High Power Highly Nonlinear Holey Fiber with Low Confinement Loss for Supercontinuum Light Sources

1.Introduction

Photonic crystal fibers are termed as holey fibers. Indexguiding holey fibers have attracted considerable attention from the optical community because they have remarkable dispersion and leakage properties[1]. As optical fiber technology advances, fibers are becoming thinner, stronger, lighter, more flexible, resistance to electromagnetic noise, large carrying capacity, longer transmission, and higher speed. To date,different index guiding highly nonlinear holey fibers (HN-HFs)have been reported for optical communications and medical applications[2]-[6]. Hao et al.[2] modeled a modified hexagonal index guiding photonic crystal fiber with a nonlinear coefficient of 37.1 W−1km−1 at 1.55 μm but this can increase the fabrication process difficulty. Liao et al.[3] presented two highly nonlinear PCFs with nonlinear coefficients of 22.83 W−1km−1 and 29.65 W−1km−1 at 1.55 μm, respectively, but both structures contain four different air holes of different diameters with hybrid claddings. Xu et al.[4] and Matloub et al.[5] designed the doped PCF structures with nonlinear coefficients of 31.5 W−1km−1 at 1.55 μm and 36.5 W−1km−1 at 1.55 μm, respectively which are lower than that of our proposed design and difficult to fabricate. In addition to the hexagonal arrangement of air holes,other structure, such as square lattice, has been proposed by Begum et al.[6]. The wavelengths near 1.0 μm and 1.3 μm are especially attractive in ophthalmology and dental applications,respectively, because they offer optical coherence tomography(OCT) imaging with minimum dispersion, deeper penetration,and improved sensitivity.

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Up to now, various highly nonlinear photonic crystal fibers(HN-PCFs) for supercontinuum (SC) generation have been recommended for optical communications and medical applications[7]-[16]. The reported model of HN-PCFs[7] had four to five different air-hole diameters, which enlarged the design complexity. Superluminescent diodes (SLDs) yield low output power of 2 mW to 15 mW[8]. Femtosecond lasers with low output power have been demonstrated experimentally or numerically by several groups[9]-[16]. Nd:YAG has been investigated at around 1.0 μm center wavelength with output power 1.3 W[9]. Generating an SC spectrum at a central wavelength of 1.07 μm was reported with 800 mW output power obtained[10]. Ultrahigh resolution OCT was demonstrated at 1.3 μm center wavelength and 48 mW output power was reported[11]. Based on the use of ytterbium-doped photonic crystal fiber, an SC was generated from a 75 mW signal wave at 1.064 μm[12]. The broadband spectrum was generated with 100 W peak power at 1.55 μm using a CS2 core photonic crystal fiber[13]. The output power of 1.44 W and 6.4 W of germania based photonic crystal fiber for high power ultrabroad band emission were achieved by pumped with a 1.06 μm or 1.55 μm laser source[14]. The stoichiometric silicon nitride integrated optical waveguide is capable of SC generation at 1.56 μm and had the total output power of 300 mW[15]. A Gedoped PCF picosecond pulse laser was investigated at 1.31 μm center wavelength which brought a fabrication challenge[16]. It should be noted that SLDs still have suffered with low output power and femtosecond pulse laser-based SC sources possess a notable drawback of high implementation cost. For the aforesaid problems, a low cost picosecond pulse laser source which can provide high power ultrabroadband light output is a crucial issue for the high performance OCT system. Therefore,a high power picosecond pulse based HN-HF is proposed in this research which is applicable in the high performance OCT and optical communications systems.

In this paper, a simple seven-ring HN-HF structure is proposed for the optical communications and medical applications. The full vector finite difference method is used to calculate the different properties of the proposed HN-HF.Numerical simulation results show that the HN-HF having high nonlinear coefficients of more than 105 W−1km−1 at 1.06 μm,71W −1km−1 at 1.31 μm, and 53 W−1km−1 at 1.55 μm, exhibits a very low confinement loss of less than 10–6 dB/km from 1.0 μm to 1.7 μm wavelength range and ultra-flattened chromatic dispersion in the targeted wavelength range. Moreover, high power broad SC spectra with extremely short fiber length are obtained at center wavelengths of 1.06 μm, 1.31 μm, and 1.55 μm, respectively.

将两组患者不同时间点血压MAP、血氧饱和度SpO2、心率HR数值作详细统计与分析，包括入手术室后基础值T0、诱导插管前即刻T1以及气管插管后即刻T2、切皮时T3等时间点数值。

2.Model of the Proposed Fiber

穿刺及手术切除标本10%中性甲醛固定，HE染色后在镜下观察。HEHE病理诊断标准：HE染色切片显示以纤维硬化区为中心，周边富于细胞，肿瘤细胞呈上皮样分化，腔内含有红细胞，免疫组织化学染色中Ⅷ因子相关抗原、CD31和CD34中的1项呈阳性。

Fig. 1. Schematic cross section of the proposed HN-HF.

3.Numerical Method

A power comparison has been made between the proposed fiber and that proposed in some other journals, which is shown in Table 2. From Table 2, it should be pointed out that the proposed fiber can achieve higher power values than those of reported papers[7]-[16],[18],[19].

Fig. 2 represents the chromatic dispersion and chromatic dispersion slope properties for the proposed HN-HF in Fig. 1.From Fig. 2, it is observed that the HN-HF possesses ultraflattened chromatic dispersion from 1.0 μm to 1.7 μm wavelength range where d1=0.31 μm, d=0.77 μm, and Λ=0.87 μm. The ultra-flattened chromatic dispersion of about 0±9.0 ps/(nm·km) is obtained in the wavelength range of 1.0 μm to 1.7 μm. A small chromatic dispersion slope of less than ±0.06 ps/(nm2·km) can be seen from 1.0 μm to 1.7 μm wavelength range with d1=0.31 μm, d=0.77 μm, and Λ=0.87 μm as shown in Fig. 2.

4.Results and Discussion

where, neff is the complex effective index, Re(neff) is the real part of the complex effective index, Im(neff) is the imaginary part of the complex refractive index, k0 is the free space wave number, λ is the operating wavelength, c is the velocity of light in a vacuum, E is the electric field, and n2 is the nonlinear refractive index coefficient in the nonlinear part of the refractive index.

The schematic cross section of the proposed seven air-hole rings HN-HF is shown in Fig. 1. In this model, the first and fifth rings’ air-hole diameters are changed to d1 and the rest rings’ air-hole diameters are kept at d with a fixed pitch Λ. It is difficult to achieve near zero flattened chromatic dispersion using a conventional holey fiber structure,therefore the first and fifth rings’ air-hole diameters are reduced compared with the air-hole diameters of the other rings. The base material of the proposed holey fiber is pure silica. In this proposed HN-HF model, the seven air-hole rings are used for reducing the confinement loss of less than 0.2 dB/km at 1.55 μm wavelength. It is known that the confinement loss could be reduced with the increase of air holes in the cladding region of the photonic crystal fiber.

Fig. 4 shows the confinement loss property of the proposed HN-HF in Fig. 1. The confinement loss is less than 10–6 dB/km at the wavelength range of 1.0 μm to 1.7 μm. From the numerical simulation result, it has been seen that the confinement loss is achieved with less than 0.2 dB/km for the proposed HN-HFs.

Fig. 2. Chromatic dispersion and chromatic dispersion slope of the proposed HN-HF as a function of wavelength.

Fig. 3. Effective area and nonlinear coefficient of the proposed HN-HF as a function of wavelength.

Fig. 3 depicts the effective area and nonlinear coefficient properties for the proposed HN-HF in Fig. 1. From Fig. 3, it is observed that the HN-HF possesses small effective areas from 1.0 μm to 1.7 μm wavelength range where d1=0.31 μm,d=0.77 μm, and Λ=0.87 μm, which are 1.82 μm2 at 1.06 μm,2.15 μm2 at 1.31 μm, and 2.44 μm2 at 1.55 μm, smaller than that of conventional fibers (about 86 μm2 at 1.55 μm).Moreover, large nonlinear coefficients have been realized ranging from 1.0 μm to 1.7 μm with d1=0.31 μm, d=0.77 μm,and Λ=0.87 μm. Obviously, the proposed HN-HF has the nonlinear coefficients of more than 105 W−1km−1at 1.06 μm, 71 W−1km−1 at 1.31 μm, and 53 W−1km−1 at 1.55 μm which are higher than those reported ones[2]-[6].

Fig. 4. Confinement loss of the proposed HN-HF as a function of wavelength.

Figs. 5 (a), (b), and (c) show the wavelength dependent SC spectrum intensity of the proposed high power HN-HF for the parameters Λ=0.87 μm, d1=0.31 μm, and d=0.77 μm at center wavelengths of 1.06 μm, 1.31 μm, and 1.55 μm, respectively.The nonlinear Schrödinger equation (NLSE) is used for numerical calculation of SC spectra[17]-[19]. The NLSE is solved by split-step Fourier method. The SC generation in the proposed high power HN-HF is numerically calculated at 1.06 μm, 1.31 μm, and 1.55 μm center wavelengths which is shown in Figs. 5 (a), (b), and (c), respectively. In Fig. 5,consider the propagation of the sech2 waveform with the full width at half maximum (FWHM) TFWHM of 2.5 ps and Raman scattering parameter TR of 3.0 fs through the proposed high power HN-HF. The propagation constants around the carrier frequencies β2 and β3 used in the calculation for Fig. 5 are shown in Table 1 at different center wavelengths. From Fig. 5(a), it can be seen that the spectrum range is acquired from about 970 nm to 1170 nm at the center wavelength of 1.06 μm.The range of spectrum is obtained about 1175 nm to 1480 nm with the center wavelength at 1.31 μm, as depicted in Fig. 5(b). Moreover, Fig. 5 (c) shows that the spectrum range is acquired from about 1360 nm to 1800 nm when the center wavelength is set at 1.55 μm. After numerical simulation, the incident pulse input power Pin and fiber length LF are obtained which are also shown in Table 1. The power of 2.0 kW,3.0 kW, and 4.0 kW are achieved at the center wavelengths of 1.06 μm, 1.31 μm, and 1.55 μm, respectively. The required fiber length LF is 1 m for all the center wavelengths.

Fig. 5. Spectrum intensity of the proposed high power HN-HF at:(a) 1060 nm, (b) 1310 nm, and (c) 1550 nm.

Table 1: Fiber parameters

Center wavelength λC (μm)　　β2 (ps2/km)　　β3 (ps3/km)　Pin (kW)LF (m)1.06　1.013　0.025　2.0　1.0 1.30　1.547　0.029　3.0　1.0 1.55　2.166　0.028　4.0　1.0

The full vector finite difference method with anisotropic perfectly matched layers is used to calculate the different properties of the proposed HN-HF. The effective refractive index neff for a given wavelength can be obtained by solving the eigen value problem from Maxwell equation. The real part of the complex effective refractive index is used to calculate the chromatic dispersion and the imaginary part of the complex effective refractive index is used to calculate the confinement loss of the proposed HN-HF. The material dispersion given by Sellmeier equation is directly included in the calculation.Therefore, in this calculation, the chromatic dispersion corresponds to the total dispersion of the proposed HN-HF[6].The chromatic dispersion, chromatic dispersion slope ,confinement loss , effective area , and nonlinear coefficient γ are calculated by the following equations[6],[17]:

The proposed HN-HF with ultraflattened chromatic dispersion, small chromatic dispersion slope, very low confinement loss, small effective area, high nonlinear coefficient, and high power SC spectrum output is applicable in high speed optical communications systems and medical applications.

Table 2: Power comparison

Reference　　λc (μm)　Coherent power[7]　1.550　　–[8]　1.310　15 mW[9]　1.064　1.3 W[10]　1.070　800 mW[11]　1.300　48 mW[12]　1.064　75 mW[13]　1.550　100 W[14]　1.550　6.4 W[15]　1.560　300 mW[16]　1.310　10 W[18]　1.060, 1.310, 1.550　50 W, 14 W, 45 W[19]　1.060, 1.310, 1.550　43 W, 8 W, 40 W Proposed fiber　1.060, 1.310, 1.550　2 kW, 3 kW, 4 kW

5.Conclusions

It has been found that the proposed HN-HF has a high nonlinear coefficient with ultra-flattened chromatic dispersion and extremely low confinement loss in the wavelength range of 1.0 μm to 1.7 μm. Moreover, it has been observed that this proposed high power HN-HF could generate a broad SC spectrum with high power of 2.0 kW, 3.0 kW, and 4.0 kW at center wavelengths of 1.06 μm, 1.31 μm, and 1.55 μm,respectively. The proposed HN-HF may be suitable for optical communications and the applications of supercontinuum including medical imaging, tunable wavelength conversion, and optical studies of photonic devices.

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