Sub-diffraction-limited fluorescent patterns by tightly focusing polarized femtosecond vortex beams in a silver-containing glass.

We report that the shape and size of fluorescent patterns can be controlled by the focused laser intensity distribution, which depends on irradiation conditions as well as on the spin and orbital angular momenta being carried by light, inducing the formation of silver cluster patterns in a silver-containing zinc phosphate glass. In particular, we demonstrate that sub-diffraction-limited inner structures of fluorescent patterns can be generated by direct laser writing (DLW) with tightly focused femtosecond laser vortex beams as Laguerre-Gauss modes (LG0l) with linear and left-handed circular polarizations. We believe this technique, further combined with dual-color DLW, can be useful and powerful for developing structured light enabled nanostructures.


Introduction
The properties and applications of optical vortex beams have been extensively investigated because of their potential to various applications, as e.g. optical tweezing or efficient laser ablation [1][2][3][4]. Direct laser writing (DLW) and processing techniques with femtosecond vortex beams have been also demonstrated to overcome limitations of accessible topologies with Gaussian beams [5,6]. Super-resolution optical STED-like lithography has recently led to remarkable nanoscale structuring in polymers [7,8] and to complex artificial architectures as chiral metamaterials [9]. However, it is still challenging to transfer such all-optical approaches in inorganic materials. In addition, even if polarization dependence of tightly focused vortex beams has already been simulated [7] or considered for material ablation [10,11], the role of the polarization state of vortex beams has not yet been investigated in transparent metalcontaining glasses, which is the aim of the present work.
Transparent silver-containing phosphate glasses show outstanding photonic response for tightly focused femtosecond laser pulses. Specifically, it has been reported that threedimensional (3D) localized fluorescent silver clusters as well as third-and second-order nonlinear optical properties can be generated in such materials by multi-pulses with TW/cm 2 peak power level [12][13][14][15][16]. Space-selective precipitation of metallic silver nanoparticles leading to oriented plasmonic metal/dielectric composite architectures has also been demonstrated [17]. Recently, ribbon fibers have also been inscribed in such photosensitive glasses, by keeping its full initial DLW abilities, enlarging thus its applicative potential to fiber sensing [18]. Although a laser-induced response by multi-pulse irradiation is expected to be influenced by both intensity and polarization of the writing light [19][20][21], to date no distinguishable polarization dependence has been observed in the fluorescence patterns in such silver-containing glass samples. Indeed, laser-induced processes seemed to depend only on the magnitude and the distribution of the light intensity. In particular, Laguerre-Gauss(LG)-like vortex beams have been shown to lead to original fluorescent patterns, such as nested double-ring cylinders [6]. Such patterns, produced with a linear polarization, were found to be independent of the sign of the topological charge of the incident vortex beam. However, previous experimental limitations of our setup prevented to address the role of the polarization state and topological charge in a systematic manner, which is now addressed in this work.
Here, we report on fluorescent patterns in a tailored silver-containing zinc phosphate glass obtained by DLW, utilizing high numerical aperture (NA) aplanatic objective lens and vortex beams with various polarization states. In particular, we find that tightly focused femtosecond laser vortex pulses with linear and circular polarizations may generate fluorescent patterns with sub-diffraction-limited inner features while considering the relevant polarizations. Indeed, such patterns show significant differences depending on the considered polarization, which is consistent with the simulated polarization-dependent intensity distribution of the vortex beams in the focal region assuming LG incident light field on the high NA objective. This supports the fact that spin-orbit coupling effects arising in highly non-paraxial light fields, especially the structure of the longitudinal field component, play a prominent role in fine optical structuring of matter. LG beams with l = 0, 1, 2 being the azimuthal index (i.e. the topological charge of the associated optical vortex) and p = 0 the radial index. The quality of the prepared beam is ensured by using a pure phase hologram formed by adding a blazed phase grating pattern to the desired LG phase distribution [Figs. 1(e)-1(h)] [22]. The irradiation duration and transmitted irradiance are controlled by an acousto-optic modulator. A quarter wave plate is introduced for controlling the polarization state of the vortex beam. LG , (g) l 0

Experimental setup
LG , and (h) Our tailored photosensitive glass is a silver-containing zinc phosphate glass with 5% Ag 2 O concentration (mol. %), prepared by a standard glass melting method and polished up to optical quality. The laser beam is focused through the microscope objective lens (MPlan N 50 × , NA 0.75, Olympus). Fluorescent images are obtained by a confocal microscope (TCS SP5, HCX PL APO CS 63 × , NA 1.4, excitation at 405 nm, emission at 440-520 nm, Leica).

Results
The influence of the topological charge of the writing vortex beam is explored by comparing the patterns obtained using linearly polarized l 0 LG beams with l = 0, 1 and 2. Figure  LG beam (number of pulses N = 5 × 10 7 , pulse energy p E = 13 nJ). In contrast, vortex beams l 0 LG and 2 0 LG create unique nested double-ring patterns [Figs. 2(h) and 2(i)], for N = 5 × 10 7 , 34 nJ p E = and 50 nJ , respectively. Note that larger topological charges require larger incident pulse energies, which is associated with a larger spatial extent of the light field and consequently leads to larger inner/outer patterns. LG , (b, e, h) l 0 LG , and (c, f, i) 2 0 LG beams, respectively. Scale bars: 2 μm.
We also investigate the polarization influence of vortex beams on the shape and size of silver cluster distributions with identical intensity distribution at the entrance pupil of the objective lens. Recalling that the azimuthal phase distribution of l 0 LG paraxial beam of the form il e ϕ is associated to an orbital angular momentum per photon lħ directed along the propagation direction, and that its polarization state is associated to a spin-angular momentum per photon of ± ħ along the propagation direction, we have selected the three following settings for the incident collimated light impinging the objective lens: (α) only the orbital angular momentum exists with no spin angular momentum; (β) the spin and orbital angular momenta are parallel, (γ) the spin and orbital angular momenta are anti-parallel [1,23,24]. LG beam with linear (Lin), left-handed circular (LHC), and right-handed circular (RHC) polarizations, which respectively refer to the cases (α, β, γ).  Fig. 3(b) and Fig. 3(c), respectively. In general, the on-axis intensity distributions strongly depend on the strength and distribution of the longitudinal electric field, a well-known fact for highly non-paraxial beams [10,23].
In particular, the LHC-polarized l 0 LG beam has zero longitudinal on-axis electric field component, resulting in zero optical intensity along the optical axis. In contrast, the RHCpolarized l 0 LG beam has significant non-zero on-axis intensity in the focal region. Finally, as the Lin-polarized l 0 LG beam corresponds to a linear combination of the two LHC and RHC polarized l 0 LG beams with equal weights, it leads to an intermediate on-axis intensity distribution compared to those of the LHC and RHC ones. LG beam versus polarization. 3D isointensity surfaces of LG beam for the different irradiation conditions. Figures 4(e) and 4(f) show the typical intensity profile of the fluorescent patterns 'iii' and 'v' of Fig. 4(a), respectively. Figure 4(e) can be well fitted with four Lorentzian functions and their peak distances are estimated to 310 ± 20 nm (inner diameter between peaks 1 and 2) and 2.12 ± 0.01 μm (outer diameter between peaks 0 and 3).
The smallest inner structure of Fig. 4(a) is obtained for 'iii' for E p = 39 nJ and N = 10 7 . Contrarily to 'v', the inner pattern 'iii' is no more transversally resolved since it appears as a single apparent peak, as shown in Figs. 4(a) and 4(f). Therefore, there are two possibilities: either this inner pattern is still a single-ring fluorescent structure (even if not resolved) or it becomes a filled fluorescent pattern. In the first hypothesis, by imposing a four-peak modeling with the same peak width parameters as those of 'v' and by allowing adjustable fitting parameters for peak positions and intensities, one estimates a sub-diffraction dimension of 185 ± 35 nm (inner diameter) and 2.33 ± 0.01 μm (outer diameter). In the hypothesis of a filled fluorescent inner pattern, the smallest inner diameter is estimated for 'iii' to be less than 390 ± 10 (FWHM). Indeed, the observed pattern is expected to be larger than the actual size since the lateral resolution of the confocal microscope was less good while imaging our structures (due to the non-matching refractive index of 1.59 of our glass) than the ideally estimated value of 220 nm by imaging sub-resolution fluorescent beads. A realistic PSF in our glass for which spherical aberrations are not ideally corrected by the imaging oil objective, should typically be 250-290 nm [6]. After a rough Gaussian deconvolution, the real diameter on the inner-structure (while supposing such fluorescent structure is filled) should be down to 260-300 nm (FWHM). Therefore, in both hypotheses, this indicates that the size of the inner fluorescent structure can be significantly smaller than 390 nm. Considering the diameter of focused Gaussian beam, ~1.5 μm under the present experimental configuration, we conclude that that LHC-polarized l 0 LG structured light can generate sub-diffraction limited inner fluorescent patterns in the silver-containing glass. As shown in Fig. 4, the dimensions and intensities of the fluorescent outer-ring patterns obtained by LHC-polarized l 0 LG beams become larger with increasing the number of pulses and/or of the energy per pulse. This is consistent with the previously reported patterns obtained with Gaussian beams [12]. In contrast, the diameter of the inner-ring patterns gets smaller while increasing the irradiation parameters [Figs. 4(a), 4(e) and 4(f)]. Indeed, it becomes smaller by increasing the pulse energy at the same number of pulses since the effective inner diameters of the donut-like focused beams decrease, forcing silver ionization, silver migration and cluster creation to occur closer to the on-axis region. Similarly, cumulative effects by increasing the number of pulses also lead to smaller inner-ring patterns since multi-pulse processes push the net formation of silver clusters towards the regions of lower beam intensities, leading to the collapse of the inner-ring pattern on the on-axis region where the laser intensity is null [6,12,25]. This remarkable collapse is expected to get even stronger for objectives with higher NA, since the on-axis intensity should remain identically null.
It should be emphasized that, till now, only 0.8 μm size fluorescent patterns have been observed by DLW with focused Gaussian beams in such glasses (tightly focusing objective Plan NEO-FLUAR, 100 × , NA 1.3 oil, Zeiss). To reach the later size, laser intensity had to be decreased and the objective NA had to be increased. Besides, a micron-size fluorescent filled ring had also been reported while structuring at the material threshold [12], but such filled pattern was unstable and weak. Thus, present results obtained from LHC-polarized l 0 LG beam irradiation represent the smallest structure dimension (below 390 nm) reported so far in our glasses, which paves the route to sub-diffraction-size fluorescent patterns by means of vortex beams. A notable difference appears for fluorescent patterns produced by RHC-polarized l 0 LG beams [Figs. 5(a)-5(d)]. As shown in Fig. 3, the modeled on-axis laser intensity of RHC