NUMERICAL SIMULATION OF ALL-NORMAL DISPERSION VISIBLE TO NEAR-INFRARED SUPERCONTINUUM GENERATION IN PHOTONIC CRYSTAL FIBERS WITH CORE FILLED CHLOROFORM

This study proposes a photonic crystal fiber made of fused silica glass, with the core infiltrated with chloroform as a new source of supercontinuum (SC) spectrum. We numerically study the guiding properties of the fiber structure in terms of characteristic dispersion and mode area of the fundamental mode. Based on the results, we optimized the structural geometries of the CHCl3-core photonic crystal fiber to support the broadband SC generations. The fiber structure with a lattice constant of 1 μm, a filling factor of 0.8, and the diameter of the first-ring air holes equaling 0.5 μm operates in all-normal dispersion. The SC with a broadened spectral bandwidth of 0.64 to 1.80 μm is formed by using a pump pulse with a wavelength of 850 nm, 120 fs duration, and power of 0.833 kW. That fiber would be a good candidate for all-fiber SC sources as cost-effective alternative to glass core fibers.


Introduction
Supercontinuum (SC) generations in all-normal dispersion fiber have been a subject of intense research because of their fascinating properties.
They have been exploited in numerous study fields and promising applications, such as optical coherence tomography [1] and ultra-short pulse generation [2]. Unlike in the anomalous dispersion regime, the SC generated by pumping in the normal regime of dispersion is achieved through the Self-Phase Modulation (SPM) and Optical Wave Breaking (OWB) mechanisms [3].
Therefore, the SC generation in the normal dispersion region enables obtaining spectra with better pulse-to-pulse temporal coherence and flatness [4].
For broadband SC generation, numerous efforts have been devoted to extending the spectral width and flatness over wavelength broadband. To achieve this, the photonic crystal fiber (PCF) requires special optical-wave-guiding designs to produce both flat all-normal dispersion and high-nonlinearity properties. Besides, the initial laser pulse properties should be optimized in terms of pump wavelength, pulse duration, and input energy [5][6]. Various complicated designs, such as different core geometries [7] and multiple air-hole diameters in different rings [8], have been exploited to achieve ultra-flattened dispersion values. Meanwhile, high nonlinear values could be obtained with the use of greaternonlinearity glasses other than silica, such as chalcogenide [9] and tellurium chalcogenide [10].
Another method for achieving materials with high nonlinear values is using hollow-core PCF filled with liquids. Much of effort has been concentrated on some liquids with high nonlinear coefficients, such as carbon disulfide (CS2) [11], toluene (C7H8) [12], carbon tetrachloride (CCl4) [13], ethanol (C2H5OH) [14], nitrobenzene (C6H5NO2) [15], and water [16]. Since the selected liquids cause such a tremendous relative index difference, it is possible to observe and control the nonlinear effects as SC generation [11][12][13][14]. The obtained results indicate that it is possible to shift the zero-dispersion wavelength (ZDW) and match it with the pump wavelength emitted by a highpower commercial laser, obtaining all-normal and flat dispersion regime of expected spectral [17][18].
Liquids have been used for applications in the near or mid-infrared wavelength range [9,10,[12][13][14]. In the meantime, the violet-visible range gets little attention although it contributes to various applications, such as fluorescence imaging, thermal sensing, photodynamic therapy, microscopy of cells, and tissue organization [19,20].
Among the liquids mentioned above, chloroform (CHCl3) emerges as an attractive candidate for the development of liquid PCFs because CHCl3 has a high nonlinear refractive index (6.17 × 10 -19 m 2 /W -higher than that of fused silica, even up to 30 times) [21]. This nonlinearity enables the PCF to generate a much broader spectrum with low input power and within a short propagating distance [12,15].
Another advantage of CHCl3 is the transparent window in the visible to near-IR (0.5-1.6 µm) range [22] and its moderate toxicity compared with other liquids, such as CS2 and C7H8 [23].
Furthermore, the refractive index of CHCl3 is very close to that of fused silica. Therefore, it would be easy to design single-mode chloroform-filled core silica PCFs with a core size similar to that of standard silica fibers.
In this report, we numerically study the

Modeling PCF structure and the study method
The cross-section of the CHCl3-filled PCF is depicted in Fig. 1.
The propagation of the optical pulse whose field amplitude changes slowly is described by using the generalized nonlinear Schrödinger where z is the spatial coordinate along the fiber; α is the total fiber loss, and βn is the n-th order of dispersion.
where Aeff is the effective cross-sectional area of the fiber, and n2 is the nonlinearity of CHCl3.
In the simulation of SC generation, we use

Numerical results
In our study, we aim at designing a new air-glass structure of photonic cladding that allows for flat slopes and low chromatic dispersion inside the all-normal regime, which is employed for supercontinuum source at pumping of 850 nm.
We   In addition, the optimal fiber structure without changing the diameter of the first-ring air holes is characterized by anomalous dispersion where the first ZDW is 0.72 μm; the second ZDW is 1.24 μm, and the dispersion at the 0.85 μm wavelength equals 66.86 ps/nm/km (Fig. 5a).     Furthermore, high nonlinearity makes chloroform a good candidate as a nonlinear medium for use in highly nonlinear liquids-core PCFs. Therefore, this fiber structure would be a good candidate for all-fiber SC sources as a cost-effective alternative to glass-core fibers. Additionally, the linear refractive index of CHCl3 is only about 0.012 lower than that of silica. The latter allows for the design of single-mode CHCl3-filled-core-silica PCFs, which have a core size similar to that of standard silica fibers.