Coherent and incoherent combining of fiber array with hexagonal ring distribution

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Abstract

Beam combining of fiber array with hexagonal ring distribution is studied in detail. The theoretical analysis and numerical calculation results are given to illustrate the propagation properties of the resulting beam through free space. A comparison between the coherent and the incoherent case shows that high peak irradiance and good beam quality for coherent combining can be obtained in the far field. The effect of phase errors and the beam quality M2 factor are also studied. Results indicate that the element numbers should be increased to achieve high power and the space between adjacent elements should be reduced to maintain good beam quality, which is basically the same for both coherent and incoherent beam combining.

Introduction

Fiber lasers are becoming an important choice for high-power solid-state laser because of proven advantages in compactness, reliability, efficiency, and beam quality. With the emergence of large mode area (LMA) fiber and the development of high-brightness semiconductor diode as pumps, there has been a rapid increase in the power produced by fiber laser system. A single-mode fiber laser producing an output of kilowatts has been demonstrated [1]. Scaling up the output power from a single-fiber laser to higher power level faces significant challenges because of the limitations imposed by nonlinear effects, such as stimulated Raman scattering and stimulated Brillouin scattering. Fortunately, fiber's geometry offers another promising approach for power scaling. Since several fibers can be easily packaged together, optical combination of the outputs of these fibers can lead to much higher powers than individual fibers can provide on their own. In the past years, various techniques have been studied for beam combination in laser arrays, including coherent beam combining [2], [3], frequency locking of coupled fiber cavities [4], [5], and wavelength combining [6], [7].

If all the elements of a fiber array are forced to operate at the same wavelength and are phase locked, their fields add coherently in the far field. This is referred to as coherent beam combining, and in this case both the power and the brightness increase with the number of elements. Robust coherent combining of a small number of a fiber lasers has been demonstrated in some proof-of-principle experiments [2]. Most of these experiments are designed as a fiber array with 1-D linear distribution. There are few reports on the characteristics of 2-D fiber arrays. The main reason is that, to achieve high beam quality, a fiber array requires high precision and stability of phase-retarding elements. This has been proved to be difficult because the allowed phase error scales inversely with the number of array elements [8]. In order to understand the influence of parameters of a fiber array on the beam quality and the intensity distribution in the far field, we investigate a fiber array with hexagonal ring distribution in this paper.

The paper is organized as follows. In Section 2, a semi-empirical model is presented to investigate the propagation properties of both coherent and incoherent beam combining. The influences of different parameters on the far field profile are analyzed in detail. Section 3 considers the effects of phase errors. The issue of beam quality is discussed in Section 4. Finally, the results are summarized in Section 5.

Section snippets

Theory

In order to simulate the far field of a fiber array, we start from the optical field in the single-mode fiberE(x,y,z)=e(x,y)exp(-ikz),where e(x, y) is the transverse electric field. k=2π/λ the wave vector in free space, and λ ithe wavelength.

Substantial insight in the physics of the radiation field can be gained by expanding e(x, y) in Gaussians. Introducing the notation r=(x,y) and using the fact that the components of e(x, y) can be chosen either real or imaginary, we considerI(r)=|e(r)|2=|jA

Effect of phase errors

Coherent beam combining requires high precision and stability of phase-retarding elements. This has been proven to be difficult, because to achieve high beam quality requires the wave-front error over the array to be within a determined fraction of the wavelength, and the optical wavelength is just of the order of 1 μm. In addition, the challenge posed by this phasing requirement increases with the number of emitter elements.

There are many kinds of phase noise sources for a fiber array [2].

M2 factor

M2 factor is a well known measurement of beam quality. In the following, we provide a detailed analysis for the beam quality obtainable from the fiber array in terms of the corresponding M2 values. Assuming that each element has a Gaussian intensity profile, we calculate the M2 value of the fiber array by using the definition of the second-order moment given by Siegman [9].

For cylindrical variances, the second-order moment is defined asσr2=|r-r¯|2I(x,y,z)dxdyI(x,y,z)dxdy,andσs2=|s-s¯|2I^(sx,s

Conclusion

In this paper, we analyze in detail the influence of the fiber array parameters on the far-field profile. The effect of phase errors and the beam quality are also studied. Results show that coherent combining can achieve high and narrow center peak in the far field compared with incoherent case, but the side lobes appear unavoidably. The number of the spacing and shape of the side lobes and the width of the centre lobe vary with the change of the ring number N and the separation distance d. The

Acknowledgments

We thank Heyuan Zhu and Xiquan Fu for technical assistance and useful discussions. This work was partially supported by grants from Science and Technology Commission of Shanghai (nos. 05 SG 02 and 05 JC 14005) and the Natural Science Foundation of China (nos. 60538010 and 10376009).

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