Characteristics of photonic crystal fibers with different lattices: Realization of constant air percentage by fixing air-filling fraction
Introduction
With the advent of photonic crystals in the field of optoelectronics, photonic crystal fibers (PCFs) have come to the forefront in fiber research. PCFs resulted from the search for fibers having superior properties to those of conventional fibers by virtue of a novel light-guiding mechanism. In 1978, Yeh et al. proposed the principle of a Bragg fiber, which led to the concept of PCFs [1]. In 1992, Russell et al. proposed a special type of fiber consisting of periodically arranged microstructures with air holes, which were either circular or hexagonal in shape [2]. The PCFs reported in subsequent years had a refractive index variation around the core, which was maintained along their entire length [[3], [4], [5]]. Compared with conventional fibers, PCFs have several key properties, such as dispersion tailoring, endless single-mode operation, and ultra-high nonlinearity, which make them useful for applications in both telecommunications and the medical field [[6], [7], [8], [9]]. It is possible to design PCFs with different structures, different air-filling fractions (AFFs), and a different number of rings, as required [5,10].
The peculiar properties exhibited by PCFs are directly related to the air-hole diameter, the hole-to-hole spacing, and the geometrical distribution of air holes around the core [[11], [12], [13], [14]]. Hence, it is interesting to investigate the dependence of mode characteristics on the geometrical arrangement of air holes in PCFs. Historically, the most common structure adopted and realized has been a hexagonal array of air holes around the core [2]. To overcome the limitations of hexagonal PCFs (H-PCFs), that is, to impart good bandgap guidance [3] and to fully exploit advances in fabrication technology [15], new lattice structures have been introduced. Recently, researchers have investigated new square [16], pentagonal [17], heptagonal [18], octagonal [19], nonagonal [20], circular [21], spiral [22], and decagonal [23] lattices of air holes.
An advantageous property of these microstructured fibers is their capacity for flexible design to attain required optical properties. By appropriate selection of lattice points for air holes in the host material (silica), it is possible to obtain different dispersion properties, such as zero dispersion at a desired wavelength, low and ultra-flattened dispersion at visible or longer wavelengths, along with small confinement losses and facilitation of infinite single-mode guidance [[24], [25], [26], [27], [28]]. The realization of high birefringence results in polarization-maintaining PCFs, and all of these properties make PCFs suitable candidates for application in the telecommunications field and as polarization controllers [6]. Although silica materials exhibit poor nonlinearity, PCFs provide sufficient index contrast between the silica core and air-hole-permeated cladding region, which permits high-intensity pulse guidance through their fiber cores, resulting in a steep nonlinear coefficient gradient. Such highly nonlinear and dispersion-tailored PCFs are good candidates for nonlinear optical applications, such as the generation of supercontinuum white-light sources, spectroscopy and microscopy, metrology and optical coherence tomography (OCT) medical instrumentation, and so on [12]. The design freedom to obtain large mode area in PCFs permits the transmission of high-power radiation with single-mode guidance, making them useful in fiber laser and fiber amplifier applications [18]. The advantageous compact structure, fast response, and efficient light-controlling techniques of PCFs have increased their prevalence in the realms of chemical/gas sensors and sensors for different blood components, pressure, refractive index, temperature, and so on [[29], [30], [31], [32]]. Amiri et al. designed and simulated a typical tri-core PCF sensor using a finite-element method (FEM) for the simultaneous sensing of salinity and temperature of aqueous media [33]. Recently, a D-shaped elliptical core PCF has been reported for the detection of plasma cells in blood samples [34]. In 2014, a low-loss highly nonlinear square-lattice PCF was proposed for applications in nonlinear optics, optical signal processing, and supercontinuum spectrum generation [35]. A 1 cm long silicon core–silica cladding PCF has been reported to produce a wideband SC spectrum in the NIR region [36]. A modified five-ring hexagonal-circular PCF structure with an asymmetric core region and a mirror-symmetric refractive index profile cladding region has recently been proposed for broadband communication and sensing applications [37].
In this context, Hossain et al. [38] designed four-ring square, circular, and hexagonal PCFs with near-zero confinement loss in the wavelength range 800–1500 nm. They reported that the square PCF (S-PCF) had a larger effective area than the H-PCF when the diameter and pitch of the air holes was kept the same. Matloub et al. [39] designed and simulated a dodecagonal PCF (Dod-PCF) and compared its optical characteristics with those of an octagonal PCF (O-PCF) and a decagonal PCF (D-PCF) with the same parameters. They reported that the Dod-PCF had a nonlinear coefficient (NLC) of 43.67 W−1 km−1 and a low confinement loss with an ultra-flattened dispersion of 0.8 ps/(nm·km) in the spectral region 1300–1700 nm. The NLC of the designed O-PCF (43.88 W−1 km−1) was nearly equal to that of the Dod-PCF. Ahmed et al. [40] carried out a numerical analysis of O-PCFs having a microstructured core, and found their relative sensitivity to be higher and their confinement loss to be lower than those of H-PCFs and S-PCFs. Another parameter relates to bending and scratches on the fiber, which result in a loss of electromagnetic energy, and is termed the bending loss.
Several PCF structures have recently been simulated and characterized for different fields of application in optics. The various fiber structures have included micro-air-hole arrangements in the core, asymmetric arrangements of air holes in the cladding, fibers based on host materials other than silica, and fibers with different dopants. Although most of these designs have their merits, the cost of their fabrication may prevent their wide implementation. Hence, simple patterns consisting of a standard configuration of circular air holes in the cladding region remain the most prevalent research topic. Nevertheless, some researchers have studied the properties of other air-hole arrangements, such as octagonal, decagonal, and so on, comparing the characteristic properties of basic higher order structures with those of currently available fiber designs. In this regard, we have attempted to systematically examine some essential characteristics, such as confinement loss, dispersion, effective mode area, and nonlinear coefficient, of fibers with different configurations of air holes, namely square, pentagonal, hexagonal, octagonal, nonagonal, decagonal, and dodecagonal. To the best of our knowledge, the simultaneous design and comparison of these structures has not been considered previously, and this study may greatly expedite the manufacture of such fibers.
In this work, the mode properties of solid-core silica PCFs having different lattice arrays of air holes, namely square, pentagonal, hexagonal, octagonal, nonagonal, decagonal, and dodecagonal, with uniform AFF, have been evaluated by a full-vector finite-element method, keeping fixed the fractional percentage of air in each silica unit cell triangle. The repeating unit cell in the H-PCFs is a regular equilateral triangle, whereas it is an isosceles triangle with a structurally dependent vertex angle in the other types. We have attempted to understand the characteristic changes in the propagation properties of these PCFs with the geometry of the fibers. The propagation characteristics were studied over the wavelength range 800–2000 nm by employing scattering boundary conditions using the software COMSOL Multiphysics 4.3. Wang et al. demonstrated a model for determining the optical properties of PCFs by combining digital image processing and the finite-element method, the results from which matched those obtained experimentally [41]. In this investigation, a type of cladding pattern conducive to the tuning process of dispersion has been identified, and attempts have been made to achieve maxima and minima in mode effective area with a corresponding nonlinear coefficient. The tuning process has also been investigated to realize flattened dispersion over a large bandwidth. In the fabrication of microstructure fibers, it is essential to realize that the geometrical parameters of the fibers that designed can be accurately developed for the realization of the characteristic results obtained from the simulation studies. Generally, slight variations in the design parameters of the fibers are likely to occur during fabrication. This may affect the optical characteristics of the designed fibers. The principal distortion in PCFs arises from variations in the air-hole radii. Hence, we have extended our investigation to the impact of air-hole size variations on the characteristics of the fibers.
Section snippets
Geometrical parameters
In the design of PCFs, to obtain a fiber with typical characteristics, various parameters first need to be defined, such as air-hole radius, the distance between adjacent air holes (pitch), the angular position of air holes around the center of the fiber, and the air-filling fraction (AFF) [9]. The AFF refers to the relative amount of air present in a silica unit triangle, and an increase therein results in strong confinement of the intensity distribution of the input light in the core of the
Numerical analysis
Input radiation of a given wavelength is guided along the fiber core of a PCF by the process of modified total internal reflection. Here, the propagation characteristics of the proposed PCFs were studied by a full-vector finite-element method using the simulation software COMSOL Multiphysics 4.3. Computational analysis in the design and characterization of PCFs has recently become an effective and extensively used technique in the field of fiber optics, as it allows an infinite platform for
Results and discussion
Contour plots of the light confinement and fundamental mode profiles of the proposed PCFs at an operating wavelength of 1550 nm are shown in Fig. 2. Contour plots are used in post-processing to visualize scalar quantities and fields in the simulation results, and are displayed with a series of colored regions or lines (Fig. 2). It is found that for higher order structures, the modes are tightly confined within the core and provide a Gaussian field output distribution at 1550 nm, as shown in
Conclusion
Three sets of solid-core PCFs with air holes arranged in square, pentagonal, hexagonal, octagonal, nonagonal, decagonal, and dodecagonal arrays, have been prepared with air-filling fractions of 0.24, 0.375, and 0.54. Their optical characteristics have been evaluated by keeping the air-filling fraction and pitch Λ constant. The studies were carried out by a full-vector finite-element method using the software COMSOL Multiphysics 4.3. It has been observed that, irrespective of the hole-to-hole
Financial support
No financial support was provided to any of the authors in the creation/writing of this manuscript.
Declaration of Competing Interest
The authors whose names are listed immediately below certify that they have NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers' bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in
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