1. Introduction

Subwavelength optical fibers, with core dimensions less than the wavelength of the light, have properties that differ significantly from conventional fibers. When the core dimensions are selected to provide optimal mode confinement (ie minimum effective mode area, A_eff), it is possible to produce fibers with extreme values of nonlinearity (γ) [1,2]. It has recently been discovered that the modes that propagate in such fibers have a significant amount of energy polarized along the propagation direction. In other words, the modes stop being transverse, which leads to significantly higher values of nonlinearity [2]. For smaller sizes, significant fractions of the mode also become located in air outside the core, which is the basis for using these fibers as gas or liquid sensing platforms [3].

When a hole of subwavelength dimension is introduced within the core region of any optical fiber, it has a notable impact on the characteristics of the propagating mode. The normal component of electric field at the interface of the hole is discontinuous; light intensity on the low index side of the interface of the air hole scales with the squared refractive index contrast at the interface [4]. Using this principle, high index silicon-on-insulator [SOI] slot waveguide structures [5] were proposed by Almeida in 2004. The air “slot” embedded between two high index silicon slabs acts as a waveguide, propagating light with its peak intensity 20 times higher than is possible using conventional silica planar waveguides. Conventional semiconductor processes allow relatively easy fabrication of such structures, and as a result research in on-chip high index SOI-based slot waveguide devices has flourished. One opportunity such devices enable is the filling of the slot with novel materials, and for example highly nonlinear silicon nanocrystals have been used to demonstrate ultrafast all-optical switching [6] and four-wave mixing [7]. Increased light-sample interaction in a slot waveguide ring resonator [8] has enabled the realization of label-free detection with a volume refractive index detection limit of 5x10⁻⁶ RIUs, the highest detection sensitivity reported for an integrated planar ring resonator [9]. A wide variety of slot waveguide structures are possible; they have been used to produce polarization-independent couplers [10], dispersion compensators [11] and polarization splitters [12]. The combination of high optical confinement and potential small sample volumes in the slot also make such structures attractive as single photon sources for quantum information processing [13]. Besides these applications, understanding ways of controlling light on the nanoscale via structuring of materials is also of fundamental interest.

Although easy to fabricate and high index, SOI slot waveguides have relatively high attenuation (of order 10 dB/cm) [14], which limits their useful length to centimeters at most. Due to long effective length, low loss and flexibility in fiber geometries, fibers with subwavelength low index holes offer a tantalizing platform for exploring light-material interactions inside nanoscale structures. The concentration of optical energy within an air hole in a fiber core was first demonstrated for a silica microstructured fiber (MOF) [15], and holes as small as 110 nm were fabricated in the silica fiber core. High index soft glasses offer an attractive alternative to silica due to the availability of high index glasses, which significantly increase light enhancement. Combining high index and low melting temperature, soft glass can be fabricated into microstructured fibers [16,17] with ultra-high nonlinearity [18] and/or strong evanescent field for sensing applications [19].

In this paper, we report subwavelength intensity enhancement in soft glass microstructured fibers. Fabrication and characterization of the first soft glass MOFs with nanoscale (i.e. subwavelength) holes in the core are presented. The centralized core hole size is as small as 20 nm, the smallest hole reported in any fiber to date.

The paper is organized as follows: in the second section, the fabrication of the MOFs with nanoholes is presented. Then the calculated light confinement in these nanoholes is shown for understanding of impact of the subwavelength hole on light confinement. The fourth section displays experimental characterization of light confinement using scanning near field microscopy. In the last section, discussion for future work and conclusions are made.

2. Fabrication of the MOFs with nanoscale hole

Commercial F2 lead silicate glass (from Schott Glass Co.) has been chosen as soft glass host material for our fabrication. The F2 glass with refractive index n = 1.61 at λ = 632nm has low softening temperature (592 °C), which has enabled us to use flexible extrusion technique to fabricate MOFs in-house for sensing and nonlinear applications [16–19].

Our target F2 MOF structure comprises four rings of micron-scale cladding holes arranged on a hexagonal array with a single nanoscale hole in the core center as shown in Fig. 1(e) . The hole array in the cladding of this fiber type is characterized by the hole-to-hole distance, Λ, and hole diameter, d, and d/Λ = 0.7 is selected to achieve tight mode confinement in the core. The fiber was fabricated by extruding preforms and jacket tubes and drawing these to s [16].

 

Fig. 1 Extruded elements: (a) tube core preform; (b) cladding-preform; (c) jacket tube. SEM images of (d) whole ; (e) fiber cladding region; (f) core region with hole of 45nm diameter; (g) images of core hole with diameters of 20nm, 45nm, and 80nm.

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Our target hole sizes (tens of nanometers) are significantly smaller than the outer diameter of the fibers and the other holes that form the cladding of the fibers, and thus one of the greatest challenges is to keep the centralized hole core open during the fiber fabrication process. The processes described in Ref [17]. have been extended by inserting a tube with a centralized hole into the centre of the ring cladding preform. The detailed steps in this fabrication process are shown in Fig. 1(a-e). We used a tube core preform as shown in Fig. 1a as the starting point for forming the core hole in the fiber. It was reduced in scale to a core cane of ~1mm outer diameter, which was inserted in the central hole of the fiber cladding preform (Fig. 1b). The fiber cladding preform contains four rings of air holes in addition to a hole in the centre of the structure that is required for the insertion of the structured core cane. This assembly was drawn down to a core/cladding cane of ~1mm, which was then inserted into the jacket tube in Fig. 1c. This assembly was drawn down to bands of fibers with outer diameters of ~150μm. The holes at the top of the structured preforms and canes were sealed to prevent hole closure via use of the self-regulating self-pressurization effect [20]. The gap between cane and cladding preform or jacket tube was closed using a slight under-pressure.

To achieve a small core hole size, we firstly explored the use of different values for the ratio of hole diameter to the outer diameter of the tube core preform (d/P = 0.16, 0.1, 0.05), and found that choice d/P = 0.10 enabled us to do this. This is because a higher ratio made the core hole too big (> 500nm) whereas a smaller ratio caused the core hole to completely close up during fiber drawing due to the effect of surface tension.

From SEM images of the fibers, we observed that the core hole diameter oscillated along the length. The oscillation period is estimated to be around 8-10 meters. The hole size varied from 500nm to complete closure, and opened again, periodically. Using careful selection of the cleaving position in the fiber, hole sizes as small as 20 ± 5 nm have been identified, as shown in Fig. 1g. This small hole extends over 50cm length of the fiber, which has been confirmed by cutting the fiber into small pieces. To the best of our knowledge, this is the smallest hole achieved in the core of any fiber. The core hole variation along the fibers is likely due to drawing instability [21] and needs further investigation to achieve more uniform hole size.

We used cut back method to measure the loss of the 3-meter length of the fiber with core hole diameter of around 250 ± 50nm. Its loss at the wavelength of 780nm is 0.25-0.55dB/m, which is similar to the loss of the MOFs without a core hole [17]. This demonstrates that no significant excess loss was introduced due to the nano/microstructure. This is in contrast to the silica MOF with 1μm core diameter and nanoscale hole in the core, in which the attenuation was of the order of decibels per meter at visible frequencies [15]. The reason for the lower loss of our fibers is anticipated to be due to the use of a relatively bigger core size (2μm), as well as the use of extrusion processes for fabrication, which result in smoother internal hole surfaces.

3. Light confinement in the nanoholes

To understand the impact of the subwavelength hole on light confinement in the holes within the MOFs, we have calculated the confined power $P_{hole}={\displaystyle {\int }_H{S}_{z}dA}/{\displaystyle {\int }_{\infty }{S}_{z}dA}$ and the average mode intensity $I_{hole}=P_{hole}/\pi {(D/2)}^2$ in the centralized core holes as a function of the hole diameter D [S_z is z-component of the Poynting vector (power flow) of the mode field, and H is the hole area]. The results are shown in Fig. 2a . It can be seen that both parameters shows similar dependence on hole size as those in an air slot within a high index 460nm wide rectangular silicon nano-waveguides as described in Ref [5]. The confined power $P_{hole}$ is maximized for a hole diameter of ≈180nm. The maximum value of $P_{hole}$ is only 0.27% for this fiber structure due to the relatively large core size of ≈2μm. The average mode intensity $I_{hole}$ increases with reduced hole size, and its value for a 50nm hole is ≈0.6 μW/μm², about 30 times lower than that in the 50nm wide air slot within the silicon waveguides mentioned above [5] due to lower refractive index and larger core size. However, it is important to recognize that our demonstrated capability to produce holes tens of nanometers in diameter within optical fibers allows us to take advantage of the extremely tight mode confinement possible in small core high numerical aperture fibers, and thus it is still possible to obtain relatively high light intensity (comparable to that in silicon slot waveguides [5]) for important applications such as nanosources for high resolution imaging.

 

Fig. 2 Modeled parameters for the fabricated F2 MOFs. (a). the confined power and average mode intensity inside the central core hole as a function of the hole diameter; (b). cross section of the power flow of the mode field for definition of the contrast. The cross section direction is parallel to the polarisation direction of the electric field; (c) and (d). contrast dependence on propagation distance to the fiber endface. (c) for the wavelength of 632nm, and (d) for 1550nm.

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The fine structure of the confined mode fields in these core holes can be observed by imaging the near field at the fiber end. However, the strong diffraction from these subwavelength features within the guided mode smears the near field distribution even over relatively short propagation distances [15]. Hence, it is necessary to understand the mode field propagation in the near field to allow any near field experimental results to be interpreted. We use a parameter, called here contrast, to describe the beam quality for recognition of the light confinement in the core hole. Figure 2b shows cross section of the power flow of the mode field in the MOF (its direction along the polarisation direction of the electric field). The contrast is defined as $C=(I_{peak}-I_{background})/I_{background}$ , where $I_{peak}$ is the intensity in the centre of the mode field, and $I_{background}$ is the maximum intensity away from the central peak of the mode field (which can be regarded as the background). When the contrast value is close to zero, it can be said that the light field confined in the core hole cannot be distinguished from the background mode field. CST Microwave studio, a commercial 3D full vectorial simulation tool based on finite integration technique is used to model light propagation in the fiber’s near field.

Figure 2(c-d) shows the contrast as a function of the propagation distance from the fiber end for fibers that have different sized core holes. Figure 2c is for the source wavelegnth of 632nm, and Fig. 2d is for 1550nm. The negative values shown in both figures imply cases in which the central intensity of the mode field $I_{peak}$ is smaller than its background signal $I_{background}$ , which is what happens when the hole is large enough that the intensity decays significantly within the hole, rather than being enhanced. It can be seen from both figures that, unsurprisingly, the contast values reduce with increased propagation distance, which indicates that the confined light in the core hole become less distinguishable (ie that the near-field fields do not survive under propagation). However, it is worth noting that for smaller holes the contrast approaches zero in a much quicker trend than those of large holes. This is due to the relatively higher diffraction of subwavelength features from small holes. For example, note tat light enhancement ( $I_{peak}>I_{background}$ ) at the wavelength of 632nm from the 20nm hole cannot be observed even after a 20nm propagation distance, whereas the propagation distance for over which the light enhancement dissapates for the 80nm hole at 1550nm is 100nm. This work provides confirmation of the working distance that needs to be achieved to detect (and exploit) this light enhancement. In order to characterise the light enhancement in these holes experimentally, Scanning Near-field Optical Microscopy (SNOM) [22] was used to observe the output patterns of the fibers in the near-field.

4. Near field characterization of light confinement in the hole

A SNOM system from NT-MDT company was used in our near field characterisation. A tiny aperture (typically 30-100nm) at the apex of the coated fiber tip enables subdiffraction resolution. The tip is controlled in close vicinity to the sample surface by detection of the shear force, which increases when the tip is closer to the sample surface. A minimum distance of 10-20nm [23] can be targeted before the risk of tip breakage becomes too severe. With one scan, the surface topography and light distribution of the fiber can be simultaneously obtained. The resolution of the SNOM is dependent on aperture size of the tips and distance of the tips to the fiber surface. In our measurement, the aperture size of the tips used is 100nm.

The first fibers used for SNOM imaging had a core hole diameter of 80nm as shown in Fig. 1g. The light source is a 675nm laser diode. The fiber surface topography and its cross sectional profile are shown in Fig. 3a and b . The fiber was cleaved manually using a blade, creating long cracks around the holes (labelled in Fig. 3a) and a slanted surface at the core region as shown in Fig. 3b (tilt angle ≈52°).

 

Fig. 3 Observation of the mode field in near field using SNOM for a MOF with a 80nm core hole size. (a) topography of the fiber endface; (b) cross sectional profile of (a) in the core region; (c) measured near field intensity; (d) modeled power flow at the plane 10nm from the fiber end; (e) cross-section profiles of (c) (red curve) and (d) (black curve).

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The intensity of the field after propagation to the SNOM tip is shown in Fig. 3c. Assuming that the tip scans at constant distance of 10nm above the fiber surface [23], the light field shown in Fig. 3c has propagated ≈10nm after exiting from the cleaved fiber surface. Figure 3d shows the modelled power flow at the plane 10nm far away from the fiber end, assuming a smooth and flat cleave for simplified calculation. Due to long calculation times for these simulations, only the first two rings are included for modelled MOF structure. Figure 3e shows the cross sectional profiles from Fig. 3c (red curve) and 3d (black curve). For comparison, the intensity of each curve has been normalised to its maximum value. From Fig. 3e, it can be seen that the hole region has been filled with light for both modeled and measured mode field intensity. However the measured mode field (red curve) displays an assymetric profile which may be caused by the very slanted surface at one side of the core region (Fig. 3a and b).

The light confinement in a 250nm core hole within a MOF at different wavelengths was also investigated, and their results are shown in Fig. 4 . The third column in Fig. 4 shows measured near field mode images at 20nm distance from the MOF endface at two wavelengths of 635nm and 1550nm. The fourth column is their corresponding intensity cross sections. The fiber was cleaved using a tension adjusted fiber cleaver, and showed smoother surface than that used in Fig. 3. Comparing measured light patterns in the third column to Fig. 3b for the 80nm hole MOF, it can be seen that light was better confined to the core in this structure, with no cladding excitation evident. This may be because a larger tip fiber gap (probably longer than 20nm) was used with this measurement in order to protect the fiber tip from breaking during scanning. Weak leaking light to the cladding had attenuated before it could be collected by the tip due to propagating a longer distance compared to that in Fig. 3b.

 

Fig. 4 Comparison of the measured and modeled field intensity from one MOF at two wavelengths of 632nm and 1550nm. The core and cetral hole diameter of the MOF is 2 μm and 250nm, respectively. The first column is the modeled power flow and the second column is their corresponding cross sections. The third column is the measured power flow at 20nm distance to the fiber endface and the fourth column is their corresponding cross sections.

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As a comparison, we calculated the power flow at a plane 20nm away from the fiber endface, as shown in the first column in Fig. 4, and the corresponding predicted intensity cross sections are displayed in the second column of Fig. 4. It is worth noting that both the modeled and measured light intensity within the hole increase with increasing wavelength due to relatively reduced hole size relative to the wavelength [15]. This is in agreement with the theoretical prediction presented in Section 3. Compared to modeled power flow, the measured patterns show higher intensity in the hole regions relative to the background signal for both wavelengths. No subwavelength features were observed in the measured pattern at the wavelength of 1500nm, which can be attributed to the large aperture of the fiber tip. Although the gauged aperture size is 100nm, the practical value might be bigger than this due to possible damage caused in the process of the scanning.

For measurement of the light enhancement with $I_{peak}>I_{background}$ , smaller hole sizes and/or longer source wavelength need to be used. Figure 5 displays calculated contrast for the power flow patterns at the 20nm distance from the fiber end as a function of core hole size with the fixed source wavelength of 1550nm. It suggests that the mode field propagating from the MOF endface with 100nm core hole has the largest contrast and the light enhancement in this core hole is the most distinguishable.

 

Fig. 5 Contrast of the power flow patterns at the 20nm distance from the fiber end as a function of the core hole diameter of the MOFs at the wavelength of 1550nm.

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As for observation of light enhancement in the 20nm hole within the MOF, it is clear from Fig. 2c that the light enhancement in the core hole region has disappeared when the light propagates about 20nm away from the endface. As mentioned in Section 4, the minimum fiber tip distance is in the range of 10-20nm. Thus it is almost impossible for the SNOM with a fixed aperture to characterize this enhancement. Other measurement tools have been considered for this purpose.

5. Discussion and conclusion

Building on existing techniques for fabricating preforms and fibers with hexagonally arranged holes, MOFs with single core holes have been fabricated and a minimum hole size of 20 nm was achieved, which is believed to be the smallest hole reported in the core of any fiber to date. Flexibility in extrusion die design, multiple drawing steps and improved process control have enabled the fabrication of this fiber.

In addition to the creation of strong localized light intensity used for increased light-material interaction, as demonstrated here, the ability to create such a small hole in the optical fibers may also enable the realization of negative refractive index in optical fiber platform [24] Negative refraction and superlensing imaging in the visible region can be implemented by metallic nanowires embedded in a dielectric matrix [25] and have been demonstrated in bulk metamaterials. This concept could be transferred into the fiber platform if suitable methods are found to create metal nanowire within the nanosized holes that have been formed here.

SNOM has been used to scan near field patterns of the MOFs with 80 nm and 250nm core hole at the visible and near infrared wavelengths. Light fills the centralized hole of the MOF. However, the light confinement in this fiber is still relatively weak due to the relatively large hole sizes compared to the wavelengths of the light sources. Therefore further SNOM experiments will be conducted for those MOFs with smaller core holes using the laser sources with a series of wavelengths for comparison. It is necessary to use a small aperture size to image light from the holes less than 50nm. The minimum aperture size from commercial fiber tips are 30nm with extremely low collection efficiency due to large leaking loss. Also with such tiny tips, it is difficult to approach the tips to the fiber surface at a distance less than 10nm without breaking tip. Thus for measurement of the light enhancement within the hole size less than 30nm, it is necessary to use apertureless SNOM, whose resolution has no wavelength related limit and allows an optical resolution of 10nm to be achieved [26].