PDF download: single mode step index optical fiber characteristics and performance

In this paper, we experimentally demonstrate that a nonlinear Kerr effect in suitable coupling conditions can introduce a spatially self-cleaned output beam for a few-mode step-index fiber. The impact of the distribution of the initial excited modes on spatial beam self-cleaning has been demonstrated. It is also shown experimentally that for specific initial conditions, the output spatial pattern of the pulsed laser can be reshaped into the LP11 mode due to nonlinear coupling among the propagating modes. Self-cleaning into LP11 mode required higher input powers with respect to the power threshold for LP01 mode self-cleaning. Our experimental results are in agreement with the results of numerical calculations.

single mode step index optical fiber pdf download

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Nonlinear pulse propagation in Multimode fibers (MMFs) has recently attracted a lot of attention in recent years due to their high transmission capacity, especially for very high data rate optical communications1,2. Research on MMF has revealed a number of nonlinear spatiotemporal phenomena such as multimode solitons, geometric parametric instability (GPI), supercontinuum (SC) generation, and nonlinear microscopy and endoscopy3,4,5,6,7,8,9,10. The input spatially Gaussian beam in MMFs, leads to an output speckled beam pattern due to the generation of a large number of guided transverse modes and this is a major problem in transmitting radiation through these fibers. After a few centimeters of the light propagation inside the fiber, the random coupling of the modes leads to a sever reduction in the quality of beam. In recent studies on nonlinear pulse propagation in MMFs it is demonstrated that the refractive index dependence on light intensity (Kerr-effect), in MMFs can lead to a spatially cleaned output beam which is robust against fiber bending11,12,13,14,15. The power threshold for frequency conversion or self-focusing of sub nanosecond to femtosecond pulses propagating in the normal dispersion regime is much higher than that required for nonlinear self-cleaning effect. Most articles in this field, reported nonlinear beam reshaping and the other nonlinear effects in MMFs with a parabolic or nearly parabolic refractive index profile16,17,18,19. We demonstrated for the first time in our previous work that the Kerr beam self-cleaning effect can be seen in step-index few-mode fiber at higher peak-powers with respect to the power threshold for self-cleaning in graded index (GRIN) fibers20. It is obvious that the role of core refractive index profile is very important in nonlinear self-cleaning process, by introducing intermodal dispersion and creation of a periodic self-imaging effect21. Kerr beam self-cleaning arises due to quasi-phase matching (QPM) induced by mode auto imagery when the refractive index is parabolic. This imagery can occur in step-index fibers but not with the same efficiency and with a smaller coherence length than GRIN fibers22. With few-mode fibers that support fewer modes than MMFs, it is easier to have the QPM condition between modes than highly multimode fibers. In this work, we demonstrate that for creation of self-cleaning effect in few-mode step-index fiber, it is necessary to manage the coupling condition and consequently the initially guided modes fractions because this arrangement affects the self-imaging distance and nonlinear modal couplings. We focus on the effect of the initial modal distributions on Kerr-beam self-cleaning in few-mode step-index fiber. To show that, we employed the second harmonic of a sub-nanosecond microchip pulsed laser propagating in a step-index fiber with a core diameter of 20 μm and a numerical aperture of 0.065 supporting more than 10 spatial modes at 532 nm wavelength. We found that there is a final limitation for the initial propagating mode distribution in order to achieve a proper Kerr-induced refractive index profile and consequently a nonlinear self-cleaned output beam in few-mode step-index fiber. Moreover, at a special input coupling angle, Kerr nonlinear self-cleaning in our considered fiber can reshape the transverse output pattern into the LP11 mode. Nonlinear self-cleaning of the LP11 mode requires a careful adjustment of the laser beam coupling at the fiber input to prepare a proper power distribution among the guided modes. Numerical simulations are consistent with our experimental results.

where summation is taken over all (\(l,m\)) excited modes with propagating constant \(\beta_lm\). Spatial self-imaging effect is one of the initial phenomena in the self-cleaning process, which its combination with Kerr nonlinearity will introduce a periodical modulation of the refractive index in the core of the fiber. Self-imaging is actually the reproduction of the input field in some positions inside the fiber where guided modes are in phase and satisfy the following condition21:

As it can be seen, by increasing the optical power of the fundamental mode with respect to the higher order modes, there will be a greater reduction in the self-imaging distance. According to our calculations, for 10 kW input peak-power Δ can be increased up to 0.36 mm for different fractions of fundamental mode with respect to the higher order modes. A reduction in the self-imaging distance facilitates nonlinear interactions, leading to a spatially cleaned output beam in a few-mode step-index fiber. On the other hand, as it has explained in Ref22, if there is a higher fraction of fundamental mode in the initial distribution of guided modes, an irreversible decoupling of the fundamental mode can be observed, which allows the power to remain in this mode. As it is demonstrated experimentally and numerically in the next sections, there is a limitation of propagating mode fractions on the observation of the self-cleaning effect in few-mode step-index fiber.

As it can be seen clearly from the figure, the excitation of the few-mode fiber at the central position with 6 propagating modes and a lower fraction of the higher-order modes lades to the Kerr beam self-cleaning at 8 kW input peak-power in 5 m long few-mode fiber. With the larger transverse shift of the input beam, the number of propagating modes and the higher order modes fraction increase, and the peak-power for Kerr-beam self-cleaning also increases. In our experiments, we observed that in cases where the index of higher order modes is much more than that of fundamental mode and lower order modes, it is impossible to reach Kerr-beam self-cleaning. Therefore, in these fibers, there is a final limitation for the initial distribution and number of propagating modes to achieve a self-cleaned output beam.

In the second series of our experiments, we varied the tilt angle of the Gaussian laser beam at the input face of the few-mode step-index fiber. The incident angle was greater than the numerical aperture of the fundamental mode. In our selected coupling condition, the highest fraction of power has been coupled into the odds modes. As has been shown in GRIN fibers26, this modal distribution generates an off-axis refractive index modulation that leads to a strong overlap with the LP11 mode, and consequently, FWM processes with participation of this mode have the highest coefficient.

Near field intensity pattern at the few-mode step-index fiber output versus input peak power for appropriate input coupling conditions for higher fraction of LP11 mode, for (a) 1 kW, (b) 3.5 kW, (c) 5 kW, (d) 7.4 kW (e) 9.2 kW, (f) 12 kW. Scale bars 10 μm.

Near field (left) and far field (right) intensity patterns at the step-index few-mode fiber output for the linear propagation regime (a, c) and Kerr nonlinear regime (b, d) for appropriate input coupling conditions for a higher fraction of the LP11 mode, scale bars 10 μm.

Numerical results of spatial reshaping of beam propagating in step-index few-mode fiber as a function of input peak power for (a) 0.5 kW, (b) 2 kW, (c) 4 kW, (d) 6 kW, (e) 7 kW, (f) 10 kW, (g) 13 kW, scale bars 10 µm. (h) Fraction of input power coupled into the different guided modes.

In conclusion, we experimentally demonstrate that Kerr nonlinear spatial reshaping of a pulsed beam to a nearly Gaussian mode at the output of a few-mode step-index fiber can be observed for specific distributions of initially excited modes. However, in the cases where the index of higher order modes is much more than that of fundamental mode and lower order modes, it is impossible to reach Kerr-beam self-cleaning. The initial distribution of guided modes affects the self-imaging distance, which has a significant rule on the Kerr-beam self-cleaning effect, and also a higher fraction of fundamental modes leads to irreversible decoupling of the central mode. Therefore, there is a final limitation for the initial coupling conditions and propagating mode numbers to achieve a condensed output beam pattern in few-mode step-index fibers.

We also demonstrated experimentally that Kerr nonlinear spatial cleaning can transform the output pattern into the LP11 mode of a few-mode step-index optical fiber while it has a speckled profile in linear regime. A necessary condition for nonlinear spatial reshaping into LP11 mode is to adjust the laser beam angle at the fiber input, which leads to a modal distribution in favor of the LP11 mode. Our numerical simulations are in agreement with experimental results. The observation of the possibility of output pattern engineering in step-index few-mode fibers may find practical importance in the delivery of high-power laser beams for a variety of applications including micromachining and nonlinear microscopy.

In its simplest form an optical fiber consists of a cylindrical core of silica glass surrounded by a cladding whose refractive index is lower than that of the core. Because of an abrupt index change at the core-cladding interface, such fibers are called step-index fibers.

where n2 is the cladding index, the ray experiences total internal reflection at the core-cladding interface. Since such reflections occur throughout the fiber length, all rays with Φ > Φc remain confined to the fiber core. This is the basic mechanism behind light confinement in optical fibers. 2ff7e9595c