1. Introduction

The integration of structures and additional materials at the end-face of optical fibers is currently the subject of great research interest [1]. The development of technology that allows the deposition of complex materials or fabrication of functional and very complex structures at the fiber end-face reveals possibilities for a range of new applications and allows miniaturization of devices, reduction of insertion losses, and easier integration with integrated optical components [1]. The optical fiber end-face has been modified for use in sensing systems (e.g., optical fiber Fabry–Perot interferometers) [2], imaging (e.g., application of the photoacoustic effect in 3D endoscopy) [3], signal processing, optical trapping [4], or optical beam shaping (e.g., by producing a phase mask on the front end of a single-mode optical fiber) [5]. Various types of periodic structures are also being extensively researched. These include 1D or 2D diffraction gratings as well as metamaterials [6]. The use of periodic structures on the optical fiber face allows optical beam forming [7], coupling of light with integrated optics systems [8], formation of plasmonic resonance [9] and surface resonance [10], and filtering of light [11]; it is also useful in sensing applications [12]. There are several techniques for fabricating periodic structures on the facet of an optical fiber, including nanoimprint [7] or nanoimprint with transfer lithography [8], as well as direct write approaches such as focused ion beam milling [9], electron-beam lithography [10], and direct laser writing [13]. Depending on the materials used, there are also numerous methods for materials depositing, for instance, metal evaporation over the mold followed by transfer onto the grating trenches within the nanoimprint method [8], magnetron sputtering of a metal film on the cleaved fiber facet [9], or the fabrication of a specialized gold membrane with a periodic structure, which can be later applied to the fiber end face [11].

Generally, periodic structures are placed on the end-faces of an optical fiber to form surface relief grating, which allows the transformation of the incident fundamental mode of the single-mode fiber (SMF) into various diffraction patterns [14]. However, it is possible to change the grating incidence angle by cleaving the optical fiber or by imprinting the grating at an angle that gives an additional degree of freedom in the modification of the angular position and produces a combination of a prism and diffraction grating, which is referred to as a grating prism or grism in the literature [15].

A grism’s main characteristic is that the dispersion curves of the prism and grating supplement each other [15], which can be used to realize various applications. For example, it is possible to produce a waveguide coupler consisting of a prism and diffraction grating to increase the spectral range of efficient light coupling [16]. Grisms are also used as dispersive elements in slitless spectroscopy [17], where a proper grism design can increase the device resolution. Other exemplary applications include the compression of ultra-short pulses [18] or increasing the sensitivity of optical coherence tomography [19]. Another interesting possibility is to design the grism so that the first-order diffraction propagates along the fiber axis [15].

This study presents the design, fabrication, and experimental characterization of a grism imprinted on an SMF facet for in-line propagation of a specific wavelength. First, we designed the grism structure on a silica SMF fiber by employing polymer resists. This allows the designing of structures for the spectral range of 500–830 nm owing to the relatively low refractive index of such materials. To extend the spectral range to 1300–2000nm, we designed a grism based on direct structurization on the end-face of chalcogenide fibers [13]. Finally, we demonstrate grisms made of task-specific ionic liquids, which have good optical properties. We used a simple nanoimprinting method to fabricate a grism on the end-face of a single-mode optical fiber (SMF-28) and achieved prism apex angles reaching 30–40°. To the best of our knowledge, for the first time we show the possibility of producing grisms on the end-face of the optical fiber that allows inline propagation of 1^st order diffraction of the specific wavelength and its control by prism/grating constructional parameters. We experimentally characterized the far-field distribution of light emanating from the fiber at different wavelengths. We managed to obtain straightforward light propagation of first-order diffraction for different combinations of prism angles and grating periods. Finally, we compared the performance of the three fabricated structures in terms of the diffraction peak position and diffraction efficiency (DE).

2. Structure design

A schematic of the structure in which the first-order diffraction propagates in the direction of the incident light is shown in Fig. 1(a), whereas in Fig. 1(b) and (c), the far-field diffraction pattern at the wavelength of 516 nm and that for supercontinuum is presented.

 

Fig. 1. (a) Grism scheme for in-line propagation: N – grating normal, Λ – period of the grating, α – angle of incidence, m - diffraction order (0, 1, 2), n_grism – refractive index of the grism. Diffraction pattern at the fiber output: (b) 516 nm diode laser source and (c) supercontinuum source (SC). In the case of SC, a cylindrical lens was positioned in front of the fiber to collect the light.

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In-line propagation of a specific wavelength can be achieved by properly adjusting the relationship between the prism angle, prism refractive index, and grating period. After a straightforward modification of the basic grating equation, the relationship can be described as [15]:

 

Fig. 2. (a) Schematic of periodic structures fabricated on the facet of an optical fiber through nanoimprinting and direct structurization of periodic structure using laser or focused ion beam (FIB) micromachining. (b) Dependence of grating constant on wavelength for two different prism angles for in-line propagation of first-order diffraction. Refractive indices of polymer resin nPOLY = 1.57, telluride glass nTE = 1.97, and chalcogenide glass nCH = 2.78.

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The use of materials with higher refractive indices allows the fabrication of grisms with smaller angles. For example, to design a grism with in-line propagation at λ $= 2000\; nm,$ a prism with an apex angle of α = 10° and grating with period of ${\Lambda _{CH}} = 6.47\; \mathrm{\mu}m,\; {\Lambda _{TE}} = 11.87\; \mathrm{\mu}m,\; \textrm{and}\; {\Lambda _{POLY}} = 20.2\; \mathrm{\mu}m$ for chalcogenide, telluride glass, and polymer resin, respectively, is needed. When choosing a grating period, the limitations imposed by the size of the fiber core need to be considered i.e. the grating period should be smaller than core diameter. These limitations can be overcome by attaching a coreless fiber to increase the mode field diameter [14]. It is also worth considering the possibility of fabricating grisms on the faces of multimode fibers. Owing to the very large diameter of the core, the material could be cured by introducing UV light directly into the optical fiber, as presented in [22]. In the case of prism angle of $\alpha = 30$°, the grating periods reduce to ${\Lambda _{POLY}} = 7.02\; \mathrm{\mu}m$, ${\Lambda _{TE}} = 4.12\; \mathrm{\mu}m$, and ${\Lambda _{CH}} = 2.25\; \mathrm{\mu}m$. It should also be noted that fabricating prisms with large apex angles can be technologically complicated.

The crucial parameter of the analyzed structure is the DE, which is related to the grating height. To analyze this parameter, we used the numerical model described in [23], which allows us to calculate the far-field distribution of light discharged from an optical fiber (e.g., SMF-28) and passing through a surface relief grating fabricated on a fiber facet. In the simulation, we assumed that the fabricated grating is rectangular.

In Figs. 3(a)-(c), we show the maps of diffraction peak maxima of the first diffraction orders, as a function of the grating height and period for the polymer GRISM fabricated on the end-face of SMF-28. The calculation was performed for the pairs of Λ and α estimated based on Eq. (1) to obtain in-line propagation for the wavelength: 516, 660, and 830 nm. We assumed that the maximum prism apex angle and the period of the grating are reached α = 45° and Λ = 4 µm, respectively, while the maximum grating height is limited by technological constraints and can reach h_gr= 1 µm. The refractive indices vs. wavelength of the fiber core and cladding (Corning in SMF 28 fiber) and polymer resin was considered in calculation based on the formula presented in [24] and [25], while the fiber core diameter was assumed to be d = 8.2 µm. The highest first-order diffraction intensities are observed at large prism apex angles-small grating pitch pairs. At low grating heights the intensity of first diffraction order is near zero because low grating heights result in a negligible phase change between light passing through the ridge and slot part of the grating. To the specific point, with increasing h_gr, the intensity of the first diffraction order increases. The highest intensities of first diffraction order at wavelengths equal to 516 nm, 660 nm, and 832 nm are observed at grating heights equal to h_gr = 0.420 µm, h_gr = 0.570 µm, and h_gr = 0.805 µm, respectively. In Fig. 3(d)-(f) we showed angular dependences of the far-field intensity distribution for structures with different prism angles and grating pitch calculated for fixed value of grating height equal h_gr= 400 nm. The results reveal the range of prism and grating parameters in which one could expect the maximum intensity of a particular diffraction order. Moreover, on the basis of this calculation, it is easy to evaluate the angular position of individual diffraction orders. It can be observed that as the prism angle increases and the grating period decreases, the separation between the angular positions of the diffraction orders increases. This observation agrees with the analytical assumptions. In Fig. 3(g)-(i) we showed intensity for first m = 1 and adjacent diffraction orders (m = 0 and m = 2) at h_gr= 400 nm. For example, for the structure designed for 516 nm, the first order intensities range from 1 to 0.7 (except Λ = 1.6 µm and α = 36°) and the zero diffraction order intensities range from 0.25 to 0, while for the structure designed for 832 nm, the first order intensities range from 0.9 to 0.4 and the zero order of diffraction from 0.7 to 0.2. In fact at period equal to 3.3 µm the intensity of m = 0 is higher than for m = 1.

 

Fig. 3. Normalized diffraction peak maxima of first diffraction orders as functions of grating height and period for grism made of polymer resin. Color map corresponds to normalized intensity (peak maxima) at λ = 516 nm (a), λ = 660 nm (b) and λ = 832 nm (c). Angular dependences of the far-field intensity distribution for structures with different prism angle and grating pitch calculated for fixed value of grating height equal to 400 nm at λ = 516 nm (d), λ = 660 nm (e) and λ = 832 nm (f). The intensity for first m = 1 (dashed lines shown in fig a-c) and adjacent diffraction orders (m = 0 and m = 2) at the grating height of 400 nm at λ = 516 nm (g), λ = 660 nm (h) and λ = 832 nm (i). The red dot represents structures that were fabricated.

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On the basis of the abovementioned observations, three grism structures made of polymer resin were designed for in-line propagation of the first-order diffraction at three different wavelengths. These three wavelengths (with corresponding periods and prism angles) were λ₁= 514 nm (Λ₁= 1800nm, α₁ = 30°), λ₂= 660 nm (Λ₂ = 1800nm, α₂= 40°), and λ₃= 832 nm (Λ₃ = 3000 nm, α₃= 30°). These structures were fabricated using the nanoimprinting method and are called structures S1, S2, and S3.

Additionally, similar calculations were performed for grisms made of chalcogenide glasses. In the case of the chalcogenide fiber, the core diameter was assumed to be 20 µm, and the refractive indices of the core and cladding were taken from the Sellmeier formula [20].

In the case of grisms made on the facet of the chalcogenide fiber, it is possible to design structures that allow inline propagation of 1^st order diffraction in the wavelength range of 2^nd, and 3^rd telecom window. In Fig. 4(a)-c, we show the maps of diffraction peak maxima of the first diffraction orders, as a function of the grating height and period for chalcogenide glass GRISM. The calculation was performed to obtain in-line propagation of 1^st diffraction order for the wavelength:1310 nm, 1550 nm and 2000nm. We chose these wavelengths because of their applicability in telecommunications. The highest intensities of first diffraction order at wavelengths equal to 1310 nm, 1550 nm, and 2000nm are observed at grating heights equal to h_gr = 0.360 µm, h_gr = 0.366 µm and h_gr = 0.469 µm, respectively. In Fig. 4(d)-(f) we showed intensity for first m = 1 and adjacent diffraction orders (m = 0 and m = 2) at h_gr= 400 nm. Moreover at low values of pitch and larger angles the angular position of m = 0 diffraction order is too high to be observed, which agrees with Eq. (1). Fabricating chalcogenide prisms with large angles may be a challenge, therefore, an alternative solution may be to create a structure with smaller angles, but with grating periods exceeding Λ > 3 µm. In this case, intensities of 1^st diffraction order decrease in comparison to its maximum value, however, is still highest than the intensity of m = 0 and m = 2 diffraction order.

 

Fig. 4. Normalized diffraction peak maxima of first diffraction orders as functions of grating height and period for chalcogenide glasses. Color map corresponds to normalized intensity (peak maxima) for $\lambda = 1310\; \textrm{nm}$ (a) $\lambda = 1550\; \textrm{nm}$ (b) and $\lambda = 2000\; \textrm{nm}$ (c). The intensity for first m = 1 (dashed lines shown in fig a-c) and adjacent diffraction orders (m = 0 and m = 2) at grating height equal 400 nm at λ = 1310 nm (d), λ = 1550 nm (e) and λ = 2000nm (f).

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3. Fabrication

To obtain a prism with apex angles of the order of 30–40°, we decided to use polymer resin based on ionic liquids (ILs), which have attracted increasing interest [26]. The main advantage of this group of materials is the chemical tunability, which owing to the possibility of synthesizing numerous combinations of anions and cations in the ILs [27]. These various combinations have resulted in the so-called task-specific ILs synthesized for specific applications [28]. In our study, we used a vinylbenzyl-based IL, N,N,N-triethyl-N-(4-vinylbenzyl) ammoniumbis trifluoromethanesulfonyl) amide, with propylene glycol. For grism fabrication using the nanoimprint method, the material was designed to maintain the liquid state and be UV curable. It has very good optical properties, namely, low losses in the VIS and near-infrared range as well as good thermal stability [25]. Moreover, it has good adhesion to silica glass.

The grism structures on the fiber end-face were fabricated using the imprint method. A setup was prepared, which consisted of a fiber holder, XYZ translation stage for controlling the mold position, an optical microscope to control the fabrication process through visual inspection, and upper goniometer for adjusting the imprint angle. In the first step, the SMF-28 fiber was positioned at the intended angle by using a goniometer. Then, by manipulating the XYZ table, the fiber tip was immersed in the IL and applied with a mask made of polydimethylsiloxane. The tip was irradiated by an ultraviolet lamp with central wavelength of 365 nm to solidify the IL. After four irradiation cycles of approximately 100 s each, the tip with the grism was detached. To ensure the hardening of the material, additional exposure was provided after demolding by directly exposing the bottom of the grism structure to 405 nm laser radiation (20 mW) for an additional 2 min. Figure 5(a) depicts the side view of the structure S3 designed for ${\lambda _3} = 832\; \textrm{nm}$.

 

Fig. 5. (a) Microscope photo of the side view of the grism imprinted on the SMF-28 fiber facet. AFM images of fabricated periodic structure on the fiber end-face and reconstructed grating profiles for: Λ = 1.8 µm (b), (d) and Λ = 3 µm (c), (e).

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In order to examine the quality of the produced structures and analyze the characteristics of the diffraction grating, we performed atomic force microscopy (AFM) images of the pattern imprinted on the end-face of a fiber for two different grating periods: ${\mathrm{\Lambda }_1} = 1.8\,\mathrm{\mu}\mathrm{m}$ and ${\mathrm{\Lambda }_2} = \; 3\,\mathrm{\mu}\textrm{m}$. The profiles reveal the sinusoidal shape of grating trenches which may be due to the high viscosity of the ionic liquid, so that the material does not completely fill the mold. The average parameters of the fabricated grating (period and heights) were as follows: ${\mathrm{\Lambda }_{1\; avg}} = 1.83\mathrm1{\mu}\textrm{m}$, h_gr1 = 366 nm and ${\mathrm{\Lambda }_{2\; avg}} = 3.06\; \mathrm{\mu}\textrm{m}$, h_gr2 = 444 nm.

Despite a very simple setup for grism fabrication, we were able to fabricate the prism with an apex angle repeatability of approximately 1.5° after several attempts. In addition, the spread of the obtained angles was checked by recording several gratings with the same period and numerically verifying that they agreed with the observations. The small deviation from the intended prism angle indicates that this parameter can be controlled with relatively high precision during the fabrication. Through atomic force microscopy, we estimated the grating height as 350 nm, whereas the intended height of the soft mold was 400 nm. This effect may be related to the viscosity of the IL and the fact that we avoided using excessive force during the imprinting process by means of the soft mold to protect the fiber output from breaking.

4. Results and discussion

The experimental characterization was performed using the technique for scanning the far-field distribution, described in [29]. We used a photodiode placed 100 mm away from the fiber tip. For the structures S2 and S3, we performed the measurements at the intended wavelengths (i.e., 660 nm and 832 nm, respectively) as well as at longer and shorter wavelengths. In the case of the structure S1, we did not perform measurements for shorter wavelengths owing to the lack of a proper diode laser source. The results are shown in Fig. 6. The data are normalized and presented in the logarithmic scale.

 

Fig. 6. Measured and calculated far-field diffraction distributions for S1 (Λ₁= 1800nm, α₁= 30°): (c),(f); S2 (Λ₂= 1800nm, α₂= 40°): (a),(d) and (g); and S3 (Λ₃= 3000 nm, α₃= 30°)(b),(e) and (h)

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Additionally, to validate our numerical model, we conducted numerical simulations of the far-field intensity distribution. In calculation we assumed that the height of the grating equals 350 nm in all cases. The numerical simulation and experimental results showed relatively good agreement. In particular, the far-field distributions for structures S1 and S3 showed very good agreement between the 1^st and 0^th order DEs. The higher-order DEs differed significantly, which may be related to the deviation of the grating relief shape from the rectangular shape. In the calculations, we assumed a rectangular grating; however, the actual grating has a more trapezoidal shape. In the case of structure S2, it was more difficult to compare the 1^st and 0^th order DEs because of the configurations, as the 0th order was close to the critical angle. Specifically, the light “slides” off the edge of the fabricated structure, which can affect its DE. Secondly, it is difficult to eliminate the higher-order modes of SMF 28 used in the experiment. These issues can be addressed by especially exciting the fundamental mode and using a higher-order-mode stripper.

The measured and simulated angular positions of the diffraction peaks demonstrated comparatively good agreement. For each structure, the difference between the experimental and computational results did not exceed 2°. The largest angular position mismatch (the difference in the angular positions of the 1^st diffraction order was 1.6°) was for the structure S3. Assuming that the grating constant was well reproduced, we estimated that the fabricated prism had an apex angle of approximately 28°.

Special attention should be paid to structure S2. The use of a large prism angle (40°) resulted in a greater separation between the adjacent diffraction peaks than in the case of structures S1 and S3. It is also worth noting that the first-order DE was the highest for this structure, which is in agreement with the results presented in Fig. 3. The use of a large grating period (structure S3) produces a greater number of diffraction peaks and results in a lower first-order DE. Thus, for a certain group of applications, it may be preferable to produce grisms with larger angles but smaller grating constants, despite the fact that large-angle prisms are more difficult to fabricate and more prone to manufacturing inaccuracies.

5. Summary

In this study, we demonstrated the design procedure of a grism attached to the end-face of an optical fiber to propagate the first-order diffraction along the fiber axis. We considered a broad range of wavelengths by properly adjusting the prism apex angle and period of the grating and by selecting the material of the grism. We also optimized the height of the grating to achieve the highest DE for the 1^st diffraction order. The estimation of angle and period for a particular wavelength is very straightforward. However, the optimal grating height needs to be estimated using numerical procedures for each design, as changing the geometrical parameters of the grism or changing the wavelength affects the DE.

We used a nanoimprint method to fabricate a grism on the fiber end-face. Our approach allowed us to fabricate prisms with angles ranging from 0° to 40°, with the largest deviation of 1.5° from the intended angle. We could also control the period of the grating with high precision in the range of 1–3 µm. However, we believe that fabrication of grisms with smaller periods is also achievable.

Finally, we fabricated grism structures with prism apex angles of 30–40° and grating pitches of 1.8–3 µm for wavelengths of 516 nm, 660 nm, and 832 nm. We used a UV-curable IL polymer resin for the fabrication, which is suitable for nanoimprinting and has excellent optical properties.