Creation of ultra-long diffraction limited optical pipe

Abstract

Engineering of highly-focused electromagnetic field has important applications in many areas including microscopic imaging, probing and controlling of particles, laser micromachining and so on. For an incident cylindrically vector beam, the strong focused field can be understood as the reversing of the field radiated by electric or magnetic dipole in the focal volume of a high numerical aperture (NA) objective lens. Inspired by this analogy, here we present a method to create an ultra-long diffraction limited optical pipe in the focal volume through reversing the radiation pattern of a magnetic dipole array. Pairs of infinitesimal magnetic dipole are introduced and placed along the optical axis in the focal volume as an array. Each pair of the magnetic dipole is mirror symmetrical with respect to the focal plane. The required incident vector beam at the pupil plane can be found with the magnetic dipole array radiation pattern. Through reversing the radiation pattern of this magnetic dipole array, a hollow optical pipe with extremely long depth of focus and excellent uniformity can be realized. The number of array elements determines the pipe's length. And the array factor, such as the amplitude, spacing, and initial phase difference of the array's paired elements, also influences the distributions of reconstructed focal volume field and pupil field. From a six-dipole array, an optical pipe with 8λ length (Fig.1 (a)) is created as an example for NA=0.95. The transverse full width of half maximum (FWHM) of the pipe is 0.315λ at the focal plane (Fig.1 (b)) and the pipe width remains almost constant throughout the total focal volume. The field distribution in the pupil plane exhibits six annular zones with varying amplitude and alternating azimuthally polarization pattern in the adjacent zones. This multi-zone azimuthally polarized beam can be focused to the desired pipe through the high-NA lens. In addition, the obtained pipe's width and length can be adjusted by changing the distribution of pupil field that relies on the array factor. We also discussed the pipe's properties under different NAs. In the case of lower NA=0.9, the optical pipe becomes shorter (7λ length) and wider (FWHM width of 0.34λ) while maintaining the pipe's uniformity. This method of synthesizing optical focal field provides a new way to engineer the field in the focal volume. The diffraction limited optical pipe may find applications in optical imaging, optical manipulation of nanoparticles and material processing on the nanometer scale.