Hole-assisted lightguide fiber (HALF) is a microstructured fiber comprising a material index profile for waveguiding and air holes for modifying optical properties. Anomalous dispersion larger than those of the conventional fibers can be realized without severe degradation in optical loss, because of low power fraction in the holes and structural simplicity. We investigate into the causes of the loss of the fabricated HALFs, and show that a GeO2-doped core, in addition to the low power fraction, is desirable for low loss. The fabricated HALF exhibits a loss as low as 0.41 dB/km and a large anomalous dispersion of +35 ps/nm/km at 1550 nm wavelength.
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Air hole is now recognized as an attractive constituent of optical fiber. Fibers having air holes running down its length, called holey fibers, air-silica microstructured fibers or photonic crystal fibers, enable a variety of novel optical properties [1,2]. Amonthem, large chromatic dispersion due to large index difference between air and silica is valuable for dispersion management applications. However, high transmission loss has been one of the problems for practical applications of the holey fibers. The transmission loss in the 1.55-µm wavelength band has been typically as high as a few tens of dB/km . Although low-loss holey fibers with losses of 3.2 dB/km  and 2.6 dB/km  have recently been reported, their losses are still significantly higher than those of the conventional fibers, which are typically 0.2 to 0.5 dB/km.
As a method for realizing novel dispersion characteristics without severe degradation in transmission loss, we have recently proposed hole-assisted lightguide fiber (HALF) . Because of the structural proximity to the conventional fibers and low power fraction in the holes, HALF exhibits low loss below 1 dB/km at 1550 nm wavelength. In addition, the holes enlarge anomalous dispersion, resulting in large chromatic dispersion above +30 ps/nm/km at 1550 nm. It has also been shown that even larger dispersion can be obtained by increasing the air filling fraction or the index difference between the core and the cladding .
In this paper, we present the properties of the fabricated HALFs and model their losses using the method for the conventional fibers. Among several samples fabricated, a HALF with a GeO2-doped core and low power fraction in the holes has showed the lowest loss of 0.41 dB/km. The model shows that the wavelength independent loss is dominant, which is consistent with Ref. . The causes of the wavelength independent loss are also discussed by comparing results of the loss modeling.
2. Hole-Assisted Lightguide Fiber
Hole-assisted lightguide fiber (HALF) is an optical fiber composed of a high index core, a low index cladding, and several holes surrounding the core, as shown in Fig. 1. This structure can enlarge chromatic dispersion, resulting in large anomalous dispersion that has been unattainable by the conventional fibers. Moreover, because of its simple structure compared to the other holey fibers, it can be fabricated with low transmission loss. We have reported a HALF with a loss of 0.82 dB/km and a dispersion of +34 ps/nm/km .
Anomalous dispersion of the HALF can be further enlarged by increasing the air filling fraction and the index difference between the core and the cladding. Figure 2 shows properties of three HALF structures (A-C). The number of holes is 4 in structure (A), and 8 in (B) and (C). The core-cladding index difference is 0.6% in structures (A) and (B), and 1.4% in (C). The radii r of the holes and their distances from the core R are 0.4a and 1.5a, respectively, where a denotes the core radius. The properties at 1550 nm wavelength are calculated with varying the core radius a within the range where the fiber operates in a single mode. Results are plotted against the effective area. The calculation is based on the full-vector finite element method, which can accurately model the properties of the HALF including the macrobend loss . As shown in Fig. 2 (d), larger anomalous dispersion can be obtained by increasing the number of holes or the index difference. In addition, Fig. 2 (e) shows that larger index difference is preferable for lowering the relative dispersion slope RDS (dispersion slope normalized by dispersion). Large anomalous dispersion and low RDS are difficult to realize in the conventional optical fibers, and hence would be valuable for dispersion management applications.
3. Experimental results
It has been predicted that novel optical properties such as large anomalous dispersion and low relative dispersion slope can be realized in HALF. For developing practical applications of these novel properties, low transmission loss should be essential. Therefore, investigation into the causes of loss in HALF would be important for further improvement in the loss and development of more valuable optical properties without degrading transmission loss. For this purpose, we have drawn three samples of HALF with different glass compositions and structures. Their structures are shown in Fig. 3. Fiber (1) has a pure silica core and a F- doped cladding. Fibers (2) and (3) have a GeO2-doped core and a pure silica cladding. The refractive index differences between the core and the cladding have been determined to be 0.4% by preform analysis. The hole sizes of Fibers (1), (2) and (3) are 5.3 µm×3.6 µm, 9.0 µm×8.3 µm, and 15 µm×15 µm, respectively. The core sizes estimated from the preform structures are 9.4 µm, 7.4 µm and 7.4 µm for Fibers (1), (2) and (3), respectively. The samples are drawn to the lengths of 1 to 3 km, and their properties are summarized in Table 1.
where A and B are supposed to correspond to Rayleigh scattering loss and waveguide imperfection loss, and αOH(λ) describes the SiOH absorption . The parameters in αOH(λ) are listed in Table 2 , where the amplitudes an are normalized so that ΔαOH gives the peak value of αOH(λ). As shown in Fig. 4, this model successfully describes the losses of the HALFs. It is also seen that the loss is not influenced by the H2O absorption, which should appear on the longer wavelength side of the SiOH absorption . In addition, although another model for better description of the OH absorption tails is known , the model in Ref.  describes more accurately the OH absorption spectra particularly near their peaks in the case of the present fibers.
As shown in Fig. 4 and Table 1, Fiber (2) has lower B and ΔαOH than those of Fiber (1), while the difference in A is small. Particularly, the reduction of B is contributing to Fiber (2)’s low loss of 0.41 dB/km at 1550 nm wavelength. It should be noted that A and B values of the present fibers are significantly lower than those of the holey fiber reported in Ref. , which has A and B values of 3.6 dB/km/µm-4 and 2.8 dB, respectively. The causes of the improvement in B are discussed later. The low ΔαOH of Fiber (2) can be explained by the difference in the fraction of optical power PF located in the holes, which can be estimated by numerical calculation from the structures shown in Fig. 3. Since the proportions ΔαOH/PF are almost the same between Fibers (1) and (2), it can be deduced that they have almost the same amount of OH groups around the holes.
Figure 5 shows comparison between Fibers (2) and (3), which have different power fractions in the holes due to the difference in the air-silica structure. It can be seen that Fiber (3) has larger B and ΔαOH than those of Fiber (2), while the difference in A is small. As in the case of the comparison between Fibers (1) and (2), the proportions ΔαOH/PF are almost the same, suggesting that the same amount of OH groups exist around the holes. Moreover, there is also an agreement in the proportion B/PF, which indicates that the holes are also contributing to the wavelength independent loss, though the mechanism is unclear at present.
The present results suggest that there are at least two causes for the wavelength independent loss B in the HALF. The dependence of the B value on PF seen in the comparison between Fibers (2) and (3) indicates the contribution of the holes to the wavelength independent loss. On the other hand, the B value of Fiber (2) lower than that of Fiber (1) cannot be explained by PF alone. The effect of the drawing tension is the most probable explanation for this. Although it is well known that there exists an optimum drawing tension that minimizes the B value of pure silica core fiber , optimization of the drawing tension has not been performed in drawing Fiber (1). It can be inferred that the high B value in the holey fiber in Ref.  is also caused by the above two causes because the reported fiber is believed to have a larger PF and to have been drawn with a higher tension than the present HALFs.
Hole-assisted lightguide fiber (HALF), which comprises a material index profile and several holes, can realize large anomalous dispersion and lower relative dispersion slope than those of the conventional fibers. In addition, the low power fraction in the holes and structural simplicity help to realize low loss. In fabrication, a HALF with a 0.41 dB/km loss and +35 ps/nm/km dispersion at 1550 nm wavelength has been demonstrated. We have modeled the loss of the HALF and confirmed that the wavelength independent loss is dominant. Moreover, comparison among results of the loss modeling for several HALFs suggests that the contribution of the holes and the drawing tension are the most probable causes of the wavelength independent loss.
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