What is a procedure for correcting a laser's beam pointing angle?
Pitch (tip) and yaw (tilt) adjustments provided by a kinematic mount can be used to make fine corrections to a laser beam's angular orientation or pointing angle. This angular tuning capability is convenient when aligning a collimated laser beam to be level with respect to a reference plane, such as the surface of an optical table, as well as with respect to a particular direction in that plane, such as along a line of tapped holes in the table.
Figure 2: The beam can be aligned to travel parallel to a line of tapped holes in the optical table. The yaw adjustment on the kinematic mount adjusts the beam angle, so that the beam remains incident on the ruler's vertical reference line as the ruler slides along the line of tapped holes.
Figure 1: Leveling the beam path with respect to the surface of an optical table requires using the pitch adjustment on the kinematic laser mount (Figure 2). The beam is parallel to the table's surface when measurements of the beam height near to (left) and far from (right) the laser's front face are equal.
Video Clip 3: The pointing angle of a laser beam from a PL202 collimated laser package was corrected using the pitch (tip) and yaw (tilt) adjusters on the laser's KM100 kinematic mount, and horizontal and vertical features on a BHM1 ruler. The resulting beam travels parallel to the optical table's surface, along a line of tapped holes.
Before Using the Mount's Adjusters First, rotate each adjuster on the kinematic mount to the middle of its travel range. This reduces the risk of running out of adjustment range, and the positioning stability is frequently better when at the center of an adjuster's travel range.
Then, make coarse corrections to the laser's height, position, and orientation. This can be done by adjusting the optomechanical components, such as a post and post holder, supporting the laser. Ensure all locking screws are tightened after the adjustments are complete.
Level the Beam Parallel to the Table's Surface Leveling the laser beam is an iterative process that requires an alignment tool and the fine control provided by the mount's pitch adjuster.
Begin each iteration by measuring the height of the beam close to and far from the laser (Figure 1). A larger distance between the two measurements increases accuracy. If the beam height at the two locations differs, place the ruler in the more distant position. Adjust the pitch on the kinematic mount until the beam height at that location matches the height measured close to the laser. Iterate until the beam height at both positions is the same.
More than one iteration is necessary, because adjusting the pitch of the laser mount adjusts the height of the laser emitter. In Clip 3 for example, the beam height close to the laser was initially 82 mm, but it increased to 83 mm after the pitch was adjusted during the first iteration.
If the leveled beam is at an inconvenient height, the optomechanical components supporting the laser can be adjusted to change its height. Alternatively, two steering mirrors can be placed after the laser and aligned using a different procedure. Steering mirrors are particularly useful for adjusting beam height and orientation of a fixed laser.
Orient the Beam Along a Row of Tapped Holes Aligning the beam parallel to a row of tapped holes in the table is another iterative process, which requires an alignment tool and tuning of the mount's yaw adjuster.
The alignment tool is needed to translate the reference line provided by the tapped holes into the plane of the laser beam. The ruler can serve as this tool, when an edge on the ruler's base is aligned with the edges of the tapped holes that define the line (Figure 2).
The relative position of the beam with respect to the reference line on the table can be evaluated by judging the distance between the laser spot and vertical reference feature on the ruler. Vertical features on this ruler include its edges, as well as the columns formed by different-length rulings. If these features are not sufficient and rulings are required, a horizontally oriented ruler can be attached using a BHMA1 mounting bracket.
In Clip 3, when the ruler was aligned to the tapped holes and positioned close to the laser, the beam's edge and the ends of the 1 mm rulings coincided. When the ruler was moved to a farther point on the reference line, the beam's position on the ruler was horizontally shifted. With the ruler at that distant position, the yaw adjustment on the mount was tuned until the beam's edge again coincided with the 1 mm rulings. The ruler was then moved closer to the laser to observe the effect of adjusting the mount on the beam's position. This was iterated as necessary.
Want additional Insights on beam alignment? Watch the full video.
How are two mirrors used to align a laser beam along a different path?
The first steering mirror reflects the beam along a line that crosses the new beam path. A second steering mirror is needed to level the beam and align it along the new path. The procedure of aligning a laser beam with two steering mirrors is sometimes described as walking the beam, and the result can be referred to as a folded beam path. In the example shown in Clip 4, two irises are used to align the beam to the new path, which is parallel to the surface of the optical table and follows a row of tapped holes.
Figure 3: The beam reflected from Mirror 1 will be incident on Mirror 2, if Mirror 1 is rotated around the x- and y-axes by angles θ and ψ, respectively. Both angles affect each coordinate (x2 , y2 , z2 ) of Mirror 2's center. Mirror 1's rotation around the x-axis is limited by the travel range of the mount's pitch (tip) adjuster, which limits Mirror 2's position and height options.
Figure 4: The adjusters on the first kinematic mirror mount are tuned to position the laser spot on the aperture of the first iris.
Video Clip 4: Two mirrors in KM100 kinematic mounts route the beam from a PL202 collimated laser package along the path defined by the two IDA25 irises. The beam is aligned when halos of laser light surround each iris' aperture and the laser spot is visible on the BHM1 ruler, which was placed behind the second iris to act as a viewing screen.
Setting the Heights of the Mirrors The center of the first mirror should match the height of the input beam path, since the first mirror diverts the beam from this path and relays it to a point on the second mirror. The center of the second mirror should be set at the height of the new beam path.
Iris Setup The new beam path is defined by the irises, which in Clip 4 have matching heights to ensure the path is level with respect to the surface of the table. A ruler or calipers can be used to set the height of the irises in their mounts with modest precision.
When an iris is closed, its aperture may not be perfectly centered. Because of this, switching the side of the iris that faces the beam can cause the position of the aperture to shift. It is good practice to choose one side of the iris to face the beam and then maintain that orientation during setup and use.
Component Placement and Coarse Alignment Start by rotating the adjusters on both mirrors to the middle of their travel ranges. Place the first mirror in the input beam path, and determine a position for the second mirror in the new beam path (Figure 3). The options are notably restricted by the travel range of the first mirror mount's pitch (tip) actuator, since it limits the mirror's rotation (θ ) around its x-axis. In addition to the pitch, the yaw (tilt) of the first mirror must also be considered when choosing a position (x2 , y2 , z2 ) for the second mirror. Each coordinate of the second mirror's location has a complex dependence on both the pitch and yaw of the first mirror, as does the spacing between the two mirrors. Be sure to place the two mirrors so that neither of the first mirror's adjusters needs to be rotated all the way to either end of its travel range.
After placing the second mirror on the new beam path, position both irises after the second mirror on the desired beam path. Locate the first iris near the second mirror and the second iris as far away as possible.
While maintaining the two mirrors' heights and without touching the yaw adjusters, rotate the first mirror to direct the beam towards the second mirror. Adjust the pitch adjuster on the first mirror to place the laser spot near the center of the second mirror. Then, rotate the second mirror to direct the beam roughly along the new beam path.
First Hit a Point on the Path, then Orient The first mirror is used to steer the beam to the point on the second mirror that is in line with the new beam path. To do this, tune the first mirror's adjusters while watching the position of the laser spot on the first iris (Figure 4). The first step is complete when the laser spot is centered on the iris' aperture.
The second mirror is used to steer the beam into alignment with the new beam path. Tune the adjusters on the second mirror to move the laser spot over the second iris' aperture (Figure 5). The pitch adjuster levels the beam, and the yaw adjuster shifts it laterally. If the laser spot disappears from the second iris, it is because the laser spot on the second mirror has moved away from the new beam path.
Tune the first mirror's adjusters to reposition the beam on the second mirror so that the laser spot is centered on the first iris' aperture. Resume tuning the adjusters on the second mirror to direct the laser spot over the aperture on the second iris. Iterate until the laser beam passes directly through the center of both irises (Clip 4). If any adjuster reaches, or approaches, a limit of its travel range, one or both mirrors should be repositioned and the alignment process repeated.
If a yaw axis adjuster has approached a limit, note the required direction of the reflected beam and then rotate the yaw adjuster to the center of its travel range. Turn the mirror in its mount until the direction of the reflected beam is approximately correct. If the mirror cannot be rotated, reposition one or both mirrors to direct the beam roughly along the desired path. Repeat the alignment procedure to finely tune the beam's orientation.
If a pitch axis adjuster has approached a limit, either increase the two mirrors' separation or reduce the height difference between the new and incident beam paths. Both options will result in the pitch adjuster being positioned closer to the center of its travel range after the alignment procedure is repeated.
Want additional Insights on beam alignment? Watch the full video.
Figure 7: The direction of the reflected beam depends on the direction of the incident beam and the pitch and yaw angles (θ and ψ, respectively) of the mirror. These angles can be used to calculate points (x2, y2, z2 ) along the reflected beam path.
Figure 6: These turning mirrors are mounted in KM100 mirror mounts, whose adjusters can tune pitch and yaw angles over a ±4° range. Note that this does not limit the yaw angle of the mirror surface, since rotating the post in the post holder also rotates the mirror's surface around the vertical axis.
Figure 9: These values were calculated using the setup described in Figure 8, except that a 1° pitch angle was assumed for the first mirror. These results demonstrate that decreasing the pitch can significantly increase the required separation between the first and second mirrors. However, stability improves when the adjusters are not extended to the limits of their travel ranges.
Figure 8: In this example, the goal is to position the second mirror on the table, so that it intercepts the reflected beam when it is 0.5" lower (y2 = -0.5") than the incident beam. It is assumed the pitch on the first mirror is 4°, the maximum possible. Setting the first mirror's yaw angle determines the x- and z-coordinates of the second mirror, relative to the first.
Figure 10: This plot views the table's surface from above, with the first mirror (star) at the origin. Curves labeled in the legend identify a few options for positioning a second mirror on the table to intercept the beam at a height (y2) that is 0.5" lower than at the first mirror. The required separation increases significantly with the first mirror's yaw angle, even when its pitch angle is held constant.
The required spacing between two steering mirrors (Figure 6) depends on the slope of the beam reflected from the first mirror and the height difference between the two mirrors. The beam's slope depends on both the pitch (tip) and yaw (tilt) angles of the first mirror. If the yaw angle is ignored when calculating the spacing, the resulting value will underestimate the required distance, often substantially.
Setting the Scene The incident beam travels along the z-axis and intersects the center of the first mirror (Figure 7). If the mirror were not rotated, the incident beam would be normally incident.
The mirror's center is at the origin of a Cartesian coordinate system. The z-axis points away from the mirror, in the opposite direction of the incoming beam, and the y-axis is vertical and perpendicular to the table.
The angles θ (pitch) and ψ (yaw) are positive when the mirror is rotated counterclockwise around the x- and y-axes respectively.
Points on the Reflected Beam When the mirror's pitch and yaw angles are known, coordinates (x2, y2, z2 ) for points along the reflected beam can be calculated with the help of some matrix algebra,
The variable A is a scaling factor: the larger its value, the larger the distance between the point and the mirror.
Example: Setting up Steering Mirrors These equations can be useful when positioning a pair of steering mirrors, which are used to route a beam from one path along another. The center of the first mirror is set at the height of the incident beam, and the center of the second mirror is set at the height of the new beam path. The second mirror must intercept the reflected beam when its height equals that of the new beam path.
For this example, both beam paths are parallel to the optical table, but the new beam path is 0.5" lower than the incident beam path. The mirrors are secured in KM100 kinematic mounts, whose pitch (tip) and yaw (tilt) adjusters each have a ±4° tuning range. Both mounts are attached to the tops of posts, which are secured in post holders (Figure 6). Note that the limited travel range of the mounts' adjusters does not actually limit the yaw angle (ψ), since rotating the post rotates the mirror around the y-axis independent of the adjuster. However, the mirror's pitch angle is limited to the range of the adjuster.
Potential x2 and z2 coordinates of the second mirror are plotted in Figure 8 for different yaw angles (ψ ) of the first mirror. These values were calculated using the desired height of the new beam path (y2 = -0.5") and a pitch angle set to the maximum value (θ = 4°). Although, for better stability, the pitch angle should be less than its maximum. The effect of keeping y2 = -0.5", but reducing the pitch angle to 1° is plotted in Figure 9.
Figure 10 plots the x2 and z2 coordinates of the second mirror as positions on the optical table. The perspective is from a point directly above the table, the first mirror's position is marked by a star, and the gray circles (guides for the eye) are concentric around it. The arrows indicate selected directions of the reflected ray, each corresponding to a different yaw angle. The curves labeled in the legend were calculated for different pitch angles and a constant -0.5" beam height difference. Comparing the curves with the gray circles illustrates that the necessary separation between the two mirrors increases significantly as the yaw angle increases. Larger separations are also required when the pitch angle is reduced.
Want additional Insights on beam alignment? Watch the full video.
参考文献  Ping-Shine Shaw, Zhigang Li, Uwe Arp, and Keith R. Lykke, "Ultraviolet characterization of integrating spheres," Appl.Opt.46, 5119-5128 (2007).  Jan Valenta, "Photoluminescence of the integrating sphere walls, its influence on the absolute quantum yield measurements and correction methods," AIP Advances8, 102123 (2018).  Robert D. Saunders and William R. Ott, "Spectral irradiance measurements: effect of UV-produced fluorescence in integrating spheres," Appl. Opt.15, 827-828 (1976).  Ping-Shine Shaw, Uwe Arp, and Keith R. Lykke, "Measurement of the ultraviolet-induced fluorescence yield from integrating spheres," Metrologia46, S191 - S196 (2009).
Figure 1: C-mount lenses and cameras have the same flange focal distance (FFD), 17.526 mm. This ensures light through the lens focuses on the camera's sensor. Both components have 1.000"-32 threads, sometimes referred to as "C-mount threads".
Figure 2: CS-mount lenses and cameras have the same flange focal distance (FFD), 12.526 mm. This ensures light through the lens focuses on the camera's sensor. Their 1.000"-32 threads are identical to threads on C-mount components, sometimes referred to as "C-mount threads."
The C-mount and CS-mount camera system standards both include 1.000"-32 threads, but the two mount types have different flange focal distances (FFD, also known as flange focal depth, flange focal length, register, flange back distance, and flange-to-film distance). The FFD is 17.526 mm for the C-mount and 12.526 mm for the CS-mount (Figures 1 and 2, respectively).
Since their flange focal distances are different, the C-mount and CS-mount components are not directly interchangeable. However, with an adapter, it is possible to use a C-mount lens with a CS-mount camera.
Mixing and Matching C-mount and CS-mount components have identical threads, but lenses and cameras of different mount types should not be directly attached to one another. If this is done, the lens' focal plane will not coincide with the camera's sensor plane due to the difference in FFD, and the image will be blurry.
With an adapter, a C-mount lens can be used with a CS-mount camera (Figures 3 and 4). The adapter increases the separation between the lens and the camera's sensor by 5.0 mm, to ensure the lens' focal plane aligns with the camera's sensor plane.
In contrast, the shorter FFD of CS-mount lenses makes them incompatible for use with C-mount cameras (Figure 5). The lens and camera housings prevent the lens from mounting close enough to the camera sensor to provide an in-focus image, and no adapter can bring the lens closer.
It is critical to check the lens and camera parameters to determine whether the components are compatible, an adapter is required, or the components cannot be made compatible.
1.000"-32 Threads Imperial threads are properly described by their diameter and the number of threads per inch (TPI). In the case of both these mounts, the thread diameter is 1.000" and the TPI is 32. Due to the prevalence of C-mount devices, the 1.000"-32 thread is sometimes referred to as a "C-mount thread." Using this term can cause confusion, since CS-mount devices have the same threads.
Measuring Flange Focal Distance Measurements of flange focal distance are given for both lenses and cameras. In the case of lenses, the FFD is measured from the lens' flange surface (Figures 1 and 2) to its focal plane. The flange surface follows the lens' planar back face and intersects the base of the external 1.000"-32 threads. In cameras, the FFD is measured from the camera's front face to the sensor plane. When the lens is mounted on the camera without an adapter, the flange surfaces on the camera front face and lens back face are brought into contact.
Figure 5: A CS-mount lens is not directly compatible with a C-mount camera, since the light focuses before the camera's sensor. Adapters are not useful, since the solution would require shrinking the flange focal distance of the camera (blue arrow).
Figure 4: An adapter with the proper thickness moves the C-mount lens away from the CS-mount camera's sensor by an optimal amount, which is indicated by the length of the purple arrow. This allows the lens to focus light on the camera's sensor, despite the difference in FFD.
Figure 3: A C-mount lens and a CS-mount camera are not directly compatible, since their flange focal distances, indicated by the blue and yellow arrows, respectively, are different. This arrangement will result in blurry images, since the light will not focus on the camera's sensor.
Figure 7: An adapter can be used to optimally position a CS-mount lens on a camera whose flange focal distance is less than 12.526 mm. This sketch is based on a Zelux camera and its SM1A10 adapter.
All Kiralux™ and Quantalux® scientific cameras are factory set to accept C-mount lenses. When the attached C-mount adapters are removed from the passively cooled cameras, the SM1 (1.035"-40) internal threads in their flanges can be used. The Zelux scientific cameras also have SM1 internal threads in their mounting flanges, as well as the option to use a C-mount or CS-mount adapter.
The SM1 threads integrated into the camera housings are intended to facilitate the use of lens assemblies created from Thorlabs components. Adapters can also be used to convert from the camera's C-mount configurations. When designing an application-specific lens assembly or considering the use of an adapter not specifically designed for the camera, it is important to ensure that the flange focal distances (FFD) of the camera and lens match, as well as that the camera's sensor size accommodates the desired field of view (FOV).
Made for Each Other: Cameras and Their Adapters Fixed adapters are available to configure the Zelux cameras to meet C-mount and CS-mount standards (Figures 6 and 7). These adapters, as well as the adjustable C-mount adapters attached to the passively cooled Kiralux and Quantalux cameras, were designed specifically for use with their respective cameras.
While any adapter converting from SM1 to 1.000"-32 threads makes it possible to attach a C-mount or CS-mount lens to one of these cameras, not every thread adapter aligns the lens' focal plane with a specific camera's sensor plane. In some cases, no adapter can align these planes. For example, of these scientific cameras, only the Zelux can be configured for CS-mount lenses.
The position of the lens' focal plane is determined by a combination of the lens' FFD, which is measured in air, and any refractive elements between the lens and the camera's sensor. When light focused by the lens passes through a refractive element, instead of just travelling through air, the physical focal plane is shifted to longer distances by an amount that can be calculated. The adapter must add enough separation to compensate for both the camera's FFD, when it is too short, and the focal shift caused by any windows or filters inserted between the lens and sensor.
Flexiblity and Quick Fixes: Adjustable C-Mount Adapter Passively cooled Kiralux and Quantalux cameras consist of a camera with SM1 internal threads, a window or filter covering the sensor and secured by a retaining ring, and an adjustable C-mount adapter.
A benefit of the adjustable C-mount adapter is that it can tune the spacing between the lens and camera over a 1.8 mm range, when the window / filter and retaining ring are in place. Changing the spacing can compensate for different effects that otherwise misalign the camera's sensor plane and the lens' focal plane. These effects include material expansion and contraction due to temperature changes, positioning errors from tolerance stacking, and focal shifts caused by a substitute window or filter with a different thickness or refractive index.
Adjusting the camera's adapter may be necessary to obtain sharp images of objects at infinity. When an object is at infinity, the incoming rays are parallel, and location of the focus defines the FFD of the lens. Since the actual FFDs of lenses and cameras may not match their intended FFDs, the focal plane for objects at infinity may be shifted from the sensor plane, resulting in a blurry image.
If it is impossible to get a sharp image of objects at infinity, despite tuning the lens focus, try adjusting the camera's adapter. This can compensate for shifts due to tolerance and environmental effects and bring the image into focus.
Why can the FFD be smaller than the distance separating the camera's flange and sensor?
Flange focal distance (FFD) values for cameras and lenses assume only air fills the space between the lens and the camera's sensor plane. If windows and / or filters are inserted between the lens and camera sensor, it may be necessary to increase the distance separating the camera's flange and sensor planes to a value beyond the specified FFD. A span equal to the FFD may be too short, because refraction through windows and filters bends the light's path and shifts the focal plane farther away.
If making changes to the optics between the lens and camera sensor, the resulting focal plane shift should be calculated to determine whether the separation between lens and camera should be adjusted to maintain good alignment. Note that good alignment is necessary for, but cannot guarantee, an in-focus image, since new optics may introduce aberrations and other effects resulting in unacceptable image quality.
Figure 9: Refraction causes the ray's angle with the optical axis to be shallower in the medium than in air (θm vs. θo), due to the differences in refractive indices (nm vs. no ). After travelling a distance d in the medium, the ray is only hm closer to the axis. Due to this, the ray intersects the axis Δf beyond the f point.
Figure 11: Tolerance and / or temperature effects may result in the lens and camera having different FFDs. If the FFD of the lens is shorter, images of objects at infinity will be excluded from the focal range. Since the system cannot focus on them, they will be blurry.
Figure 10: When their flange focal distances (FFD) are the same, the camera's sensor plane and the lens' focal plane are perfectly aligned. Images of objects at infinity coincide with one limit of the system's focal range.
A Case of the Bends: Focal Shift Due to Refraction While travelling through a solid medium, a ray's path is straight (Figure 8). Its angle (θo ) with the optical axis is constant as it converges to the focal point (f ). Values of FFD are determined assuming this medium is air.
When an optic with plane-parallel sides and a higher refractive index (nm ) is placed in the ray's path, refraction causes the ray to bend and take a shallower angle (θm ) through the optic. This angle can be determined from Snell's law, as described in the table and illustrated in Figure 9.
While travelling through the optic, the ray approaches the optical axis at a slower rate than a ray travelling the same distance in air. After exiting the optic, the ray's angle with the axis is again θo , the same as a ray that did not pass through the optic. However, the ray exits the optic farther away from the axis than if it had never passed through it. Since the ray refracted by the optic is farther away, it crosses the axis at a point shifted Δf beyond the other ray's crossing. Increasing the optic's thickness widens the separation between the two rays, which increases Δf.
To Infinity and Beyond It is important to many applications that the camera system be capable of capturing high-quality images of objects at infinity. Rays from these objects are parallel and focused to a point closer to the lens than rays from closer objects (Figure 10). The FFDs of cameras and lenses are defined so the focal point of rays from infinitely distant objects will align with the camera's sensor plane. When a lens has an adjustable focal range, objects at infinity are in focus at one end of the range and closer objects are in focus at the other.
Different effects, including temperature changes and tolerance stacking, can result in the lens and / or camera not exactly meeting the FFD specification. When the lens' actual FFD is shorter than the camera's, the camera system can no longer obtain sharp images of objects at infinity (Figure 11). This offset can also result if an optic is removed from between the lens and camera sensor.
An approach some lenses use to compensate for this is to allow the user to vary the lens focus to points "beyond" infinity. This does not refer to a physical distance, it just allows the lens to push its focal plane farther away. Thorlabs' Kiralux™ and Quantalux® cameras include adjustable C-mount adapters to allow the spacing to be tuned as needed.
If the lens' FFD is larger than the camera's, images of objects at infinity fall within the system's focal range, but some closer objects that should be within this range will be excluded. This situation can be caused by inserting optics between the lens and camera sensor. If objects at infinity can still be imaged, this can often be acceptable.
Not Just Theory: Camera Design Example The C-mount, hermetically sealed, and TE-cooled Quantalux camera has a fixed 18.1 mm spacing between its flange surface and sensor plane. However, the FFD (f) for C-mount camera systems is 17.526 mm. The camera's need for greater spacing becomes apparent when the focal shift due to the window soldered into the hermetic cover and the glass covering the sensor are taken into account. The results recorded in the table beneath Figure 9 show that both exact and paraxial equations return a required total spacing of 18.1 mm.
Does PM fiber preserve every input polarization state?
No polarization-maintaining (PM) fiber preserves an arbitrary input polarization state. Typical PM fiber only preserves the polarization state of input light that is both linearly polarized and polarized parallel to one of the fiber's two orthogonal axes. The orientation of the linearly polarized light input to the PM fiber matters, since the refractive indices of its two orthogonal axes are different. Light polarized along the high-index direction (slow axis) travels more slowly than light polarized along the orthogonal direction (fast axis).
If the input polarization state does not meet these criteria, the light output from the fiber will be elliptically polarized. However, the elliptical polarization state cannot be predicted and is not stable, since it depends on the fluctuating temperature and stress conditions over the length of the fiber.
Figure 1: Polarimeter measurements of light output by a PM fiber patch cable are plotted on a Poincaré sphere. The points indicated by the arrows result when there is optimal alignment between the linearly polarized input and one of the fiber's axes. These input states are preserved by the fiber. All other points correspond to the elliptically polarized output states resulting when the input light's polarization direction is not parallel with one of the fiber's axes.
PM Fibers Do Not Polarize Light A PM fiber does not behave like a linear polarizer, and a PM fiber will not convert an arbitrary input polarization state into a linearly polarized output state.
A linear polarizer has two orthogonal axes, but these are not the slow and fast axes of a PM fiber. In the case of a linear polarizer, the light polarized parallel to one of the axes is attenuated, while the light polarized parallel to the other is transmitted. Since only one polarization component is transmitted, the output light is linearly polarized.
Because a PM fiber transmits both orthogonal polarization components, instead of attenuating one, PM fiber cannot be used as a linear polarizer.
Comparison with Wave Plates Since PM fibers and wave plates both have fast and slow axes, they have a lot in common. If the polarization axis of a linearly polarized light beam is aligned parallel to either the slow or the fast axis, both PM fibers and wave plates will preserve that polarization state. However, if the input beam has components polarized along both slow and fast axes, neither a PM fiber nor a wave plate will preserve the input polarization state.
Both PM fibers and wave plates change the polarization state of a light beam by delaying the component of light polarized parallel to the slow axis more than the component polarized parallel to the fast axis. But, a PM fiber cannot be used to replace a wave plate, since the delay induced by the PM fiber fluctuates unpredictably as the temperature and stress applied over the length of the fiber changes.
Output Polarization States The polarimeter measurements plotted on the Poincaré sphere in Figure 1 illustrate the range of elliptically polarized output states a PM fiber patch cable can provide, when the input is a linearly polarized beam with arbitrary orientation to the fiber's axes. The polarimeter measurement of the output light has one of the two values indicated by the black arrows, when the fiber preserves the input polarization state. These values result when there is optimal alignment between the polarization direction of the input polarization state and one of the fiber's axes. All other points on the sphere indicate elliptical output polarization states occurring when the input polarization state is not aligned parallel to either fiber axis.
Each data trace in the figure was generated by rotating the polarization direction of the linearly polarized input light once around the optical axis. The traces do not overlap, since the temperature of the fiber was changed after every rotation. Each temperature change resulted in a different set of elliptically polarized output states, due to the fiber's temperature sensitivity. Note that each data trace crosses the points indicated by the arrows. This indicates that when the linearly polarized input state is well-aligned to one of the fiber's axes, the output polarization state is not sensitive to changes in temperature and applied stress.
How does polarization-maintaining fiber preserve linearly polarized light?
There is a significant refractive index difference (birefringence) between the orthogonal "slow" and "fast" axes of a polarization-maintaining (PM) fiber, and this birefringence is the reason PM fiber is effective in preserving the polarization state of input linearly polarized light. However, the input linear polarization state can only be preserved if it is aligned parallel to one of the fiber's axes.
Because PM fibers are birefringent, there are different velocity, or more accurately propagation constant, requirements for light polarized parallel to the fiber's slow vs. fast axes. In order for light to switch to being polarized parallel to the orthogonal axis, the light would have to change its velocity (propagation constant) to meet the requirements of the orthogonal axis. This creates such a barrier that a switch is unlikely to occur unless the fiber's birefringence is reduced.
Figure 3: Bow-tie polarization-maintaining fibers use two wedge-shaped stress rods to place the core in tension and make it birefringent. The stress is directed along the slow axis, and it results from the stress rods contracting more than the cladding as the fiber cooled after fabrication.
Figure 2: PANDA polarization-maintaining fiber uses two cylindrical stress rods to place the core in tension, making it birefringent. The stress, which is directed along the slow axis, results from the stress rods contracting more than the cladding as the fiber cooled after fabrication.
Figure 4: To minimize microbends, spool fiber by winding it loosely in parallel rows (top). Microbends result from winding fiber so that it crosses over the bumpy surface created by deeper layers of the wound fiber (bottom).
A Stressful Situation One approach to creating a PM fiber is to apply a mechanical stress to the fiber's core, since stress causes glass to become birefringent (photoelasticity). The two most common stress-birefringent fibers, PANDA and bow-tie, apply tension to the fiber's core.
In these designs, glass structures called stress rods extend down the length of the fiber, parallel to fiber's core. In cross section, the stress rods and the core of the fiber are linearly arranged, as shown in Figures 2 and 3. As the fiber cools after fabrication, the glass in the stress rods contracts more than the glass in the surrounding cladding. The pull from the contraction of the stress rods creates a line of tension (slow axis) across the core, with comparatively little stress applied in the orthogonal direction (fast axis). This creates an index difference between the two axes.
Stress Relief is not Always a Good Thing The tension across the core in stress-birefringent PM fibers is temperature dependent, since the stress results from the glass in the stress rods and the glass in the cladding having different rates of thermal expansion (CTEs). The tension provided by the stress rods decreases as the operating temperature increases. Since this reduces the birefringence, and therefore the fiber's ability to preserve polarization, it can result in a reduced extinction ratio (ER).
The tension in the core can also be reduced by stress from handling, such as coiling the fiber in a small-diameter ring, routing it around sharp corners, and fixing it to a bumpy surface. Microbends at localized stress points scatter light into the orthogonal polarization state, which reduces ER. Winding a fiber across itself (Figure 4), or pressing a bare fiber against a surface, can cause microbending.
Attaching fiber connectors typically reduces ER, since the cured potting compound that secures the fiber can induce asymmetric stress, hardened bubbles within the compound can press into the fiber, and there can be contact between the fiber and the ferrule's bore. To increase the maximum ER the fiber can provide, manufacturers typically take steps to suppress these sources of stress, but they cannot be eliminated.
Form is Function If the temperature-dependence of stress-birefringent fibers is unacceptable, form-birefringent fibers offer a largely temperature-insensitive alternative. These PM fibers are birefringent due to their elliptically shaped cores, rather than tension induced by stress rods (Figure 5).
Form-birefringent fibers, which include PM photonic crystal fibers, are not well-suited to every application. Their elliptical cores, attenuation, and small mode sizes are not ideal for telecommunications applications, and they find most use in fiber optic sensors.
References  Chris Emslie, in Specialty Optical Fibers Handbook, edited by Alexis Mendez and T. F. Morse (Elsevier, Inc., New York, 2007) pp. 243-277.  Malcolm P. Varnham et al., "Analytic Solution for the Birefringence Produced by Thermal Stress in Polarization-Maintaining Optical Fibers," J. Lightwave Technol., LT-1(2), 332-339 (1983).  Zhenyang Ding et al., "Accurate Method for Measuring the Thermal Coefficient of Group Birefringence of Polarization-Maintaining Fibers," Opt. Lett., 36(11), 2173-2175 (2011).  M. Shah Alam and Sarkar Rahat M. Anwar, "Modal Propagation Properties of Elliptical Core Optical Fibers Considering Stress-Optic Effects," World Academy of Science, Engineering and Technology, Open Science Index 44, International Journal of Electronics and Communication Engineering, 4(8), 1170 - 1175 (2010).
Figure 6: Due to the effects of cross talk, PM fibers typically output light that is slightly elliptically polarized. Varying the temperature applied to a PM fiber will change the output elliptical polarization state in a controlled manner. The polarization measurement values will trace a circle on the Poincaré sphere and can be used to characterize the output light.
Figure 7: Three different data traces, each corresponding to a different angular mismatch between input linear polarization state and PM fiber axis, are plotted on a Poincaré sphere. Each trace was acquired while using a heat gun to vary the fiber's temperature, which cycled the output polarization state. As the angular mismatch decreased, the range of temperature-dependent polarization states decreased, and the extinction ratio increased. Extinction ratios are given for each trace in decibels (dB)
The extinction ratio (ER) of the light output from a PANDA and bow-tie polarization-maintaining (PM) fiber will be reduced, relative to the ER of input light, due to a combination of non-ideal coupling conditions, the effects of external stress applied to the fiber, and interactions between the light and fiber imperfections. All can worsen (decrease) the ER by transferring some light to the orthogonal polarization state.
Approximate Cross Talk Due to Misalignment Cross talk (cross coupling) occurs when some fraction of light becomes polarized parallel to the orthogonal direction. Coupling light into a PM fiber can cause cross talk if there is misalignment (rotation) between the polarization axes of the source and the fiber. In this case, the linearly polarized light from the source would be split between two orthogonally polarized components, which are guided separately by the slow and fast axes of the fiber.
Cross talk due to misalignment can be significant, and it can be estimated by varying the fiber's temperature while measuring the output polarization state. If the output light includes both orthogonally polarized components, the delay between them will vary with temperature. This will cause the output light's elliptical polarization to vary with temperature.
When the temperature-dependent polarization measurements are plotted on a Poincaré sphere, they will trace out a circle (Figures 6 and 7). The approximate value of cross talk due to misalignment can be found from the angle (2φ) of the arc from the point at the circle's center to a point on its circumference.
If the point in the center of the circle is used as a reference, the angle 2φ is the incremental ellipticity needed to reach the circle's circumference. When the half-angle (φ ) is expressed in radians, the approximate amount of cross talk in decibels is,
Cross Talk (dB) ≈ -20 log (tan(φ )).
One way to improve the alignment between the source and fiber is to rotate the polarization angle of the source around the optical axis until the temperature-dependent fluctuations in the fiber's output polarization state are minimized.
Approximating ER of the Output Light A minimal amount of cross talk will occur as the light propagates down the fiber and interacts with fiber imperfections, but externally applied stress can significantly reduce the ER. Small diameter coils, tightly winding the fiber over bumpy or sharp features, and fixing the bare fiber against hard surfaces can also lower the ER. Fiber connectors can also be a significant source of cross talk, due to the stresses arising from interactions among the bare fiber, connector ferrule, and potting compound.
The extinction ratio (ER) can be calculated using different approximations. One,
ERδ (dB) ≈ -20 log (tan(φ + |δ |)).
is similar to the equation used to calculate cross talk due to misalignment but includes cross talk arising from fiber imperfections, microbends, and other perturbations distributed along the length of the fiber. These effects displace the center of the circular trace from the equator of the Poincaré sphere by an angle 2δ. A more exact approximation,
takes into account the degree of polarization (DOP), which is the intensity of polarized light divided by the total light intensity.
References  Chris Emslie, in Specialty Optical Fibers Handbook, edited by Alexis Mendez and T. F. Morse (Elsevier, Inc., New York, 2007) pp. 243-277.  Edward Collett, Polarized Light in Fiber Optics (Elsevier, Inc., New York, 2007) pp. 45-53.
What is beat length and why is it often specified for PM fiber, instead of polarization extinction ratio?
It is difficult for manufacturers to specify a polarization extinction ratio (PER) for light output by polarization-maintaining (PM) fibers, since this parameter depends on the length of the fiber, how it is routed, and the polarization and alignment of the input light. Beat length is independent of these factors, which makes it a convenient parameter for quantifying the fiber's potential to preserve polarization. A smaller beat length is better, and it is a useful parameter to reference when choosing a PM fiber and its operating temperature. While beat length provides information about a PM fiber's potential to perform well, its actual performance and the PER of the light output by the fiber ultimately depend on the details of the fiber's deployment.
Figure 8: The blue and green curves represent waves polarized parallel to the PM fiber's slow and fast axes, respectively. Since the two axes' refractive indices are different, the two waves oscillate at different rates with respect to the distance along the fiber's optical axis (gray line). The beat length is the distance, measured in air, between the two red spheres, in which the sphere on the left selects a reference phase for the two waves (0° in this example), and the sphere on the right marks the next time both waves are again at this same reference phase. As long as the fiber's birefringence remains constant, the beat length is the same at any location along the length of the fiber.
Beat Length of a PM Fiber The beat length of a PM fiber is found by comparing waves propagating along the fiber's two orthogonal axes, fast and slow. These waves can be provided by a single, monochromatic, linearly polarized beam whose polarization angle is oriented midway between the orientations of the fiber's fast and slow axes. The orthogonally polarized waves oscillate with the same phase before, but not after, entering the fiber. Since the refractive index of the slow axis is greater than that of the fast axis (nslow > nfast ), the wave polarized parallel to the slow axis will oscillate with a shorter period than the wave polarized parallel to the fast axis.
The phases of these two sinusoidal waves cycle through angles from 0 to 2 (0° to 360°). But, the two waves do not stay in phase with one another as they propagate (Figure 8). The wave polarized parallel to the slow axis cycles more times per unit distance, where "distance" refers to the length measured in air.
The beat length is a measure of how often the difference between the two waves' phases cycles through a full 2. This is illustrated in Figure 8, in which both waves happen to have a phase of 0° at the origin. The beat length is the distance between this reference point and the next point at which both waves simultaneously return to the phases they had at the reference point. Beat length (Lp ),
is proportional to wavelength () and inversely proportional to the fiber's birefringence (B = nslow - nfast ).
Typical Beat Lengths The larger the refractive index difference between the two fiber axes, the larger the birefringence, the shorter the beat length, and the better the polarization-preserving performance of the fiber. The beat length remains constant along the length of the fiber, as long as the fiber's birefringence does not change. Manufacturers often specify beat length for selected wavelengths and limited temperature ranges.
To date, PM fibers with beat lengths <1 mm have had elliptical cores and mode field diameters (MFDs) significantly smaller than those of standard single mode optical fibers. Many applications require fibers with circular cores and MFDs close to those of standard single mode fibers. Typical PM fibers that meet these criteria and perform well have beat lengths between 1 mm and a few millimeters. It is interesting to note that standard single mode fibers also have measurable beat lengths, although they are meters long. This is due to their cores not having a perfectly circular cross section. Since the ellipticity of their cores is slight and changes randomly along the length of the fiber, standard single mode fibers are not useful as PM fibers.
The Amplitude Does not Beat In the case of PM fibers, beat length refers to a repeating phase relationship between waves polarized parallel to the orthogonal slow and fast axes of a PM fiber. The sum of these waves at any point along the fiber determines the polarization state of the light beam at that point. For example, when the waves are in phase, the light is linearly polarized, and the waves are out of phase by /2 (90°), the light is circularly polarized.
An amplitude beat pattern does not occur, since these waves are polarized orthogonal to one another. Two waves only produce an amplitude beat pattern when they have components polarized parallel to one another. For the same reason, a signal with an interference term equal to zero will result when a photodetector is used to measure the combined intensity of two orthogonally polarized waves with different periods.
References  Chris Emslie, in Specialty Optical Fibers Handbook, edited by Alexis Mendez and T. F. Morse (Elsevier, Inc., New York, 2007) pp. 243-277.  Malcolm P. Varnham et al., "Analytic Solution for the Birefringence Produced by Thermal Stress in Polarization-Maintaining Optical Fibers," J. Lightwave Technol., LT-1(2), 332-339 (1983).
Figure 9: The PANDA PM fiber has stress rods embedded in its cladding. These cylinders are aligned parallel to the core. Since the glass of the stress rods contracts more than the surrounding cladding as the fiber cools from fabrication temperatures, the core is pulled in tension along the slow axis.
Figure 11: Since the effect of the temperature-dependent birefringence dominates in Figure 10, the red trace from that figure is plotted alone to better show its range. These values were calculated using the assumption that the length of the fiber increases with temperature, while the fiber's birefringence remains constant with temperature.
Figure 10: The relative delay (y-axis) between orthogonal polarization components propagating through a PANDA PM fiber changes as the fiber's temperature changes (x-axis). As the temperature increases, the polarization-maintaining performance decreases. Performance is improved by reducing the temperature. The blue and red traces were calculated using the assumption that only the birefringence or fiber length, respectively, changed with temperature.
The larger the refractive index difference between the orthogonal slow and fast polarization axes of a polarization-maintaining (PM) fiber, the better its PM performance. However, the magnitude of this difference (birefringence) decreases with increasing temperature, since the thermally dependent tension across the core drops with increasing temperature. The decrease in the fiber's birefringence is approximately proportional to the increase in temperature.
Temperature-Dependent Birefringence Stress-birefringent PM fibers like PANDA and bow-tie fibers have stress rods embedded in their claddings (Figure 9). Since the stress rod's glass has a higher coefficient of thermal expansion (CTE) than the cladding's glass, the glass in the stress rods contracts at a higher rate than the rest of the cladding as the fiber cools immediately after fabrication. Due to their greater contraction, the stress rods pull on the surrounding cladding, which places the core under significant tension around room temperature. This creates birefringence in the fiber's core.
A proportionality constant () relates the birefringence (B ),
to the difference between the temperature of the glass when it transitions between its liquid and glassy states (To , the fictive temperature), and the operating temperature (T ).
Estimating the Impact of Temperature If all of the light propagating in a PM fiber is polarized parallel to the same fiber axis, the polarization state of the light output by the fiber will be independent of temperature. If the light includes components polarized parallel to each of the fiber's axes, changing the operating temperature will change the elliptical polarization state of the light output by the fiber.
This is due to the relative delay between the two orthogonal components determining the output polarization state. That delay depends on the fiber's birefringence and the length of the fiber, which are both temperature dependent. But, only the change in birefringence significantly affects the fiber's polarization-maintaining performance.
Estimates of the relative significance of these two effects on the output polarization state were calculated using the equations in the table, a 1550 nm operating wavelength, and a 2 m length (L ) of PANDA PM fiber (PM980-XP), whose beat length is ~2.7 mm. The coefficient was assumed to be -5.6 x 10-7 . A fused silica glass fiber core, with a CTE of 5.5 x 10-7/°C, was also assumed.
The calculated results are plotted in Figures 10 and 11. The delay changes (y-axis), when the temperature changes (x-axis). This indicates that monitoring the temperature-dependent delay can provide information about the fiber's temperature-dependent birefringence and the fiber's potential to preserve polarization.
Temperature and Beat Length While the fiber's birefringence determines the strength of a PM fiber's ability to preserve polarization, birefringence is not usually specified by the manufacturer. Beat length is a related and typically specified parameter. The beat length (Lp),
is the ratio of wavelength () and birefringence and is shorter for higher-performance PM fibers. Note that for stress-birefringent PM fibers, beat length increases with temperature.
References  Chris Emslie, in Specialty Optical Fibers Handbook, edited by Alexis Mendez and T. F. Morse (Elsevier, Inc., New York, 2007) pp. 243-277.  Malcolm P. Varnham et al., "Analytic Solution for the Birefringence Produced by Thermal Stress in Polarization-Maintaining Optical Fibers," J. Lightwave Technol., LT-1(2), 332-339 (1983).  Zhenyang Ding et al., "Accurate Method for Measuring the Thermal Coefficient of Group Birefringence of Polarization-Maintaining Fibers," Opt. Lett., 36(11), 2173-2175 (2011).  M. Cavillon, P. D. Dragic, and J. Ballato, "Additivity of the coefficient of thermal expansion in silicate optical fibers," Opt. Lett, 42(18), 3650 - 3653 (2017).
参考文献  Edward Collett, Polarized Light in Fiber Optics (Elsevier, Inc., New York, 2007) pp. 45-53.  Russell A. Chipman, Wai-Sze Tiffany Lam, and Garam Young, Polarized Light and Optical Systems (CRC Press, New York, 2019) pp. 80-83.
Is there a rule for choosing the mirror's diameter based on the laser beam's diameter?
The diameter of the laser beam should be significantly smaller than the clear aperture of the mirror (Figure 1). A general rule restricts the diameter of the beam to no more than a third of the mirror's diameter. This limits the risk of introducing aberrations into the beam, which will occur if it interacts with the coating boundary near the perimeter of the surface and / or is clipped by the edge of the optic.
Figure 1: The clear aperture of the mirror should have a larger diameter than the beam. A general rule recommends the mirror's diameter be at least a factor of three larger than the beam's 1/e2 diameter.
Figure 2: A larger-diameter mirror provides the flexibility to preserve optical beam quality despite situations in which the laser spot is not perfectly centered on the mirror or is elongated due to oblique incidence.
Beam Diameter and Optical Power When the laser beam has a Gaussian intensity profile, it is common to measure its diameter across the 1/e2 intensity points. If a visible wavelength beam is observed, the 1/e2 diameter generally appears to enclose the beam. However, the intensity of the beam is 13.5% of the peak intensity along the 1/e2 perimeter, and there is measurable power beyond this diameter.
A mirror would optimally have a diameter (D ) large enough to reflect all of the beam's power. The fraction of the reflected optical power (PT ),
can be calculated using D and the 1/e2 beam intensity diameter (d ), or using the mirror's radius (r ) and the 1/e2 beam intensity radius (w ). 
When the diameter of the mirror is a factor of 1.52 larger than the beam's 1/e2 diameter, the mirror can reflect 99% of the power. Increasing the mirror's diameter to twice the beam's diameter will reflect over 99.96% of the power. If the beam is not perfectly centered on the mirror, the fraction of reflected light will be lower.
Beam Position and Clear Aperture The mirror's optical performance is specified over the area of the clear aperture, which typically includes all but a thin annulus around the perimeter of the mirror. It is good practice to confine the laser beam to the clear aperture, since nothing is known about the mirror's performance in the surrounding region. In addition, a beam that extends beyond the clear aperture risks being clipped by the edge of the mirror.
If the mirror's diameter is twice the beam's diameter, and the beam is perfectly centered on the mirror, the optical quality of the beam will be preserved and approximately all of the beam power will be reflected. However, any misalignment will impact beam quality. A larger mirror diameter provides additional flexibility during alignment and accommodates situations in which the beam is not perfectly centered in the clear aperture. Due to this, it can be more convenient to work with mirrors that have clear apertures at least a factor of three larger than the beam diameter.
Want additional Insights on beam alignment? Watch the full video.
Reference  Bahaa E. A. Saleh and Malvin Carl Teich, Fundamentals of Photonics (John Wiley & Sons, Inc., New York, 1991) p. 85.
Figure 4: There are six possible sequences of reflections for a beam. The zone in which the first reflection occurs determines the sequence. These maps apply to beams approximately parallel with the retroreflector's normal axis. The beam paths are indcated by arrows, and dots mark reflections.
Figure 3: The three reflective faces of a corner-cube retroreflector are shown in false color and with numerical labels assigned to each half. Retroreflectors are designed to reflect an incident beam once from each face and provide an output beam parallel to the input.
Figure 6: Shifting the position of the first reflection to below the diagonal of the red face causes the next reflection to occur from the yellow face. After the third reflection, from the blue face, the beam exits the retroreflector travelling parallel to but shifted from the output beam in Figure 5.
Figure 5: When the first reflection occurs above the diagonal of the red face, and the beam is parallel to the retroreflector's normal axis, the second reflection occurs from the blue face. The beam then reflects from the yellow face before exiting the retroreflector.
Beams output from corner-cube retroreflectors travel parallel to the input beam, but in the opposite direction. The input beam can be aligned to the vertex or to a point on one of the three faces. The input and output beams are colinear if the input beam is aligned to the vertex. The two beams will be separated if the input beam spot does not overlap the vertex.
Input beams aligned to one of the retroreflector's faces will reflect from that face and then the other two before exiting the retroreflector. For a range of incident angles, there are six possibilities for the order in which the beam will reflect from the three different faces. lt can be useful to select the path through the retroreflector for reasons that include optimal beam positioning and minimizing polarization effects.
For a beam to follow a particular sequence of reflections, it is not sufficient to align the beam so that it is incident on a specific face. The beam must also be incident on the proper half of that face.
Tracing the Beam Path When looking into the vertex of the retroreflector, reflective effects make it possible to see the six halves of the three faces. Here, they are identified using dashed diagonal lines (Figure 3). In addition, the three faces of the retroreflector are shaded with false color for illustrative purposes. The normal axis is not shown, but it passes through the vertex and is equidistant from all three faces.
The six different possible reflection sequences can vary with angle of incidence. The maps in Figure 4 apply to beams nearly parallel with the normal axis. While a hollow retroreflector is used for these illustrations, these sequences of reflections also apply to prism retroreflecting mirrors.
The position of the first reflection determines which sequence of reflections the beam will follow through the retroreflector. The beam always exits from a different face than it entered.
Example Figures 5 and 6 illustrate the two orders of reflections that can occur when the first reflection occurs from the left-most vertical face. The incident beam is parallel to the retroreflector's normal axis.
When the first reflection occurs above the diagonal, as shown in Figure 5, the last reflection occurs from the horizontal (yellow) mirror. However, locating the first reflection below the diagonal results in a last reflection from the other vertical (blue) mirror. The output beams of these two cases are parallel to, but shifted from, one another.
Figure 8: Vertically polarized beams were input to a TIR solid prism retroreflector (PS975M) and a backside-gold-coated solid prism retroreflector (PS975M-M01B). The polarization ellipse of each output beam is shown in the zone that provided the beam's third reflection. For a plot of the ellipticity angle ( χ ) and orientation angles ( ψ ) with respect to the horizontal axis, click here.
Figure 7: Horizontally polarized beams were input to a TIR solid prism retroreflector (PS975M) and a backside-gold-coated solid prism retroreflector (PS975M-M01B). The polarization ellipse of each output beam is shown in the zone that provided the beam's third reflection. For a plot of the ellipticity angles ( ψ ) with respect to the horizontal axis, click here.
Figure 10: Retroreflectors convert some of the input light to the orthogonal polarization. Over 90% of the light output from the backside-gold-coated solid prism retroreflector (PS975M-M01B) remained polarized in the input state. In the case of the TIR solid prism retroreflector (PS975M), that percentage strongly depended on beam path and did not exceed 80%.
Figure 9: A retroreflector is designed to reflect an input beam once off of each face. When the beam is approximately normal to the viewing plane illustrated in Figures 7 and 8, the beam will follow one of six beam paths.
When the backsides of solid prism retroreflectors are coated with metal, polarization changes induced in the output beam are significantly reduced.
This is due to the difference between specular reflections, which occur from interfaces between glass and the higher refractive index metal, and reflections that occur due to total internal reflection (TIR), which require the backside material, like air, to have a lower refractive index.
Compared with TIR, a specular reflection from a glass-metal interface better preserves the input beam's polarization ellipticity.
Polarization and Beam Path Diagrams Beam paths through a retroreflector can be described by dividing its three reflective faces into six wedge-shaped zones (Figures 7, 8 and 9). Solid gray boundary lines mark physical lines of contact between reflective faces. Dotted gray lines indicate boundaries between the halves of each face.
The retroreflectors in these figures are oriented with one face-to-face interface aligned with the vertical axis. When the input beam is normal to these figures' viewing planes, Figure 9 describes the order in which the input beam reflects from the three faces before being output.
Output Polarization State Two sets of six measurements were made for both a PS975M TIR solid prism retroreflector and a PS975M-M01B backside-gold-coated solid prism retroreflector. Input light was linearly polarized, vertically for one set of measurements and horizontally for the other. In a set, each measurement was taken with the beam aligned to a different zone. At all three reflections, the beam was confined within a single zone.
In Figures 7 and 8, the polarization states of the output beam are represented using polarization ellipses. Each output beam's polarization ellipse is shown in the zone that provided the third reflection.
Ideally, the output beam would have the same polarization state as the input beam. However, these measurements indicate the retroreflectors converted some of the incident light to the orthogonal polarization. The plot in Figure 10 is a measure of the fraction of light in the output beam that was polarized parallel to the input.
The backside-gold-coated solid prism retroreflector was significantly more successful in maintaining the polarization state of these linearly polarized input beams.
Figure 12: Since the refractive indices of glass and air are different, the beam reflects at the front face. Reflected light can make multiple passes through the retroreflector before being output. Coherent overlapping beams produce interference effects.
Figure 11: The beam path through a corner-cube retroreflector includes a reflection from each of the three back faces, in an order determined by the position of the incident beam. The incident beam shown above has a 0° AOI and is displaced from the vertex.
The beam power output by solid prism retroreflectors may oscillate around an average value as the angle of incidence (AOI) varies. This is due to a multiple-beam interference effect that can occur when the coherence length of the light source is at least twice the optical path length through the retroreflector.
When the front face of a solid retroreflector has an anti-reflective coating, oscillation amplitudes for all AOIs are substantially reduced. Hollow metal-coated retroreflectors provide output beams whose power is approximately independent of AOI.
Beam Path These corner-cube retroreflectors provide an output beam that travels in a direction parallel and opposite to the incident beam. Figure 11 shows one beam path.
The AOI is determined using a reference axis normal to the front face of the retroreflector. This axis passes through the vertex and is equidistant from the three back faces.
Reflections from the Front Face As illustrated in Figure 12, light can make multiple passes through a solid prism retroreflector, depending on whether the light reflects from or is transmitted through interfaces between the front face and the surrounding medium.
When a glass retroreflector is surrounded by air, ~96% of the light is in the primary output beam, which makes a single pass through the retroreflector, and ~0.16% is in the beam that completes an additional round trip. In this work, light making additional round trips had negligible intensity.
Conditions for Interference Since the output of solid prism retroreflectors consists of beams that have travelled different optical path lengths, they will interfere if:
The beams overlap, which is more likely when the AOI of the incident beam is near 0° and the output is measured closer to the retroreflector. At larger distances, the beam deviation specified for the retroreflector and the AOI will more widely separate the first- and third-pass beams.
The coherence length of the source is longer than the difference in path length between the primary beam and the overlapping beam that has made more than one pass through the retroreflector.
Figure 14: Output power as a function of AOI differed depending on the type of corner-cube retroreflector. Data from measurements, made as described in Figure 13, were normalized to the same scale, and traces were vertically shifted as a visual aid. Oscillation amplitude was strongly suppressed when the front face was AR-coated (PS975-C). Oscillations were not observed for the hollow retroreflector (HRR201-M01).
Figure 13: The power output by a TIR solid prism retroreflector (PS975M) was measured as a function of AOI. The incident beam was provided by a DBR1064S 1064 nm laser source, whose coherence length was several meters. The largest-amplitude oscillations resulted around 0° AOI, where the first- and third-pass beams overlapped. The 1/e2 beam diameters did not overlap for AOIs larger than ±1° at a distance of 30 cm from the front face of the retroreflector.
Corner-Cube Retroreflectors Compared The variation of output power with small AOI was compared for four different types of corner-cube retroreflectors: a PS975M TIR solid prism retroreflector, a PS975M-M01B backside-gold-coated solid prism retroreflector, a PS975M-C TIR solid prism retroreflector with an antireflective-coated front face, and a HRR201-M01 that has a hollow construction. The input source was a DBR1064S 1064 nm laser diode with a coherence length of several meters, and the power detector was placed 30 cm from the front face of the retroreflectors. The beam size was small enough to ensure that each reflection occurred from a single face.
Figure 131 plots the normalized measurements made for the TIR solid prism retroreflector. As the AOI increased, the centers of the first- and third-pass beams shifted away from one another. At AOIs greater than around ±1°, the beams' 1/e2 diameters no longer overlapped. This resulted in the oscillation amplitude decreasing with AOI. The range of AOIs over which oscillations were significant would increase if the detector were located closer to the front face.
Figure 14 plots the trace from Figure 13, as well as traces measured for the other three retroreflectors, on the same scale but vertically shifted as a visual aid. These results indicate that an antireflective-coated front face suppresses power oscillations in beams output by solid prism retroreflectors. The power output by hollow retroreflectors does not oscillate, since there is no material boundary at the front face.