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Abstract
The development of gradient index free-form micro-optic components dedicated to the mid-infrared range is challenging due to the lack of appropriate technology. We propose a method for developing gradient index components for broadband infrared range beyond the transmission window of silicate glass based on nanostructurization using a stack-and-draw fiber drawing technique. A proof-of-concept microlens is developed and verified experimentally in the wavelength range 1.5–4.3 µm. The microlenses are composed of a set of nanorods with a diameter of 940 nm made of a pair of SiO2-PbO-Bi2O3-Ga2O3 based glasses ordered into the preliminary calculated binary pattern. The pattern forms effectively continuous parabolic refractive index distribution for infrared range according to Maxwell-Garnett effective medium model. The development of individual microlenses with a diameter of 118 µm and focal length of 278 µm at the wavelength of 3.75 µm are reported. A large array of 737 microlenses with an individual diameter of 125 µm and focal length of 375 µm is also presented and analyzed.
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1. Introduction
The development of imaging systems, sensors, and beam delivery methods has led to an increased demand for appropriate optical systems. Additional pressure is imposed by the trend for miniaturization and cost reduction [1,2]. Progress is particularly evident in the visible and near-infrared (IR) range, where optical components are mainly fabricated from silica and silicate glasses. However, its strong absorption above 2 µm limits its mid-infrared applications. For longer wavelengths, other materials and often other fabrication technologies must be used. Particular types of optical components are gradient refractive index (GRIN) elements. Their optical functionality is based on a continuous internal change of the refractive index distribution. This change can be either in the axial direction or in the radial direction [3]. A particular type of GRIN elements, which function as lenses, are rod-shaped elements with flat interfaces and a parabolic refractive index profile. This makes them easy to align and integrate with optical fibers, detectors, sources, and other micro-optical elements [4]. In particular, they have been widely used in fiber optic communication systems for fiber coupling [5], optical computers [6] in imaging systems, and optical medical devices [7–9].
There are many methods for GRIN optics fabrication, although they focus primarily on solutions for visible light. The two primary ones commonly used in mass production are ion exchange and chemical vapor deposition (CVD). The main role in the ion exchange method is played by diffusion-controlled by temperature and optionally an external electric field [10–14]. Only a limited group of silicate glasses can be processed this way since only Na and Ag ions can be exchanged this way. Other disadvantages of this method are the limitation of refractive index changes to monotonic functions and a small refractive index gradient achieved, typically on the order of 0.1 per 250 µm [4]. In the CVD method, successive layers of different glasses with various dopants are deposited on a glass tube or capillary [15,16]. The advantage is the possibility of a quite free shaping of the radial refractive index distribution, but the main disadvantage is the fabrication cost and the limited set of materials that can be used that determines limits in optical transmission range.
Less common fabrication methods that have mainly not achieved commercial success are: neutron irradiation, which changes the composition of the glass and thus changes the refractive index [17]; laser or electron beam irradiation [1,18–20]; ion filling where, after heating, the glass separates into phases, one of which is dissolved to form a glass sponge and is then filled with other ions [21]; sol-gel where dopants diffuse through a gel which is then dried and sintered to a glass [22]; thermal poling [3,23]; laser-induced vitrification [19,24]; layering of multiple layers of glass or polymer (lamination) [25,26]; copolymer diffusion [27]; layer diffusion [28,29]; printing [30]; and electrophoresis of surface-modified ZrO2 nanoparticles [31]. These methods were not successfully used for the development of GRIN micro-optical components dedicated to the mid-infrared range.
Only very recently, a few approaches to overcome the limitations were considered and demonstrated to development of new GRIN materials for the midIR has been proposed. The starting point is multi-component chalcogenide glass-ceramic nanocomposite, including compounds based on Ge-As-Se-Pb [19,32] or Ge-Ga-Se [33]. These are partially crystallized glasses in which nanocrystals are suspended in volume, and the higher local concentration of nanocrystals causes a local increase of RI in the volume. Thus, by modifying the spatial concentration of nanocrystals, it is possible to obtain a GRIN material [1,18–20,34,35] with a variable refractive index distribution in 3D with the RI constant contrast up 0.2 for a nanocrystalline glass with RI higher than 3. Modifications of nanocrystal concentration are possible in two directions. First, it is possible to induce nucleation and crystal phase formation using thermal processing or high-power laser pulses [18,20,24,32,34–36]. Secondly, it is also possible to induce local vitrification (remorphization) i.e. to force a phase transition from the crystalline phase back to the glass phase [19,24,32]. This new nanocrystalline glass is potentially attractive for optical applications. However, control of the ceramic phase in chalcogenide glasses also has significant limitations. All processes require accurate temperature control since nanocrystal distribution determines the final RI distribution in the fabricated components. These requirements can limit the flexibility of the RI distributions and the RI gradients [19,33]. One of the proposed solutions is using a pulsed laser for local temperature change and, consequently, the local RI change in the laser-induced vitrification (LIV) technique [19]. However, the lateral feature size of the smallest structures that can be fabricated by this method is currently of the order of 4.5 µm, and the vertical resolution is even lower [19]. Moreover, laser processing requires high power because the laser power necessary for vitrification is in the order of 66.5 W/cm2 [19]. Furthermore, the high absorption of near-infrared radiation by the crystalline phase can lead to glass damage. High absorption also indicates light scattering on the nanocrystals. The disadvantage of the method is also the fabrication time of a single element. Therefore, the method is not suitable for mass production and can be used more for very low scale manufacture since several hours are needed to perform small-scale growth of nanocrystals and then their vitrification in case of the individual component.
In this paper, we demonstrate for the first time the development of GRIN microlenses with a parabolic refractive index distribution dedicated to working in the hyperspectral range from visible to mid-infrared (4.5 um). A stack-and-draw fiber drawing technique was used for nanostructuring GRIN microlens and arrays of GRIN microlenses development. The use of nanostructurisation is an alternative generic approach for developing GRIN optical components [37–39] referred to as nGRIN. Nanostructurisation opens new perspectives for the development of GRIN micro-optics using glasses with broadband mid-infrared transmission. The nanostructuring also allows for a straightforward integration of multiple elements into densely packed array structures [39]. In this method, micro-optical components are composed of a set of nanorods made of a pair of thermally matched glasses ordered into a preliminary calculated binary pattern.
According to Maxwell-Garnett's effective medium model, the binary patterns mimic continuous gradient index distribution for wavelengths much larger than the size of an individual nanorod [40]. It allows fabricating GRIN flat-surface micro-optical components with the arbitrary 2D distribution of the refractive index. The capabilities of this method were previously demonstrated for the visible and near-infrared wavelength range by fabricating parabolic and elliptical GRIN microlenses [37], axicons, diffractive optical elements (DOE), and birefringent artificial glass materials [38]. An essential advantage of this method is the development of components with an extremely high contrast of refractive indices up to 0.4 and a lack of restriction on glass composition. It is possible to use crystallization-free glasses that are thermally matched, and resistant to multiple thermal processing. For the nanostructure composition in this study we applied lead-bismuth oxide glass, which is resistant to crystallization.
2. Selection of glasses with ultra-broadband transmission range
In general, glass, polymers [41–43], ceramic materials [44] as well as glass with ceramic inclusions [1,18–20,34,35] can be considered for GRIN components fabrication. In the infrared range, the choice becomes more and more limited [1]. The operating wavelength range of polymers is fundamentally limited only to the short wavelength IR band up to 1700nm. Strong absorption above 2 µm limits the application range of silica and silicate glasses [45]. Above this band, only some heavy metal oxide, chalcogenide, and fluoride glasses are characterized by high transmission above 2.5 µm [37,46] and can be considered for nanostructured gradient index (nGRIN) lenses development.
There is a growing interest in chalcogenide glasses due to the possibility of changing their chemical composition and thus the possibility of tuning or extending the transmission into the range from visible light to longwave IR (LWIR 8-15 µm) [36,47–49]. The possibility of using chalcogenide glasses to fabricate GRIN elements is based on the above-described ability to locally grow nanocrystals that modify the refractive index locally, However, their applicability to the development of nGRIN fibers is limited due to susceptibility to crystallization during multiple thermal processing. Moreover, these types of glasses are not transparent in the visible range, which introduces difficulties in complex system alignment and limits their applications.
Therefore we consider for development of nGRIN components a heavy metal oxide glasses based on the PbO-Bi2O3-Ga2O3 system. They are characterized by high transmission, up to 8 µm, but showed a high tendency to crystallization [46]. An improvement in thermal stability was achieved by adding mixtures of oxides such as GaO2, SiO2, Tl2O, CdO, Nb2O5, ZnO [50]. As optimal, we consider a modified composition of SiO2-PbO-Bi2O3-Ga2O3 glasses labeled as PBG81 and PBG89. Their chemical compositions are given in Table 1. These glasses were developed in-house for optical fiber drawing and successfully used to develop microstructured fibers [46,50].
Table 1. Chemical compositions of PBG glasses (% mol).
The enhancement of thermal stability and crystallization resistance of the modified glasses resulted in a blue shift of the IR absorption limit with respect to 3-compound PbO-Bi2O3-Ga2O3. The PBG81 and PBG89 glasses are characterized by high transmission in the range from visible light up to 4.5 µm (Fig. 1). The absorption peak of around 3 µm for PBG89 glass is related to the absorption of OH- ions during thermal processing. This can be reduced by maintaining thermal processes in a protective atmosphere. Notably, both glasses are thermally matched. They have similar rheology, i.e., they have very similar viscosity-temperature characteristics and can be drawn on the optical tower at similar temperatures (Fig. 2). Moreover, they show high resistance to crystallization so that they can be thermally processed several times. The temperature that the drawing process is carried out determines the drawn rate and the amount of diffusion. In both cases, for the fabrication of single lenses and lens arrays, the drawing temperature was 630–640°C. The coefficient of thermal expansion is also similar for both glasses and is αPBG81 = 8.21×10−7 K-1 and αPBG89 = 8.12×10−7 K-1 in the range from 20 to 400°C.
Fig. 1. Transmission characteristics of PBG81 and PBG89 glass. The thickness of the measured samples is 2 mm.
Fig. 2. The viscosity characteristics of the PBG81 and PBG89 glasses (Tg – transformation temperature, Tsp – dilatometric softening point, Tz – oval creation, Tk – sphere creation, Tpk – hemisphere creation, Tr – spreading of the sample temperature).
The dispersion properties of the glasses were measured using a Michaelson interferometer in the range 0.5–1.7 µm due to a limit of the spectrometer (Fig. 3). Based on experimental characteristics, the Sellmeier coefficients were determined (Table 2) based on Sellmeier's formula:
Table 2. Sellmeier coefficients for PBG glasses.
3. Lens designing
The basis of the nanostructuring technique is the concept of effective medium, which is described by the Maxwell-Garnett effective medium approximation model (EMA) [51]. In this approach, the physical properties of a dielectric material composed of discrete elements with different physical properties are assumed to be a weighted average of the properties of the individual components in a local neighborhood. In the case of electrical permeability, it can be written as [51]:
where fi determines the concentration and ɛi electrical permeability of the i-th component. The condition is met that: For the material properties to be considered effective, a size criterion must be fulfilled, stating that the size of the individual components must be no greater than λ/2π [51]. This theoretical limitation can be significantly mitigated in real layouts where diffusion occurs. As we have verified experimentally in our previous work on nGRIN lenses, the effective medium condition is fulfilled for individual component sizes comparable to λ/3 [40]. When the size of individual elements increases, diffraction effects start to play a more important role [52] and degrade a lens's performance.The nanostructuring method allows obtaining arbitrary effective refractive index distribution within limits determined by the used glasses. In the case of the nanostructure composed of two considered glasses, the lower limit of the refractive index is determined by the properties of PBG89 glass and the upper one by the PBG81 glass. Equation (2) can be written to determine an effective electrical permeability in the form:
where ɛPBG81 and ɛPBG89 are the electrical permeability of the glasses and f is the local fill factor. The starting point for designing a new structure is defining a target continuous refractive index distribution given by an analytical formula or a two-dimensional distribution map. This distribution is then converted into the corresponding distribution of two glasses. Various numerical methods can be used for this purpose as simulated annealing [53], dithering [54,55], genetic algorithms [56], or direct binary search [57]. In our case, we have used a custom-developed in-house algorithm based on dithering, genetic algorithms, and binary search.For GRIN lenses, in general, the distribution of the refractive index n is a polynomial function with circular symmetry given by the formula [58]:
where n(r) is the refractive index at a normalized distance r from the optical axis (units: mm), n 0 is the index of refraction in the center of the lens, and nr i is the radial index – coefficients of a polynomial. For simplicity, only the first two terms of the expression are used, which corresponds to a lens with a parabolic distribution of the refraction index [59]: where g is a geometrical gradient constant (units: mm-1), determined by the difference between the refractive indices at the center n 0 and periphery n 1 of the lens:4. Lens fabrication
A stack-and-draw technique commonly used to develop photonic crystal fibers is used to fabricate the nanostructured GRIN lenses (nGRIN) [60]. A process flow chart is shown in Fig. 4. The preform is stacked by hand, layer by layer, according to the calculated pattern from (Fig. 4(a)) 15 cm long glass rods with a diameter of 0.3 µm made of PBG81 and PBG89 glasses (Fig. 4(b)). Then, in the next thermal process, the preform is drawn to a diameter of about 0.5 mm on an optical tower. In this way, a hexagonal sub perform is obtained (Fig. 4(c)). When a single GRIN lens is developed, the sub perform is first inserted into a glass capillary made of glass with a lower refractive index (PBG89), and then the third thermal process is used to thinner it to the desired thickness (Fig. 4(d)). The result is an optical fiber whose refraction index on the diagonal cross-section corresponds to the GRIN lens. The fiber prepared in this way is cut into slices and polished on both surfaces, while the thickness of the lens determines its optical properties (Fig. 4(e)) [37]. For the fabrication of GRIN microlens arrays, the hexagonal sub perform is divided into rods about 15 cm long and arranged in the form of a hexagonal or rectangle array, and the arrays are placed in a capillary. Possible larger gaps are filled with rods made of the same glass as the capillary. In the subsequent thermal process, this structure is drawn and thinned to the desired size (Fig. 4(f)) and cut and polished (Fig. 4 (g)) [39]. In both cases, the fabricated optical element consists of subwavelength-sized glass rods.
Fig. 4. Scheme of the modified stack-and-draw technique used for fabrication nanostructured elements: a) design of nGRIN parabolic lens, b) glass rods preparation, c) stacked hexagonal preform of the lens and drawing to hexagonal sub-preform, d) for a single lens, drawing hexagonal sub-preform inside the capillary, e) cut and polished final nGRIN lenses, f) stacking hexagonal sub-preform to the lenses array and drawing, g) cut and polished final arrays of nGRIN lenses.
Using the method described above, GRIN lenses with diameters in the range of 60 to 120 um and arrays consisting of 737 lenses arranged in a 100% filled hexagonal array were fabricated (Fig. 5). Each lens, independently of the diameter, was composed of 12097 rods. The basic geometrical and optical parameters of the sampled lenses and lens arrays are shown in Table 3.
Fig. 5. Example of fabricated structures: a) beam focusing through the nGRIN lens (see Visualization 1) b) nGRIN lens glued to an edge of a glass coverslip, c) SEM image of 80 µm diameter lens consisting of 12097 rods, d) SEM image of an enlarged section of 80 um diameter lens, e) and 140 um diameter lens, f) microscope image of the array of 737 lenses, g) enlarge part of the lenses array.
Table 3. Geometrical and optical parameters for wavelength λ=3.1 µm of the lenses and lens arrays.
5. Measurement systems
The optical properties of the fabricated lenses and lens arrays have been verified by measuring the working distance WD for several wavelengths (Fig. 6). For the 1.55 µm wavelength, a diode laser and a phosphor-enhanced CCD camera (Edmund Optics, 1460-1600 nm Near-Infrared Camera) were used. For wavelengths 2.4, 2.9, 3.6, and 4.3 µm LEDs were used as the source and a Thermosensorik SM 640 camera with InSb detector (range 1.1 - 5.3 µm) as the detector. FWHM measurements of the beam were made in 1 µm increments, which allowed to determine the working distance (Fig. 7).
Fig. 6. Scheme of the setup, sources, and detectors used for working distance measurements of nGRIN lenses.
Fig. 7. Measurement of working distance of lens #L1 based on FWHM analysis using 3.6 µm LED and InSb camera, a) evolution of the FWHM of the beam, b-e) example of the registered beam images.
For the other wavelengths: 2.75, 3.1, and 3.75 µm the NKT SuperK MIR supercontinuum source operating in the range from 900 nm to 4.2 µm was used, together with bandpass filters with FWHM = 500 nm. A single-pixel scanning camera based on an HgCdTe photovoltaic detector (VIGO PVI-4TE-4) operating in the range of 2.2-4.2 µm was used as a detector. The architecture of the single-pixel scanning camera and a scheme of work is shown in Fig. 8. The signal was collected in successive planes spaced 5 um apart by a single-mode Zirconium Fluororide patch fiber (core diameter = 9 µm) placed on a computer-controlled XYZ table. In a particular plane, the displacement was performed with a constant speed in the X direction and a step of 1 µm in the Y direction (Fig. 8(b)). The HgCdTe detector recorded the collected signal. An example of the focal plane for the single lens and the lens array registered by the single-pixel scanning camera and then deblurred using deconvolution [61] is shown in Fig. 8(c).
Fig. 8. Single-pixel scanning camera: view of the measuring system, b) measurement scheme, c) raw measurement result for lenses array after deblurring.
6. Optical properties
The focal length and working distance for all considered nGRIN microlenses measured at wavelength λ=3.1 µm are shown in Fig. 9.
Fig. 9. The dependence of a) focal length and b) working distance on the length and diameter of the lenses made of PBG81 and PBG89 glasses for wavelength λ=3.1 µm. The #L1 and #L2 denote individual lenses, and #LA1 and #LA2 are arrays of the nGRIN lenses. The horizontal, dashed lines indicate a fixed lens diameter is determined at the fiber drawing stage. The focal length and working distance depend in this case only on the lens length L.
Each microlens was examined for several wavelengths. The results are shown in Fig. 10. These prove that both the single lenses and the nGRIN lens arrays operate as predicted.
Fig. 10. Working distance - comparison of experimental results with theoretical predictions for a) lens #L1, b) lens #L2, c) lens array #LA1, d) lens array #LA2.
7. Discussion
The nanostrurisation method described in this paper allows for obtaining a relatively large refractive index contrast Δn = 1.7e-2, which is difficult (irradiation methods [17,18]) or impossible (CVD [4]) to obtain by other methods. Moreover, unlike most other methods, except the vitrification [18] and the crystal-based method [1], nanostructuring enables producing an arbitrary refractive index distribution. It offers high control and reproducibility of the obtained structures by using the well-controlled stack-and-draw technology to fabricate all-glass optical fibers. However, unlike vitrification [18] and nanocrystal-based methods [1], the nanostructurisation technique is adequate for high-volume fabrication. Tens or hundreds of meters of fiber can be obtained from a single preform. This results in obtaining thousands of identical elements with the thickness of a single lens of several hundred micrometers. Moreover, the selection of parameters of the drawing process such as temperature, preform application rate, and drawing velocity allows to change the diameter of the lens, and what follows, the g parameter (the gradient constant). In this way, a whole series of elements differing in their optical parameters can be fabricated in a single process.
8. Conclusions
We have applied the nanostructured medium concept to develop flat-surface gradient index microlenses with the extended transmission in the mid-infrared range up to 5 µm. The microlenses are composed of a discrete set of high and low refractive indices nanorods ordered into a precalculated binary pattern on a hexagonal lattice that mimics parabolic refractive index distribution in gradient index medium. The nGRIN microlens is composed of 12097 rods. We have used a pair of lead-bismuth-gallium glasses with an RI difference of 0.017 at the wavelength of 3 µm to form high and low refractive index nanorods. A standard stack-and-draw technology, commonly used to develop imaging fiber bundles and photonic crystal fibers, has been applied to draw a rod with embedded nanostructured microlenses. The microlenses are further cut and polished into individual components. We have also shown that using the same method the fabrication of nGRIN microlens arrays is possible.
We have developed proof-of-concept nGRIN microlenses with a total diameter of 80 and 118 µm and verified their performance experimentally in the wavelength range between 1.5 µm and 4.3 µm. The tested samples with 1859 and 2743 µm pitch (for λ=3.1 µm) have an effective focal length of 159 and 278 µm respectively that corresponds to the f-number of 1.99 and 2.36 respectively. We verified their performance experimentally and measured a focal spot diameter. The measured M2 = 3.1 proves the good quality of the microlenses. Imaging properties of developed lenses were not verified since the diameter of the lens is small with respect to wavelength and the unstructured pad area of the glass around the microlens introduces high background noise. We also fabricated arrays consisting of 737 nGRIN microlenses. The lens diameters were 125 and 60 µm and the measured effective focal lengths were 375 and 139 µm, respectively, corresponding to f-numbers of 3 and 1.99, respectively. The proposed method of GRIN element manufacture is not limited to the development of microlens with parabolic refractive index distribution. With the same fabrication method and workload, any arbitrary free-form GRIN components as axicon, vortex, or diffractive element can be obtained since only rods have to assemble into the alternative binary pattern, as we have shown previously for near infra-red components [37,38].
The proposed method of microlens manufacture is ready for mass manufacture and flexible for developed GRIN microlenses with various pitch fractions. We develop GRIN microlens in the form of a few hundred meters long fibers in one process using an optical fiber drawing tower. Next, the fiber can be cut into thousands of individual components with a dedicated pitch fraction since a single 0.23 pitch lens length corresponds to 426 µm length (for #L1 lens, for λ=3 µm).
Currently, this technology is limited, with a total diameter of developed microlenses to 125 µm. It is related to the practical limits of manual assembly of the microlens preform with a maximum of 20 thousand rods in the structure. Further increase of assembled rods and hence the total diameter of the fibers is possible if robot assembly of preforms will be applied. Therefore this method is also scalable in size of the components without fundamental limits, although further processing technology modification is needed.
The introduction of gradient index optics microoptical components dedicated to the mid-IR range may significantly impact miniaturized robust integrated optical systems due to their compactness, ease of alignment, and compatibility with fibers optics.
Funding
Horizon 2020 Framework Programme (grant No. 722380 [SUPUVIR]); H2020 Industrial Leadership (644192, 644192 [MIREGAS], EU-H2020-ICT-2014); Fundacja na rzecz Nauki Polskiej (TEAM TECH/2016-1/1); European Regional Development Fund (POIR.04.04.00-00-1C74/16).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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