Polarization controller

A polarization controller converts light in an arbitrary, usually unknown polarization state into a chosen one, for example linear polarization aligned to the TE mode of a grating coupler. Standard single-mode fiber does not preserve polarization: bends, twists, stress and temperature give it small, randomly oriented birefringence, so the state at the fiber output differs from the state launched and drifts as the fiber moves or warms. A controller adds a known, adjustable birefringence to undo that change. The manual fiber paddle controller is the common bench form: three paddles, each carrying a few loops of fiber, act as quarter-wave, half-wave and quarter-wave waveplates, and tilting the paddles about the fiber axis turns their optical axes.

Bend birefringence in a fiber loop

A fiber bent to radius $R$ is compressed on the inside of the bend and stretched on the outside, and through the photoelastic effect the two transverse axes acquire different indices. For a fiber of cladding radius $r$,

$$\Delta n = \frac{n^3}{4}\,|p_{11}-p_{12}|\,(1+\nu) \left(\frac{r}{R}\right)^2$$

with the refractive index $n$, the strain-optic coefficients $p_{11}$ and $p_{12}$ and Poisson's ratio $\nu$ of silica. With $n$ = 1.444, $|p_{11}-p_{12}|$ = 0.15 and $\nu$ = 0.17, the prefactor is 0.132, so $\Delta n \approx 0.132\,(r/R)^2$. $N$ loops of length $2\pi R$ each give a retardance of $\lambda/m$ when

$$R = \frac{2\pi \cdot 0.132\, N m\, r^2}{\lambda}.$$

For 125 µm fiber ($r$ = 62.5 µm) at 1550 nm, a quarter-wave plate ($m$ = 4) made of two loops needs $R$ = 16.7 mm, a loop diameter of about 33 mm, where $\Delta n$ is $1.8 \times 10^{-6}$ and each loop contributes one eighth of a wave. Four loops on the same diameter make a half-wave plate. These are elastic-model estimates; coating, loop tension and the exact material constants shift the required diameter, so practical paddles are dimensioned from measurement. Because the retardance in waves scales as $1/\lambda$, a paddle that is a quarter-wave plate at 1550 nm gives about 0.30 wave at 1310 nm.

Three paddles on the Poincaré sphere

On the Poincaré sphere built from the Stokes parameters, a linear retarder rotates the polarization state about an axis in the equatorial plane by its retardance, and tilting the paddle moves that axis around the equator. The first quarter-wave paddle, set at the right angle, brings any elliptical state to the equator, which is linear polarization; the half-wave paddle rotates the linear azimuth to any value; the last quarter-wave paddle converts that linear state into any target ellipse. In the Jones calculus the controller is the product of three retarder matrices with adjustable axes, and this product can represent any lossless polarization transformation.

Other types

In-line controllers clamp the fiber in a squeezer, whose pressure sets the retardance, and rotate the squeezer about the fiber, which sets the axis; together these carry any input state to any output state. Electronic controllers drive several piezoelectric squeezers at alternating angles, liquid-crystal cells, or electro-optic waveplates in lithium niobate, under a feedback loop that holds a monitored signal at its maximum or minimum. Following drift indefinitely, called endless or reset-free control, needs more stages than the minimum, so that one element can be reset while the others hold the state. Coherent receivers now separate the polarizations digitally in the coherent DSP; trackers remain in use for compensating polarization mode dispersion, for polarization-sensitive receivers and in laboratory automation.

Use in the lab

A controller is set by watching a polarization-sensitive signal: the power behind a polarizer, the coupled power of a TE grating coupler, whose dependence on input state can exceed 20 dB, or a polarimeter reading. Motorized controllers that step the input through many states spread over the sphere are the basis of the all-states method for polarization-dependent loss, described in Measuring PER and PDL.

Pitfalls

The fiber after the controller is part of the transformation, so movement or temperature change downstream alters the delivered state; it is taped down and the setting rechecked before each measurement. The setting is correct at one wavelength only, and with a broadband source or a swept laser the output state varies across the band where the downstream fiber is birefringent. Tight loops add bend loss, which grows toward 1625 nm in standard fiber. Where the state must stay fixed without adjustment, polarization-maintaining fiber from the source to the device is the alternative to a controller.

Common questions

How does a fiber paddle polarization controller work?

Loops of bent single-mode fiber are birefringent, so each paddle is a fixed retarder whose axis turns as the paddle is tilted; with quarter-, half- and quarter-wave paddles, the tilt angles map any input state onto any output state.

Why does a polarization controller have three paddles?

A quarter-wave plate first makes the light linear, a half-wave plate rotates it to the required azimuth and a second quarter-wave plate adds the required ellipticity. Three retarders in this quarter-half-quarter arrangement, each with an adjustable axis, are the minimal set that can realize any lossless polarization transformation (Simon and Mukunda 1990).

Why does the polarization keep drifting after it has been set?

The fiber between the controller and the device changes its birefringence with temperature and handling. The setting compensates the fiber only as it was when the setting was made.

References: R. Ulrich, S. C. Rashleigh and W. Eickhoff, "Bending-induced birefringence in single-mode fibers," Optics Letters 5, 273 (1980); H. C. Lefevre, "Single-mode fibre fractional wave devices and polarisation controllers," Electronics Letters 16, 778 (1980); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019); R. Simon and N. Mukunda, "Minimal three-component SU(2) gadget for polarization optics," Physics Letters A 143, 165 (1990); E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1993).