Polarization Field Rotation
...values. NOTE: values less than unity are preceded by 0, i.e. 0.1. Clicking OK redraws the plot with the current parameter values. Clicking Defaults resets the program defaults. Clicking Cancel exits the program. Display The Plot window displays a graph of intensity on the slow axis (in dB) for three wavelengths (1.5 microns = orange; 1.5 microns - Wavelength Range = green; 1.5 microns + Wavelength Range = violet) vs. distance. Parameters Input Default Value Meaning (refer to Figure 1 above) Select Rot/Osc 0/1 0 Chooses simulation mode: 0=Continuous Rotational; 1=Continuous Oscillatory Input angle 0 (radians) Input angle of the plane polarized beam with respect to fast axis in radians. Rotation Max 0.2 (radians) Total rotation of the length of fiber in radians (continuous rotational mode) Period 5 (mm) Period of oscillation of the fiber for an alternating rotation; Rotation Max is taken as the amplitude of the oscillation. Wavelength Range 0.01 (microns) Three wavelengths are determined by this range centered at 1.5 microns. Resolution 500 (data points) Number of slices that determine resolution of the output. Beat Length 2 (mm) Beat length of the fiber. The defaults illustrate a beam launched on the fast axis of a fiber continuously rotated by 0.2 radians. The beat length is 2 mm with a wavelength range of 0.01 (plotted are wavelengths: 1.49 microns, 1.5 microns, and 1.51 microns). The polarization isolation is determined by the light on the slow axis and can be seen to vary in sync with the beat length, becoming -52 dB at the half beat positions. $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Polarization maintaining (PM) fiber has orthogonal slow and fast axes with substantially different propagation constants. The common method of fabrication is by inclusion of stress members to cause stress induced birefringence. Plane polarized light launched at a random orientation into PM fiber will be resolved into components along each axis and these components will propagate at different rates. The result is a repetitive phase difference of 2which causes the light to beat from plane1-elliptical-circular-elliptical-plane2--- plane 1. This occurs over typically 1 to 2 mm of fiber which is termed the beat length. There is very little coupling between the polarization modes as their propagation constants are substantially different. Light launched on one axis therefore remains in that axis, unless there is some stress or thermally induced disturbance, that causes a local shift in axes orientation that is misaligned with the incident plane polarized beam. Polarization Mode Dispersion In a real fiber residual birefringence from the manufacturing process and that induced by bending and thermal effects creates differing optical axes that generally correspond to the maximum and minimum of the refractive index profiles across the diameter of the fiber. Such axes are usually orthogonal due to the mechanical stress distribution and have different propagation constants. These axes can be thought of as corresponding to the LP polarization modes or principal states of polarization. Plane polarized light propagating along the fiber will be resolved into components in these axes and as they propagate at different speeds, phase differences are created resulting in elliptically polarized light. The sum of all phase change mechanisms along a fiber is the measure of polarization mode dispersion. The following references are a representative sample of literature describing PMD and its measurement. Polarization Isolation and Cross Coupling Single Devices Cross coupling is defined as the coupling of light from one axis to the orthogonal axis and can be expressed as a ratio, either a percentage or in dB (0.01 = 1% =-20dB) It occurs where polarization maintaining fiber has been stressed, modified or processed to form a device such as an end termination. Connector key misalignment to an axis is another cause of cross coupling as plane polarized light would be launched on both axes. The region over which the fiber is supported in any device can result in residual stress-induced birefringence which causes a small amount of cross coupling between the fast and slow axes. In an evanescent wave coupler, made with two fibers, any misalignment of the polarization axes will also contribute to cross coupling. Cascaded Devices Download "Cascade" Interactive Example Program "Cascade" Installation and Program Instructions Mathematical Model Behind "Cascade" Usually, couplers are used with light launched on the slow axis. At each successive device in a chain the cross coupled components that are resolved along the fast axis are summed with respect to phase and amplitude to give resultants. The square of the resultant is the intensity. A set of components in series will therefore have a resultant state of cross coupling at each device that is dependent on the phase difference between the fast and slow axis and the magnitudes of cross coupling for each preceding device, including the input state of polarization. As intensity is the square of amplitude and in coherent light, superposition of waves is performed with respect to amplitude and phase, the final intensity variations can be unexpectedly high, when all the contributing cross coupling components are in phas...