1. Introduction

The hollow core microstructured optical fibers (HC MOFs) are a special kind of optical fibers [1] which confine the electromagnetic field inside a hollow core surrounded by a microstructured cladding. Such HC MOFs as hollow core photonic crystal fibers (HC PCFs) or Kagome lattice HC MOFs now have a wide range of applications such as light-gas interactions [2], high power and ultra short pulse delivery [3], terahertz applications [4] and others. The key advantage of HC MOFs is that the radiation propagates mostly in the air core and the optical damage threshold is raised. HC PCFs usually have a circular core-cladding boundary and a complicated photonic crystal cladding with a triangular arrangement of air holes. The localization of light occurs due to the presence of a full photonic bandgap over appropriate optical frequencies. The light guidance occurs when the photonic band gap coincides with a core resonance. Kagome lattice HC MOFs guide the light due to inhibited coupling mechanism [5]. Furthermore, it was shown that single-layer cladding is an efficient way to simplify the kagome lattice HC MOFs [6].

Recently, a new type of HC MOFs with a negative curvature of the core-cladding boundary and a simplified cladding has been proposed [7, 8]. The advantage of using the negative curvature of the core boundary for decreasing the optical loss was first demonstrated in [7], where the core boundary had the form of a hypocycloid. In [8] the term “negative curvature” was introduced and it was demonstrated that in the case of a silica negative curvature hollow core fiber (NCHCF) it was possible to guide the light in the mid infrared spectral range (> 3.5 μm) where the material loss of silica glass is very high. Such constructions led to a complication of the boundary conditions for the core modes and strengthened their localization in the air core [8]. In [9] CO₂ laser power delivery was demonstrated at a wavelength of 10.6 μm using a fiber with the same cross section design but made of chalcogenide glass. In [10] the authors demonstrated silica NCHCF for a transmission in the mid IR with a minimum attenuation of 34 dB/km at wavelength of 3.05 μm. It was also shown that the NCHCF had a transmission band above the wavelength of 4 μm. The authors of [11] demonstrated the delivery of high energy microsecond pulses through NCHCF described in [10] at 2.94 μm. In authors’ opinion the delivery system can be useful for minimally invasive surgical laser procedures. In work [12] it was demonstrated that a flexible NCHCF with capillaries in the cladding made of polymethylmethacrylate could be used for THz guidance.

It should be also noted that a negative curvature of core-cladding boundary is a necessary but not sufficient condition for a low optical loss [13]. Moreover, it is known that the cladding elements in HC PCFs such as interstitial apexes or struts are optical resonators that form the lower or upper frequency band gap edges [5]. In this paper we show that the touching points between the cladding capillaries can be considered as additional optical resonators that cause optical loss increase in the transmission bands. It is shown that it is possible to achieve a low-loss light transmission under extremely high material loss in the mid infrared spectral range > 5 μm using silica NCHCF by removing the touching points between the cladding capillaries. The paper has four sections. In Section 2 we show the impact that touching points of cladding capillaries have on the optical loss inside the transmission bands by using numerical simulations as well as describe the fiber fabrication process. In Section 3 the optical loss measurements are described. Section 4 contains the conclusions.

2. Fiber development

In this section we demonstrate the impact that optical resonators occurred at the touching points between the cladding capillaries have on the optical loss level. The numerical simulation was carried out using the Femlab 3.1 commercial packet. Two silica NCHCFs with the same cross-section were analyzed. Each fiber had eight capillaries in the cladding, the outer diameter of the capillaries was 63 μm and the inner diameter was 51 μm. The distance between the capillaries was 1.3 μm. The difference between the considered fibers was that in the first sample the capillaries in the cladding didn’t touch while in the second sample the capillaries were in contact with each other Fig. 1. The loss spectrums were calculated for both structures in the spectral range of 3 – 6.5 μm Fig. 2(a). The presence of additional optical resonators in the cladding led to an increase in the density of electromagnetic states in the cladding Fig. 2(b) and, consequently, to an increase in total optical losses in the transmission bands Fig. 2(a).

 

Fig. 1 The analyzed fiber geometries; a) NCHCF with non touching capillaries; b) NCHCF with touching capillaries in the cladding.

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Fig. 2 (a) the calculated fundamental mode loss for a silica NCHCF with capillaries touching and not touching in the cladding; (b) the output end of the NCHCF with touching capillaries excited by visible light.

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In terms of production it is much more difficult to fabricate a NCHCF with touching capillaries in the cladding because the high temperature reduces the silica glass viscosity and the surface tension forces straighten the capillary walls. In this case, it is much more difficult to obtain a negative curvature of the core boundary. In the case of a NCHCF with non touching capillaries in the cladding it is possible to keep the negative curvature of the core boundary even at high drawing temperature.

To demonstrate the possibility of the fabrication of a NCHCF with capillaries not touching in the cladding, a fiber was made by the stack and draw technique. Eight identical capillaries were drawn from a silica tube (Suprasil F300, Heraeus) and were installed into a tube with a larger diameter and soldered to it. The resulting preform was drawn on a standard drawing tower into a fiber with a core diameter of 119 µm and with a capillary wall thickness of 6 µm Fig. 3.

 

Fig. 3 Cross section of a NCHCF with non touching capillaries.

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3. Measurements and numerical simulations

In this subsection we discuss the experimental results obtained with the fabricated NCHCF. The attenuation was measured in a wide spectral region from 2.5 to 7.9 μm by cut-back method using Infrared Fourier Transform Spectrometer IFS-113v with a resolution of 2 cm⁻¹. As a light source a globar was used, a ZnSe lens was used for launching light into the fiber. The measurements were carried out with fiber lengths from 90 to 23 cm which allowed to measure the loss values up to 80 dB/m. The resulting spectral dependence of the losses is shown in Fig. 4 (red).

 

Fig. 4 a) The measured loss (red); the loss measured with He-Ne at 3.39 µm (red asterisk); the material loss in silica glass (black); the calculated loss (by left scale) and Re(n_eff) (by right scale) of the fundamental mode(orange); the calculated loss (by left scale) and Re(n_eff) (by right scale) of next higher order modes (green, navy, blue); b) the intensity distribution of the first several air core modes (the color of the frame corresponds to the color of the line in the plot).

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It is seen in Fig. 4 that there are three transmission bands in the spectral range of 2.5 – 5 μm with a minimum loss level of 4 – 5 dB/m. The average losses measured in the spectral bands at 5.8 and 7.7 µm were 30 and 50 dB/m, respectively. The bands at 3.3 and 4.3 µm have a number of absorption peaks. The location of the peaks in the band at 3.3 µm Fig. 4 (inset) can be explained by the presence of HCl in the core and they are identical to the peaks observed in [10]. The peaks in the band at 4.3 µm correspond to absorption peaks of CO₂ in the atmosphere.

To analyze the experimental data a fiber with the same geometric parameters was modeled and the dependences of the total loss and the real part of the effective index Re(n_eff) were calculated for different core modes Fig. 4 (orange, green, navy, blue) using the Femlab 3.1 commercial packet. The dependence of imaginary and real parts of silica glass refractive index was taken according to [14, 15].

As one can see from Fig. 4, the simulated and experimental band edges superpose very well. Note that the transmission band at 7.7 µm is especially interesting as the silica glass refractive index becomes equal to one and enters the anomalous region (n<1) at 7.3 µm [15]. Thus, the light transmission in the transmission band at 7.7 µm occurs due to a superposition of two guiding mechanisms, namely, total internal reflection and the ARROW [16]. For example, similar light guidance was demonstrated in hollow core oxide-glass cladding optical fibers [17]. In the case of NCHCFs the nature of light localization in the anomalous region requires further investigations.

The discrepancy between the measured loss level and the calculated one for the fundamental mode Fig. 4 in the wavelength range < 5 µm is mainly due to the presence of multimode waveguide regime. The imperfect launching conditions leads to an excitation of high-aperture modes which can propagate along the fiber length at some distance. Moreover, as the wavelength decreases the values of Re(n_eff) Fig. 4 become closer to each other and an intermodal interaction occurs. All this leads to an increase in the total loss. Thus, the measurements defined only the upper limit of the loss values. To find the lower limit of the loss values it is necessary to improve the excitation conditions, for example, by using of a high-bright source and larger fiber lengths.

To confirm this finding we carried out several experiments with a few-mode He-Ne laser at a wavelength of 3.39 µm. The loss was measured by cut-back method with a fiber length from 11 to 1 meter. The bend radius of the fiber was 20 cm. The He-Ne laser radiation intensity versus fiber length is shown in Fig. 5. The intensity distributions in the near field in the case of different lengths of the fiber are shown in the insets of Fig. 5. These pictures were obtained with Electrophysics PV320 thermal imaging camera. The striped structure of the images Fig. 5 (insets) is due to an interference of coherent laser radiation on the entrance window of the camera. There are two different ranges of the fiber length which are clearly seen in Fig. 5. The first range of the fiber length is up to 2 m and in this range the multimode waveguide regime still exists. The second range of the fiber length > 3 m and in this range the signal decreases exponentially. As one can see from Fig. 5, the mode structure of the fiber is stabilized at the fiber lengths over 3 m and only the first several modes are present in the fiber. The part of the signal dependence from 3 to 11 m was approximated by an exponential curve. The value of the optical loss estimated with this curve at a wavelength of 3.39 µm was 50 ± 8 dB/km Fig. 4 (red asterisk).

 

Fig. 5 The He-Ne laser radiation intensity versus fiber length. The straight line is an approximation of the exponential curve. The insets show the intensity distribution in the near field at the fiber length of 1 and 11 m.

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It should be noted, that the level of the transmitted signal and the mode structure are strongly dependent on the local tensions. Therefore, the stress was not applied to the fixing input and output ends of the fiber. In our opinion, the tension created the micro bends which strongly increased the loss level.

4. Conclusion

The light propagation through silica NCHCF in transmission bands at 4.5, 5.8 and 7.7 µm in extremely high material loss region was demonstrated. The total loss was at least three orders of magnitude lower than the material loss of silica glass. It confirms a very weak coupling of the air core modes with the cladding structure. The NCHCFs with non touching capillaries in the cladding allow to decrease the loss level in the transmission bands due to an absence of additional optical resonators in the cladding. It should be noted that the considered NCHCF has a great potential for different applications and for the light guidance from UV to mid IR spectral regions. To decrease the loss level in the required spectral range it is necessary to carry out an optimization of the NCHCF structure. The main parameters of the considered NCHCFs to optimize are the air core diameter, the number of capillaries in the cladding, the outer and the inner diameters of the capillaries.