Polarization mode dispersion
Encyclopedia
Polarization mode dispersion (PMD) is a form of modal dispersion
where two different polarizations of light in a waveguide, which normally travel at the same speed, travel at different speeds due to random imperfections and asymmetries, causing random spreading of optical pulses. Unless it is compensated, which is difficult, this ultimately limits the rate at which data can be transmitted over a fiber.
) that travel at the same speed
. The signal that is transmitted over the fiber is randomly polarized, i.e. a random superposition of these two polarizations, but that would not matter in an ideal fiber because the two polarizations would propagate identically (are degenerate
).
In a realistic fiber, however, there are random imperfections that break the circular symmetry, causing the two polarizations to propagate with different speeds. In this case, the two polarization components of a signal will slowly separate, e.g. causing pulses to spread and overlap. Because the imperfections are random, the pulse spreading effects correspond to a random walk
, and thus have a mean polarization-dependent time-differential Δτ (also called the differential group delay
, or DGD) proportional to the square root of propagation distance L:
DPMD is the PMD parameter of the fiber, typically measured in ps
/√km, a measure of the strength and frequency of the imperfections.
The symmetry-breaking random imperfections fall into several categories. First, there is geometric asymmetry, e.g. slightly elliptical cores. Second, there are stress-induced material birefringence
s, in which the refractive index itself depends on the polarization. Both of these effects can stem from either imperfection in manufacturing (which is never perfect or stress-free) or from thermal and mechanical stresses imposed on the fiber in the field — moreover, the latter stresses generally vary over time.
to compensate for PMD in fiber
s. Essentially, one splits the output of the fiber into two principal polarizations (usually those with dτ dω = 0, i.e. no first-order variation of time-delay with frequency
), and applies a differential delay to bring them back into synch. Because the PMD effects are random and time-dependent, this requires an active device that responds to feedback
over time. Such systems are therefore expensive and complex; combined with the fact that PMD is not yet the limiting factor in the lower data rates still in common use, this means that PMD-compensation systems have seen limited deployment in largescale telecommunications systems.
Another alternative would be to use a polarization maintaining fiber (PM fiber), a fiber whose symmetry is so strongly broken (e.g. a highly elliptical core) that an input polarization along a principal axis is maintained all the way to the output. Since the second polarization is never excited, PMD does not occur. Such fibers currently have practical problems, however, such as higher losses than ordinary optical fiber and higher cost. An extension of this idea is a single-polarization fiber in which only a single polarization state is allowed to propagate along the fiber (the other polarization is not guided and escapes).
Strictly speaking, a circular core is not required in order to have two degenerate polarization states. Rather, one requires a core whose symmetry group admits a two-dimensional irreducible representation
. For example, a square or equilateral-triangle core would also have two equal-speed polarization solutions for the fundamental mode; such general shapes also arise in photonic-crystal fiber
s. Again, any random imperfections that break the symmetry would lead to PMD in such a waveguide.
Modal dispersion
Modal dispersion is a distortion mechanism occurring in multimode fibers and other waveguides, in which the signal is spread in time because the propagation velocity of the optical signal is not the same for all modes...
where two different polarizations of light in a waveguide, which normally travel at the same speed, travel at different speeds due to random imperfections and asymmetries, causing random spreading of optical pulses. Unless it is compensated, which is difficult, this ultimately limits the rate at which data can be transmitted over a fiber.
Overview
In an ideal optical fiber, the core has a perfectly circular cross-section. In this case, the fundamental mode has two orthogonal polarizations (orientations of the electric fieldElectric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
) that travel at the same speed
Group velocity
The group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....
. The signal that is transmitted over the fiber is randomly polarized, i.e. a random superposition of these two polarizations, but that would not matter in an ideal fiber because the two polarizations would propagate identically (are degenerate
Degeneracy (mathematics)
In mathematics, a degenerate case is a limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class....
).
In a realistic fiber, however, there are random imperfections that break the circular symmetry, causing the two polarizations to propagate with different speeds. In this case, the two polarization components of a signal will slowly separate, e.g. causing pulses to spread and overlap. Because the imperfections are random, the pulse spreading effects correspond to a random walk
Random walk
A random walk, sometimes denoted RW, is a mathematical formalisation of a trajectory that consists of taking successive random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the...
, and thus have a mean polarization-dependent time-differential Δτ (also called the differential group delay
Differential group delay
In optics, differential group delay is the difference in propagation time between the two eigenmodes X and Y polarizations. Consider two eigenmodes that are the 0° and 90° linear polarization states. If the state of polarization of the input signal is the linear state at 45° between the two...
, or DGD) proportional to the square root of propagation distance L:
DPMD is the PMD parameter of the fiber, typically measured in ps
Picosecond
A picosecond is 10−12 of a second. That is one trillionth, or one millionth of one millionth of a second, or 0.000 000 000 001 seconds. A picosecond is to one second as one second is to 31,700 years....
/√km, a measure of the strength and frequency of the imperfections.
The symmetry-breaking random imperfections fall into several categories. First, there is geometric asymmetry, e.g. slightly elliptical cores. Second, there are stress-induced material birefringence
Birefringence
Birefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...
s, in which the refractive index itself depends on the polarization. Both of these effects can stem from either imperfection in manufacturing (which is never perfect or stress-free) or from thermal and mechanical stresses imposed on the fiber in the field — moreover, the latter stresses generally vary over time.
Compensating for PMD
A PMD compensation system is a device which uses a polarization controllerPolarization controller
A polarization controller is an optical device which allows one to modify the polarization state of light.- Types and operation :Polarization controllers can be operated without feedback, typically by manual adjustment or by electrical signals from a generator, or with automatic feedback...
to compensate for PMD in fiber
Fiber
Fiber is a class of materials that are continuous filaments or are in discrete elongated pieces, similar to lengths of thread.They are very important in the biology of both plants and animals, for holding tissues together....
s. Essentially, one splits the output of the fiber into two principal polarizations (usually those with dτ dω = 0, i.e. no first-order variation of time-delay with frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
), and applies a differential delay to bring them back into synch. Because the PMD effects are random and time-dependent, this requires an active device that responds to feedback
Feedback
Feedback describes the situation when output from an event or phenomenon in the past will influence an occurrence or occurrences of the same Feedback describes the situation when output from (or information about the result of) an event or phenomenon in the past will influence an occurrence or...
over time. Such systems are therefore expensive and complex; combined with the fact that PMD is not yet the limiting factor in the lower data rates still in common use, this means that PMD-compensation systems have seen limited deployment in largescale telecommunications systems.
Another alternative would be to use a polarization maintaining fiber (PM fiber), a fiber whose symmetry is so strongly broken (e.g. a highly elliptical core) that an input polarization along a principal axis is maintained all the way to the output. Since the second polarization is never excited, PMD does not occur. Such fibers currently have practical problems, however, such as higher losses than ordinary optical fiber and higher cost. An extension of this idea is a single-polarization fiber in which only a single polarization state is allowed to propagate along the fiber (the other polarization is not guided and escapes).
Related phenomena
A related effect is polarization-dependent loss (PDL), in which two polarizations suffer different rates of loss in the fiber due, again, to asymmetries. PDL similarly degrades signal quality.Strictly speaking, a circular core is not required in order to have two degenerate polarization states. Rather, one requires a core whose symmetry group admits a two-dimensional irreducible representation
Group representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication...
. For example, a square or equilateral-triangle core would also have two equal-speed polarization solutions for the fundamental mode; such general shapes also arise in photonic-crystal fiber
Photonic-crystal fiber
Photonic-crystal fiber is a new class of optical fiber based on the properties of photonic crystals. Because of its ability to confine light in hollow cores or with confinement characteristics not possible in conventional optical fiber, PCF is now finding applications in fiber-optic...
s. Again, any random imperfections that break the symmetry would lead to PMD in such a waveguide.