Modal decomposition of fiber modes based on direct far-field measurements at two different distances with a multi-variable optimization algorithm.

We present a novel method for modal decomposition of a composite beam guided by a large-mode-area fiber by means of direct far-field pattern measurements with a multi-variable optimization algorithm. For reconstructing far-field patterns, we use finite-number bases of Hermite Gaussian modes that can be converted from all the guided modes in the given fiber and exploit a stochastic parallel gradient descent (SPGD)-based multi-variable optimization algorithm equipped with the D4σ technique in order for completing the modal decomposition with compensating the centroid mismatch between the measured and reconstructed beams. We measure the beam intensity profiles at two different distances, which justifies the uniqueness of the solution obtained by the SPGD algorithm. We verify the feasibility and effectiveness of the proposed method both numerically and experimentally. We have found that the fractional error tolerance in terms of the beam intensity overlap could be maintained below 1 × 10-7 and 3.5 × 10-3 in the numerical and experimental demonstrations, respectively. As the modal decomposition is made uniquely and reliably, such a level of the error tolerance could be maintained even for a beam intensity profile measured at a farther distance.

Metallic Fresnel zone plate implemented on an optical fiber facet for super-variable focusing of light.

We propose and investigate a metallic Fresnel zone plate (FZP/MFZP) implemented on a silver-coated optical fiber facet for super-variable focusing of light, the focal point of which can be drastically relocated by varying the wavelength of the incident light. We numerically show that when its nominal focal length is set to 20 µm at 550 nm, its effective focal length can be tuned by ~13.7 µm for 300-nm change in the visible wavelength range. This tuning sensitivity is over 20 times higher than that of a conventional silica-based spherical lens. Even with such high tuning sensitivity with respect to the incident wavelength change, the effective beam radius at the focal point is preserved nearly unchanged, irrespective of the incident wavelength. Then, we fabricate the proposed device, exploiting electron- and focused-ion-beam processes, and experimentally verify its super-variable focusing functionality at typical red, green, and blue wavelengths in the visible wavelength range, which is in good agreement with the numerical prediction. Moreover, we propose a novel MFZP structure that primarily exploits the surface-plasmon-polariton-mediated, extra-ordinary transmission effect. For this we make all the openings of an MFZP, which are determined by the fundamental FZP design formula, be partitioned by multi-rings of all-sub-wavelength annular slits, so that the transmission of azimuthally polarized light is inherently prohibited, thereby leading to super-variable and selective focusing of radially polarized light. We design and fabricate a proof-of-principle structure implemented on a gold-coated fused-silica substrate, and verify its novel characteristics both numerically and experimentally, which are mutually in good agreement. We stress that both the MFZP structures proposed here will be very useful for micro-machining, optical trapping, and biomedical sensing, in particular, which invariably seek compact, high-precision, and flexible focusing schemes.