A new type of index-guided photonic crystal fiber is proposed to enhance chemical sensing capability by introducing a hollow high index ring defect that consists of the central air hole surrounded by a high index GeO2 doped SiO2 glass ring. Optical properties of the fundamental guided mode were numerically analyzed using the full-vector finite element method varying the design parameters of both the defects in the center and the hexagonal air-silica lattice in the cladding. Enhanced evanescent wave interaction in the holey region and lower confinement loss by an order of magnitude were achieved simultaneously, which shows a high potential in hyper sensitive fiber-optic chemical sensing applications.
© 2011 OSA
Index guiding photonic crystal fibers (PCFs) consisting of the central silica defect and periodic arrays of air holes have realized unique optical properties that could not be achieved in conventional single mode fibers (SMFs) such as endless single mode, high nonlinearity, high birefringence, and flexible chromatic dispersion, to name a few [1, 2]. Other than those transmission related properties, the evanescent wave interaction of the guided mode in index-guiding PCFs in the holes has recently brought intense interests due to its enhanced performances compared to the prior fiber-optic chemical sensing schemes such as D-shaped fiber  and tapered fibers . Thus, PCFs have recently initiated novel chemical sensing applications for various bio-chemical analytes in both gas and liquid phases [5, 6]. Another type of PCF, the hollow core photonic band gap fiber (PBGF), has further increased light-matter interaction by maximizing the overlap between the light and analyte along the central hole . However, it has suffered from narrow and discrete transmission windows that significantly reduce species of analytes as well as the inherent lack of geometrical uniformity along the axial direction. Therefore, the index guiding PCFs are regarded to provide higher potential in practical sensing applications.
In conventional index guiding PCFs, the principal waveguide parameters are: hole diameter (d), pitch size (Λ), and air filling ratio (d/Λ). It has been widely accepted that the large air-filling ratio and small pitch size (Λ<1μm) can increase the evanescent interaction [6, 8], which unavoidably induces very weak tolerance against geometrical variations and also suffers from significant fabrication difficulties. Recently, attempts to replace the solid silica defect of conventional index-guided PCFs with a smaller air hole have been reported to enhance sensing capability , which is schematically shown in Fig. 1-(a) . In this prior PCFs [9-11], the larger central hole diameter dc, showed the higher evanescent field fraction, nevertheless it should be less than cladding hole diameter d, to satisfy the effective index guiding criterion. Despite the improved evanescent interaction, the prior PCFs with a larger dc, suffered from an excessive confinement loss, which raised a critical trade-off between the sensitivity and the confinement loss in PCF design for sensing applications . In order to cope with ever increasing demands for chemical- and bio-sensing PCF devices, there exist compelling needs to develop a novel waveguide structure to overcome this critical trade-off in prior PCFs.
In this paper, we proposed a new index-guided PCF for chemical sensing applications with a hollow GeO2-doped high index ring defect to simultaneously achieve a higher evanescent wave interaction efficiency, a lower confinement loss, and a lower splicing loss than prior PCFs, for the first time to the best knowledge of the authors. The schematic structure of the proposed PCF is shown in Fig. 1-(b), where the hollow high index ring defect at the center is depicted along with its structural parameters in Fig. 1-(c). In addition to the central hole diameter dc, the proposed defect provides two additional waveguide parameters as indicated in Fig. 1-(c): the thickness wring and relative index difference Δring, of doped ring, which can endow a new degree of freedom in waveguide design. The defect is adopted from the hollow optical fiber , which has a high index GeO2 doped silica ring core, and has been successfully implemented in index guiding PCFs for dispersion and polarization control [13, 14].
In this paper, the proposed structure efficiently decreases the confinement loss by the single hollow high index ring defect at the center that can replace a number of additional air holes in the outer rings in prior PCFs. Moreover, it also allows a new degree of freedom to control the diameter of the central defect equal or larger than those of cladding holes in order to further enhance the sensitivity, which has not been possible in prior PCFs. Due to the unique adiabatic collapse of the Ge-doped ring into a solid high index core, the proposed PCF also provides an order of magnitude lower splice loss. Throughout the whole analyses, we assumed 5 layers of air holes in the cladding with the diameter d = 1.4μm, the hole to hole pitch Λ = 2.3μm, and the refractive index of holey region to be ns = 1 for both PCFs in Fig. 1-(a) and (b).
2. Numerical analysis on optical properties
In order to investigate optical properties of the proposed PCF, a full-vectorial finite element method (FEM) was applied for solving Maxwell’s equations, because of its well-proven reliability and accuracy for PCF analyses [15,16]. We assumed the circular perfectly matched layer (PML) , where the electric field satisfies Maxwell’s equations:
Here μr and εr are relative permeability and permittivity, respectively. k0 is the free-space wave number, ω is angular frequency, and σ is electric conductivity. Material dispersion of SiO2 glass  and germanosilicate glass (GeO2-SiO2)  were also used for precise calculation of effective indices of the guided modes.
In real PCFs, the holey cladding region is surrounded by the outer silica clad to result in a confinement loss (dB/m), which is given in terms of neff is the complex effective refractive index of the guided mode and λ is the light wavelength [20, 21]:
If the index contrast between the core and the clad gets weaker by the central air hole as in the prior PCF in Fig. 1-(a), a significantly high confinement loss occurs to trade off the sensing capability [9-11]. In prior PCFs, reduction of the confinement loss have been attempted by increasing the number of hole layers in the cladding [21, 22]. However, imbedding additional air hole layers into PCFs requires highly elaborated processes in practical manufacturing, especially to keep the hole uniformity along both the lateral and axial directions. For example, if we add more air hole layers, it requires to have additional 36 capillaries in the 6th layer and 42 capillaries in the 7th layer properly arranged in the hexagonal structure. Even in the state of art PCF fabrication process, it is very demanding to keep the uniformity of extra 36~78 layers in addition to 91 holes of the 5 layer hexagonal structure. Non-uniformity in holes will inevitably result in an irregular length-dependent mode field distribution, and chromatic dispersion to seriously damage the repeatablity of optical measurements . Here we proposed a unique and efficient method to decrease the confinement loss by the single hollow high index ring defect at the center that can replace 36~78 additional air holes in the outer rings in prior PCFs.
According to the modified Beer-Lambert law , absorbance, A, is given by:
Using FEM, the impact of the proposed ring defect over Re[neff(λ)] was analyzed, and the results are summarized in Fig. 2 . We will use the term “effective index” to represent Re[neff(λ)] in the following discussion. In Fig. 2, we could confirm that the effective index can be flexibly controlled by either the ring thickness wring or the relative index difference Δring of the proposed PCF, which enables the control of the light intensity distribution near the center and over the air holes.
The modal intensity distribution of the fundamental mode for the proposed PCF and the prior PCF at λ = 1.5μm are shown in Fig. 3 . For both PCFs, the central hole diameter was set as dc = 0.8μm and dc = 1.2μm in Fig. 3-(a) and (b). In the proposed PCF, we set the relative index difference Δring = 1.2% and the ring width wring = 0.6μm.
It is noted that the ring defect in the proposed PCF is tightly binding the fundamental mode as shown in Fig. 3-(a). In contrast, in the prior PCFs, the mode spreads throughout the silica cladding region as in Fig. 3-(b). This trend gets more prominent with the larger central hole diameter, dc = 1.2μm: the mode did spread out further beyond the third hole layers of the prior PCF. In Fig. 3-(c) and (d), the proposed PCF with a larger central hole diameter d c = 1.2μm simultaneously provided an almost equivalent relative sensitivity and orders of magnitude lower confinement loss in comparison to prior PCF, which confirms that the proposed PCF can efficiently deal with the critical issue of trade-off between the confinement loss and the sensitivity that has been a design bottleneck in prior PCF. In the following sections, we will focus on the cases of d c≥1.2μm.
2.1 Achievement of a lower confinement loss in the proposed PCF (dc<d)
We investigated the effects of the relative index difference Δring and the ring width wring in the proposed defect on the confinement loss assuming gas sensing, ns = 1. The spectral range (λ) was confined to the near infrared from 0.8 to 2.0μm where the absorption lines of various standard sensing gas molecules are located [25, 26]. For instance stretch bands and their overtones of C-H, N-H, and O-H bonds are located in the spectral range . We especially focused on the longer wavelength region to take the advantage of stronger absorption intensity of lower order overtones of molecular vibrations.
In the proposed PCF, Δring was varied from 0.4 to 2.0% and its effects over the confinement loss and relative sensitivity were analyzed in Fig. 4-(a) and -(b), respectively. Here we fixed other parameters; Λ = 2.3μm, d = 1.4μm for the cladding, and dc = 1.2μm, and wring = 0.6 μm for the hollow ring defect. Higher Δring could reduce the confinement loss by orders of magnitude, to achieve a low confinement loss less than 8.1dB/m in the whole operating wavelength range for Δring = 2.0%. At the wavelength of λ = 1.5μm, the confinement loss of the proposed PCF was 0.023dB/m, while that of the prior PCF was as large as 32dB/m.
Similar results were obtained by increasing wring or equivalently expanding the GeO2 doped region as shown in Fig. 5-(a) and -(b). We varied the ring width wring from 0.2 to 0.8μm while the other parameters were set as Λ = 2.3μm, d = 1.4μm, ns = 1, dc = 1.2μm, and Δring = 1.2%. The wider wring provided the lower confinement loss as in Fig. 5-(a). For wring = 0.8 μm, the confinement loss of the proposed PCF was less than 15dB/m in the whole operating wavelength range, and at λ = 1.5 μm, it was 0.026dB/m, which is two orders of magnitude smaller than the prior PCF. On the other hand, the relative sensitivity did not show significant variation for modification of Δring and wring, especially in the shorter wavelength range as shown in Fig. 4-(b) and Fig. 5-(b).
The effective V number of the proposed PCF increases either by thicker ring width wring or higher index difference Δring, which can allow higher order modes guidance. For example, when we take the extreme defect parameters of wring = 0.6μm and Δring = 2.0%, the proposed PCF guides 2 modes at λ = 1.5 μm. In the intensity based sensing using a few-mode PCF, it is reported that the effective sensitivity can be approximated with a fair accuracy to an average sensitivity of individual modes, if the modes have similar field overlap with the analytes . We confirmed that all the core modes of the proposed PCF did have almost the same power fraction in the air holes with the average value of 4.07% and the maximum of 5.39% in the relative standard deviation in the entire wavelength range of interests. This is due to the nature of the ring defect to confine the higher order mode around the central defect .
2.2 Higher sensitivity and lower confinement loss with optimal parameters (dc = d)
The prior PCF is known to provide a higher relative sensitivity, r, with increasing central air hole diameter dc . However, dc must be kept smaller than the cladding air hole diameter d, (dc<d), otherwise the effective index guiding is not realized physically. One of the contrasting advantages of the proposed PCF is that the diameter of the central hole can be enlarged to be the same as the cladding holes (dc = d) due to the high index ring.
By systematic analyses, we found optimal waveguide parameters for the proposed PCF: dc = d = 1.4 μm, Λ = 2.3 μm, wring = 0.6μm, and Δring = 1.2%. As shown in the orange plot in Fig. 6 , the optimal PCF provides not only a lower confinement loss but also a higher relative sensitivity for the entire spectral range than prior PCF. As indicated by the arrows in Fig. 6, at λ = 1.5μm, the relative sensitivity, r, of the optimal PCF was 5.09% significantly larger than 4.79% of the prior PCFs. The confinement loss of the optimal PCF was 1.25dB/m, while that of the prior PCFs was 32.4dB/m. In this optimal condition, the proposed PCF provided a tighter confinement of optical field than the prior PCF, especially at holes at the center and the first ring. This local confinement capability of the optical PCF contributed to a larger power fraction in the air holes and subsequently a higher relative sensitivity. Therefore, we could confirm that the proposed PCF can successfully overcome the critical trade-off between the confinement loss and sensitivity in prior PCFs, providing a fundamentally new degree of freedom in waveguide design to explore sensing application capabilities.
To measure the absorbance after filling the chemical analyte into the sensing PCF, efficient light launching is highly demanded. Fusion splicing between conventional single mode fiber (SMF) and PCF has been widely used, yet it requires sophisticate optimization of arc parameters. Especially, the air holes in PCFs are easily collapsed by high temperature arcs as schematically shown in Fig. 7-(a) . The GeO2 doped ring in the proposed PCF adiabatically collapses to a solid core  and keeps the guided beam confined to the center to have a larger overlap with the fundamental mode of SMF. In Fig. 7-(b), the splicing loss between SMF and PCFs were estimated as a function of collapsed hole diameter using the reported formulae in reference . The proposed PCF showed a significantly lower loss as the air hole collapses and its splicing loss was estimated to be as low as 0.22dB in contrast to 12.75dB of prior PCF.
A novel index-guided photonic crystal fiber for sensing applications was successfully demonstrated to provide a unique solution to the trade-off between the confinement loss and the sensitivity in prior designs, by embedding a hollow high index ring defect at the center. The proposed defect provided new waveguide design parameters: the ring index difference Δring and the ring width wring to efficiently control the optical guidance and the power fraction over the air holes. At λ = 1.5μm, the proposed PCF with optimal parameters provided a high relative sensitivity of 5.09% significantly improved from 4.79% of the prior PCFs, and a low confinement loss of 1.25dB/m, an orders of magnitude reduced from 32.4dB/m of the prior PCFs. This excellent optical properties were made possible by extending the central hole diameter dc to the cladding hole diameter d (dc = d), which was not achievable in prior PCFs. A low splicing loss of 0.22dB was also estimated between the conventional single mode fiber due to adiabatic mode conversion along the GeO2-doped ring defect, which enables practical applications in chemical sensing.
This work was supported in part by the Brain Korea 21 Project and in part by the National Research Foundation of Korea (NRF) grant funded by the Korean Ministry of Education, Science, and Technology (MEST) (Nos. 2010-0018442, 2009-00479, EC-FP7/2007-2013, 219299 GOSPEL, and 2010-0017286).
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