Birefringent masks that are optimal for generating bottle fields

Abstract

An optical bottle field containing a three-dimensional intensity null at the focal point can be generated by placing a spatially inhomogeneous birefringent mask at the pupil of an aplanatic high-NA focusing system. We derive the optimal birefringence distribution for which a uniformly polarized input beam is converted into a bottle field with the sharpest possible null in intensity. We show that a stress engineered optical (SEO) window, which has a radially varying retardance, followed by a half-wave plate, performs nearly as well as the optimal solution. Experimental results corroborate that an SEO element can be used to generate a bottle field.

Poincaré sphere representation for spatially varying birefringence

“…These results are also relevant to non-imaging applications that use similar configurations. For example, the birefringence distribution in the pupil plane can be tailored such that the focused field forms an optical bottle (S = 0) for circular input polarization [21,22]. The formalism introduced here can also be applied to optimize the polarimetry technique used in [17][18][19].…”

“…Stress-induced birefringence in optical elements can result from their manufacture process or be caused by their mount, and often has undesirable effects on their optical performance [15]. It is worth mentioning, though, that stress can also be tailored to produce birefringence distributions [16] that are useful in polarimetry [17][18][19] or for the generation of beams with interesting polarizations [20][21][22].…”

Birefringent distributions tailored for imaging and other applications

“…For example, simple geometric interpretations in terms of the Poincaré hypersphere were given to both the widening of the PSF and the reduction of the Strehl ratio of imaging systems, due to spatially-varying birefringence of its elements [6]. This formalism has also been used for the design of birefringence distributions that are optimal for different goals, such as the generation of bottle beams [11] and of polarimetric systems [12]. In both cases, the optimal distributions have been found to be extremely similar to the stable birefringence pattern that results from subjecting a glass window to a pressure distribution with trigonal symmetry at the edges [5].…”

“…In both cases, the optimal distributions have been found to be extremely similar to the stable birefringence pattern that results from subjecting a glass window to a pressure distribution with trigonal symmetry at the edges [5]. These so-called stress-engineered optics (SEOs) have been applied already for generating beams with interesting polarization distributions [13], [14], imaging polarimetry [15]- [17] and bottle beam generation [11], and they are currently being considered for applications in microscopy [18].…”

Vector measurement and performance tuning of a terahertz bottle beam

“…In 2017, Vella et al . proposed a generation method of an optical bottle field by placing a stress engineered optical window at the pupil of an aplanatic high numerical aperture focusing system 7 .…”