An intuitive approach to structuring the three electric field components of light

Abstract

This paper presents intuitive interpretations of tightly focused beams of light by drawing analogies with two-dimensional electrostatics, magnetostatics and fluid dynamics. We use a Helmholtz decomposition of the transverse electric field components in the transverse plane to introduce generalized radial and azimuthal polarization states. This reveals the interplay between transverse and longitudinal electric field components in a transparent fashion. Our approach yields a comprehensive understanding of tightly focused laser beams, which we illustrate through several insightful examples.

Interference and polarization beating of independent arbitrarily polarized polychromatic optical waves

“…This fact can be used to extract additional information about the field source and propagation medium. Furthermore, significant progress has been recently achieved in structuring the polarization state of optical beams [15][16][17][18][19]. As an example, it has been shown that interference of an optical wave * andriy.shevchenko@aalto.fi with its orthogonally polarized frequency-shifted copy, such as its second harmonic, can result in complex polarization Lissajous curves instead of polarization ellipses and form optical beams with fractional-order angular momenta [15].…”

“…As an example, it has been shown that interference of an optical wave * andriy.shevchenko@aalto.fi with its orthogonally polarized frequency-shifted copy, such as its second harmonic, can result in complex polarization Lissajous curves instead of polarization ellipses and form optical beams with fractional-order angular momenta [15]. Such beams, as well as other optical fields with designed twoand three-dimensional polarization profiles [16][17][18][19], can show a variety of new spatially distributed dynamic polarization and interference effects.…”

Shaping the longitudinal electric field component of light

“…For meeting the second condition we use the same filtering in spatial Fourier space as in. 3,4 The effect is shown in Fig. 1(a-d).…”

“…Let us now return to our equations of motion Eqs. (3)- (4). At this point it is important to notice that E f cannot be arbitrarily prescribed in all three components due to the coupling of different components via Eq.…”

“…The exception arises for the special case of the beam's transverse electric field components being divergence free in the two-dimensional transverse plane; under these circumstances the longitudinal polarization component exactly vanishes despite tight focusing. 3,4 The simplest example for that is azimuthal polarization. 2 Whereas technically this additional electric field component does not actually introduce a new degree of freedom in the sense that all electric and magnetic field components are still fixed if we fix two electric or magnetic field components in a plane, it allows new interesting beams with spatially varying polarization, where all three electric field components are relevant.…”