Simultaneous achievement of high birefringence, broadband normal dispersion, and endlessly single-mode operation for an optical fiber would provide a new platform for optical communications and optical-fiber sensing systems. By controlling polarization cross-talk, high birefringence in fiber optics has found various applications in fiber-optic sensors, gyroscopes, interferometers, fiber lasers, and coherent optical communications [1, 2]. Broadband normal dispersion in an optical fiber is needed to compensate for chromatic dispersion in a conventional single-mode fiber (SMF) over a wide range of wavelengths in wavelength-division multiplexed communication systems [3]. In addition, stable single-mode operation in photonic waveguides is a fundamental requirement in many areas of modern photonics and optical communications systems, and broadband operation with single-mode guidance is very important for improving overall system performance. Several types of optical fibers with a conventional step-index design have been proposed to address these issues individually, but there has been no integrated solution that addresses all of these issues simultaneously. An integrated solution to combining various optical functions (
In this study we propose a hybridsquare-lattice PCF based on the conventional square lattice and just two different-size air holes to control various optical properties simultaneously such as high birefringence, large normal dispersion, and single-mode operation. The proposed PCF has circular air holes of two different diameters alternating in the cladding, plus a silica defect at the center. Preliminary results for the proposed design have been published in conference proceedings [19-21]. However, in this paper, we show progress in control of multiple optical properties such as high birefringence, large normal dispersion, and single-mode operation at the same time. The optical properties of the guided modes are analyzed numerically by the finite-element method with a perfectly matched layer as the boundary condition. The proposed fiber structure is based on the conventional square-lattice cladding, which can be readily fabricated by the stack-and-draw method using fused-silica glass capillaries of two different wall thicknesses [4].
The new PCF design in this study is based on a hybrid-square-lattice cladding structure. The core of the HS-PCF is based on that of a conventional HB-PCF. To illustrate the design algorithm for a proposed fiber, the cross sections of a proposed HS-PCF and a conventional HB-PCF are shown in Figs. 1(a) and (b) respectively. Both PCFs have a central silica defect and smaller air holes on both sides, which introduce asymmetry in the core. The lattice of the cladding region is defined by the distance between consecutive holes Λ, the larger hole diameter
III. COMPARATIVE STUDY OF A CONVENTIONAL HB-PCF AND THE PROPOSED HS-PCF
To demonstrate the effect of smaller air holes in the cladding of the proposed HS-PCF on its modal properties, we compared the modal properties of a conventional HB-PCF and a proposed HS-PCF using the finite-element method (FEM) with the circular perfectly matched layer (PML) boundary condition. An efficient boundary condition must be used to simulate the leakage. PMLs are the most efficient absorption boundary conditions, producing no reflection at the boundary [23].
In an optical fiber with mode guiding by total internal reflection (TIR), single-mode operation is cut off when the effective refractive index of the guided mode becomes equal to the effective index of the fundamental space-filling mode of the cladding [5]. Using FEM, the effective indices of guided modes and the cladding mode can be swept as a function of the wavelength. We found the crossing point as a cutoff wavelength by plotting the effective index of each mode obtained by FEM. Figure 2 shows the modal dispersion curves for the guided modes and cladding modes for the proposed HS-PCF (Fig. 2(a)) and the conventional HB-PCF (Fig. 2(b)) with Λ = 1 μm,
Reducing the index contrast between core and cladding by adding small air holes in the cladding is a simple design strategy for a HS-PCF to yield a single-mode fiber while maintaining high birefringence. This is a key result, and the reason to introduce small air holes into the cladding for a proposed HS-PCF.
Next, to study the effect of small air holes in the cladding of the HS-PCF on its optical properties, the guided-mode shape, modal birefringence, chromatic dispersion, and confinement loss of the fundamental modes for both HB-PCFs are numerically analyzed. Once the modal complex effective index
where
Figure 3 shows the
To compare other optical properties of both PCFs, the modal birefringence and chromatic dispersion of the
Now we discuss the confinement losses of the two PCFs. As expected, the confinement loss for the HS-PCF becomes slightly greater than that for the conventional HB-PCF, because of the lower index contrast between core and cladding. However, the confinement loss is still quite small (< 0.205 dB/km) and comparable to that of a conventional SMF. From the simulation results, the proposed HS-PCF shows slightly lower birefringence and higher confinement loss than the conventional HB-PCF. However, there is a key advantage in the proposed HS-PCF beyond the conventional HB-PCF: The HS-PCF can support true single-mode operation over the entire communication band, with high birefringence and normal dispersion at the same time.
IV. OPTIMIZATION OF THE PROPOSED HS-PCF
To apply the proposed HS-PCF to an optical communication system, the optical properties of the proposed fiber should be optimized over the S, C, and L communication bands. Figs. 5(a) and (b) show the effects of the structural parameters Λ and
The optimized
According to the above results, the proposed HS-PCF can act as a DCF to compensate for the accumulated dispersion of an SMF, and can be used to eliminate the effect of PMD in optical communication systems, and in many other areas where polarization-maintaining properties are required, such as sensing applications [25]. Fibers with highly flat birefringence and dispersion compensation are extensively used in fiber-loop mirrors, as a major component for optical-fiber sensing applications, with better performance for fiber-sensor design. In addition, true single-mode operation is also required for a long-distance data transmission system.
A simple fabrication process is a key advantage for a PCF. Other HB-PCFs, dispersion-compensating PCFs, or PCFs with both properties, have very complicated structures to enhance performance, such as elliptical air holes [12], five types of different air holes, and unconventional cladding structure [13-14, 25], which are difficult to fabricate using the stack-and-draw method. Another strong point of the proposed HS-PCF design is its easy fabrication process. All the air holes of the HS-PCF are circular, and the structure of the cladding is a conventional square lattice. Therefore, using the conventional stack-and-draw method, the proposed HS-PCF can be easily fabricated [26-29]. The most important issue in the optical-communication industry lately has been the reduction of price in the development of optical devices. To accoplish this, the functions of various optical components should be combined in a single device, to minimize the system. The proposed HS-PCF is a good example of a combined integrated waveguide with the multiple functions of polarization maintenance, broadband dispersion compensation, low loss, and true single-mode operation for optical-communication and smart-sensing applications.
In this paper we have proposed a true single-mode, highly birefringent, and broadband dispersion-compensating HS-PCF over a wideband optical-communication region. By the simple design strategy of introducing small air holes into the cladding of a conventional HB-PCF, broadband single-mode operation, high birefringence, and large normal dispersion can be achieved simultaneously in the proposed HS-PCF. The optimized HS-PCF has a normal dispersion coefficient of −601.67 ps nm−1 km−1 and birefringence of 1.025×10−2 at 1.55 µm. In addition, in the S+C+L+U wavelength bands the proposed HS-PCF has ultraflat birefringence with a slope of the order of 10-5. The confinement loss of this HS-PCF is comparable to that of a conventional SMF, according to numerical results using an imaginary effective index. The proposed HS-PCF can be used as a multifunction waveguide in optical-communication and smart-optical-sensor applications.