Introduction to Polarization
As light passes through a point in space, the direction and amplitude of the vibrating electric field traces out a path in time. A polarized lightwave signal is represented by electric and magnetic field vectors that lie at right angles to one another in a transverse plane (a plane perpendicular to the direction of travel). Polarization is defined in terms of the pattern traced out in the transverse plane by the electric field vector as a function of time.
Polarization can be classified as linear, elliptical or circular, in them the linear polarization is the simplest. Whichever polarization can be a problem in the fiber optic transmission.
More and more telecommunication and fiber optic measuring systems refer to devices that analyse the interference of two optical waves. The information given by the interferences cannot be used unless the combined amplitude is stable in time, which means, that the waves are in the same state of polarization. In those cases it is necessary to use fibers that transmit a stable state of polarization. And polarization-maintaining fiber was developed to this problem. (The polarization-maintaining fiber will be called PM fiber for short in the following contents.)
What Is PM Fiber?
The polarization of light propagating in the fiber gradually changes in an uncontrolled (and wavelength-dependent) way, which also depends on any bending of the fiber and on its temperature. Specialised fibers are required to achieve optical performances, which are affected by the polarization of the light travelling through the fiber. Many systems such as fiber interferometers and sensors, fiber laser and electro-optic modulators, also suffer from Polarization-Dependent Loss (PDL) that can affect system performance. This problem can be fixed by using a specialty fiber so called PM Fiber.
Principle of PM Fiber
Provided that the polarization of light launched into the fiber is aligned with one of the birefringent axes, this polarization state will be preserved even if the fiber is bent. The physical principle behind this can be understood in terms of coherent mode coupling. The propagation constants of the two polarization modes are different due to the strong birefringence, so that the relative phase of such copropagating modes rapidly drifts away. Therefore, any disturbance along the fiber can effectively couple both modes only if it has a significant spatial Fourier component with a wavenumber which matches the difference of the propagation constants of the two polarization modes. If this difference is large enough, the usual disturbances in the fiber are too slowly varying to do effective mode coupling. Therefore, the principle of PM fiber is to make the difference large enough.
In the most common optical fiber telecommunications applications, PM fiber is used to guide light in a linearly polarised state from one place to another. To achieve this result, several conditions must be met. Input light must be highly polarised to avoid launching both slow and fast axis modes, a condition in which the output polarization state is unpredictable.
The electric field of the input light must be accurately aligned with a principal axis (the slow axis by industry convention) of the fiber for the same reason. If the PM fiber path cable consists of segments of fiber joined by fiber optic connectors or splices, rotational alignment of the mating fibers is critical. In addition, connectors must have been installed on the PM fibers in such a way that internal stresses do not cause the electric field to be projected onto the unintended axis of the fiber.
Types of PM Fibers
Circular PM Fibers
It is possible to introduce circular-birefringence in a fiber so that the two orthogonally polarized modes of the fiber—the so called Circular PM fiber—are clockwise and counter-clockwise circularly polarized. The most common way to achieve circular-birefringence in a round (axially symmetrical) fiber is to twist it to produce a difference between the propagation constants of the clockwise and counterclockwise circularly polarized fundamental modes. Thus, these two circular polarization modes are decoupled. Also, it is possible to conceive externally applied stress whose direction varies azimuthally along the fiber length causing circular-birefringence in the fiber. If a fiber is twisted, a torsional stress is introduced and leads to optical-activity in proportion to the twist.
Circular-birefringence can also be obtained by making the core of a fiber follows a helical path inside the cladding. This makes the propagating light, constrained to move along a helical path, experience an optical rotation. The birefringence achieved is only due to geometrical effects. Such fibers can operate as a single mode, and suffer high losses at high order modes.
Circular PM fiber with Helical-core finds applications in sensing electric current through Faraday effect. The fibers have been fabricated from composite rod and tube preforms, where the helix is formed by spinning the preform during the fiber drawing process.
Linear PM Fibers
There are manily two types of linear PM fibers which are single-polarization type and birefringent fiber type. The single-polarization type is characterized by a large transmission loss difference between the two polarizations of the fundamental mode. And the birefringent fiber type is such that the propagation constants between the two polarizations of the fundamental mode are significantly different. Linear polarization may be maintained using various fiber designs which are reviewed next.
Linear PM Fibers With Side Pits and Side Tunnels
Side-pit fibers incorporate two pits of refractive index less than the cladding index, on each side of the central core. This type of fiber has a W-type index profile along the x-axis and a step-index profile along the y-axis. A side-tunnel fiber is a special case of side-pit structure. In these linear PM fibers, a geometrical anisotropy is introduced in the core to obtain a birefringent fibers.
Linear PM Fibers With Stress Applied Parts
An effective method of introducing high birefringence in optical fibers is through introducing an asymmetric stress with two-fold geometrical symmetry in the core of the fiber. The stress changes the refractive index of the core due to photoelastic effect, seen by the modes polarized along the principal axes of the fiber, and results in birefringence. The required stress is obtained by introducing two identical and isolated Stress Applied Parts (SAPs), positioned in the cladding region on opposite sides of the core. Therefore, no spurious mode is propagated through the SAPs, as long as the refractive index of the SAPs is less than or equal to that of the cladding.
The most common shapes used for the SAPs are: bow-tie shape and circular shape. These fibers are respectively referred to as Bow-tie Fiber and PANDA Fiber. The cross sections of these two types of fibers are shown in the figure below. The modal birefringence introduced by these fibers represents both geometrical and stress-induced birefringences. In the case of a circular-core fiber, the geometrical birefringence is negligibly small. It has been shown that placing the SAPs close to the core improves the birefringence of these fibers, but they must be placed sufficiently close to the core so that the fiber loss is not increased especially that SAPs are doped with materials other than silica. The PANDA fiber has been improved further to achieve high modal birefringence, very low-loss and low cross-talk.
PANDA Fiber (left) and Bow-tie Fiber (right). The built-in stress elements made from a different type of glass are shown with a darker gray tone.
Tips: At present the most popular PM fiber in the industry is the circular PANDA fiber. One advantage of PANDA fiber over most other PM fibers is that the fiber core size and numerical aperture is compatible with regular single mode fiber. This ensures minimum losses in devices using both types of fibers.
Linear PM Fibers With Elliptical Structures
The first proposal on practical low-loss single-polarization fiber was experimentally studied for three fiber structures: elliptical core, elliptical clad, and elliptical jacket fibers. Early research on elliptical-core fibers dealt with the computation of the polarization birefringence. In the first stage, propagation characteristics of rectangular dielectric waveguides were used to estimate birefringence of elliptical-core fibers. In the first experiment with PM fiber, a fiber having a dumbbell-shaped core was fabricated. The beat length can be reduced by increasing the core-cladding refractive index difference. However, the index difference cannot be increased too much due to practical limitations. Increasing the index difference increases the transmission loss, and splicing would become difficult because the core radius must be reduced. Typical values of birefringence for the elliptical core fiber are higher than elliptical clad fiber. However, losses were higher in the elliptical core than losses in the elliptical clad fibers.
Linear PM Fibers With Refractive Index Modulation
One way to increase the bandwidth of single-polarization fiber, which separates the cutoff wavelength of the two orthogonal fundamental modes, is by selecting a refractive-index profile which allows only one polarization state to be in cutoff. High birefringence was achieved by introducing an azimuthal modulation of the refractive index of the inner cladding in a three-layer elliptical fiber. A perturbation approach was employed to analyze the three-layer elliptical fiber, assuming a rectangular-core waveguide as the reference structure. Examination of birefringence in three-layer elliptical fibers demonstrated that a proper azimuthal modulation of the inner cladding index can increase the birefringence and extend the wavelength range for single-polarization operation.
A refractive index profile is called Butterfly profile. It is an asymmetric W profile, consisting of a uniform core, surrounded by a cladding in which the profile has a maximum value of ncl and varies both radially and azimuthally, with maximum depression along the x-axis. This profile has two attributes to realize a single-mode single-polarization operation. First, the profile is not symmetric, which makes the propagation constants of the two orthogonal fundamental modes dissimilar, and secondly, the depression within the cladding ensures that each mode has a cutoff wavelength. The butterfly fiber is weakly guiding, thus modal fields and propagation constants can be determined from solutions of the scalar wave equation. The solutions involve trigonometric and Mathieu functions describing the transverse coordinates dependence in the core and cladding of the fiber. These functions are not orthogonal to one another which requires an infinite set of each to describe the modal fields in the different regions and satisfy the boundary conditions. The geometrical birefringence plots generated vs. the normalized frequency V showed that increasing the asymmetry through the depth of the refractive index depression along the x-axis increases the maximum value of the birefringence and the value of V at which this occurs. The peak value of birefringence is a characteristic of noncircular fibers. The modal birefringence can be increased by introducing anisotropy in the fiber which can be described by attributing different refractive-index profiles to the two polarizations of a mode. The geometric birefringence is smaller than the anisptropic birefringence. However, the depression in the cladding of the butterfly profile gives the two polarizations of fundamental mode cutoff wavelengths, which are separated by a wavelength window in which single-polarization single-mode operation is possible.
Applications of PM Fibers
PM fibers are applied in devices where the polarization state cannot be allowed to drift, e.g. as a result of temperature changes. Examples are fiber interferometers and certain fiber lasers. A disadvantage of using such fibers is that usually an exact alignment of the polarization direction is required, which makes production more cumbersome. Also, propagation losses are higher than for standard fiber, and not all kinds of fibers are easily obtained in polarization-preserving form.
PM fibers are used in special applications, such as in fiber optic sensing, interferometry and quantum key distribution. They are also commonly used in telecommunications for the connection between a source laser and a modulator, since the modulator requires polarized light as input. They are rarely used for long-distance transmission, because PM fiber is expensive and has higher attenuation than single mode fiber.
Requirments for Using PM Fibers
Termination: When PM fibers are terminated with fiber connectors, it is very important that the stress rods line up with the connector, usually in line with the connector key.
Splicing: PM fiber also requires a great deal of care when it is spliced. Not only the X, Y and Z alignment have to be perfect when the fiber is melted together, the rotational alignment must also be perfect, so that the stress rods align exactly.
Another requirement is that the launch conditions at the optical fiber end face must be consistent with the direction of the transverse major axis of the fiber cross section.