Evaluation of Spiral-Shaped Photonic Crystal Fiber's Performance in Nonlinear Optical Applications

2025-02-14 Fri
photonic crystal fiber nonlinearity birefringence beat length confinement loss
Evaluation of Spiral-Shaped Photonic Crystal Fiber’s Performance in Nonlinear Optical ApplicationsResearch Background and Problem StatementPhotonic crystal fiber (Photonic Crystal Fiber, PCF) is a new type of optical waveguide with unique microstructures. The periodic arrangement of air holes within it enables it to achieve optical properties that traditional optical fibers cannot reach. Since its introduction in the late 1990s, PCF has attracted widespread attention due to its potential applications in fields such as communication, sensing, medical imaging, and nonlinear optics. However, despite numerous studies on PCFs, how to further improve its nonlinearity coefficient (Nonlinearity, γ), birefringence (Birefringence, BR), numerical aperture (Numerical Aperture, NA), and reduce confinement loss (Confinement Loss, LC) remains a challenge.
To address these issues, researchers have begun exploring the impact of different materials and geometric structures on PCF performance. For example, using highly nonlinear materials such as graphene, gallium phosphide, and tellurite glass as core materials has been shown to significantly enhance the nonlinear performance of PCFs. Additionally, designing unique geometries (such as spiral structures) is also considered an effective method to enhance birefringence and numerical aperture.
This study aims to optimize the nonlinear optical performance by designing a novel spiral-shaped photonic crystal fiber (Spiral-Shaped Photonic Crystal Fiber, SS-PCF) and combining it with highly nonlinear materials (such as graphene, gallium phosphide, and tellurite glass). The goal is to evaluate the performance of SS-PCF in nonlinear optical applications and explore its potential application value in future optical communications, supercontinuum generation, and bioimaging.
Paper SourceThis paper was co-authored by Bipul Biswas and Erik M. Vartiainen, both from the School of Engineering Sciences at LUT University, Finland. The paper was published in the journal Optical and Quantum Electronics in 2025, article number 57:148, DOI: 10.1007/s11082-025-08052-z.
Research Process and Methodsa) Research Process and Experimental DesignThis study mainly includes the following steps:
1. Design and Modeling of SS-PCFThe study first modeled the SS-PCF using COMSOL Multiphysics 5.1 software. The cross-section of the SS-PCF consists of an elliptical core surrounded by 10 spiral-shaped air holes. The semi-axis lengths of the core are 0.35 µm and 0.17 µm, respectively, while the diameters of the cladding air holes are set to 0.96 µm, 1.26 µm, and 2 µm. To simulate the boundary conditions of the fiber, two perfectly matched layers (PML1 and PML2) were set up, with their thickness accounting for 10% of the entire fiber. Moreover, silica was used as the background material, while gallium phosphide (GaP), graphene, and tellurite glass were chosen as the core materials.
2. Finite Element Method (FEM) AnalysisThe study used the Finite Element Method (FEM) to conduct a detailed analysis of the optical properties of SS-PCF. A total of 235,430 mesh elements were divided, and key parameters including nonlinearity coefficient (γ), birefringence (BR), beat length (Beat Length, (Lb)), confinement loss (LC), numerical aperture (NA), and effective mode area (Effective Mode Area, (A{eff})) were calculated within the wavelength range of 0.1 µm to 1.5 µm. All calculations were completed based on the Sellmeier equation (Equation 1) and relevant theoretical models.
3. Material Performance TestingTo evaluate the performance of different core materials, the study separately tested gallium phosphide, graphene, and tellurite glass. The nonlinearity coefficients ((n_2)) and refractive indices (RI) of these materials were calibrated according to literature data. The study also demonstrated the mode field distribution of the fiber at wavelengths of 0.1 µm and 1 µm under X and Y polarization modes.
4. Data Analysis and Result VerificationThe study employed various algorithms for data analysis, including power fraction (Power Fraction, η) calculation (Equation 4), confinement loss (LC) calculation (Equation 5), effective mode area ((A_{eff})) calculation (Equation 6), and numerical aperture (NA) calculation (Equation 7). All results were verified by comparing them with existing literature data.
b) Main Research Results1. Birefringence (BR) and Beat Length ((L_b))The study found that within the wavelength range of 0.1 µm to 1.5 µm, the birefringence value of SS-PCF increases with wavelength. Among them, gallium phosphide achieved a maximum birefringence value of 0.33 at a wavelength of 1.5 µm, which is nearly an order of magnitude higher than previously reported results. The beat length ((L_b)) shortens as the wavelength increases; at a wavelength of 0.1 µm, the maximum beat lengths for gallium phosphide, tellurite glass, and graphene are 1247.48 µm, 496.94 µm, and 687.26 µm, respectively.
2. Confinement Loss (LC) and Power Fraction (η)The confinement loss of SS-PCF remains between 1×10⁻⁵ and 3×10⁻⁵ dB/m within the wavelength range of 0.4 µm to 1.5 µm. Graphene exhibits the lowest confinement loss (1.0×10⁻⁵ dB/m) at a wavelength of 0.6 µm. The power fraction (η) decreases as the wavelength increases; at a wavelength of 0.1 µm, the power fractions for gallium phosphide, tellurite glass, and graphene are 99.998%, 99.989%, and 99.995%, respectively.
3. Nonlinearity Coefficient (γ) and Numerical Aperture (NA)Graphene exhibits extremely high nonlinearity coefficients at a wavelength of 0.1 µm, reaching 6.13×10¹² W⁻¹km⁻¹ and 5.31×10¹² W⁻¹km⁻¹ under X and Y polarization modes, respectively. In comparison, the nonlinearity coefficients of gallium phosphide and tellurite glass are 3.70×10⁶ W⁻¹km⁻¹ and 3.28×10⁵ W⁻¹km⁻¹, respectively. Furthermore, the numerical aperture of SS-PCF reaches 0.86 (gallium phosphide), 0.72 (tellurite glass), and 0.80 (graphene) at a wavelength of 1.5 µm, far exceeding the numerical aperture of traditional silica optical fibers (usually less than 0.40).
c) Research Conclusions and SignificanceScientific ValueThis study shows that by combining a spiral structure with highly nonlinear materials, the nonlinear optical performance of photonic crystal fibers can be significantly improved. The SS-PCF proposed in this study exhibits excellent performance in terms of birefringence, numerical aperture, and nonlinearity coefficient, providing important references for the design of future nonlinear optical devices.
Application ValueThe high nonlinearity and low confinement loss of SS-PCF make it widely applicable in fields such as supercontinuum generation, short pulse generation, optical communications, and bioimaging. Additionally, its high numerical aperture and strong birefringence characteristics also offer new possibilities for medical imaging and optical coherence tomography (OCT).
d) Research HighlightsInnovative Spiral Structure: The spiral design of SS-PCF significantly enhances birefringence and numerical aperture.
Ultra-High Nonlinear Performance: Graphene achieves a nonlinearity coefficient as high as 6.13×10¹² W⁻¹km⁻¹ at a wavelength of 0.1 µm.
Comparison of Multiple Material Performances: The study systematically compares the performances of gallium phosphide, graphene, and tellurite glass, providing scientific basis for material selection.
e) Other Valuable InformationThe study also discusses the manufacturability of SS-PCF, pointing out that the sol-gel method and capillary stacking technique are ideal methods to realize this design. Additionally, the study emphasizes the importance of open access to data, and all data can be obtained by contacting the authors.
Summary and OutlookThrough the design and analysis of a novel spiral-shaped photonic crystal fiber, this study successfully demonstrates its outstanding performance in nonlinear optical applications. The study not only provides new ideas for the design of high-performance photonic crystal fibers but also lays the foundation for their practical applications in communication, sensing, and biomedical fields. Future research can further explore the stability of SS-PCF in extreme environments and its integration potential with other optical devices.