Cylindrically polarized (CP) beams [1] find numerous applications in nanoscale optical imaging and manipulation, e.g., stimulated emission depletion (STED) microscopy [2], particle trapping [3], sub-diffraction focussing [4], and excitation of subwavelength plasmonic modes on tapered metallic nanowires (NW) [5]. CP beams can be generated actively using laser intracavity devices [6], or passively using spatial light modulators [7], holographic phase-masks [8], metasurfaces [9], or lenses containing laser-written nanostructures [10]. Such devices can be integrated into existing, typically linearly polarized (LP), laser setups; however, CP beam generating setups are often expensive, narrow-band, and can produce beams of rather poor quality.

CP beams are also general eigenstates of optical fibers [11]; the two lowest higher-order modes (${\mathrm{TM}}_{01}$ and ${\mathrm{T}\mathrm{E}}_{01}$ modes) have no azimuthal intensity variations and thus, completely resemble radially polarized (RP) and azimuthally polarized (AP) states, respectively. However, being higher order modes, they generally coexist with the fundamental ${\mathrm{HE}}_{11}$ mode and the ${\mathrm{HE}}_{21}$ mode. If one of the CP modes can be isolated from the entire set of modes, such a fiber serves as an effective cylindrical polarizer which is flexible and can be easily integrated into photonic circuitry. This principle has been harnessed in a number of experiments demonstrating in-fiber generation of CP beams, although performance is typically inefficient ($\sim 1\%$) [12] or narrow band (40 nm) [13].

Here, we present a novel monolithic step-index fiber with a gold NW in its central core, and demonstrate that it efficiently converts an input LP state into AP beams. The complete device is composed of two sections, as shown in Fig. 1. The first section [Fig. 1(i)] is formed by a cylindrical silica step-index fiber with a ${\mathrm{GeO}}_2$ doped core (radius 2 μm, doping level 9 wt.%) and a central nanochannel (referred to as nanobore) of 550 nm radius. This fiber is fabricated by preparing a centimeter-thick fused silica preform with a ${\mathrm{GeO}}_2$ doped core and a central hole. The preform is thermally drawn at high temperatures. The nanobore diameter is set by the size of the initial hole and the outer diameter, which is monitored during the draw. Its diameter is measured after drawing using scanning electron microscopy (SEM). The empty fiber can support four waveguide modes for $\lambda <735\mathrm{nm}$ (${\mathrm{T}\mathrm{E}}_{01}$, ${\mathrm{TM}}_{01}$, ${\mathrm{HE}}_{11}$, and ${\mathrm{HE}}_{21}$), two of which have very similar field patterns to CP beams. In the second section [Fig. 1(ii)], which actually provides the AP state conversion functionality, a gold NW is included in the central nanohole. This section provides very strong polarization discrimination i.e., the ratio of the attenuation coefficient of the ${\mathrm{T}\mathrm{E}}_{01}$ polarization state to that of all other states is small, since the four supported modes have different overlaps with the lossy metal in the center [Fig. 2(a)]. In this case the modal absorption coefficient $\gamma$ at a wavelength $\lambda$ can be obtained via [14]

 

Fig. 1. Gold NW enhanced step-index fiber device schematic: LP light propagates through the unfilled fiber (i) and couples to the gold-filled fiber modes over a finite transition region (ii a), resulting in AP light at the output due to the loss discrimination between ${\mathrm{T}\mathrm{E}}_{01}$ modes and all other supported modes in region (ii b). This device is then spliced to a commercial single-mode fiber (SMF). Inset: SEM micrograph of a gold-filled nanobore fiber end-face.

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Fig. 2. (a) Calculated axial Poynting vector profiles (normalized log scale) for the supported modes of the gold-filled step index fiber at 600 nm. White arrows are snapshots of the electric field. (b) Absorption coefficient $\gamma$ of the gold-filled fiber modes calculated from the complex eigenvalue equation (solid lines) and from the integral on the right-handed side of Eq. (1) (circles).

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The principle of the transverse electric (TE) mode having lower loss than all other modes in hybrid metal-dielectric waveguides has been harnessed in several designs of TE polarization filters [14,18,19]. It was recently shown that a photonic crystal fiber (PCF) with a gold NW along its core axis provides a broadband AP output [20]. However, device design and fabrication procedures were complex (requiring precise PCF design and selective hole filling). Our fiber device is simpler, gives a comparably homogenous output mode, and can be integrated into a fiber loop using an industrially produced fiber [21].

The different modal propagation losses are a result of the finite penetration of the tangential magnetic field (i.e., the $\varphi$ and $z$ components in a cylindrical coordinate system) into the metal, which imposes surface currents in the vicinity of the interface, and leads to energy dissipation (ohmic loss) [22]. The ${\mathrm{T}\mathrm{E}}_{01}$ mode possesses only a very small tangential magnetic field (i.e., a small $z$- and no $\varphi$-component), since the azimuthal electric field is dominant, resulting in low ohmic loss.

The device in Fig. 1 is fabricated by filling a 2 m long nanobore fiber with gold using pressure-assisted melt-filling [23], yielding a sample having an empty and a filled section. By identifying the end of the metal NW and cleaving at the appropriate location, we obtain a device formed by a long (90 cm) unfilled nanobore fiber, where light is coupled into, and a short (3.5 cm) gold-filled section, which acts as an azimuthal polarizer (Fig. 1). Note that the gold NW is integrated into the device without requiring splicing, leading to optimum launching modal conditions between the empty and the gold-filled section. We find occasional μm-sized breaks in the gold wire, which have little effect on the device loss, and in fact contribute to modal conversion in the transition region, as addressed below.

The experimental analysis relies on coupling broadband LP light from a supercontinuum (SC) source (500–1700 nm) into the fiber and carefully evaluating the output state. The transmitted light is spectrally analyzed using an optical spectrum analyzer [OSA, Fig. 3(a)]. The output transmission is normalized to the input intensity for both an unfilled and the gold-filled nanobore fiber [Fig. 3(b)]. Undesired cladding light is removed by bending the unfilled section into a loop. The modal attenuation was experimentally obtained by cutting a gold-filled fiber in eight successive steps (2–3 mm lengths), measuring the transmission after each cut, and fitting the transmission value at a fixed wavelength with an exponential function. Mode patterns are imaged onto a charge-coupled device (CCD) camera, where AP modes can be identified by a distinct double lope pattern when a polarizer is inserted into the output beam path [a schematic of this setup is shown in Fig. 4(a)].

 

Fig. 3. (a) Experimental setup schematic. (b) Transmission spectra of the empty (unfilled) and gold-filled fiber. (c) Loss of the ${\mathrm{T}\mathrm{E}}_{01}$ mode (right axis) and loss discrimination with respect to other modes (left axis). Circles show the experimentally measured cut-back loss.

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Fig. 4. (a) Schematic of experimental setup. Different band-pass filters (BPF) and a polarizer are placed after fiber output. Modal images are measured with a CCD camera. (b) Experimental modal images for different filter wavelengths. Black arrows indicate the orientations of the polarizer. Background colors (yellow and light blue) correspond to the wavelength regions shown in Fig. 2. Angle values refer to $\overline{\mathrm{\Delta }\psi }$ as defined in the text.

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The empty fiber possesses a flat transmission spectrum with $\sim 3\mathrm{dB}$ coupling loss [Fig. 3(b)]. For the short fiber lengths considered, the propagation losses in the unfilled fiber are negligible. In contrast, the gold-filled sample yields a transmission which increases toward longer wavelengths as expected from the evolution of the modal attenuation [Fig. 2(b)]. The resulting loss values of the AP mode [blue circles in Fig. 3(c)] are in good agreement with the calculated losses of a purely ${\mathrm{T}\mathrm{E}}_{01}$ mode (dashed blue line), indicating an effective suppression of the other modes inside the NW section. Calculations show that the ${\mathrm{HE}}_{11}$, ${\mathrm{HE}}_{21}$, and ${\mathrm{TM}}_{01}$ modes are highly discriminated relative to the ${\mathrm{T}\mathrm{E}}_{01}$ mode with more than 10 dB/cm [Fig. 3(c)], except in those regions where the ${\mathrm{HE}}_{21}$ and ${\mathrm{TM}}_{01}$ modes cut off.

The modal imaging shows symmetric doughnut-shaped modes over the entire operation range [583–720 nm, Fig. 4(b)]. The slight observed intensity asymmetry could be attributed to an ellipticity of the gold wire and bore or core, or due to a scattering of the output mode as a result of the gold wire partially screening the core section (SEM in Fig. 1). The latter effect emerges during the cleave of the gold filled part, as gold is a ductile material. By placing the polarizer in front of the camera, we observe a two-lobe pattern that rotates in accordance with the polarizer axis. The orientations of the lobes, relative to the orientation of the polarizer, confirm the azimuthal polarization state of the output beam across the entire spectral operation range. We observe that the purest azimuthal beams (663–720 nm) are produced at those wavelengths where only the ${\mathrm{HE}}_{11}$ and the ${\mathrm{T}\mathrm{E}}_{01}$ modes exist. These images allows us to calculate $\overline{\mathrm{\Delta }\psi }$, i.e., the average deviation of the orientation angle [24] with respect to an ideally AP state [inset of Fig. 4(b)]. The lowest value of $\overline{\mathrm{\Delta }\psi }=2.6°$ is observed at 701 nm, whereas between 583–640 nm where all four modes are supported, we observe a gradual increase of $\overline{\mathrm{\Delta }\psi }$ to 5.7°.

To demonstrate that our device can be integrated into fiber circuitry, we fusion-spliced the unfilled section of the nanobore fiber to a commercially available step-index fiber with a ferrule connector (Thorlabs HP460), thus forming a completely connectorized device for use with any commercial light source. Although splice losses for this particular connectorized prototype are 10–12 dB in this wavelength range, we observe splice losses $<1\mathrm{dB}$ using a different input single-mode fiber (SMF). To better comprehend the coupling mechanisms between the unfilled and the gold-filled fiber sections, we coupled light to our device via a fiber-optic visual fault tester (FS1565D, $\lambda =650\mathrm{nm}$) and recorded the sideways scattered light using an optical microscope ($10\times$ microscope objective). A side image of the laterally scattered light in the vicinity of the NW/air interface is shown in Fig. 5(a). A bright-field view of the unfilled/filled boundary is shown in Fig. 5(b). The initial dark region in Fig. 5(a) (i.e., no scattering) corresponds to the unfilled fiber section; light scattering begins with the gold-filled region and continues until the output. We observe an initial 6 mm length region of random (“chaotic”) light scattering, over which coupling between the input modes of the unfilled fiber and the modes of the gold-filled section occur. Uniform scattering is observed over the remaining 29 mm. This observation indicates that the gold NW induces a strong perturbation in the direction of propagation, giving rise to a complex coupling region over this 6 mm length. This is an important observation since a single filled/unfilled junction would give rise to only one coupling event and thus only to small amount of light in the TE mode. As a result, the nonuniformity of the NW along the fiber axis presumably distributes the electromagnetic energy evenly across all four modes, which is key for the efficient polarization discrimination. We find this transition behavior to be sample-dependent (a comparison with a second sample yields comparable transition lengths and conversion efficiencies between 25%–45% in the same wavelength region), however, we observe a high-quality azimuthal mode output for all samples. A further investigation will be the object of a future study.

 

Fig. 5. (a) Scattered light at the boundary between the unfilled and gold-filled region of the step-index fiber ($\lambda =650\mathrm{nm}$). An initial transition region of the 6 mm length with irregular light scattering is followed by a region of regular scattering. Point A and B respectively represent the beginning and the end of the gold-NW transition region over which modal conversion occurs. (b) Microscope image of the first section of the transition region. The gold wire begins with the white vertical dotted line. (c) Launching efficiency of the AP beam (left axis), and estimated modal conversion efficiency (right axis).

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The azimuthally polarizing launching efficiency ${\eta }_{\text{launch}}$ of the device can be obtained from the ratio of the transmission of the filled portion of the fiber $T_{\mathrm{NW}}$, with respect to the transmission of the unfilled fiber $T_{\text{empty}}$, i.e., ${\eta }_{\text{launch}}=T_{\mathrm{NW}}/T_{\text{empty}}$. This includes the losses over both the 6 mm long transition section over which modal conversion occurs, and modal attenuation over the remaining 29 mm gold filled region [Fig. 5(c), blue]. The launching efficiency can thus be improved using a shorter device. By subtracting the contribution of propagation loss over the 29 mm propagation region, we can estimate the modal conversion efficiency over the 6 mm transition region. In this case, we define the modal conversion efficiency as ${\eta }_{\text{conv}}=I_B/I_A$, where $I_A$ is the field intensity in the unfilled region immediately before the gold wire (equivalent to the intensity transmitted by the empty fiber), and $I_B$ is the intensity immediately after the 6 mm transition region [obtained from the transmission of the gold-filled fiber, taking into account the experimentally measured ${\mathrm{T}\mathrm{E}}_{01}$ modal loss over 29 mm, Fig. 3(c)]. This yields a modal conversion efficiency of the input mode to the ${\mathrm{TE}}_{01}$ mode of up to 37% over the entire transmission bandwidth [Fig. 5(c), red].

The device specifications can be further tailored, for example by changing the geometry and constituent materials. By reducing the wire radius to 100 nm (keeping all other parameters constant), the cutoff wavelength of the ${\mathrm{TE}}_{01}$ mode can be increased up to 796 nm, pushing the device performance to longer wavelengths. The operation domain on the short-wavelength side is limited by a larger penetration of the fields into the metal and the inverse wavelength dependence [cfr. Eq. (1)]. Increasing the core/cladding material refractive index contrast, or larger core diameters, would also extend the operation bandwidth of the device. Furthermore, other metals with higher optical loss could be incorporated as a central wire to increase the modal discrimination even further.

In conclusion, we have experimentally demonstrated that a step-index fiber with a central gold NW acts as an efficient azimuthal polarizer, providing low-loss transmission for the ${\mathrm{TE}}_{01}$ mode and high discrimination to all other modes, on an integrated step-index fiber platform. The direct integration of the gold NW into the device core provides optimum launching modal conditions, and enables the direct observation of the modal conversion behavior via the multiple junction scattering. We found a complex transition section in the first part of the NW, leading to a surprisingly high coupling efficiency into the AP propagating mode of about 37%. This integrated fiber-based polarizer has the advantage of being broadband and effectively single mode. The device was produced without having to resort to a cumbersome PCF platform, yielding azimuthal states of comparable quality, simplifying both the fabrication of the fiber and the gold filling procedure.

High quality CP beams are essential for many applications, since AP beams can be converted into their radial counterparts or vice versa simply by using two half-waveplates. Due to its unique properties, this device will find immediate applications in STED microscopy, laser tweezer experiments and superfocussing, as well as providing a novel platform for the investigation of fiber-based plasmonics.