## Abstract

An effectively single-mode all-solid photonic bandgap fiber with large effective area and low bending loss for compact high-power all-fiber lasers is fully investigated. The pitch dependencies of effective area, bending loss, and effectively single-mode operation are discussed numerically and experimentally. The calculation results indicate that an effectively single-mode all-solid photonic bandgap fiber with an effective area of more than 500 μm^{2} and a bending loss of less than 0.1 dB/m at a bending radius of 10 cm can be realized by choosing optimum fiber parameters. In a fabricated effectively single-mode all-solid photonic bandgap fiber with 48.0 μm core, the effective area of 712 μm^{2}, the effectively single-mode operation, and the bending loss of less than 0.1 dB/m at a bending radius of 10 cm are achieved simultaneously at 1064 nm.

©2012 Optical Society of America

## 1. Introduction

A high-power all-fiber laser with high beam quality is an attractive laser source. It has been applied to various application areas such as material processing, medicine and display. In such high-power all-fiber laser, the issue is nonlinear effects which are caused by high optical intensity in the core. The nonlinear effects limit laser output power. A good solution to the issue is using a large-mode-area (LMA) fiber in the high-power all-fiber laser. In the LMA fiber, optical intensity in the core becomes small. As a result, the nonlinear effects are suppressed.

A conventional LMA fiber is a step-index fiber with large core size and low core numerical aperture (NA). The increase of the core size leads to the enlargement of effective area directly. On the other hand, the core NA has to be decreased for single-mode operation. The single-mode operation is a requirement for the high beam quality. In standard fabrication methods such as the modified chemical vapor deposition, it is difficult to control a core NA of less than 0.06 precisely. The limits of the core diameter and the effective area are around 15 μm and 200 μm^{2}, respectively [1].

A lower core NA is achieved by introducing small air holes around a silica core in a rod-type photonic crystal fiber (PCF) [2, 3]. The core size is increased beyond the limit of the step-index LMA fiber. A rod-type PCF with a core diameter of 60 μm and an effective area of more than 1000 μm^{2} has been reported [2]. The rod-type PCF with a fiber diameter of more than 1 mm is not bendable, which makes laser size larger. The bendable LMA fiber is preferred for realizing a high-power all-fiber laser in practical size.

Another promising approach for increasing the core size with maintenance of single-mode operation is to design a multi-mode fiber to operate as an effectively single-mode fiber. A chirally-coupled-core (CCC) fiber is one of the bendable and effectively single-mode LMA fibers [4-7]. The higher order mode (HOM) of a multi-mode central core is coupled to a side core helically wrapped around the central core and attenuated selectively. Effectively single-mode operation of a CCC fiber has been demonstrated in an Yb-doped fiber laser [7]. A CCC fiber with a core diameter of 35 μm has been reported [4]. Another bendable and effectively single-mode LMA fiber is a Bragg fiber with a large low-index silica core and alternative high-index and low-index layers [8–11]. The attenuation coefficient of the HOM is larger than that of the fundamental mode (FM). Only the FM can be propagated effectively. Effectively single-mode operation of a Bragg fiber has been confirmed in an Yb-doped fiber laser [11]. A Bragg fiber with a core diameter of 40 μm and a mode field diameter of 27.2 μm has been reported [9]. Its effective area is estimated to be about 600 μm^{2}. However, its bending loss is about 0.4 dB/m at a bending radius of 10 cm, which is not enough low for compact packaging. In general, the enlargement of effective area while maintaining effectively single-mode operation causes high bending sensitivity. In the LMA fiber, bending loss is also an important characteristic. A bending loss of less than 0.1 dB/m at a bending radius of 10 cm is required for compact packaging.

Recently, an effectively single-mode all-solid photonic bandgap fiber (AS-PBGF) with large effective area has attracted a great attention [12–15]. The effectively single-mode AS-PBGF is a bendable LMA fiber. The HOM is suppressed selectively by the large bending loss difference between the FM and the HOM. It has been shown that the effectively single-mode AS-PBGF has a potential to achieve large effective area and low bending loss simultaneously [15]. Larger effective area could be achieved while maintaining low bending loss for compact packaging by doing detailed analysis on the characteristics of the effectively single-mode AS-PBGF.

In this paper, an effectively single-mode AS-PBGF with an effective area of more than 500 μm^{2} and a bending loss of less than 0.1 dB/m at a bending radius of 10 cm is investigated numerically and experimentally. In section II, a fiber structure is explained. Leakage loss, bending loss, and effective area are numerically estimated for various fiber parameters. In section III, the measurement results of fabricated effectively single-mode AS-PBGFs with different fiber parameters are shown. The effectively single-mode operations, the allowable bending radius ranges, and the effective areas of the fabricated effectively single-mode AS-PBGFs are discussed.

## 2. Fiber design and concept of proposed effectively single-mode AS-PBGF

Figure 1(a) shows the schematic cross-sectional view of a proposed effectively single-mode AS-PBGF. The periodically arranged high-index rods are embedded in the low-index background. The seven high-index rods at the center of the fiber are removed to form the low-index core (seven-cell core). The seven-cell core is surrounded by the five high-index rod rings. Light is confined into the seven-cell core thanks to photonic bandgap effect. Large core size and low leakage loss is expected by employing this cross-sectional structure.

The leakage loss of the proposed effectively single-mode AS-PBGF was calculated by using the finite element method [14]. Figure 1(b) shows the calculated leakage losses as a function of the normalized frequency. The normalized frequency *V* is represented as,

*d*is the diameter of the high-index rods,

*λ*is the wavelength,

*n*is the refractive index of the high-index rods,

_{1}*n*is the refractive index of the low-index background. The

_{2}*Δ*is the relative refractive index difference between the high-index rods and the low-index background. The pitch between adjacent high-index rods

*Λ*was 12.0 μm, which corresponds to a core diameter of 48.0 μm. The bandwidth of the first photonic bandgap was wider than those of the second and third photonic bandgaps. The leakage loss at the center frequency

*V*= 1.6 of the first photonic bandgap for

*Δ*= 2.0% was around 10

^{−12}dB/m. The second photonic bandgap was not affected by varying the

*Δ*. The lowest leakage loss of the second photonic bandgap was around 10

^{−4}dB/m. The leakage loss around the center frequency

*V*= 4.65 of the third photonic bandgap decreases with increasing the

*Δ*. The lowest leakage loss of the third photonic bandgap reached to 10

^{−10}dB/km for

*Δ*= 2.5%. The large core diameter of around 50 μm and low leakage loss of less than 10

^{−10}dB/m can be achieved simultaneously in the proposed effectively single-mode AS-PBGF with the seven-cell core and the five high-index rod rings.

Figure 2
shows the calculated bending losses of the FM and the HOM at the center frequency *V* = 1.6 of the first photonic bandgap as a function of the bending radius for *Δ* = 2.0% and *λ* = 1064 nm. For the bending loss calculation, the geometrical deformation and the change of the refractive index due to the elasto-optic effect were taken into account [16]. The equivalent refractive index profile of the fiber bent in the x-direction *n _{eq}*(

*x*,

*y*) is expressed as,

*n*(

*x*,

*y*) is the refractive index profile of the straight fiber,

*ρ*is the correction factor of the elasto-optic effect,

*R*is the bending radius. The

*ρ*was fixed to 1.25 since a large part of the cross-section area of the effectively single-mode AS-PBGF is pure silica [16]. The bending losses of the FM and the HOM increased with the increment of the

*Λ*. In general, the acceptable bending loss of the FM is 0.1 dB/m or below. For

*Λ*= 12.0 μm, the minimum bending radius R

_{min}was around 10 cm, which is small enough for compact packaging. When the bending loss of the HOM is more than 10 dB/m, the HOM is eliminated selectively thanks to the large bending loss difference between the FM and the HOM. Therefore, effectively single-mode operation is achieved. The maximum bending radius R

_{max}was around 14 cm for

*Λ*= 12.0 μm. As a result, allowable bending radius range for

*Λ*= 12.0 μm was from 10 cm to 14 cm. The large bending loss difference between the FM and the HOM leads to the wide allowable bending radius range. Figure 3 shows the calculated bending losses of the FM and the HOM at the center frequency

*V*= 4.65 of the third photonic bandgap as a function of the bending radius. The bending losses of the FM were less than 0.1 dB/m at a bending radius of 10 cm. However, the bending loss difference between the FM and the HOM was small. The HOM is not suppressed selectively. Effectively single-mode operation is not achieved. There is no allowable bending radius range. From these results, we could say that it is preferred to employ the first photonic bandgap for simultaneous achievement of the low bending loss of the FM and the effectively single-mode operation.

Figure 4
shows the calculated effective area of the FM at the center frequency *V* = 1.6 of the first photonic bandgap as a function of the bending radius for *Δ* = 2.0% and *λ* = 1064 nm. The effective area *A*_{eff} is expressed as

*I*(

*x*,

*y*) is the intensity distribution at near field region and

*S*is the whole fiber cross section. The effective area increased with increasing the bending radius and the

*Λ*. For

*Λ*= 12.0 μm, the effective area was around 600 μm

^{2}in the allowable bending radius range from 10 cm to 14 cm. There is the peak at a bending radius of about 6.5 cm (

*Λ*= 12.0 μm), which is caused by coupling the FM to cladding radiation modes. The above-mentioned numerical simulations show that the effectively single-mode AS-PBGF with an effective area of more than 500 μm

^{2}, effectively single-mode operation, and a bending loss of less than 0.1 dB/m at a bending radius of 10 cm can be realized.

## 3. Characteristics of fabricated effectively single-mode AS-PBGFs

Three effectively single-mode AS-PBGSs (Fiber A, Fiber B and Fiber C) were fabricated by the stack-and-draw technique. The fiber parameters of the fabricated effectively single-mode AS-PBGFs are summarized in Table 1
. The *Δ*s and the *d*/*Λ*s of the effectively single-mode AS-PBGFs were the almost same. The *V*s at 1064 nm were slightly different. The *Λ*s of the effectively single-mode AS-PBGFs were 10.6 μm (Fiber A), 11.2 μm (Fiber B), and 12.0 μm (Fiber C), respectively. The core diameter of the fiber C reached to 48 μm. Figure 5
shows the cross-sectional photo of the fiber C. The Ge-doped silica rods were precisely arranged in the silica cladding. The Ge-doped silica rods were slightly graded-index profile. The cross-sectional structure with the seven-cell core and the five high-index rod rings was fully realized. Figure 6(a)
shows the measured transmission spectra of the effectively single-mode AS-PBGFs with a fiber length of 1 m. The effectively single-mode AS-PBGFs had the wide transmission bands which correspond to the first photonic bandgap. The 10 dB bandwidths of the transmission bands are estimated to be more than 1000 nm. The shift of the transmission band was observed since the effectively single-mode AS-PBGFs had the different *d*s. The *V*s of the effectively single-mode AS-PBGFs with different *d*s were not the same as shown in Table 1. Only short wavelength edge of the first photonic bandgap of the fiber C was observed. The short wavelength bandgap edge of the fiber C was shifted to longer wavelength by bending the fiber. Figure 6(b) shows the measured transmission losses of the FM of the effectively single-mode AS-PBGFs in the wavelength range from 1000 nm to 1300 nm. The cut-back method was used. The cut length was 10 m. The input part of the effectively single-mode AS-PBGFs was coiled to eliminate the HOM. The transmission losses were less than 60 dB/km in the measurement wavelength range. The transmission loss at 1064 nm of the fiber C was 25 dB/km. The minimum transmission loss of the fiber C was 5.6 dB/km around 1270 nm.

Figure 7(a)
shows the measured bending losses at 1064 nm of the effectively single-mode AS-PBGFs as a function of the bending radius. The calculated bending losses are also plotted for comparison. The bending loss increased with increasing the *Λ*. As the acceptable bending loss is 0.1 dB/m, the minimum bending radii of the effectively single-mode AS-PBGFs were 5 cm (Fiber A), 7 cm (Fiber B), and 10 cm (Fiber C), which are small enough for compact packaging. The effectively single-mode operations of the effectively single-mode AS-PBGFs were investigated by offset-launching technique. Figure 7(b) shows the transmission spectra around 1064 nm and the near field patterns at 1064 nm for the coiled fiber C with different bending radii. The length of the fiber C was 1.5 m. The end of the fiber C was set to be straight. The spectral beating by the mode interference between the FM and the HOM was observed at a bending radius of 15 cm. The near field pattern at a bending radius of 15 cm was not Gaussian shape because of the existence of the HOM. The content of the HOM is estimated to be about 0.5% from the amplitude of the spectral beating. On the other hand, no spectral beating was generated at a bending radius of 14 cm. The near field pattern at a bending radius of 14 cm was nearly Gaussian shape. A measured M-squared factor of output light was 1.05. In the calculations, the bending loss of the HOM of the 1.5-m fiber C at a bending radius of 14 cm was about 10 dB higher than that at a bending radius of 15 cm. The content of the HOM would be decreased to about 0.05%. As a result, spectral beating was not observed at a bending radius of 14 cm. The effectively single-mode operation of the fiber C was clearly confirmed. In the fiber A and the fiber B, the effectively single-mode operations were also confirmed by the same method. The maximum bending radii of the effectively single-mode AS-PBGFs were 7.5 cm (Fiber A), 10 cm (Fiber B), and 14 cm (Fiber C), respectively.

The effective areas of the fabricated effectively single-mode AS-PBGFs were evaluated by far field scanning technique. The end of the fiber under test was set to be straight. The fiber under test was coiled for effectively single-mode operation. Figure 8
shows the measured effective areas at 1064 nm of the FM of the effectively single-mode AS-PBGFs as a function of the *Λ*. The effective areas calculated from the fiber parameters of the effectively single-mode AS-PBGFs are also plotted in Fig. 8. The effective area of the fiber A with the smallest *Λ* was more than 500 μm^{2}. The effective area of the FM increased with the increment of the *Λ*. The effective area of the fiber C with the largest *Λ* reached to 712 μm^{2}. The measurement results were slightly smaller than the calculation results. The end of the fiber under test would not be perfectly straight.

The allowable bending radius range affects laser size and output power. The minimum bending radius of the allowable bending radius range R_{min} is determined by the condition of low bending loss of the FM (0.1 dB/m). The maximum bending radius of the allowable bending radius range R_{max} is also determined by the condition of effectively single-mode operation. Figure 9
shows the measured minimum bending radius and maximum bending radius as a function of the *Λ*. The calculated minimum bending radius and maximum bending radius are also plotted in Fig. 9. The allowable bending radius range of the fiber A with the smallest *Λ* was from 5 cm to 7.5 cm, which make highly compact deployment possible. The allowable bending radius range increased with increasing the *Λ*. The measurement results are similar to the calculation results. The allowable bending radius of the fiber C with the largest *Λ* was from 10 cm to 14 cm, which is still small enough for compact packaging. The optimum *Λ* has to be chosen to realize required fiber laser size and output power.

## 4. Conclusions

An effectively single-mode AS-PBGF with large effective area and low bending loss has been fully investigated. The effectively single-mode AS-PBGF having the seven-cell core and the five high-index rod rings can achieve an effective area of more than 500 μm^{2}, effectively single-mode operation, and a bending loss of less than 0.1 dB/m at a bending radius of 10 cm simultaneously. In the fabricated effectively single-mode AS-PBGF with a core diameter of 48.0 μm, the effective area of 712 μm^{2} was successfully achieved while maintaining the bending loss of less than 0.1 dB/m at a bending radius of 10 cm. The effectively single-mode operation was confirmed at a bending radius of 14 cm. The near field pattern was nearly Gaussian shape. The M-square factor of output light was 1.05. The allowable bending radius range was from 10 cm to 14 cm. The proposed effectively single-mode AS-PBGF provides the compact deployment and the strong suppression of the nonlinear effects.

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