Open Access
Add to BibSonomy
Abstract
The high refractive index of lithium niobate crystal (n = 2.2) and the highly transparent range (300-5000 nm), makes it a perfect material for refractive lenses and other types of micro-optical elements. This material already finds extensive use in waveguides and photonic crystals, however, little work has been done on producing refractive optical components in lithium niobate, presumably due to the challenges associated with its fragility and difficulties in three-dimensional micromachining. In this study, we fabricated high-quality refractive micro-lenses and micro-axicons with low surface roughness (< λvis / 20), with 220 µm diameters and sag heights up to 22 µm in single-crystal LN using focused Xe beam milling. Xe ion beam milling is a flexible and rapid technique allowing realization of complex three-dimensional surface reliefs directly in lithium niobate. We characterized the optical performance of the fabricated elements showing sub-µm focusing capabilities of both the lenses and axicons.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The excellent optical properties of single crystal lithium niobate (LN) make it a perfect material for optics and photonic applications [1–6]. In particular, its large transparent range of 0.35-5 µm and high refractive index of n = 2.2 (comparable to that of diamond, yet significantly more affordable) make it ideal for integration in microfluidic devices for operation in aqueous environments (n = 1.33). Single-crystal LN also has the peculiarity of presenting strong linear and non-linear electro-optical responses [7], for this reason, it found applications in optics and photonics [8–12], e.g., electro-optical modulators, tunable filters, waveguides and wavelength converters. In parallel to the optical properties, LN displays a strong electromechanical coupling (piezoelectricity), therefore those are employed in the generation of surface acoustic waves (SAW) in SAW-based RF communication devices. Recently SAW found a broad range of application in microfluidics [13–15], in atomization [16,17], trapping [18,19], mixing [20,21] and many others. Due to its resistance to most etchants, LN has the reputation of being difficult to use for the realization of photonic micro- and nanostructures. Nevertheless, a variety of micromachining techniques has been successfully applied to fabricate various devices, such as waveguides, fibre optics, photonic crystals and microring resonators. Some of these techniques include Ti in-diffused proton exchange [22], mechanical machining [23,24], wet etching [25,26], and argon plasma sputtering often combined with fluorine-based reactive ion etching [5,27]. These techniques are, however, mainly limited to planar or two-dimensional structure geometries. Even though both femtosecond laser ablation [4,28,29] and focused ion beam (FIB) milling [30–34] are in principle capable of three-dimensional (3D) surface machining, it is surprising, that little work has been reported on the realization of miniaturized refractive lenses and other micro-optical components in LN crystals. FIB milling is a very flexible method for realization of complex surface profiles in practically any material. The method is based on scanning a finely focused beam of accelerated ions (typically Ga) across a substrate and sputtering controllably the substrate material carving out the desired profile with high precision. Recently introduced high-brightness plasma-source FIBs (P-FIBs) allow replacing metallic Ga with noble gas ions, such as Ar or Xe. Although the resolution of P-FIBs is reduced as compared to Ga-FIBs, the available Ar/Xe ions currents can be more than an order of magnitude higher than those available from Ga-FIBs without the loss of resolution. Higher milling currents, with high-quality beam profile, allow speeding up the milling process significantly (up to 50 times). In addition, replacing Ga with noble gas ions eliminates possible optical performance degradation of milled components associated with metallic Ga contamination due to its implantation [35,36]. This study reports, to the best of our knowledge, the first realization of high-quality refractive micro-lenses and micro-axicons with sub-µm focusing properties in single crystal LN. While lenses with spherical shape are useful for light concentration in a focal spot and image formation, axicons have a conical shape and generate non-diffracting Bessel beams with extended depth-of-focus [37]. Micro-axicons may allow miniaturization and find, therefore, their use in applications where their macro counterparts have been proven to be useful (e.g. in optical manipulation, particle trapping and imaging) [38].
2. Experimental
Microlenses and micro-axicons were fabricated on chips diced from single crystal 128° Y-cut (SAW grade) LN double side polished wafers (Precision Micro-Optics). The chips were coated with 400 nm of Al. Prior to milling LN, openings in the Al layer were milled to expose the LN surface. In addition to serving as an optical aperture of the lenses, the Al layer provided conductivity necessary to remove charging effects during the milling. The milling was performed using focused 30 keV beams of Ar or Xe ions at 200 nA current from a ThermoFisher Helios P-FIB Ux-G4 system. The desired surface profiles (spherical or conical) were digitized into 8-bit bitmaps with pixel coordinates corresponding to the position within the lens, and the pixel value (0-255) proportional to the depth of the milled profile. P-FIB milling using Xe was previously shown to generate high-quality microlenses in glass [39]. Here, we followed similar procedures to generate smooth profiles in LN. Comparison between similar devices milled with Ar and Xe ions reveals that, generally, Ar-milling is capable of producing smoother surfaces compared to Xe, albeit at the expense of more than two-fold increase in the milling times. In this study, we concentrate on the components fabricated with Xe beams. We estimated the milling rate experimentally to be 0.5 ± 0.04 µC3/nC when using 30 keV Xe ions. This compares adequately with the value of 0.4 µC3/nC obtained from simulation [40]. The mismatch between the numerical and experimental results can be attributed to uncertainties in the beam current measurement and sputtered volume estimations from SEM images of milled shapes. The milling rate with Xe is two thirds higher compared to Ga (0.3 µC3/nC [34]) due to the significantly higher mass of Xe ions. Furthermore, with high-quality beams available at currents up to 200-500 nA from a P-FIB (compared to 20-65 nA when using Ga-FIB), the milling times of components can be reduced by more than an order of magnitude.
Figure 1 shows both: focusing microlenses with a spherical profile and micro-axicons with conical profiles. The diameter of both components was kept constant at 220 µm, while their sag height (corresponding to the milled depth) varied up to ~22 µm. The surface quality and their profiles were characterized using white light interferometry [Figs. 1(c) and 1(d)]. The measurements reveal very smooth profiles with an average roughness < 20 nm (< λvis / 20) and only minor defects due to redeposition mostly present on the surface around the lens. The curvature of the microlenses matches a perfect sphere even for the lenses with the highest sag height [Figs. 1(c) and 1(e)]. Similarly, the fabricated micro-axicons maintain constant sloped profiles throughout their diameters.
Fig. 1 Micro-optical components milled with Xe beam using a P-FIB. For focusing microlenses and micro-axicons, respectively: (a,b) Scanning electron microscopy (SEM) images with inlet showing magnified image of the component with the highest sag (stage tilt 52°); (c,d) surface profiles of the components with the highest sag measured with a white light optical profilometer; (e,f) Fitted profiles (spherical and linear) to selected components.
The optical performance of the fabricated micro-optical elements was characterized by a beam profiler composed of a microscope with a high NA objective (0.85) and a CCD camera (Andor Zyla 4.2 sCMOS). The selected micro-optical components were illuminated with a laser beam (λ = 475 nm) with the light incident on the flat unpatterned surface of the LN chips. The intensity profile was recorded by collecting the light emerging from the patterned lenses or axicons on the opposite surface of the LN chip with the beam profiler. With a physical pixel size of 6.5 µm and the objective magnification of 40 × the nominal sampling of the image plane is 162.5 nm, allowing oversampling of the imaging resolution (Abbe limit) of the objective of ~280 nm. This enables us to duly characterize the microoptical elements which have lower NAs than the objective in use and generate comparatively larger beamspots. A series of such profiles obtained at different positions from the chips were used to reconstruct the three-dimensional light intensity field downstream of the chip.
3. Lithium niobate microlenses optical characterisation
The cross-section views through the beams formed by few selected LN microlenses are presented in Fig. 2 and the summary of the measurements are shown in Table 1. The beam cross-section of a microlens with a relatively long (0.86 mm) focal distance [Fig. 2(a)], shows a uniform and symmetrical intensity distribution about the focal spot. The measured focal distance and the focal spot at full-width at half-maximum (FWHM) of 1.9 µm are in good agreement with the expected design parameters from ray tracing simulations (Table 1). The numerical aperture (NA) of the lenses is defined as the sine of the half-angle of the cone of light converging into the focus. The Abbe diffraction limit is the theoretical limit of the beam spot size equal to λ/(2NA) with λ being the wavelength. The agreement with the design parameters decreases as the sag height of the lenses increases. At a focal distance of 0.46 mm, the focal spot becomes slightly asymmetric and elongated [Fig. 2(b)]. This effect is even more pronounced for the lenses with shorter focal distances [Figs. 2(e) and 2(f)]. The beam profiles in Figs. 2(b), 2(e) and 2(f) indicate that the lenses are affected by positive spherical aberration (i.e., the peripheral rays are focused stronger). As the lens sag height increases, the radius of curvature of the surface relief is increased (Table 1). As the focal distance is decreased, the lens diameter becomes comparable with the radius of curvature, leading to increased spherical aberrations. The aberration prevents the lenses from reaching the diffraction-limited focusing performance, nevertheless, sub-µm beam spots could be achieved [Figs. 2(d), 2(g) and 2(h)].
Fig. 2 Focal spot characterization of selected lithium niobate microlenses with a diameter of 220 µm. Normalized intensity maps and profile cross-sections, respectively, for a lens with a (a,c) sag height of 6.46 µm and focal distance of 0.86 mm, (b,d) sag height of 10.62 µm and focal distance of 0.46 mm, (e,g) sag height of 14.92 µm and focal distance of 0.33 mm, and (f,h) sag height of 21.46 µm and focal distance of 0.23 mm. The profile cross-sections were taken along points of maximum intensity (denoted by A) and in case of (e,g) and (f,h) also ~10 µm upstream of the maximum intensity point (denoted by B).
Table 1. Summary of the lithium niobate microlenses optical characterization. Due to high aberrations, theoretical estimation of the focal distance of the lens 4 is uncertain
Selected lenses were tested in projection imaging experiments using a Cu TEM (transmission electron microscopy) grid as a test object [Fig. 3(a)]. Due to the short focal distance of the lenses compared with the thickness of the LN chips (0.5 mm), the test object was positioned in front of the patterned surface of microlenses. The Cu grid was illuminated with incoherent light (λ = 625) and projected images were recorded [Figs. 3(b) and 3(c)]. As expected, the microlens with a longer focal distance projects an image with a lower resolution, albeit with lower spherical aberration. It is worth noting that the microlenses in the inverted configuration (light incident on the curved surface and exiting from the flat backside of the chip) perform differently compared with the configuration summarized in Table 1. Thus, according to ray tracing simulations (Zemax OpticsStudio), the microlens 4 (Table 1) forms the focal spot ~10 µm downstream the backside of the chip. By adjusting the lens curvature it is possible to concentrate the light at the very surface of the chip enabling solid-immersion mode of imaging.
Fig. 3 Imaging of a reference sample, (a) Cu TEM grid (SEM image), using (b,c) lithium niobate microlenses with 220 µm diameter and with focal distances of 0.86 mm and 0.23 mm, respectively.
4. Pockel effect and solid-state variable focal length
Lithium niobate is a material with one of the strongest electro-optical effects (Pockel effect), i.e. with a refractive index dependent on the applied electrical field. A microlens or an array of microlenses with patterned electrodes allows realization of adaptive optical elements without moving parts. We attempted to observe focal distance variation of LN microlenses, however, the changes were typically small and within the depth of focus even for very high voltages applied (>2500 V over 0.5 mm of LN). The induced change in the refractive index is, although one of the highest amongst a variety of materials, still relatively small (depending on the crystal cut, up to ~1.5 × 10−4 for 103 V/mm [8]). To achieve even 1% variation in the refractive index, voltages in excess of 70 kV need to be applied over a 0.5 mm thick slab of LN. Even though thinner crystals of LN require reduced voltages to achieve a considerable effect, nevertheless, the required voltages are still prohibitively high for practical applications.
5. Lithium niobate micro-axicons optical characterization
Axicons are optical elements consisting of a conical surface and can be described as rotationally symmetric prisms. The optical performance of an axicon is determined by its radius R, the axicon angle (cone or base angle) α [Fig. 1(f)] and the refractive index of the material. It can be shown that after a ray passing through an axicon is refracted, it intersects the optical axis at an angle β = arcsin(n sin α) – α. The axicon forms a Bessel-like non-diffracting beam with a central spot radius of r0 = (2.4048/kβ), where k = 2π/λ is the wave number. The corresponding FWHM of a Bessel beam is (2.25273/kβ). The beam spot size can be minimized either by increasing the axicon angle α or by using a material with a higher refractive index n. By using lithium niobate (n = 2.2) as the axicon material, the beam spot size can be reduced by a factor of >2.4 compared to the axicon made of glass (n = 1.5) when the geometry is maintained. One of the greatest advantages of an axicon is a considerably extended DOF compared to focusing lenses. The DOF extends from the tip of the axicon and up to the distance of R/tan(β), although the usable DOF containing higher intensity beam is somewhat smaller.
Figure 4 shows intensity maps formed by micro-axicons with a varying sag height with a summary of measurements presented in Table 2. Figures 4(e)-4(h) show zoomed areas around the central beam rod, while Fig. 4(i) shows the beam profile cross-sections with the central peak fit. The measured performance of all the micro-axicons is in very good agreement with the theoretical values (Table 2).
Fig. 4 Optical characterisation of selected lithium niobate micro-axicons with a diameter of 220 µm. (a,b,c,d) Intensity map (log scale) from micro-axicons with sag heights of 6.34 µm, 10.65 µm, 15.16 µm and 21.56 µm, respectively. (e,f,g,h) Intensity maps of the areas of maximal intensity along the optical axis from axicons corresponding to (a,b,c,d). (i) Profile cross-sections of (a-d) denoted as 1-4 (Table 2), respectively.
Table 2. Summary of the lithium niobate micro-axicons optical characterization
The micro-axicon with the highest α of 11.11° generates a rod of light with sub-µm size extending to over >200 µm depth of focus (DOF), see Figs. 4(h)-4(i). The most comparable microlens is able to maintain the DOF over only <5 µm [Fig. 2(f)]. On the other hand, the micro-axicons with reduced cone angles generate light rods with ~1 mm DOF [Figs. 4(e)-4(f)], albeit with reduced resolution. The observed intensity variations and oscillations within the light rods [Figs. 4(e)-4(f)] are consistent with the performance of a classical linear axicon with a hard aperture [38].
6. Conclusion
In this work, we demonstrated, for the first time, the ability to fabricate high-quality micro-optical components (microlenses and micro-axicons) on single-crystal LiNbO3. The fabricated microlenses with 220 µm diameter had sag heights up to 21.2 µm. The microlenses were capable of producing sub-µm focused beam spot, although the intensity profiles and projection imaging indicate that the microlenses are affected by spherical aberrations due to the high curvature of their surface profiles. Similarly, micro-axicons with 220 µm diameter had sag heights of up to 21.6 µm, corresponding to the cone’s base angle of 11.11°. The micro-axicons generate rods of light with the depth of focus exceeding 200 µm for sub-µm beam spots, >400 µm for a micron-sized beam and in excess of 1 mm for larger beam spots. This work is a promising foundation for applications where LN is already in use, for example, it could be advantageous for embedding micro-optics and microfluidics.
Acknowledgement
LiNbO3 dies were provided by A. Fakhouri and A. Nield from Laboratory for Microsystems, Department of Mechanical and Aerospace Engineering, Monash University, Australia. This work was performed in part at the Melbourne Centre for Nanofabrication (MCN) in the Victorian Node of the Australian National Fabrication Facility (ANFF).
References
1. F. Chen, “Photonic guiding structures in lithium niobate crystals produced by energetic ion beams,” J. Appl. Phys. 106(8), 081101 (2009). [CrossRef]
2. G. Poberaj, H. Hu, W. Sohler, and P. Gunter, “Lithium niobate on insulator (LNOI) for micro-photonic devices,” Laser Photonics Rev. 6(4), 488–503 (2012). [CrossRef]
3. M. Bazzan and C. Sada, “Optical waveguides in lithium niobate: Recent developments and applications,” Appl. Phys. Rev. 2(4), 040603 (2015). [CrossRef]
4. J. Wang, F. Bo, S. Wan, W. Li, F. Gao, J. Li, G. Zhang, and J. Xu, “High-Q lithium niobate microdisk resonators on a chip for efficient electro-optic modulation,” Opt. Express 23(18), 23072–23078 (2015). [CrossRef] [PubMed]
5. I. Krasnokutska, J. J. Tambasco, X. Li, and A. Peruzzo, “Ultra-low loss photonic circuits in lithium niobate on insulator,” Opt. Express 26(2), 897–904 (2018). [CrossRef] [PubMed]
6. S. Y. Siew, E. J. H. Cheung, H. Liang, A. Bettiol, N. Toyoda, B. Alshehri, E. Dogheche, and A. J. Danner, “Ultra-low loss ridge waveguides on lithium niobate via argon ion milling and gas clustered ion beam smoothening,” Opt. Express 26(4), 4421–4430 (2018). [CrossRef] [PubMed]
7. R. S. Weis and T. K. Gaylord, “Lithium-Niobate - Summary of Physical-Properties and Crystal-Structure,” Appl. Phys. Adv. Mater. 37, 191–203 (1985).
8. W. Sohler, “Integrated-Optics in LiNbO3,” Thin Solid Films 175, 191–200 (1989). [CrossRef]
9. S. Diziain, R. Geiss, M. Steinert, C. Schmidt, W. K. Chang, S. Fasold, D. Fussel, Y. H. Chen, and T. Pertsch, “Self-suspended micro-resonators patterned in Z-cut lithium niobate membranes,” Opt. Mater. Express 5(9), 2081–2089 (2015). [CrossRef]
10. R. Geiss, J. Brandt, H. Hartung, A. Tunnermann, T. Pertsch, E. B. Kley, and F. Schrempel, “Photonic microstructures in lithium niobate by potassium hydroxide-assisted ion beam-enhanced etching,” J. Vac. Sci. Technol. B 33(1), 010601 (2015). [CrossRef]
11. R. Geiss, S. Saravi, A. Sergeyev, S. Diziain, F. Setzpfandt, F. Schrempel, R. Grange, E. B. Kley, A. Tünnermann, and T. Pertsch, “Fabrication of nanoscale lithium niobate waveguides for second-harmonic generation,” Opt. Lett. 40(12), 2715–2718 (2015). [CrossRef] [PubMed]
12. A. Sergeyev, R. Geiss, A. S. Solntsev, A. A. Sukhorukov, F. Schrempel, T. Pertsch, and R. Grange, “Enhancing Guided Second-Harmonic Light in Lithium Niobate Nanowires,” ACS Photonics 2(6), 687–691 (2015). [CrossRef]
13. M. K. Tan, L. Y. Yeo, and J. R. Friend, “Rapid fluid flow and mixing induced in microchannels using surface acoustic waves,” EPL- Europhys. Lett. 87(4), 47003 (2009). [CrossRef]
14. L. Y. Yeo and J. R. Friend, “Ultrafast microfluidics using surface acoustic waves,” Biomicrofluidics 3(1), 012002 (2009). [CrossRef] [PubMed]
15. J. Friend and L. Y. Yeo, “Microscale acoustofluidics: Microfluidics driven via acoustics and ultrasonics,” Rev. Mod. Phys. 83(2), 647–704 (2011). [CrossRef]
16. J. R. Friend, L. Y. Yeo, D. R. Arifin, and A. Mechler, “Evaporative self-assembly assisted synthesis of polymeric nanoparticles by surface acoustic wave atomization,” Nanotechnology 19(14), 145301 (2008). [CrossRef] [PubMed]
17. D. Ashtiani, H. Venugopal, M. Belousoff, B. Spicer, J. Mak, A. Neild, and A. de Marco, “Delivery of femtolitre droplets using surface acoustic wave based atomisation for cryo-EM grid preparation,” J. Struct. Biol. 203(2), 94–101 (2018). [CrossRef] [PubMed]
18. H. Li, J. R. Friend, and L. Y. Yeo, “Surface acoustic wave concentration of particle and bioparticle suspensions,” Biomed. Microdevices 9(5), 647–656 (2007). [CrossRef] [PubMed]
19. H. Li, J. R. Friend, and L. Y. Yeo, “A scaffold cell seeding method driven by surface acoustic waves,” Biomaterials 28(28), 4098–4104 (2007). [CrossRef] [PubMed]
20. J. Friend, L. Yeo, M. Tan, and R. Shilton, “Concentration and mixing of particles in microdrops driven by focused surface acoustic waves,” IEEE Ultrasonics Symposium, 930–933 (2008). [CrossRef]
21. R. Shilton, M. K. Tan, L. Y. Yeo, and J. R. Friend, “Particle concentration and mixing in microdrops driven by focused surface acoustic waves,” J. Appl. Phys. 104(1), 014910 (2008). [CrossRef]
22. D. Y. Zang and C. S. Tsai, “Single-Mode Wave-Guide Microlenses and Microlens Arrays Fabrication in LiNbO3 Using Titanium Indiffused Proton-Exchange Technique,” Appl. Phys. Lett. 46(8), 703–705 (1985). [CrossRef]
23. R. Takigawa, E. Higurashi, T. Kawanishi, and T. Asano, “Lithium niobate ridged waveguides with smooth vertical sidewalls fabricated by an ultra-precision cutting method,” Opt. Express 22(22), 27733–27738 (2014). [CrossRef] [PubMed]
24. Z. Y. A. Al-Shibaany, Z. J. Choong, D. Huo, J. Hedley, and Z. X. Hu, “CNC Machining of Lithium Niobate for Rapid Prototyping of Sensors,” IEEE Sensors 2015, 442–445 (2015).
25. P. de Nicola, S. Sugliani, G. B. Montanari, A. Menin, P. Vergani, A. Meroni, M. Astolfi, M. Borsetto, G. Consonni, R. Longone, A. Nubile, M. Chiarini, M. Bianconi, and G. G. Bentini, “Fabrication of Smooth Ridge Optical Waveguides in LiNbO3 by Ion Implantation-Assisted Wet Etching,” J. Lightwave Technol. 31(9), 1482–1487 (2013). [CrossRef]
26. S. Sugliani, P. De Nicola, G. B. Montanari, A. Nubile, A. Menin, F. Mancarella, P. Vergani, A. Meroni, M. Astolfi, M. Borsetto, G. Consonni, R. Longone, M. Chiarini, M. Bianconi, and G. G. Bentini, “High quality surface micromachining of LiNbO3 by ion implantation-assisted etching,” Proc. SPIE 8612, 86120E1 (2013).
27. Z. Ren, P. J. Heard, J. M. Marshall, P. A. Thomas, and S. Yu, “Etching characteristics of LiNbO3 in reactive ion etching and inductively coupled plasma,” J. Appl. Phys. 103(3), 034109 (2008). [CrossRef]
28. L. Gui, B. X. Xu, and T. C. Chong, “Microstructure in lithium niobate by use of focused femtosecond laser pulses,” IEEE Photonics Technol. Lett. 16(5), 1337–1339 (2004). [CrossRef]
29. J. M. Lv, Y. Z. Cheng, W. H. Yuan, X. T. Hao, and F. Chen, “Three-dimensional femtosecond laser fabrication of waveguide beam splitters in LiNbO3 crystal,” Opt. Mater. Express 5(6), 1274–1280 (2015). [CrossRef]
30. F. Lacour, N. Courjal, M. P. Bernal, A. Sabac, C. Bainier, and M. Spajer, “Nanostructuring lithium niobate substrates by focused ion beam milling,” Opt. Mater. 27(8), 1421–1425 (2005). [CrossRef]
31. X. J. Li, K. Terabe, H. Hatano, and K. Kitamura, “Nano-domain engineering in LiNbO3 by focused ion beam,” Jpn. J. Appl. Phys. 44(51), L1550–L1552 (2005). [CrossRef]
32. X. F. Xu, S. Yan, J. M. Xue, Y. G. Wang, K. M. Wang, and X. L. Wang, “Investigation of etching two-dimensional microhole lattice array on lithium niobate with focused ion beam for fabricating photonic crystals,” J. Vac. Sci. Technol. B 27(4), 1851–1855 (2009). [CrossRef]
33. G. Y. Si, A. J. Danner, S. L. Teo, E. J. Teo, J. H. Teng, and A. A. Bettiol, “Photonic crystal structures with ultrahigh aspect ratio in lithium niobate fabricated by focused ion beam milling,” J. Vac. Sci. Technol. B 29(2), 021205 (2011). [CrossRef]
34. M. Sridhar, D. K. Maurya, J. R. Friend, and L. Y. Yeo, “Focused ion beam milling of microchannels in lithium niobate,” Biomicrofluidics 6(1), 012819 (2012). [CrossRef] [PubMed]
35. Y. Q. Fu and N. K. A. Bryan, “Investigation of physical properties of quartz after focused ion beam bombardment,” Appl. Phys. B 80(4-5), 581–585 (2005). [CrossRef]
36. M. T. Langridge, D. C. Cox, R. P. Webb, and V. Stolojan, “The fabrication of aspherical microlenses using focused ion-beam techniques,” Micron 57, 56–66 (2014). [CrossRef] [PubMed]
37. B. Chebbi, I. Golub, and P. Breygin, “Characterization of a refractive linear axicon with distant depth of field and no central blocking,” Appl. Opt. 52(35), 8572–8575 (2013). [CrossRef] [PubMed]
38. D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005). [CrossRef]
39. S. Gorelick and A. De Marco, “Fabrication of glass microlenses using focused Xe beam,” Opt. Express 26(10), 13647–13655 (2018). [CrossRef] [PubMed]
40. J. F. Ziegler, “Stopping of energetic light ions in elemental matter,” J. Appl. Phys. 85, 1249–1272 (1999).
