axis of the Corning polarizer. The front polarizer of the scanner (“polarizer 3” in Ref. [21]) was a half-inch diameter wire-grid polarizer from Meadowlark Optics Inc. (VLR-050-IR). It was mounted substrate-first after the Corning polarizer, and the pass axis angle of this polarizer was aligned to the incident polarization state. The Faraday rotator was attached to the polarizer mount on the wire grid side, so that the two components would scan together and there was minimal space between them. The tilt angle of the front polarizer and Faraday rotator was also controlled by a Thorlabs PRM1Z8 high-precision motorized rotation stage, which was positioned with its rotation axis perpendicular to the optical table. In this setup, the motorized rotation stage controlled the precision to which the scan angle of the beam could be steered. With the 0.1° bidirectional repeatability of the front polarizer tilt angle $\theta$, we had a precision of 0.2° on the scan angle of the transmitted beam. The rear polarizer (“polarizer 5” in Ref. [21]) was a one inch wire-grid polarizer, also from Meadowlark Optics Inc. (VLR-100-IR). It was positioned with the wire grid side first behind the Faraday rotator and with the pass axis rotated to maximize transmission through the system so that the offset between the pass axes of the two polarizers was 45°. The power in the beam transmitted through the scanner was measured by an integrating sphere detector (Newport 819C-IG-2-CAL).
B. Predicted System Performance
The predicted system efficiency was calculated by cascading the measured efficiencies of each component for the relevant input polarization state $\delta$ and incidence angle (which is related to the front polarizer tilt angle $\theta$). The characterization of the Faraday rotator is described in Appendix A, and the characterization of the commercial WGPs used in this scanner device are described in Ref. [21].
The system could be rotated such that it accepts any linear polarization state; however, our individual component characterizations only included measurements at $\delta \in\def\LDeqbreak{} {\{0^ \circ}, + {45^ \circ},{90^ \circ}\}$. Assuming the component efficiencies are symmetric at $\delta = \pm {45^ \circ}$ and that the Faraday rotation angle $\alpha = {45^ \circ}$, the measured component efficiencies can be used to predict the scanner’s performance for linear input states $\delta \in {\{0^ \circ}, \pm {45^ \circ},{90^ \circ}\}$ using Eq. (1), where the subscript “1” indicates the front polarizer, the subscript “2” indicates the rear polarizer, and the subscript “F” indicates the Faraday rotator:
Note that this method predicts the scanner’s output efficiency in units of power, not electric field amplitude and phase. For our purposes this was sufficient since we measured the scanner’s relative output power (averaged over wavelength to suppress etalon effects), and cascading the measured component efficiencies accounted for the coherent substrate effects mentioned above. If a more complete analysis were desired, the system could be modeled using Jones calculus [22], which would require additional component phase data to be measured. The predicted scanner efficiencies for $\delta \in {\{0^ \circ}, \pm {45^ \circ},{90^ \circ}\}$ as a function of beam scan angle are shown in Fig. 3.
Fig. 3. Predicted transmission efficiency of the transmissive-reflective scanner for several input polarization states computed using individual component characterization data. This model assumes perfect 45° polarization rotation from the Faraday rotator and perfect rotational alignment of the optics in the scanner.
Considering the full range of beam scan angles, the scanner had the best predicted performance for an input polarization state $\delta = - {45^ \circ}$, which meant the pass state of the rear polarizer was horizontal. For this polarization state the Brewster effect increases the transmission efficiency through the rear polarizer. For the scan range shown in Fig. 3, the scanner behavior for the other input polarization states tended to decrease as $|\theta |$ increased. In general, the scanner’s predicted performance largely had the same characteristics that were seen in the individual component performance results, as expected. Because these results are based on experimental component data, we expect the experimental measurements of the scanner transmittance to approximately match the transmission efficiencies and trends shown in Fig. 3.
C. Demonstration of Symmetric forward Beam Scanning
In this system, the maximum possible front polarizer tilt angle $\theta$ is limited by vignetting by the rear polarizer. Assuming a normally incident input beam, on the last pass through the device the light reflected from the front polarizer is deflected at an angle $2\theta$, so if the distance to the rear polarizer is too large, light would walk off the edge of the rear polarizer. However, the front and rear components cannot come too close together, or else they will mechanically interfere when the front components are rotated. In this configuration, the axial distance between the front and rear polarizers was approximately 1 cm and the diameter of the rear optic was 2.54 cm, so the optical elements in the scanner occupied a volume of approximately $5\;{{\rm cm}^3}$.
For this demonstration, we aligned the rear polarizer such that at $\theta = { 0^ \circ}$ the beam passed through its center, which allowed the front optics to scan equally to both sides. The distance between the front and rear polarizers was minimized to achieve the maximum scan range while avoiding mechanical interference between the front and rear optics. We tested the scanner in this symmetric configuration for one input polarization $\delta = {90^ \circ}$. It should be noted that these scanner measurements were performed with a slightly different characterization system setup (shown in Fig. 6 in Appendix A, with the scanner system as the “device under test”). The results are shown in Fig. 4, with four different individual measurements shown in gray, the trial-averaged efficiency shown in red, and the predicted efficiency for $\delta = {90^ \circ}$ shown in black.
Fig. 4. Transmission efficiency versus beam scan angle for the symmetric scanner configuration. Four trials for vertically polarized incident light are shown along with the trial-averaged efficiency (in red) and the predicted efficiencies (in black) for this input polarization state (adapted from Ref. [18]).
For this symmetric scan configuration, the front optics could achieve tilt angles up to $\theta = \pm {22.5^ \circ}$, or a 90° total beam scan range (from ${-}{45}^\circ$ to ${+}{45}^\circ$). The maximum difference in measured efficiency between the four trials was about 1%, which establishes the measurement variation present in our characterizations. The maximum difference between transmittance measured at symmetric scan angles was 0.8%, so to within our measurement error the scanner did perform symmetrically for left- and right-scanning beams, as expected. The average maximum measured transmittance (which occurred at $\theta = { 0^ \circ}$) was 75.6%, with a maximum difference of 0.7% between trials. The average transmittance remained ${\gt}73\%$ over the entire beam scan range of ${-}{45^ \circ} \le 2\theta \le + {45^ \circ}$. The measured transmission efficiency of the scanner is slightly larger than what was predicted by the cascaded component model, which may reflect small measurement errors present in the measured scanner efficiency and/or in the individual component characterizations. Overall, the results demonstrate that this scanner can achieve both high transmission efficiency and a large angular scan range in a transmissive footprint beam scanner.
D. Measurement of Polarization Sensitivity over a One-Sided Scan Region
In this section, we characterized the scanner performance over wider scan angles and measured the polarization dependence seen in the predicted efficiencies. To increase tilt range for characterization, the rear polarizer was shifted such that a normally incident beam did not pass through the center of the polarizer, and instead was horizontally closer to one side. By doing this, the scanned beam had a larger distance to travel before it walked off the rear polarizer, and the front polarizer could swing around the edge of the rear polarizer to achieve a higher tilt angle before mechanical interference occurred. In this asymmetric configuration, the beam could only be scanned to one side, but this allowed us to characterize the scanner’s behavior at larger beam scan angles. Even after optimizing the distance between the components within the scanner in the asymmetric configuration, the tilt angle was limited to $[\theta] { \lt 35^ \circ}$.
Provided that the offset between the pass axes of the two polarizers is 45°, the polarizers forming the scanner can be rotated to accept any input linear polarization state. We performed three trials each with the front polarizer oriented to accept four input polarization states $\delta \in \{- {45^ \circ},{0^ \circ},\def\LDeqbreak{} + {45^ \circ},{90^ \circ}\}$. For each trial, the front polarizer tilt angle $\theta$ was increased in 2.5° steps (5° beam angle steps) from $\theta = { 0^ \circ}$ to $\theta = - {35^ \circ}$, where walk-off of the scanned beam from the rear polarizer was observed. All of the transmitted power measurements occurred at a fixed distance after the scanner system. The measured efficiency of the scanner as a function of beam scan angle is shown in Fig. 5. The individual trial measurements are shown in gray, with the three-trial average for each input state $\delta \in \{- {45^ \circ},{0^ \circ}, + {45^ \circ},{90^ \circ}\}$ overlaid in color. The predicted scanner efficiency for each input polarization state calculated from the measured efficiencies for each individual component in the scanner is shown in black, with corresponding line markers.
Fig. 5. Asymmetric scanner configuration measured efficiency as a function of beam scan angle $2\theta$. The individual measurements are shown in gray, with the average for each input state $\delta$ shown in color and the predicted efficiencies shown in black.
E. Discussion
The maximum spread between the three trials for each input state was ${\sim}1\%$ and never exceeded 1.2% for $|\theta | \le {32.5^ \circ}$ (where no vignetting was observed), which provides an estimate of our measurement repeatability. The grouping of the measurements for each input state indicates that certain input states may be desirable to increase the scanner throughput efficiency for a given scan range (which is also consistent with the predicted efficiencies). The transmission efficiency for the $\delta = - {45^ \circ}$ and $\delta = { 0^ \circ}$ states was improved at larger beam scan angles due to the Brewster effect when transmitting through the glass substrate in the WGPs. The Brewster angle for the glass substrate occurs for incidence angles ${\simeq }{56^ \circ}$ when horizontally polarized light transmits through the WGPs. For the $\delta = { 0^ \circ}$ (horizontal) state, the incidence angle to the front polarizer is equal to the tilt angle $\theta$, so the Brewster effect improves the scanner transmission as $|\theta |$ increases. The peak scanner efficiency is expected to occur for $|\theta {| \gt 35^ \circ}$, which is supported by the rising trend in the measured data for this input state at large $\theta$. We do not expect the peak transmission efficiency for this input state to occur at $|\theta | \simeq {56^ \circ}$, since the transmission efficiency of all of the components begins to drop off for incidence angles larger than 20°. For the $\delta = - {45^ \circ}$ (negative diagonal) incident polarization state, the light transmitted through the rear polarizer is horizontally polarized with an incidence angle $2\theta$; therefore, the Brewster effect is maximized for $\theta \simeq {28^ \circ}$. For $\delta = - {45^ \circ}$, the maximum measured efficiency of the scanner occurred for $\theta = - {25^ \circ}$. For the other two input states $\delta = { 45^ \circ}$ and $\delta = { 90^ \circ}$, there were no cases of transmission of horizontally polarized light through the WGPs, so the Brewster effect did not improve the component efficiency at high tilt angles. Therefore, the efficiency of the scanner remained relatively constant until $\theta \simeq - {20^ \circ}$, where the transmission/reflection efficiency of the individual components began to decrease. The efficiency of the $\delta = { 90^ \circ}$ input state was measured to be higher than for the $\delta = { 45^ \circ}$ state, which is also consistent with the predicted values from the individual component characterizations. This suggests that this difference in scanner efficiency is due to the polarization sensitivity of the individual components.
The measured scanner efficiency agrees well with the transmission efficiency predicted using the individual component characterization data. However, the predicted transmission efficiencies were slightly lower than the average measured efficiency of the scanner, which may be indicative of measurement error present in our individual component characterizations as well as the scanner transmission characterization. Even with the slight disagreement in absolute scanner efficiency between the model and the measured data, the model does well predicting the trend in scanner performance as the tilt angle $\theta$ increases; there is never more than a 3% difference between the predicted and measured scanner transmittance for ${-}{25^ \circ} \le \theta \le {0^ \circ}$ (corresponding to beam deflection angles from ${-}{50^ \circ}$ to 0°). Finally, for three of the four input polarization states, the experimentally measured efficiency of the scanner remained ${\gt}{72}\%$ for beam deflection angles up to ${-}{60}^\circ$.
The demonstration system used half-inch and one inch optics and occupied a volume of approximately ${5}\;{{\rm cm}^3}$. The minimum axial length of the scanner is limited by the thicknesses of the two WGPs and the Faraday rotator, plus space to allow for tilting of one WGP. A MEMS implementation might use substrates that are 0.5 mm thick, so that the full length could be less than 2 mm including freedom for tilt motion. Depending on beam size, the full scanner could occupy a volume of less than ${10}\;{{\rm mm}^3}$. Such a miniaturized scanner would be comparable in volume to other MEMS transmissive scanners (e.g., Refs. [8,9]), while delivering high throughput efficiency, a large angular scan range, and high scanner resolution. Using off-the-shelf optics and mounting hardware we demonstrated an unvignetted symmetric scan range of ${\theta _b}= { 90^ \circ}$. With a clear aperture of ${ D} = {10}\;{\rm mm}$, this large scan range results in a large potential angular resolution ${N_\theta} = {\theta _b}D/\lambda \approx 10{,}100$ resolvable spots. It should be noted that a beam traveling backwards through the scanner will not be descanned (due to the nonreciprocity of the Faraday rotator). Nevertheless, this combination of large scan angle, high resolution, and good efficiency is a promising result for this new transparent beam scanner architecture.
Fig. 6. Schematic diagram of the system used to control the power, linear polarization orientation, and wavelength of the input light used to characterize the individual components used in the scanner system. All optics are optimized for use at 1550 nm.
3. CONCLUSION
A double-reflection transmissive beam scanner was constructed using two wire-grid polarizers with a 45° Faraday rotator placed between them. The average normal-incidence ($\theta = { 0^ \circ}$) efficiency of the scanner for all input orientations was 74.8%, and the efficiency of the scanner for $|\theta {| \gt 0^ \circ}$ varied with the input polarization state. The polarization dependence of the scanner means that the input polarization orientation should be thoughtfully selected to maximize the scanner efficiency for a desired scan range. In the symmetric scan configuration (the more typical configuration for a laser beam scanner), we were able to achieve a full beam deflection range of 90° (${-}{45^ \circ} \le 2\theta \le + {45^ \circ}$) and a scanner resolution of more than 10,000 resolvable spots, maintaining ${\gt}{73}\%$ transmission efficiency over the entire scan range for the vertical input polarization state ($\delta = { 90^ \circ}$). This demonstrates that this scanner device can achieve high efficiencies over a large beam scan region with high resolution while in a compact in-line footprint, which fills a previously unoccupied niche in scanner devices.
This concept could also be capable of two-dimensional forward scanning if the rear WGP were scanned orthogonal to the current scan direction, or if either of the WGPs were capable of two-dimensional tilting. The volume size reduction of this device when compared to a traditional z-fold system for two-dimensional scanning is significant. Importantly, the device is well-suited for miniaturization and MEMS integration, with the static and scanning WGPs and Faraday rotator packaged together in a very small footprint. Such a fully integrated device could meet an increasing demand for small and lightweight optical beam scanners in applications such as autonomous vehicles, endoscopy, wearable displays, and many others.
APPENDIX A: MEASURED PERFORMANCE OF CONSTITUENT COMPONENTS
In order to predict the transmission efficiency of the double-reflection transmissive beam scanner, the individual components were first characterized as a function of incidence angle for select input polarization states. The individual components had to be characterized for each input polarization orientation encountered in the scanner, which meant each component had to be characterized for input polarization states where $\delta \in {\{0^ \circ}, + {45^ \circ},{90^ \circ}\}$ (with the assumption that the characterization results for $\delta = - {45^ \circ}$ would be the same as those found for $\delta = + {45^ \circ}$). In this appendix we describe the measured performance of the Faraday rotator over a range of incidence angles and for different input polarization orientations.
1. CHARACTERIZATION SYSTEM
A system was built to measure the transmission efficiency of a device under test while also measuring the laser output power via a pickoff beam. A wedged-plate beam pickoff was positioned near 45° incidence after the wave plate to monitor fluctuations in incident power. The clean-up polarizer and half-wave plate are the same as those in Fig. 2. The devices under test were placed after these initial polarization-controlling optics, as seen in the schematic shown in Fig. 6.
2. FARADAY ROTATOR: TRANSMISSION EFFICIENCY AND POLARIZATION ROTATION
We characterized a Bismuth-doped rare-earth iron garnet latching Faraday rotator (MGL-1550-1.0-AA-11.0 from Coherent Corp.) for use in the scanner. The latching Faraday rotator is a nonreciprocal magneto-optic material that has been poled and does not require an externally applied bias magnetic field in order to rotate the polarization of light transmitted through it. The devices are 485 µm thick, and achieve 45° rotation for light at 1550 nm wavelength [23]. Because the magneto-optic effect is nonreciprocal, a round trip through the Faraday rotator results in a 90° total rotation, whereas the net rotation after a round trip through a reciprocal rotator is 0°. When used in the scanner, the folded beam passes through the Faraday rotator three times, and the orientation of the polarization is different each time the beam is incident on the Faraday rotator. The transmission efficiency and polarization rotation performance of the Faraday rotator were characterized for incidence angles up to ${\pm}{50^ \circ}$ in 5° steps. As described in Section 2.A, a wavelength sweep of 1546–1554 nm was performed at each incidence angle. Taking the arithmetic mean of the transmitted power over this range suppressed angle-dependent etalon effects and reduced the uncertainty on the measured transmitted power.
Fig. 7. (a) Normalized transmission through the Faraday rotator as a function of incidence angle for horizontal, diagonal, and vertical orientations of linearly polarized incident light. Reprinted by permission from SPIE: Baker et al., Proc. SPIE 12428, 98 (2023) [18]. Copyright 2023. (b) Rotation of polarization orientation after transmission through the Faraday rotator as a function of incidence angle for horizontal, diagonal, and vertical orientations of linearly polarized incident light.
Fig. 8. DoLP of light after transmission through the Faraday rotator as a function of incidence angle for horizontal, diagonal, and vertical orientations of linearly polarized incident light.
Before each Faraday rotator characterization measurement, a polarization analyzer, inserted after the device under test, was set to minimum transmission to find the rotation reference position and then rotated 360° in 5° steps, performing a wavelength sweep at each angle to determine the unattenuated power prior to insertion of the Faraday rotator. This measurement yielded 73 wavelength sweeps where the transmitted power was recorded at each wavelength with a simultaneous pickoff power reading. The raw transmitted power readings were each divided by the associated pickoff power reading and then the arithmetic mean was taken over each wavelength sweep, resulting in one pickoff-normalized power value for each analyzer angle. The pickoff-normalized measurements were then fit to a sine-squared curve as a function of analyzer angle where the amplitude, period, angle offset, and amplitude offset parameters were free. This fit was the baseline against which the transmission efficiency and polarization rotation angle of the Faraday rotator were determined.
The Faraday rotator was then placed in the system in front of the polarization analyzer, and the new minimum transmission state of the polarization analyzer was found. The polarization analyzer was rotated 360° from the minimum transmission position in 5° steps, with a wavelength sweep performed at each analyzer position. Once again, the pickoff-normalized wavelength-averaged power was fit to a sine-squared curve as a function of analyzer angle. Comparing the best-fit parameters of the Faraday characterization data to the best-fit parameters of the baseline data allowed us to determine the transmission efficiency of the Faraday rotator by taking the ratio of the maxima of the characterization and baseline fits. This procedure was then repeated for incidence angles to the Faraday rotator ranging from ${-}{50^ \circ}$ to 50°, and the results are shown in Fig. 7(a).
The manufacturer specified the insertion loss of the Faraday rotator to be ${\le} 0.05\;{\rm dB}$ (or greater than 98.9% transmission) when operated at normal incidence at a wavelength of 1550 nm [23]. Our measured transmission efficiency of the Faraday material exceeded this specification, with a transmission efficiency of $99.4\% \pm 0.2\%$ for all input polarization states for incidence angles up to ${\pm}{20^ \circ}$, and remained above 94.5% for incidence angles up to ${\pm}{50^ \circ}$ for all tested input polarization states. Excluding the endpoints (${\pm}{50^ \circ}$), the maximum difference between the transmission efficiencies of the three incident polarization states tested was less than 0.5%. High transmission efficiency of the Faraday rotator is vital to the overall efficiency of the scanner because light passes through the Faraday rotator three times. By scanning the Faraday rotator with the front polarizer (as shown in Fig. 1), light is always incident at the polarizer tilt angle ${\pm}\theta$.
Table 1. Comparison of the DoLP of the Light Incident on and Transmitted by the Faraday Rotator for Various Input Polarization States, at Normal Incidence
The polarization rotation angle ($\alpha$) for light passing through the Faraday rotator can be found at each incidence angle by comparing the polarization orientation of the light before ($\delta$) and after ($\delta + \alpha$) it transmits through the Faraday rotator. This is done by comparing the maximum transmission angle of the analyzer from the curve fits of the baseline and Faraday transmission data. The calculated polarization rotation of the light transmitted through the Faraday rotator as a function of incidence angle is shown in Fig. 7(b). The manufacturer specified the polarization rotation to be ${45^ \circ} \pm {1^ \circ}$ at normal incidence. Our measured polarization rotation agreed, and was within the range ${45^ \circ} \pm {1^ \circ}$ for all tested cases. For the tested input polarization states, the polarization rotation angle for incidence angles up to ${\pm}{20^ \circ}$ was $|\alpha {| = 45.3^ \circ} \pm {0.25^ \circ}$. Over all tested incidence angles, the rotation was always ${45.3^ \circ} \pm {0.8^ \circ}$. This is important for the scanner because the incident linear polarization state is different at each transmission through the Faraday rotator, and for good scanner efficiency, each rotation must be close to 45°.
3. FARADAY ROTATOR: DEGREE OF LINEAR POLARIZATION
The degree of linear polarization (DoLP) of the light transmitted by the Faraday rotator at each incidence angle can be calculated using the maximum and minimum power transmitted through the analyzer as it was rotated behind the Faraday rotator using Eq. (A1):
The DoLP of the light transmitted by the Faraday rotator for each input polarization state as a function of incidence angle is shown in Fig. 8.
In order to correctly characterize any change in the linear polarization state due to transmission through the Faraday rotator, we also needed to characterize the purity of the linear polarization state incident on the Faraday rotator, which changes as a function of the position of the half-wave plate. We characterized the DoLP of the light transmitted by the half-wave plate using a Corning Polarcor glass polarizer with a stated extinction ratio ${\gt}100{,}000{:}1$ at 1550 nm. The DoLP of the light incident on the Faraday rotator could then be compared to the DoLP of the transmitted light to determine the effect of the Faraday rotator. These values for the incident and transmitted DoLP are summarized in Table 1.
From this comparison, we can see that the Faraday rotator slightly degrades the DoLP of the transmitted state. The degradation increases as angle of incidence increases, but even at $\theta = {40^ \circ}$ the transmitted DoLP remains above 98.5% for all incident polarization states tested.
Funding
Air Force Research Laboratory (FA8650-16-C-1954).
Acknowledgment
This project was funded by the Air Force Research Laboratory via a subcontract from S2 Corp with a fundamental research exemption.
Disclosures
The authors declare no conflicts of interest.
Data availability
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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