Polarization Characterization of LEDs by Stokes Parameters Measurements

Stokes parameters have been measured by using a polarimeter consisting of a rotating phase plate before a fixed polarizer for bullet-shaped red, green and blue LEDs at 3 different directions of 0°, 45° and 90° from the principal axis. The degree of polarization is minimum at the observation angle 0° (observed head-on) for all colors as expected but has non-zero values (1-9%). As for the possible cause for the partial polarization, it is likely to be brought by striae inside the transparent epoxy resin that can be easily visible. Data at observation angle 90° have features common for all colors; the degree of polarization is highest, the long axis azimuth of the polarization ellipse is nearly in the horizontal direction, and the ellipticity is small. These features can be explained as follows. At observation angle 90°, only small fraction of the beam emitted nearly horizontally is detected possibly through multireflection (the plane of incidence is in the vertical plane) inside the top- and bottom-surfaces (in the horizontal direction) of the chip substrate. Since the reflectance for s-polarization (horizontal component) is higher than that for p-polarization, the emerging beam becomes horizontally polarized. The hypotheses that geometrical asymmetry generates polarization is experimentally supported.

On the concept of a filtered bundle

We present the notion of a filtered bundle as a generalization of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more general polynomial transformation laws. The key examples of such bundles include affine bundles and various jet bundles, both of which play fundamental roles in geometric mechanics and classical field theory. We also present the notion of double filtered bundles which provide natural generalizations of double vector bundles and double affine bundles. Furthermore, we show that the linearization of a filtered bundle — which can be seen as a partial polarization of the admissible changes of local coordinates — is well defined.