Ultra-High Nonlinear Lead Silicate Photonic Crystal Fiber with Two Zero Dispersion for Supercontinuum Generation Applications

This paper presents an unique type of Lead silicate (SF57) photonic crystal fiber (PCF) with eleven rings of air holes. The PCF promises to yield very large nonlinearity . The PCF has two zero dispersion at wavelength 0.3 𝜇𝑚 and 1.50 𝜇𝑚 . The value of nonlinearities is highest reported till now. The PCF contains very low optical mode field, causes large nonlinearity which makes it best suitable PCF for generating supercontinuum.


Introduction
Photonic crystal fiber (PCF) was first discovered by knight et. al. in 1996 [1] and generally have the defected central core surrounded by air holes cladding in a regular triangular or hexagonal lattice pattern. The effective refractive index contrast between core and cladding with flexibility of design promises excellent optical properties like high nonlinear coefficient [2,3], zero dispersion [2,3], endless single mode propagation [4], and high birefringence [4] etc. PCFs can achieve a high effective nonlinear coefficient by keeping effective mode field area as small as possible. The chromatic dispersion of the PCFs can be tuned by tailoring the air holes pitch and air holes cladding arrangement. These properties are the best suitable for a variety of novel application including optical soliton parametric amplification and supercontinuum generation [5][6][7][8]. The high value of nonlinear coefficient can be achieved by tight mode confinement with the use of glasses with greater intrinsic material nonlinearity coefficients than silica. Lead Silicate PCFs, especially SF57 glass PCF has a high nonlinear refractive index (4.1 × 10 −19 2 ⁄ ), transmission up to wavelength 3.5 , good thermal and crystallization stability [3] as compared to the fused silica glass PCF, where fused silica has a nonlinear refractive index (2.1 × 10 −20 2 ⁄ ) and transmission limit upto wavelength 2 .
In a PCF large nonlinearity can be realized by making a very tight confinement of the optical mode in the core region, which could be achieved either by decreasing the core area with some modification in the cladding design or increasing the refractive index contrast between core and cladding by introducing shown to lead silicate glass with nonlinear coefficient which is 20 times larger than that of silica glass and has good thermal and crystallization stability [13,14]. Lead silicate glass fibers exhibit attenuation ~1-3 dB/m at the operating wavelength 1.55 , whereas chalco-sulfide glass has fiber attenuation 3-4 dB/m at 1.55 [14] and it has higher thermal expansion coefficient than silica, which may allow more flexibility in the fabrication process. A brief comparison of thermal, crystalline and other properties of soft glasses have been discussed by Feng et al. [14]. PCFs with large effective optical nonlinearity require very low threshold power to generate broadband supercontinuum, which make them attractive for application in supercontinuum (SC) generation.
Due to large effective nonlinearity, PCFs made of SF57 glass have remain very attractive nonlinear medium for SC generation. Extensive investigations have been carried out towards evolving designs of SF57 glass PCFs to achieve large effective nonlinearity and small dispersion so as to get flat broadband supercontinuum in these fibers. Along this direction, several authors have studied effective nonlinear coefficient of SF57 glass PCFs. For example, effective nonlinear coefficient of 112, 500 and 1860 −1 −1 at 1.55 µ operating wavelength were respectively reported by Xing-Ping et al. [9], Tiwari et al. [10] and Leong et al. [12]. Several efforts have been made to achieve wideband SC spectra in SF57 glass PCFs [9][10][11][12]. For example, Xing-Ping et al. [9] generated SC spectra from 1300 nm to 1900 nm, Leong et al. [12] were able to generate SC spectra spanning more than 1000 nm by using 300 fs pulses in a 6.8 cm long fiber. Miret et al. [11] have reported 3 dB flat SC spectra spanning over ~1500 nm by using femtosecond pulse in a 15 cm PCF which exhibits normal dispersion. Buczynski et al. [13] have also reported about wavelength 1540 nm. Tiwari et al. [10] generated SC spectra from 1000 nm to 3200 nm by using 50 fs pump pulse of peak power 2 kW in a 15 cm long PCF. Along this direction, we focus our attention to achieve broadband SC generation at low input power. The objective of the present study is to two-fold.
First, to design a SF57 glass PCF which exhibits large nonlinearity and low dispersion and then we use this fiber to achieve broadband SC spectra employing pump pulses with low peak power. The proposed fiber can be fabricated without many difficulties since several authors have demonstrated the fabrication of PCFs with soft glass. For example, Leong et al. [12] have fabricated a soft glass PCF with core diameter 0.95 µ , Xing-Ping et al. [9] have studied SF57 PCF with small air hole of diameter 0.5 µ which was fabricated by Institute of Photonics and Advance Sensing at University of Adelaide, Australia. Buczynski et al. [13] have also demonstrated the fabrication of lead silicate PCF with core diameter 3.36 µ by using extrusion technique [15].
The organization of the paper is as follows: In section 2, we have described the necessary computational procedure. In section 3, we have described the PCFs. Important results have been discussed in this section. A brief conclusion has been added in section 4.

Theoretical Model
Fiber dispersion is one of the most important parameters relevant to supercontinuum generation. . The single modeness of a PCF is characterized by the normalized V parameter whose effective value can be expressed as = 2 Λ √ 2 − 2 , where Λ is the hole pitch, is the refractive index of the core. The single mode cut-off for photonic crystal fiber is ≤ 4.1 [17]. The confinement loss is calculated by using finite element method (FEM) [18,19], which is numerically represented as = 8.686 0 ( ), where ( ) is the imaginary part of the effective refractive index and 0 = 2 ⁄ is the wavenumber in free space [20].

Result and discussion
With the aim of achieving high nonlinearity with two zero dispersion. We designed a unique type of body centered hexagonal PCF by confining its optical mode field as small as possible to achieve high nonlinearity with two zero dispersion, whereas the simple fiber design was unable to confine the optical mode field small as compared to the proposed design with desired two zero dispersion wavelengths. We therefore modify the design by additional introduction of small air holes in each hexagonal lattice layer of air holes. This modification leads a very tight confinement of optical mode field in the core region, which helps to achieve large nonlinearity ( Fig. 1(a)).  The schematic of the fiber is shown in Fig. 1(b), which has eleven rings of circular air holes with unique geometry, where a small air hole of diameters d 3 = 0.6 × Λ μm is surrounded by the large air holes with d 2 = 0.8 × Λ μm in a periodic hexagonal pattern. The air hole diameter d 1 of the first ring ( d 1 = 0.9 × Λ μm) is slightly larger than the neighboring air hole which ensures small effective area and outermost ring d 2 = 0.8 × Λ μm. Fig.2 illustrate the leakage of the optical mode from simple design of PCF with = 0.9 × Λ μm. It may be observed that the PCF is not able to confine the optical mode inside the core. Hance, start leaking from the cladding. After several alteration, the optical mode is able to remain in the core of the fiber, which may be seen from Fig.1(a).  . The effective area gradually increases at higher wavelengths, which cause of getting high nonlinearity at hole pitch Λ = 0. 8 (Fig. 3). Table.1 depicts the large nonlinearities with effective area at variation of different pump wavelength for supercontinuum generation.

Conclusion
We have designed a highly nonlinear photonic crystal fiber, which contains eleven rings of air holes. These air holes are arranged in a body centered hexagonal lattice pattern. The diameter of the air holes in the innermost ring is the largest while that of the outermost ring is smallest. By optimizing the structure parameters, the nonlinear coefficient value is achievable up to ~4640 W −1 km −1 at 1.55 and the two zero dispersion wavelength is at 0.3 and 1.55 . Finite difference time domain method has been adopted to study the optical fiber dispersion and non-linear characteristics of the fiber. This proposed highly nonlinear PCFs is easy to fabricate by using flam brushing technique. With regard to the two zero dispersion wavelength, highly nonlinearity PCFs are a good candidate to the supercontinuum generation at wavelength 1.55 .