There has been a drastic increase in the output power of solid-state lasers with diffraction limited beam quality in recent years. Their commercial success is to a large extent owing to the possibility of a flexible light guiding with large-mode-area optical fibers. But the deliverable power is inversely proportional to the fiber length and vice versa owing to the onset of several nonlinear effects [1
1. R. H. Stolen, Proc. IEEE 68, 1232 (1980). [CrossRef]
2. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).
] inside the waveguide material. These effects occur in fiber amplifiers as well as in passive beam delivery fibers. Increasing the effective mode area
will decrease the optical power density and therefore increase the threshold of these effects, but it will generally result in a higher bending sensitivity of the single-mode (SM) fiber. Several approaches, such as photonic crystal fibers (PCF) [3
], leaky channel fibers (LCF) [4
4. W. S. Wong, X. Peng, J. M. McLaughlin, and L. Dong, Opt. Lett. 30, 2855 (2005). [CrossRef] [PubMed]
], and the use of a single higher-order mode (HOM) [5
5. S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, Laser Photonics Rev. 2, 429 (2008). [CrossRef]
], are being investigated to improve the trade-off between effective area and bending sensitivity in comparison to standard step-index fibers (SIFs).
In this Letter, we present a different approach. Instead of using one large core with a special cladding we utilize several evanescent-field coupled cores in a simple cladding of pure silica glass. These multicore fibers (MCFs) [6
6. Y. Huo and K. Peter, J. Opt. Soc. Am. B 22, 2345 (2005). [CrossRef]
7. U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, Opt. Express 15, 6894 (2007). [CrossRef] [PubMed]
] are multimode in general but with a proper design of the core-to-core distance as well as the size and the NA of the single cores the resulting structure will guide a single transverse supermode only.
In the following, we present the theoretical and experimental results of a new kind of SM fiber with 19 coupled cores, manufactured by the Institut für Photonische Technologien (IPHT) in Jena. The 19 identical cores can only be visualized with a white-light microscope if the other end of the fiber is illuminated, but the cores can be directly observed with the help of a scanning electron microscope (SEM), as can be seen in Fig. 1
. Each single core has a diameter of
and an NA of 0.108. Their center to center distance is
, and the cladding diameter of the fiber is
. Calculated and measured near-field (NF) intensity distributions of the fiber are shown in Fig. 2
; the measurements correspond well to the calculations. Linescans of the intensity distributions along the x
- and y
-axes are shown (solid curves), Gaussian fits are imposed (dotted curves) to show that the so called in-phase supermode is close to Gaussian. Hence, it is possible to use the present fiber like a standard SM fiber without the need for mode conversion or lens arrays. Therefore, the far-field (FF) distribution (Fig. 2
) is essentially Gaussian. Our simulation shows that the overlap with the NF of an SI fiber with the same
as the MCF can reach more than 99%; this is essential for a fiber splice to an SM fiber laser. From the measured NF and FF pictures an NA of 0.028 and an
represents the electric field,
the complex conjugate) have been determined, which are very close to the design values of
. All measurements have been performed with a broadband (50 nm FWHM) amplified spontaneous emission (ASE) fiber source (Multiwave ASE) with a center wavelength of
. The simulation results have been obtained with fully vectorial finite element calculations performed with the commercial software Comsol Multiphysics [8
]. A user-defined and well-optimized circular perfectly matched layer (PML) [9
9. J. -P. Berenger, J. Comput. Phys. 127, 363 (1996). [CrossRef]
] in association with a perfect electric conductor was used to truncate the computational domain. All modeling results have been obtained with second-order hybrid mesh elements of subwavelength size. The bending of the fiber was taken into account by modifying the refractive indices [10
10. D. M. Shyroki, IEEE Trans. Microwave Theory Tech. 56, 414 (2008). [CrossRef]
11. D. Marcuse, J. Opt. Soc. Am. 66, 216 (1976). [CrossRef]
is the new equivalent refractive index of the bent fiber, n
is the refractive index of the material, and R
denotes the bending radius along the x
To verify that the designed and fabricated 19-core fiber is SM, the beam propagation factor
was measured for different lengths and bending radii of the fiber. Using a Spiricon
beam propagation analyzer, all measurements were performed according to the ISO 11146-1999 standard and revealed
factors of less than 1.03. A typical result of the beam caustic measurement of the MCF under study is displayed in Fig. 3
. Furthermore, a single-frequency laser beam with a wavelength of 1030 nm has been coupled into a curled multimode fiber (
core diameter), which resulted in a highly multimode output on the other end of the fiber. This end has then been butt-coupled to a short piece (1.6 m) of the 19-core fiber, thus, massively overfilling the core diameter as well as the NA of the MCF. Without any mode stripping, similar beam caustic measurements as described above revealed an
factor of 1.1. This clearly shows that the fiber worked as an efficient SM filter and therefore does not guide any HOMs.
shows the measured as well as the calculated bending losses of the fiber versus the bending radius. As can be seen, the measurements [solid (blue) circles], which are based on a cut-back method are in good agreement with the theoretical predictions (open circles). One can see that, for small bending radii, the measured losses are lower than calculated. This may be attributed to the high refractive index of the coating, which was not taken into account by the simulations. To illustrate that this new structure exhibits an improved bending performance in comparison to state of the art SIFs, the same calculations have been performed for a hypothetical SM SIF with the same
, core diameter
). It turned out that the bending induced losses of the 19-core fiber are much lower, e.g., at a bending radius of
the losses of the 19-core fiber are 0.6 dB/m (0.1 dB/m measured), whereas the losses of the SIF are 144.7 dB/m. This somewhat astonishing result can be explained by comparing the effective refractive indices of the fundamental modes
with the refractive index of the cladding material
. The index difference
in the case of the 19-core fiber and only
for the SIF. Therefore, the fundamental mode of the SIF can couple more easily to cladding modes, resulting in a higher sensitivity to distortions.
Additionally, the dependence of the mode field area (MFA) on the bending radius R
is more pronounced for the SIF, as can be seen in Fig. 5
. According to the definition of the MFA [Eq. (2
)], both SM fibers have the same MFA if they are straight, but the MFA of the SIF is strongly increased for moderate bending radii, whereas the MFA of the 19-core fiber is minimally affected (reduction of 2% at
). This is because a considerable part of the intensity distribution inside the SIF is shifted into the fiber cladding owing to the bending, as can be seen in the inset of Fig. 5
. The field distribution of the MCF does not change perceptibly. This is another aspect that indicates the highly stable light guiding properties of the MCF and it shows that the fiber can even be used in a coiled configuration, which is particularly interesting for active fibers (more details about the MCF concept will be published elsewhere).
In conclusion, we presented what is to the best of our knowledge the first demonstration of a truly single-mode multicore fiber. Using this concept, we were able to demonstrate large effective mode areas without the need of a complicated cladding structure, high-index contrasts (i.e., air holes), or mode conversion. In fact, the structure can be fabricated by standard stack and draw techniques and might even be simpler to fabricate than very low NA SIFs. According to our investigations, the realized 19-core fiber is orders of magnitude less sensitive to bending than a comparable SIF. Moreover, the multicore SM concept is further scalable (we are currently working on a 37-core fiber with an even higher ) and suitable for passive as well as for active fibers.