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UĞUR TEĞICHRISTOPH

Published 4 November 2019

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Spatiotemporal self-similar fiber laser: supplementary material

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This document provides supplementary information to “Spatiotemporal self-similar fiber laser,” https://doi.org/10.1364/optica.6.001412. It contains details on the numerical and experimental studies on output beam profile measurements of the laser.

1Optics Laboratory, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland2Laboratory of Applied Photonics Devices, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland*Corresponding author: ugur.tegin@epfl.ch

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rofiles of amplifined with [60%, 2obtained with [n. Beam profilut 1 (a’) obtainendition and (b’) oing condition. a factor 1.5 in bsimilariton puhan the dissipaticondition. An inde analysis, whefiber modes: ,d modes he multimode fspatial beam propes , (s are the saen a Gaussian (d(similariton or ahape has more cNumerical simral distribution tribution, thus bass Spatio

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ier-similariton pu25%, 5%, 5%, 2.5[25%, 60%, 5%,les of dissipativd with [60%, 25obtained with [2beam diameter iulses, the outpuive soliton and ntuitive explanaere the comple, ,and propagatiofiber. For the saofile is determinsince the eigename for both cdissipative solitoamplifier similaonfined tempormulations showtranslated to better beam qual

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ion cases of thee power, 37.8med considerinrical symmetrygate power exear Schrödingernt initial conditioitial energy diste given in Table e Case 11 30% 2 20% 3 10% 4 10% 5 10% 6 10% 7 10% 8 0% 9 0% 0 0% 2. Initial energy dmulation case. ,Case 1, low ordesented in Fig. Spropagation, eneed. After propgating energy incdecreases for LP0

For simulation C(blue) and z = 2 m

e GIMF fiber fo8 MHz repetitng the lowest y. Coupled-modxchange betwer Equation (S2ons. tributions of the2. Case 2 10% 10% 10% 10% 10% 10% 10% 10% 10% 10% distribution betw

, ,er modes are favS3, although funergy coupling tpagating 2 m creases for LP02,01, LP04 and LP06

Case 1, Percentagm (red).

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As an extreme case when all the modes excited equally in the beginning, percentage of the propagating energy increases for LP03, LP05, LP06, LP07, LP09 and LP10 increase while decreases for LP01, LP02 and LP04.

Fig. S4. For simulation Case 2, Percentage of the total energy per mode at z = 0 (blue) and z = 2 m (red). For Case 3, higher order mode dominant initial condition is simulated and energy transfer to lower order modes from higher order modes observed. After propagating 2 m GIMF, energy percentage at LP05, LP06 and LP07 increased while LP04, LP08 and LP10 lost energy (see Fig. S5).

Fig. S5. For simulation Case 4, Percentage of the total energy per mode at z = 0 (blue) and z = 2 m (red). For Case 4, a more realistic scenario is simulated and a drastic energy transfer to lower order modes from higher order modes observed. At the end of 2 m GIMF, energy percentage at LP03, LP05 and LP08 increased while LP04, LP06 and LP10 lost energy. More than 10% energy coupled to LP05 and energy coupling to an initially empty mode such as LP03 is observed (see Fig. S6).

Fig. S6. For simulation Case 4, Percentage of the total energy per mode at z = 0 (blue) and z = 2 m (red). III. Experimental MeasurementsTwo-dimensional beam profiles presented in Fig.3 are presented in three dimensions. For mode-locked beam, high-order background is observed from both output ports (see Fig.S7 and Fig.S8). Continuous-wave beam profile measured as larger than the mode-locked beam profile. We observed that beam profile vibrates and breathes cyclically since the lasing wavelength is not stable and changes continuously for continuous-wave regime. Here we present the beam shape which occurs most of the time for continuous-wave regime (see Fig. 3.d and Fig. S9). We observed that beam profile vibrates and breathes cyclically since the lasing wavelength is not stable and changes continuously for continuous-wave regime. Here we present the beam shape which occurs most of the time for continuous-wave regime (see Fig. 3.d and Fig. S9). Since NPE mode-locking mechanism is employed in the cavity, perturbations which can cause changes in the polarization state of the propagating light are affecting the laser operation we observed that mode-locked operation is preserved with small perturbations in the cavity. These perturbations (touching the GIMF) do not introduce significant changes in the output beam profile.

Fig. S7. Mode-locked beam profile measured from output 1 (before spatiotemporal filtering).

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Fig. S8. Mode-locked beam profile measured from output 2 (after spatiotemporal filtering).

Fig. S9. Continuous-wave beam profile measured from output 1 (before spatiotemporal filtering). References

1. L. G. Wright, D. N. Christodoulides, and F. W. Wise, Science 358, 94 (2017).

2. J. Hult, Journal of Lightwave Technology 25, 3770 (2007).

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