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OPTICS LETTERS / Vol. 38, No. 23 / December 1, 2013

Measurement of higher-order mode propagation losses in effectively single mode fibers Christian Schulze,1,* Daniel Flamm,1 Sonja Unger,2 Siegmund Schröter,2 and Michael Duparré1 1

Institute of Applied Optics, Abbe Center of Photonics, Friedrich Schiller University, Fröbelstieg 1, 07743 Jena, Germany 2 Institute of Photonic Technology, Albert-Einstein-Straße 9, 07745 Jena, Germany *Corresponding author: christian.schulze@uni‑jena.de. Received August 14, 2013; accepted October 18, 2013; posted October 23, 2013 (Doc. ID 195749); published November 20, 2013 We present a direct and nondestructive measurement of the propagation loss of higher-order modes (HOMs) in effectively single-mode fibers. Lossy HOMs are excited by applying local stress at various points alongside a straight single mode fiber. The change of the HOM power as a function of the propagation distance is recorded at the fiber end by performing a modal decomposition with a correlation filter. The results for the HOM propagation loss are compared to simulations yielding very good agreement. © 2013 Optical Society of America OCIS codes: (060.2270) Fiber characterization; (060.2400) Fiber properties; (030.4070) Modes; (060.2430) Fibers, single-mode; (090.1760) Computer holography. http://dx.doi.org/10.1364/OL.38.004958

To transport and generate high optical powers while simultaneously maintaining high beam quality, the core diameters of optical fibers are increased to the limit of effective single mode operation [1]. Even beyond the onset of higher-order modes (HOMs) and entering the multimode regime, fibers can be effectively single mode, which is achieved by selective excitation of the fundamental mode [2], fiber bending [3,4], tapering [5], or alternatively, by the use of Bragg gratings for mode selection [6]. In addition, the use of index-antiguiding fibers (in case of active fibers), where a particular gain [7] or temperature profile [8] prefers fundamental mode operation, the specific design of the fiber’s refractive index structure [9–11], and the application of the selfimaging property in a multimode fiber [12], have been shown to improve the single mode property of fiber systems. However, also in fibers, where only the fundamental mode is supported by the fiber structure and the next HOMs already reached cutoff, such HOMs can propagate inside the fiber if excited but will then experience losses. Excitation might be caused by slight misalignment of the injected beam or by fiber coupling and splicing processes. The propagation of HOMs is crucial, especially when the fiber is short [13]. Whereas the treatment of mode propagation losses in a certain fiber structure based on mode solvers is well covered theoretically [14], an experimental technique that measures these losses without destroying the fiber (as with cut-back experiments) is not yet available. In this Letter we demonstrate the direct measurement of the HOM propagation loss at the example of a largemode area multicore fiber, which is designed for single-mode high-power applications at the operating wavelength 1064 nm [15]. By applying local stress, HOMs are selectively excited at various positions along the length of the fiber. With the aid of a correlation filter, which enables a modal decomposition of the beam at the fiber end into the given set of modes, the power of each mode as a function of propagation length is measured, from which the HOM propagation loss can be inferred. 0146-9592/13/234958-04$15.00/0

Such correlation filters are diffractive optical elements that act as matched filters [16], thus optically correlating the incident field with a predefined set of modes, which is implemented in the filter. Physical realizations of such filters include spatial light modulators [17], which impact solely on the phase of an incident light field, and metalcoated glass masks [18], which only have an effect on the field’s amplitude. The coding of the complex-valued mode fields for decomposition into both filter structures is detailed in [19] and [20], and aims to convert the complex fields into practicable phase-only or amplitude-only representations, which then yield the desired optical field in a certain diffraction order. To obtain the correlation signal, which indicates the presence of a mode, a camera is simply placed within the Fourier plane of the filter, as schematically shown in Fig. 1. The intensity I l on the optical axis then appears to be proportional to the power of a mode Ψl , provided the transmission function of the filter is Tr  Ψl r;

(1)

where r  x; y denotes the spatial coordinates and “” complex conjugation. To give a physical picture, if the

Fig. 1. Sketch of the match filter principle. CFΨl , correlation filter displaying the conjugate complex of the signal Ψl ; L(f), lens of focal length f; D, detection plane; and I l , correlation intensity signal. © 2013 Optical Society of America

December 1, 2013 / Vol. 38, No. 23 / OPTICS LETTERS

conjugate complex of the incident field is displayed on the filter, all the phase curvature of the field will be cancelled, producing plane waves, which are focused by a 2f-setup to a bright central spot. Any other field distribution will not experience a phase cancellation and hence not focus to a bright spot [16]. Accordingly, the content of a mode is measured by recording one single intensity value only. By displaying a superposition of many mode patterns on the filter, each with a different carrier frequency Kl , the powers of several modes can be measured simultaneously from one camera image [18]. The respective transmission function then takes the form Tr 

X Ψl r expiKl · r:

(2)

l

Figure 2 depicts the experimental setup to measure the mode propagation loss with the aid of a correlation filter, which was realized in this experiment by a metal-coated glass mask. The fiber under test was a large mode area fiber with 19 cores of 2 μm diameter in a hexagonal arrangement and a core-to-core distance of 5.5 μm [15] (cf. Fig. 3). Accordingly, the fiber depicts a typical example for a fiber, whose core diameter is increased to the very limit of single mode operation to satisfy the requirements of both high-power transmission and maintenance of high beam quality at the same time. So, at the operation wavelength of 1064 nm the fiber is single mode, which means that only the fundamental mode propagates in good approximation lossless (see below). A Nd:YAG laser at 1064 nm wavelength was used to excite the fundamental mode of the fiber with a Gaussian beam with the waist diameter adapted to the mode field diameter of 25 μm. The fiber end facet was relay imaged onto a camera (CCD1 ) to record the near field intensity, and onto the correlation filter performing the modal decomposition. An additional camera (CCD2 ) was placed in the Fourier plane of the correlation filter to measure the correlation signals, i.e., to extract the modal powers of the fundamental mode LP01 and the next HOMs LP11e and LP11o. The fiber cross section and the corresponding mode profiles are illustrated in Fig. 3. To prove that the fiber is indeed single mode when no stress is applied, the fiber mode spectrum was recorded as a function of transverse misalignment Δx. Accordingly, the Gaussian input beam was shifted in steps of 1 μm across the fiber core. The results are depicted in Fig. 4, showing a local maximum for the fundamental mode power ρ201 at the optimal coupling

Fig. 2. Schematic experimental setup. LS, laser source; MO, microscope objectives; L, lenses; BS, beam splitter; CF, correlation filter; CCD1;2 cameras. Dashed section depicts the side view of the fiber holder consisting of a 50 cm long straight groove, on which the local pressure is applied with a magnet.

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Fig. 3. Fiber cross section in white light illumination (a) and simulated modes relevant at 1064 nm wavelength (b)–(d), which are denoted in the LP system due to their similarity to step-index fiber modes.

position Δx  0, and a drop to both sides to 40% of the maximum value when moving 10 μm away from the core center. However, the relative content of the fundamental mode is constant with ≈100% and independent of the shift Δx. This behavior is also evident from the measured near field intensities (insets in Fig. 4), which do not change in shape, but only in brightness during misalignment. Hence, the fiber is single mode and no HOMs can be excited at the fiber front facet. However, the fiber can be susceptibly perturbed by applying local stress. To measure the HOM loss, a constant force of ≈65 N was applied at various points along the fiber length by using a cylindrical magnet of 15 mm diameter, which pressed the fiber to the magnetic subsurface. The local perturbations could be used to selectively excite the LP11o mode (lobes orientated in direction of the applied force, cf. Fig. 3) at various distances from the fiber end facet. Using the correlation filter, a modal decomposition was performed for each position of mode excitation, and the power of all modes as well as the near field intensities were measured. To avoid the additional influence of bending losses and other disturbances, e.g., from fiber holders, the fiber was placed in a straight and even groove of 50 cm length and fixed by UV-curable glue at its ends. The fixing, which is essential to keep the adjustment of the correlation filter, was done without applying stress and while monitoring the fiber output modally to ensure pure single modeness as an indicator for the absence of any perturbation. Figure 5 depicts the mode content and the recorded near field intensities of the unperturbed fiber, as well as of the fiber with local pressure applied at three distinct points along the fiber length. As can be seen, in its initial state the fiber is single mode (cf. Fig. 4) with a measured

Fig. 4. Fundamental mode power ρ201 in absolute (mW) and normalized (%) units as a function of transverse misalignment Δx. Insets depict the near field intensities at the positions marked with red circles.

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Fig. 5. Measured relative mode content of LP01 (1), LP11e (2), and LP11o (3) mode, with corresponding near field intensities without applied stress (a), (e) and when stress is applied at three different positions z measured from the fiber end facet: z  1 cm (b), (f), z  22 cm (c), (g), z  45 cm (d), (h). Blue circles mark the central fiber core.

fundamental mode content of about 98% [Fig. 5(a)], and a corresponding near field, which is symmetric and undistorted [Fig. 5(e)]. The remaining power is distributed between the HOMs LP11e and LP11o. Note that their mode content of 1% each depicts the lower detection limit of the correlation filter technique, since background light in the camera and the low detection efficiency at 1064 nm inevitably influence the determination of modal powers. As mentioned above, the single mode regime of the fiber can be disturbed when stress is applied on the fiber. Pressing directly in front of the fiber end facet (1 cm) yields a strong excitation of the LP11o mode of 31% of total power, whereas the LP11e remains unaffected [Fig. 5(b)]. This is reasonable, since the applied force acts in the direction of the orientation of the LP11o-mode lobes, whereas the lobes of the LP11e-mode are orientated perpendicularly. At the same instance, the near field is strongly distorted and the beam center appears shifted due to the coherent superposition of fundamental mode LP01 and the LP11o [Fig. 5(f)]. If the same stress is applied at a larger distance from the fiber end facet (22 cm), the LP11o-content decreases [Figs. 5(c) and 5(g)]. At a distance of 45 cm finally, the HOM content has the same value as without applied stress and the corresponding near field is symmetric and dominated by the fundamental mode [Figs. 5(d) and 5(h)]. Since the same pressure is applied each time, it is reasonable to assume that the LP11o-mode is excited with the same power content within the fiber, independent of the position of applied stress. Note that the fiber is single mode when no stress is applied. Accordingly, the LP11o-mode constantly loses power when propagating from its point of excitation to the fiber end, yielding less and less power guided in this mode, the larger the distance between fiber end and point of excitation gets. After removing the stress completely, the fiber still showed its initial single mode behavior, which indicates that the fiber was not damaged and the perturbation was only temporary. The measured power of the LP11o-mode as a function of the position of applied stress is depicted in Fig. 6, with the selected positions of Fig. 5 marked with red circles. As already pointed out by the previous discussion, the power of the LP11o-mode decreases continuously when moving the point of local stress away from the fiber end facet at which the mode content is analyzed. An

Fig. 6. Measured (me) decay of HOM power ρ211o with increasing propagation distance z. An exponential fit yields a propagation loss of αdB  19  2 dB∕m. Red circles mark the positions given in Fig. 5.

exponential fit of the measured mode power of the kind ρ2  ρ20 exp−z∕z0   ρ2∞ , where ρ2∞ was set to zero, allows one to determine the propagation power loss αdB  4.34∕z0 m, yielding a value of 19  2 dB∕m, whereas the error originates from the fit uncertainty. Note that the associated LP11e mode is in good approximation degenerated with the LP11o mode, and is hence expected to possess the same propagation loss. To estimate the meaningfulness of the measured power loss, and to decide if its origin is a pure result of the fiber’s refractive index profile or of potential manufacturer imperfections, we modeled the fiber under test using the commercial software Comsol Multiphysics, which provides a full-vectorial finite element method mode solver. Accordingly, the refractive index structure of the fiber was implemented and surrounded by a perfectly matched layer, which was adapted to the cladding region regarding refractive index, to introduce losses in the system. The propagation loss of a mode can then be determined from its imaginary part of the effective refractive index neff [14]: αdB 

20 2π Ineff ; ln10 λ

(3)

where λ is the wavelength. Following this approach the propagation loss of the LP11 -modes is about αdB  17 dB∕m, which is in good agreement with the measurement. Accordingly, a strong influence of manufacturer imperfections on the modal loss can be excluded. Regarding the fundamental mode LP01 , its power loss is expected (from simulation) to be at least three orders of magnitudes smaller than the LP11 loss. Consequently, the LP01 mode power was assumed to be constant along the investigated fiber length. In conclusion, we presented a versatile tool to measure the propagation loss of HOMs in quasi-single mode fibers in a nondestructive way. It has been shown that although fibers might be single mode from their refractive index specifications, HOMs can still propagate for certain distances, albeit experiencing losses. From local HOM excitation along the length of the fiber in combination with a modal decomposition using a correlation filter, the propagation loss of the LP11o-mode in a multicore fiber was measured to be 19 dB∕m. A comparison with

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numerical modelling (finite element solver) showed very good agreement proving the reliability of the approach. We consider our technique to be a valuable tool in the fields of fiber design, generation and transportation of high optical powers while maintaining a high beam quality. References 1. A. Tünnermann, T. Schreiber, and J. Limpert, Appl. Opt. 49, F71 (2010). 2. F. Dubois, P. Emplit, and O. Hugon, Opt. Lett. 19, 433 (1994). 3. J. P. Koplow, D. A. V. Kliner, and L. Goldberg, Opt. Lett. 25, 442 (2000). 4. C. Schulze, A. Lorenz, D. Flamm, A. Hartung, S. Schröter, H. Bartelt, and M. Duparré, Opt. Express 21, 3170 (2013). 5. Y. Jung, Y. Jeong, G. Brambilla, and D. J. Richardson, Opt. Lett. 34, 2369 (2009). 6. J. M. O. Daniel, J. S. P. Chan, J. W. Kim, J. K. Sahu, M. Ibsen, and W. A. Clarkson, Opt. Express 19, 12434 (2011). 7. A. E. Siegman, J. Opt. Soc. Am. B 24, 1677 (2007). 8. F. Jansen, F. Stutzki, H.-J. Otto, C. Jauregui, J. Limpert, and A. Tünnermann, Opt. Lett. 38, 510 (2013). 9. W. Wong, X. Peng, J. McLaughlin, and L. Dong, Opt. Lett. 30, 2855 (2005).

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10. C.-H. Liu, G. Chang, N. Litchinister, D. Guertin, N. Jacobson, K. Tankala, and A. Galvanauskas, in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, 2007), paper CTuBB3. 11. F. Stutzki, F. Jansen, C. Jauregui, J. Limpert, and A. Tünnermann, Opt. Express 19, 12081 (2011). 12. X. Zhu, A. Schülzgen, H. Li, L. Li, Q. Wang, S. Suzuki, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, Opt. Lett. 33, 908 (2008). 13. A. Grassi, F. Casagrande, M. D’Alessandro, and S. Marinoni, Opt. Commun. 273, 127 (2007). 14. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1996). 15. M. M. Vogel, M. Abdou-Ahmed, A. Voss, and T. Graf, Opt. Lett. 34, 2876 (2009). 16. J. W. Goodman, Introduction to Fourier Optics (McGrawHill, 1968). 17. D. Flamm, D. Naidoo, C. Schulze, A. Forbes, and M. Duparré, Opt. Lett. 37, 2478 (2012). 18. T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, Opt. Express 17, 9347 (2009). 19. V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, J. Opt. Soc. Am. A 24, 3500 (2007). 20. W.-H. Lee, Appl. Opt. 18, 3661 (1979).

Measurement of higher-order mode propagation losses in effectively single mode fibers.

We present a direct and nondestructive measurement of the propagation loss of higher-order modes (HOMs) in effectively single-mode fibers. Lossy HOMs ...
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