Progress In Electromagnetics Research Symposium Proceedings, Moscow, Russia, August 19–23, 2012 1083

Proposal for Large Mode Area Photonic Crystal Fibers

Yaw-Dong Wu, Jian-Jang Lee, and Tien-Tsorng ShihDepartment of Electronic Engineering

National Kaohsiung University of Applied Sciences415 Chien Kung Road, Kaohsiung 807, Taiwan, R.O.C.

Abstract— Conventional single-mode fibers suffer from small core, leading to limited outputpower due to generally a single-mode fiber diameter about 8 µm ∼ 10 µm. In order to allow higheroutput power and improve the influence of external force, currently photonic crystal fibers (PCFs)have overcame the mentioned shortcomings, such as endlessly single-mode operation, large modearea (LMA), and high birefringence et al.. These properties provide scaling potential for fiberlaser and amplifier systems. We present the results of numerical analysis showing that largeperiod can be obtained in LMA PCFs. One of analysis methods corresponds to finite-elementmethod (FEM) with perfectly matched layer boundary conditions. This method respects thesufficient reliability, efficiency, and accuracy for the PCFs. In this paper, we proposed severalPCF models to increase the effective mode area up to 1000 µm2. The confinement loss is reducedto 0.486 dB/km at the wavelength of 1.064 µm for the improved PCF with d/Λ = 0.28.

1. INTRODUCTION

Fiber lasers have attracted much interest in recent years. Ytterbium in particular is capable of highefficiency and may be pumped directly by diode lasers at 915 or 980 nm. For high power, the effectivearea of optical fiber is limited by the fact that an increasing core size requires a correspondinglydecreasing index step between the core and the cladding in order to maintain single-mode operation.On the other hand, the intensity within the core of an optical fiber becomes very large and thiscan give rise to optical nonlinearity and physical damage. In order to avoid these effects, highpower lasers based on conventional Ytterbium doped step-index fibers have used relatively largemode area [1]. Some literatures have reported the ytterbium-doped fiber lasers with output powerbeyond 1 kW [2, 3]. The photonic crystal fiber (PCF) has attracted growing attention owing toits many unique properties, such as low nonlinearity, endlessly single-mode operation, large modearea (LMA), and high birefringence [4–6]. The development of LMA fibers is important for a widerange of practical applications most notably those requiring either the delivery or generation ofhigh power optical beams. Thus, an interesting research of PCF is the realization high power laserapplications by means of endlessly single mode PCFs with very LMA. These properties providescaling potential for fiber laser and amplifier systems.

An all-silica PCF with the different ratio of hole diameter to pitch d/Λ was studied in this paper.One of important requirement is maintained low loss for a practical application to optical fiber.It is shown form our numerical results that it is possible to design a low loss PCF with LMA at1.064µm.

2. ANALYSIS AND SIMULATION

All the analyses of the PCF properties have been performed by using the finite-element method(FEM) [7]. This method respects the sufficient reliability, efficiency, and accuracy for the PCFs.In particular, the FEM is suited for studying fibers with non-periodic air-hole arrangements. Asit has been previously shown, triangular-lattice PCFs present a wider effective area for large Λvalue so that they can be practical applied for high power delivery. In order to successfully usetriangular-lattice PCFs for this kind of applications, it is necessary to define their single-modeoperation regime. Typically the PCF is operated close to cut-off where V = π, the V -parametercan be written as [8]:

V =2π

λΛ

√n2

eff − n2FSM (1)

where neff and nFSM are the effective indices, respectively. FSM is the fundamental guided modeof the fundamental space-filling mode (FSM) in the air-hole cladding. The Λ is the air-hole pitchthat choices as the effective core radius can be adopted also for the PCF. In general, they consist ofan ordered array of air-holes running along its length. PCFs can divide into two kinds of guidingmechanisms: one is photonic bandgap fibers [9], such a fiber with low loss and low nonlinearity

1084 PIERS Proceedings, Moscow, Russia, August 19–23, 2012

(a) (b)

Figure 1: Schematic of the cross-section of the two kinds of PCFs: (a) Photonic bandgap fiber that guidesin a hollow core by a band gap. (b) Holey fiber that confines light in a solid core by index guiding.

Figure 2: Cutoff value of the normalized frequencyV according to the Λ/λ for the proposed PCF.

Figure 3: The MFD of the PCF with Λ = 9 µm anddifferent d/Λ.

transmission over a hollow core, which can not be obtained with conventional fibers based on totalinternal reflection (TIR), as shown in Figure 1(a). Band gap confinement is attractive because itallows light to be guided within a hollow core. Furthermore, the effective index of the guided modeis lower than unity, the electric field localizes in the hollow core. The other one is index-guidingfibers [10]. The air-holes arranged in a triangular lattice a PC in the cladding, and a defect is madein the core by replacing an air-hole with silica glass, as shown in Figure 1(b). Since the averagerefractive index at the defect is higher than that in PC, such a PCF operates via TIR.

In this paper, we focus on all-silica holey fiber with large effective area at 1.064µm. In order toensure at single-mode operation, the resulting curves of the normalized frequency V against Λ/λ forvarious relative hole sizes and hole pitches Λ are shown in Figure 2. The horizontal line correspondsto the single mode condition when V value of PCF is lower than π. Thus we further calculate themode field diameter (MFD) of d/Λ < 0.28 with hole pitch Λ = 9µm, as shown in Figure 3.However, the numerical results show the limited MFD by changing hole diameter. Table 1 showsthe properties of several PCF models with different hole pitch Λ and d/Λ, increasing Λ can causeapparent an increase for MFD. The effective area of the fundamental mode is up to ∼ 1000µm2,corresponding to a MFD larger than 26µm. The effective area Aeff of fiber is calculated as follows:

Aeff =

(∫∫ |E|2 dxdy)2

∫∫ |E|4 dxdy(2)

where E is the propagation electrical field. The hole diameter increases opposite to decrease MFD,the model of MFD17-5 especially.

Progress In Electromagnetics Research Symposium Proceedings, Moscow, Russia, August 19–23, 2012 1085

Table 1: The properties of several PCF models with different hole pitch Λ and d/Λ.

Λ d/Λ MFD Aeff

MFD15-1 15 µm 0.1 26 µm 1017 µm2

MFD17-1 17 µm 0.1 28 µm 1256 µm2

MFD17-5 17 µm 0.5 20 µm 531 µm2

MFD21-1 21 µm 0.1 35 µm 1963 µm2

MFD21-2 21 µm 0.2 32 µm 1425 µm2

Figure 4: Confinement loss property of MFD21 with the different d/Λ.

According to the previous results, the PCF model of MFD21 is considered and further changesthe geometry structure. Figure 4 shows the confinement loss property of the MFD21 with thedifferent d/Λ from 600 nm–1700 nm. However, MFD21-1 is not available in high power deliveringbecause acute loss. Besides, we have since reduced to 0.486 dB/km at the wavelength of 1.064µmby increasing d/Λ. We proposed several PCFs with large effective area and low loss for furtherapplications, such as polarization-maintaining fiber, amplifier, and fiber laser etc..

3. CONCLUSION

In this paper, we proposed several PCF models to provide an available in high power delivering.All the analyses of the PCF properties have been performed by using the FEM. The effective areaof the fundamental mode is up to ∼ 1000µm2, corresponding to a MFD larger than 26µm. Thenumerical results show low loss and large effective area with the confinement loss of 0.486 dB/kmat 1.064µm. This is done by increasing d/Λ of MFD21 reduced effective index. These interestingproperties may find applications for polarization-maintaining fiber, amplifier, and fiber laser.

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