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Abstract
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.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
How to focus light remains an important issue at all times for a variety of optical applications, including micro-machining [1], optical trapping [2–4], and biomedical sensing [5]. In particular, high flexibility and controllability in determining the beam-waist position of light when focused down, is of great criticality for practical implementation. A traditional approach for varying the position of the beam waist is to move either the location of the focusing lens or the location of the target object. Obviously, such mechanical adjustments cannot help but give rise to relatively large inaccuracy and uncertainty in controlling the resultant focal point. To resolve such an issue, one can consider exploiting an all-optical technique via a clever combination of fiber-optic and metal-optic technologies [6–12], excluding the use of a conventional lens-based focusing apparatus. In fact, fiber-optic technology can bring in a lot of advantages, such as high flexibility, compactness, cost-effectiveness, and abundant availability of efficient fiber-based light sources in both continuous-wave (CW) and pulsed regimes [6–17]. On the other hand, metal-optic technology can also bring in a lot of fascinating features that the conventional optical technology does not offer [18–23], including high flexibility and precision in fabrication as well as super-resolution and ultrashort focusing when distinct characteristics of surface plasmon polaritons (SPPs) are additionally exploited. Recently, optical focusing by means of plasmonic lenses and meta-surfaces has been receiving a considerable amount of research attention. Most of the studies were devoted to reducing the size of the focal spot or diminishing the chromatic aberration, so that various novel optical focusing effects were obtained, such as the capability of generating a focal spot smaller than the diffraction limit (i.e., super-resolution focusing) or flattened chromatic aberration properties [24–26]. However, few studies have attempted to change the focal point, exploiting relatively high chromatic aberration that is often observed in such flat-optical lenses. In fact, we believe that the combination of various fiber-optic and metal-optic technologies offers the practicality of flat-optical features being realized in an all-fiberized platform [6–12].
Building upon our preliminary studies [6,7], we here investigate a metallic Fresnel zone plate (FZP/MFZP) structure [27,28] implemented on a silver-coated optical fiber facet, i.e., a metallic Fresnel-zone-plated optical fiber facet (MFZP-OFF), and verify both numerically and experimentally that it can exhibit a novel super-variable focusing functionality in a very compact, efficient, and flexible form. To the best of our knowledge, there have been no studies analyzing such a structure from a super-variable focusing perspective although a handful of FZP fiber facet structures have been investigated [4,29,30]. We stress that this MFZP-OFF is also capable of maintaining its beam-waist size, irrespective of the wavelength of the incident optical radiation. These novel properties are obtained thanks to the fact that unlike conventional counterparts of spherical or aspherical lenses, the change of its effective focal length is directly dependent on the fractional change of the incident wavelength rather than the chromatic dispersion of the lens material [27,28]. In particular, this type of super-variable focusing functionality will be very useful and effective in optical trapping [2–4], spectrometry [31], and nano-machining applications [1]. We note that although the transmission efficiency of such an FZP device tends to be relatively low in comparison with that of a conventional optical lens, which is limited to approximately 10% at the maximum if it is based on a binary-type amplitude zone plate [32], it may not be a severe issue for some specific applications, such as in bio-medicine [5] or nano-particle manipulation areas [33], which often require substantially low-power focal spots.
Thus, our investigation and discussion on the novel MFZP-OFF scheme are presented in the following order: First, we explain the design principle of an MFZP to be implemented into an MFZP-OFF and its characteristic features in comparison with those of a conventional focusing lens. Second, we analyze the detailed characteristics of an MFZP-OFF designed and fabricated for visible light both numerically and experimentally. Third, we present a further discussion on potential perspectives of the MFZP-OFF scheme into super-variable focusing of radially polarized light [27,34–36] in an SPP regime, for which we carry out a proof-of-principle analysis on an all-sub-wavelength-scaled MFZP implemented on a gold-coated fused-silica substrate both numerically and experimentally. Finally, we summarize and conclude our investigation.
2. Design principle of super-variable focusing of light through an MFZP-OFF
The focal length of a conventional optical lens, such as a spherical or aspherical lens, varies with respect to the wavelength of the incident optical radiation mainly on account of the chromatic dispersion of the given lens material. For example, the focal length of a bi-convex lens is determined via the lens maker’s equation given by [37]
where f is the resultant focal length; R1 and R2 the radii of curvatures of both lens facets; nlens the refractive index of the lens material. In general, the chromatic dispersion of nlens is given in the order of ~10−5/nm [38], so that the variation of focal length with respect to the incident wavelength is relatively very small. In contrast, focusing by an FZP is drastically different from the aforementioned feature of a conventional lens [27,28]. An FZP utilizes multiple concentric annular slits to squeeze down light onto a specific plane. All the annular slits are designed such that all the light paths through them lead to constructive interference at a fixed focal point on the center axis of them, thereby effectively producing a hotspot there. Thus, without loss of generality, the inner and outer radii of the individual annular slit can be determined by the following mathematical formula [27]:where rm denotes the inner radius for an odd integer m or the outer radius for an even integer m; N the total number of the annular slits; α, f0, and λ0 the phase-offset constant, the nominal focal length, and the reference wavelength, respectively. Once all the geometric parameters of the annular slits are determined for a fixed parameter set of f0 and λ0, detuning of the incident wavelength will subsequently lead to a shift of the focal point as illustrated in Fig. 1. For example, elongation of the incident wavelength gives rise to increase of the optical path difference between two adjacent slits (see Δl in Fig. 1) in order for keeping the constructive interference condition at the target point on the center axis. This subsequently leads to a considerable amount of shift of the focal point towards the FZP. From Eq. (2), one can also estimate the change of the focal point with respect to the incident wavelength: If one neglects the second term in the square-root symbol in the right side of Eq. (2), assuming that the focal length is substantially longer than the incident wavelength, the product of the wavelength and the corresponding focal length becomes approximately invariant for a fixed FZP geometry, even when the incident wavelength is substantially detuned to a new wavelength λ, such as λfλ ≈λ0f0. The new focal length fλ for the detuned wavelength λ is now determined byAs a result, an FZP has a characteristic feature that its focal length becomes inversely proportional to the incident wavelength. This property leads to a subsequent feature that the beam radius at the focal point tends to remain nearly unchanged, irrespective of the incident wavelength as the following: Without loss of generality, the minimum beam radius at the focal point is approximately determined by the optical diffraction principle as [37]where k, NA, and R denote the wavenumber of the incident optical radiation, the numerical aperture, and the radius of the clear aperture of the lens, respectively. In fact, combining Eqs. (3) and (4) gives rise to the fact that the beam radius at the focal point of an FZP is preserved approximately invariant, regardless of the detuning of λ. In addition, it is worth noting that an FZP can also give rise to higher-order focal points at f/3, f/5, etc [4], which we do not take into account in our current investigation, mainly because their intensities are substantially low in comparison with that of the fundamental-order focal spot and we are more interested in the super-variable nature of the fundamental-order focal spot.We now consider implementing the MFZP structure discussed so far onto an optical fiber platform, the schematic of which is shown in Fig. 2. For this, we assume the following conditions: The fiber is a standard multi-mode fiber (MMF), which has a step-index core of 50-μm diameter and 0.22 numerical aperture (NA). The incident optical radiation is in the visible wavelength range from 400 to 700 nm, and is approximated by a uniform beam in normal incidence having no specific polarization state for the sake of simplicity, assuming that all the lateral spreads of the annular slits are well within the core region of the MMF. We note that unless the width of slit opening is reduced to a sub-wavelength scale or many peculiar high-order modes are excited in the core, it is not really necessary to take into account the specific modal feature of the MMF and its polarization dependence, because even in an MMF a single mode can be selectively excited and efficiently preserved through the fiber length [13,39]. Notwithstanding, we will take such aspects into consideration more rigorously in Section 4 when investigating sub-wavelength-scaled annular slits. The metal layer put onto the MMF facet is based on silver, and its thickness is 100 nm, which is sufficiently thicker than the skin depth of silver [40]. The detailed material parameters of silver and fused silica, including their refractive indices and extinction coefficients, can be found in Refs. 37 and 38. All the annular-slit parameters are determined based on Eq. (2) up to N = 6 for f0 = 20 μm, λ0 = 550 nm, and α = 0. They are all concentric with the core of the MMF. It is worth noting that we design the MFZP pattern such that a fraction of its central part is blocked. This geometrical choice brings in a considerable advantage in suppressing the inherent optical diffraction from the central aperture, thereby increasing its focusing power, although the overall transmissivity of the MFZP may drop to some degree [32]. The detailed design and corresponding fabrication parameters are summarized in Table 1.
Fig. 2 Schematic of an MFZP-OFF: (a) Perspective view and (b) cross-sectional view of an MFZP-OFF together with the illustration of its operational principle.
Table 1. Design Parameters Of An MFZP-OFF
3. Characteristics of an MFZP-OFF
We first perform numerical simulations to justify the general focusing characteristics of the MZFP-OFF structure designed in the preceding section, relying on the finite-element method (FEM: COMSOL Multiphysics®). Figure 3(a) shows the numerical results of the field-intensity patterns of the transmitted light from the top surface of the MFZP-OFF for incident optical radiations at 473, 527, and 612 nm, respectively, which represent typical visible optical radiations for blue, green and red (RGB) colors to be utilized in our experiment, respectively. All the incidence conditions and simulation parameters are as specified in the preceding section. It is worth noting that the MFZP-OFF is located at the bottom of the illustration and that the region enclosed by a black semi-open cylinder simply means free space above the MFZP-OFF. One can see that it focuses down the incident optical radiation at significantly different locations, depending on the incident wavelength. In fact, the location of the focal point shifts towards the fiber facet as the incident wavelength increases, such that the individual focal points take place at 23.8, 21.0, and 17.6 μm for 473, 527, and 612 nm, respectively.
Fig. 3 Numerical results on the characteristics of the MFZP-OFF: (a) Normalized field-intensity patterns formed above the MFZP-OFF for incident wavelengths of 473, 527 and 612 nm, respectively. (b) Field intensity along the z-axis with respect to the incident wavelength along with the analytical estimation of the locus of the beam waist (dashed line). (c) Beam radius and depth of focus of the fundamental focal spot with respect to the incident wavelength.
It is also worth noting that one can observe some higher-order focal spots formed nearby the top surface of the MFZP-OFF in Fig. 3(a). While the generation of such sub-focal spots is another inherent characteristic of an FZP [4], we note that their intensities are relatively very low in comparison with that of the fundamental focal spot at f, such that their maximal intensities are given by 2.06, 3.73, and 5.91% for RGB radiations, respectively. We also note that they are fully out of the tuning range of the fundamental focal spot, which ranges approximately from 15 to 30 μm, so that their impacts on the super-variable focusing nature of the fundamental focal spot are negligible.
Figure 3(b) shows the field-intensity distribution along the z-axis formed above the MFZP-OFF with respect to the incident wavelength, in which the bright trace represents the locus of the focused light. It is worth noting that the intensity has been integrated and averaged within the range of r ≤ 768 nm that is the average beam radius over the whole visible spectral window. In fact, the distance from the facet of the MFZP-OFF to the effective focal point varies from 28.6 to 14.9 μm for the wavelength range from 400 to 700 nm. As a result, the relative focal-length change per unit wavelength is given by 45.5. We emphasize that this relative change rate is over 20 times higher than the rate that can be obtained with a conventional silica-based lens [38]: In the latter case Eq. (1) indicates that the focal length of a conventional silica-based bi-convex lens can only vary from 20.2 to 19.6 μm for the same spectral detuning range. It is also worth noting that the dashed black line in Fig. 5(b) denotes the analytical result determined by Eq. (3) under the first-order approximation, which is more or less in good agreement with the full numerical result. The yellow dotted line in Fig. 3(c) represents the change of the beam radius at the focal point with respect to the incident wavelength. As expected from the preceding discussion with Eq. (4), one can readily see that the beam radius is well maintained, regardless of the incident wavelength that varies in the whole visible spectral range. The mean beam radius averaged out over the whole visible spectral window is 768 nm with a standard deviation of 14.2 nm, which means the relative change is limited to only 1.84%. The red dotted line in Fig. 3(c) represents the change of the depth of focus (DOF) of the focal spot along the optical axis with respect to the incident wavelength. It is worth noting that the DOF determines the axial resolution of a focusing lens [41]. We note that the DOF is, in general, proportional to λ/NA2 [41], so that it tends to be inversely proportional to wavelength, taking into account the consequence of Eq. (4):
In fact, the simulation results show that the DOF varies inverse-proportionally with respect to wavelength, which is consistent with the diffraction theory [41]. In addition, we note that in the given MFZP structure the maximum transmission efficiencies for the RGB inputs were estimated to be 8.6, 9.0, and 8.9%, respectively, which can be thought to be as normal as a typical binary-type amplitude zone plate [32].Finally, to demonstrate the real performance of the proposed scheme we fabricated an MFZP-OFF as specified in the preceding section, and experimentally analyzed its characteristics as the following. We utilized an electron-beam evaporation system to deposit the flat-cleaved facet of the standard MMF with silver of 100-nm thickness, and exploited a focused ion beam (FIB) milling process [42,43] to implement the designed FZP pattern as specified in Table 1. Figure 4 shows the scanning electron microscope (SEM) image of the processed silver-coated MMF facet. We note that the extra ring patterns located on the left side denote the traces of the pre-process taken for the initial alignment of the FIB system. In fact, these patterns were in the cladding region far enough from the core, so that they had no influence onto the incident optical radiation that was primarily guided in the central core.
Fig. 4 Characterization of the fabricated MFZP-OFF: (a) SEM image of the fabricated MFZP-OFF. (b) Schematic of a microscope system to characterize the super-variable focusing functionality of the fabricated MFZP-OFF.
We characterized the fabricated MFZP-OFF by launching visible light of three different colors (RGB) into the other end of the MMF in normal incidence condition in order to excite the lowest-possible modes in its core, which were obtained by means of applying appropriate bandpass color filters to a supercontinuum source (SC400-2-PP, Fianium), the peak wavelengths of which were 612 (R), 527 (G), 473 (B) nm. In fact, a fiberized supercontinuum laser [15–17] can be an ideal light source for exploiting the super-variable focusing functionality of the MFZP-OFF if one can continually and selectively choose an appropriate spectral band out of it. The variable focal length of the MFZP-OFF was measured using an optical microscope system, which is depicted in Fig. 4(b). Varying the longitudinal location of the MFZP-OFF via controlling the linear stage with a micrometer, on which the MFZP-OFF pigtailed with an MMF was set up, we continually took the images of the output optical radiation from the MFZP-OFF framed at around the focal plane of the optical microscope system.
For example, a set of images taken at different locations (which are distant by approximately 18, 20, and 23 μm from the top surface of the MFZP-OFF) for different color inputs were shown in Fig. 5(a). The corresponding field-intensity distributions along the transverse directions, i.e., along the x and y axes at different longitudinal locations are also shown in Fig. 5(b). From them one can readily see that the RGB colors were focused at z = 18, 20, and 23 μm, respectively. Actually, these measured values are in good agreement with the values obtained via the numerical simulations shown in Fig. 3(a), which correspond to z = 17.6, 21.0, and 23.8 μm, respectively. (It is worth noting that while we also observed the higher-order focal spots as was briefly discussed in the simulation results shown in Fig. 3(a), we do not take them into account in our current investigation.)
Fig. 5 Experimental results on the super-variable focusing functionality of the fabricated MFZP-OFF: (a) Microscope images of the optical radiations at various incidence and distance conditions. (b) The corresponding field-intensity distributions along the transverse directions, i.e., along the x and y axes, at different longitudinal locations.
In Fig. 6 we illustrate the experimental results and the corresponding numerical results at the same time, which were reproduced from the numerical data shown in Fig. 3, incorporating the experimental data points obtained for the RGB lights centered at 612, 527, and 473 nm, respectively. In general, the experimental and numerical results are in good agreement, so that we emphasize that the fabricated MFZP-OFF demonstrated excellent super-variable focusing functionality as designed and predicted by theory.
Fig. 6 Comparison between the numerical results and experimental measurements: (a) Numerical results on the normalized field intensity distributions along the z-axis with respect to the incident wavelength along with the corresponding experimental data points (the dots with error bars). (b) Numerical results on the normalized field-intensity distributions for incident wavelengths of 612, 527 and 473 nm, respectively, along with the corresponding experimental data points (the dots with error bars).
4. Further discussion on an all-sub-wavelength-scaled MFZP
In the preceding section, we have analyzed and verified wavelength-dependent, super-variable focusing characteristics of an MFZP-OFF, in which the widths of the concentric annular slits were presumably set larger than the nominal wavelength of the incident optical radiation λ0. In this case the transmission through the MFZP-OFF tended to be dominated by optical diffraction rather than SPP-mediated radiation, i.e., the extra-ordinary transmission (EOT) via SPPs [23], so that one may not expect a drastic, characteristic enhancement by the EOT effect out of it, e.g., an enhancement in terms of polarization selectivity, in particular. Thus, it is necessary to consider a novel, modified design rule in order for fully exploiting an EOT-based functionality out of it. That is, one makes an MFZP be entirely comprised of sub-wavelength-scaled annular slits, so that its transmission is solely mediated by SPPs [23]. Such an MFZP will bring in significantly distinct characteristics in terms of polarization selectivity, because SPPs are primarily excited in the direction perpendicular to the metal-dielectric boundary (i.e., in the radial direction of the annular slits), which will be the only component that can produce a hotspot at the effective focal point. Thus, it can be utilized for focusing of radially polarized light, which has considerable advantages over the linearly polarized counterpart in a variety of applications, including micro-machining [1], optical trapping [2–4,44], and biomedical sensing [5], thanks to the cylindrical symmetry of its polarization state [34–36]. We, thus, extend our discussion on the application of the MFZP scheme to super-variable focusing of radially polarized light, exploiting the polarization-selective, EOT-effect via an all-sub-wavelength-scaled MFZP, i.e., an SPP-MFZP, in the following.
Before fully investigating the characteristics of the proposed SPP-MFZP structure, we had performed a basic numerical simulation to verify how the transmission of a single, sub-wavelength-scaled annular slit would vary in terms of the relative slit width s/λ, considering two orthogonal polarization states of the incident optical radiation, one polarized in the radial direction and the other polarized in the azimuthal direction. For this we set the numerical parameters as the followings: The incident wavelength was 660 nm, the nominal radius of the annular ring without accounting for its width was 11 μm, and the metal layer was based on 195-nm-thick (~0.3 in terms of the relative thickness t/λ) gold. The numerical simulation result is shown in Fig. 7.
Fig. 7 Transmission of radially and azimuthally polarized light through a single annular slit with respect to its relative slit width.
As expected, one can readily observe a significant polarization-selective characteristic from the sub-wavelength-scalded annular slit, such that the transmission of azimuthally polarized (i.e., parallel-polarized) light becomes drastically reduced once the relative slit width s/λ is < ~0.3, whereas the transmission of radially polarized (i.e., perpendicular-polarized) light does not vary with it significantly [45,46]. It is worth noting that in the cases of the relative slit widths of > ~0.4, the transmission of radially polarized light tends to be slightly lower than that of azimuthally polarized light. This is mainly due to the plasmonic loss incurred by the metal slit surface, because the former can be converted into SPPs by some fractions even in such relatively wide slit widths whereas the latter cannot. Nevertheless, in sufficiently narrow slit conditions (i.e., s/λ < ~0.3), azimuthally polarized light is not allowed to pass it through, suffering extremely high transmission loss, whereas radially polarized light can selectively be transmitted with a good transmission rate.
We further analyzed the characteristics of the proposed SPP-MFZP structure, utilizing a full numerical model, which was based on the application of the novel modification rule into the conventional MFZP, such that all the concentric annular slits were partitioned with sub-slits in sub-wavelength scales, as depicted in Fig. 8(a). We assumed that the SPP-MFZP was implemented on a gold-coated fused-silica substrate and was parameterized for the incident wavelength of 660 nm and the focal length of 20-μm, such that the six original concentric annular slits were determined based on Eq. (2), all of which had as many sub-wavelength-slit partitions of 120-nm opening (~0.18 in terms of s/λ) with a duty ratio of 50% as they can fit in, and the thickness of the gold coating layer was set to 195 nm (~0.3 in terms of t/λ). Figures 8(b) and 8(c) show the corresponding numerical simulation results on its transmission characteristics for radially polarized light and azimuthally polarized light, respectively. One can clearly see that the SPP-MFZP selectively transmits and focuses radially polarized light at z = ~20 μm. The resultant polarization extinction ratio (PER) between radially polarized light and azimuthally polarized light was calculated to be as high as ~24.4 dB. We note that the design parameters were indeed optimized to maximize the focal spot intensity for radially polarized light; however, the resultant intensity was slightly reduced by ~8.1% in comparison with that of the conventional MFZP without having auxiliary sub-wavelength slits.
Fig. 8 Numerical results on the characteristics of the proposed all-sub-wavelength-scaled SPP-MFZP: (a) Schematic of the SPP-MFZP. Normalized field-intensity patterns formed above the SPP-MFZP for incident light at 660 nm for different polarization states: (b) Radially polarized light and (c) azimuthally polarized light.
Based on the numerical design and simulation, we have carried out a proof-of-principle experiment, fabricating and characterizing an SPP-MFZP implemented on a gold-coated fused-silica substrate. It is worth noting that we fabricated it with the same structural parameter set determined for the numerical model discussed above. A SEM image of the fabricated SPP-MFZP is shown in Fig. 9(a). To characterize its transmission and focusing properties, we utilized linearly polarized light as the incident radiation, rotating its principal direction of polarization to be parallel to the x or y axis. Since the SPP-MFZP selectively let the perpendicular-polarization components pass, whereas drastically attenuating the parallel-polarization counterparts, one can readily expect that the transmitted light pattern through the SPP-MFZP measured right after its top surface must be shaped as a “figure of eight”. This is evidently due to the fact that linearly polarized light can always be decomposed into radial and azimuthal components with different ratios depending on its location of radiation in the SPP-MFZP plane. In Fig. 9(b), we illustrate the optical microscope images of the transmitted light patterns obtained just after the top surface of the SPP-MFZP and of the focused hotspots at the focal points for the two different linear polarization states of the incident radiation at 660 nm. We experimentally verified that the fabricated SPP-MFZP functioned as expected by the numerical simulation, such that only the polarization components in the radial direction could efficiently pass it through and be focused on the target focal plane. (Additional images for different incident polarization states can also be viewed in a movie version available in a separate file: Visualization 1.) In addition, we are confident that such an SPP-FZP structure can also be implemented onto a fiber platform without having any big difference from the case of the MFZP-OFF. The only difference is that we have to consider a slight modification of its pattern design, because the lowest fiber mode of radial-polarization state, i.e., TM01 mode, has a ring shaped intensity pattern in the core [14], unlike that of the fundamental fiber mode or a Gaussian beam. It is worth noting that we are currently putting fabrication efforts on the fiberization of the SPP-FZP, so that its detailed characteristics and performances will be reported elsewhere.
Fig. 9 Characterization of the fabricated SPP-MFZP: (a) SEM image of the SPP-MFZP fabricated on a gold-coated fused-silica substrate. (b) Dark-field optical microscope images of the transmitted light at different image planes and for different incident polarization states. Left: for x-polarized incident light. Right: for y-polarized incident light.
5. Conclusion
We have proposed and demonstrated an MFZP implemented on an optical fiber facet (i.e., an MFZP-OFF) that can efficiently focus light within tens of micrometers in free space without relying on conventional optical components. We numerically and experimentally verified that its focal length was super-variable by means of detuning the incident wavelength while the spot size of the focused light was well maintained, irrespective of the incident-wavelength detuning. The numerical result showed that when its nominal focal length was set to 20 μm at 550 nm, its focal length could vary from 28.6 to 14.9 μm as the wavelength of the incident optical radiation was detuned from 400 to 700 nm, so that the relative focal-length change per unit wavelength was obtained to be 45.5, which is more than 20 times higher than the rate that can be obtained with a conventional silica-based spherical lens. Even with such a large change in the effective focal length with respect to the incident wavelength, the relative change of the focused beam spot size was estimated to be as low as 1.84% over the whole visible wavelength range. We implemented the proposed scheme onto a silver-coated flat-cleaved MMF facet, utilizing electron-beam evaporation and FIB milling processes. We experimentally characterized the fabricated MFZP-OFF particularly at three specific red, green, and blue wavelengths of 612, 527, and 473 nm, and measured that the focal length was variable to 18, 20, and 23 μm with respect to the corresponding RGB wavelengths, which were in good agreement with the numerical results.
We have, moreover, proposed a novel all-subwavelength-scaled MFZP (i.e., an SPP-MFZP) based on the EOT effect via SPPs. We numerically verified that the SPP-MFZP could inherently have substantially high attenuation to azimuthally polarized light, so that it could selectively transmit and focus radially polarized light with a sufficiently high PER (e.g., ~24.4 dB) against azimuthally polarized light. We fabricated the proposed SPP-MFZP on a gold-coated fused-silica substrate and experimentally demonstrated its polarization-selective focusing capability in good agreement with the numerical result.
We see that the proposed schemes, including the MFZP-OFF and the SPP-MFZP, can be usefully exploited for various scientific and engineering applications that require super-variable focusing functionality, such as nano-machining, sensing, and optical trapping. In particular, the proposed schemes combined with multi-wavelength incident radiation can readily produce multi-focal points with different depths in a very compact and precise manner, so that we expect they can make significant impacts on nano-machining and bio-medical research fields.
Funding
National Research Foundation of Korea (NRF) grant funded by the government of Korea (2017R1D1A1B03036201); Ministry of Trade, Industry and Energy (Project no. 10060150); Brain Korea 21 Plus Program.
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