1. Introduction

Ultrafast fiber lasers in the 1 µm spectral range have become a key element in numerous fields of science and production. Their main advantages are an adjustment-free design, compactness, reliability and high efficiency. At the same time, decreasing the pulse duration down to a few hundred femtoseconds is problematic for 1-µm fiber lasers because of the lack of standard fibers with anomalous dispersion (which is required for dispersion compensation). This problem could be solved by utilizing volume elements (e.g., diffraction gratings) in a laser scheme, but this addition would break the integrity of the system and eliminate the advantages of the all-fiber design.

Different types of fibers with zero dispersion that are wavelength shifted down to 1 µm (DS-fiber) have been proposed. Among these fibers are hollow core fibers [1], photonic crystal fibers [2,3] and photonic bandgap fibers [4, 5]. An anomalous dispersion at 1 μm has also been obtained by utilizing a higher order mode (LP₀₂) in few-mode fibers [6,7].

Unfortunately, each of these proposed DS-fibers has drawbacks that prevent their wide spread implementation. For instance, hollow core fibers support the propagation of several modes. Photonic crystal fibers are characterized by high nonlinearity. In addition, both fiber types require a careful choice of the splicing regime to prevent the collapse of air holes in its structure. Utilizing a few-mode fiber is quite cumbersome as it requires careful excitation of only the LP₀₁ mode, which then has to be converted into the operating mode (LP₀₂) using a long-period fiber grating. After pulse compression, the LP₀₂ mode must be converted back into the fundamental LP₀₁ mode. Photonic bandgap fibers have anomalous dispersion at the edge of the bandgap, so it is difficult to obtain a low optical loss in such fibers. Also it should be noted that a lot of low-loss DS-fiber designs was proposed theoretically (for example [8,9],), but its practical realization might be difficult because of fabrication technology limitations or effects that were not taken into account (resonances with cladding modes, bend loss etc). Partially this problem could be solved by utilization of hybrid fibers [10], but to the best of our knowledge there is still no clear demonstration of simultaneous achievement low-loss propagation and anomalous dispersion in the 1 µm spectral region.

In this Letter, we have realized a novel DS-fiber design. The operating mode is confined in the low-index core owing to two mechanisms: total internal reflection (TIR) and coherent Fresnel reflection (a photonic bandgap mechanism). This hybrid mode combines properties of the photonic bandgap fiber mode (anomalous dispersion near 1 μm and simple splicing to common step-index fibers) and properties of the TIR fiber modes (zero leakage loss). The proposed fiber design is suitable for mass production using the conventional fiber fabrication MCVD techniques.

2. Hybrid fiber design - modeling

To design the DS-hybrid fiber, we used the dispersion shifted photonic bandgap Bragg fiber (BF) design described in [5] as a base. In the refractive index profile (RIP), there is a depressed index core (Δn_core = −0.004) with a diameter of 9 µm and a cladding formed by eight high-index (Δn = 0.025) ring layers alternating with pure silica layers (Fig. 1(a)). Thickness of high and low index layers was 0.75 μm and 1.9 μm, correspondingly. The refractive index of the whole structure (core and cladding up to r = 24 µm) was increased by 0.009 over the pure silica value (Fig. 1(b)). This new structure could be considered as usual multi-mode TIR-based fiber and its modes could be easily found by solving of the scalar wave equation. Material dispersion was taken from [11]. Our calculation has shown that there is TIR-guided mode LP₀₉, which is almost identical to the Bragg mode of the initial structure in term of electrical field distribution and dispersion. Moreover it is the only mode that is localized in the low-index core region (>90% of the power is confined within the core radius r_core<4.5 µm, whereas the portion of power for other modes does not exceed 17% in this region). Thus, this mode could be considered as a hybrid mode that propagates owing to TIR (so it does not have leakage loss), but is formed by coherent Fresnel reflection from the alternating low- and high-index layers in the cladding (because the mode is identical to the fundamental mode of the photonic bandgap Bragg fiber in term). It is interesting to note, that as well as Bragg mode of the initial structure the LP₀₉ mode can be excited easily by splicing with a typical step-index fiber that has an appropriate mode field diameter (MFD) (in our case, the value is approximately 6 µm).

 

Fig. 1 Refractive index profiles of the BF [3] (a) and the hybrid fiber (b) and intensities of the guided mode.

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It is worth noting that design of dispersion-shifted BF requires 8 high-index ring layers to decrease the leakage losses. In the proposed hybrid fiber, this number of layers is excessive because there is zero leakage loss; as a result, the design can be simplified significantly. As can be seen in Fig. 2(b), the dispersion of the hybrid mode is mainly defined by the first few high-index ring layers.

 

Fig. 2 a – refractive index profile of hybrid fiber with different number of high index layers (1, 4 and 8); b - calculated dispersion of the hybrid mode in hybrid fibers with different number of high-index layers (1, 2, 3, 4 and 8).

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Our primary goal was to find the simplest hybrid fiber design with high anomalous dispersion at 1064 nm. To this end, we chose a design with only one high-index ring (i.e., a three-layer structure, see Fig. 2(a)). A drawback of this structure is the presence of normal dispersion for all wavelengths near 1 μm (it can only reach zero point). It is interesting to note that a similar structure was described previously in [12].

According to our calculations, the dispersion of the hybrid mode can be increased by further raising the refractive index of the whole structure (the core and high-index layer) over that of silica. However, this will result in the propagation of a second hybrid mode (LP₁₂) in the core, which is undesirable from a practical point of view. Alternatively, a depressed index layer can be placed outside the high-index ring layer to increase the dispersion (see Fig. 3(a)). We have found that the dispersion of the hybrid mode in the region from 1 to 1.1 µm approaches that of the BF mode if the index value of this depressed layer is decreased (see Fig. 3(b)). The RIP of the developed design and the intensity distributions of the electrical fields for all propagating modes are shown in Fig. 3(a). It can be seen that only the hybrid mode has a significant intensity near the fiber axis while the other modes are localized in the high-index ring. Thus, splicing this fiber to a standard, single-mode at 1 μm step-index, 6/125 μm fiber (SMF) will mainly excite the hybrid mode.

 

Fig. 3 a – RIP of the hybrid fiber with outer depressed layer (Δn_(-) = 0.010) and electrical field intensity distributions of the propagating modes; b - calculated dispersion for a Bragg fiber (1), a three-layer hybrid fiber design (2), a four-layer hybrid fiber design with Δn_(-) = 0.005 (3) and a four-layer hybrid fiber design with Δn_(-) = 0.010 (4).

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Thus we proposed a simple fiber design that allows simultaneous achievements of a low-loss guidance and anomalous dispersion near 1 µm. It is worth to note, that in spite of the fact that the final hybrid fiber design is very different from those of the initial Bragg fiber structure [5], the properties of the hybrid LP₀₂ mode (dispersion and electric filed distribution) are rather close to that of the Bragg mode. The reason is that both the modes are formed by the coherent Fresnel reflection from the first high index layer and this defines mode properties.

3. Properties of the realized hybrid fiber and its practical application

According to the proposed fiber design, the preform was fabricated by a modified chemical vapor deposition (MCVD) method, and fibers with outer diameters (OD) of 110, 115 and 120 μm were drawn. The measured RIP of the hybrid fiber with OD = 120 μm is plotted in Fig. 4(a). A study of the mode composition at 1064 nm showed that only the hybrid mode LP₀₂ was propagating in the core for the fibers with OD = 110 and 115 μm. Measured mode field diameter (at the 1/e level) of the fiber with outer cladding 110 μm was about of 7 μm. The second hybrid mode (LP₁₂) was observed in the fiber with OD = 120 μm. Measured near-field intensity distributions of the LP₀₂ and LP₁₂ hybrid modes are shown in the insets of Fig. 4(a).

 

Fig. 4 a - RIP of the fabricated hybrid fiber, insets are mode field distributions of the LP₀₂ operating mode (top) and the LP₁₂ second hybrid mode (bottom); b - measured dispersion of the hybrid fibers and optical losses of the hybrid fiber with outer diameter of 110 mm.

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The dispersion of the fabricated hybrid fibers was measured by a standard interferometric method [13] (see Fig. 4(b)), and it was found to be anomalous at 1.064 µm (11-15 ps/nm/km). Optical losses were measured by the cut-back method, and they did not exceed 6 dB/km at 1.064 μm. Optical loss of the hybrid fiber with outer cladding 110 μm is plotted on Fig. 4b. Optical losses of the other fibers with larger cladding diameter (OD = 115 μm and OD = 120 μm) are the same (except position of the high loss peaks, that are wavelength shifted). The splicing losses between the fabricated hybrid fibers and a SMF were approximately 1.5 dB at 1064 nm for all fibers. The splicing loss spectrum is shown in Fig. 5(b). The dotted and dashed lines in Fig. 5(b) show an approximation of the splicing loss for the fundamental mode (LP₀₁) in the 1000-1100 nm spectral region and for the hybrid mode (LP₀₂) in the spectral region near its cut-off.

 

Fig. 5 a: dispersion curves for the hybrid fiber modes; b: measured splicing losses between the hybrid fiber with OD = 110 µm and a SMF.

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It could be seen that the splicing loss for the fundamental mode is higher by approximately 4.2 dB than that of the hybrid mode. Thus, suppression of the fundamental mode will exceed 8.4 dB if the hybrid fiber is spliced with SMFs at both ends. It is interesting to note that much higher suppression of the LP₀₁ and higher order modes (such as LP₁₁, LP₂₁, LP₃₁ and LP₄₁) could be achieved by placing a thin absorbing ring layer at r = 3.6 µm where the hybrid mode has zero intensity. This layer will not influence the loss of the hybrid mode, but the losses in all other modes would be increased by many orders of magnitude.

It is worth noting that there are narrow peaks at 755, 771,846,867 and 1011 nm in the spectrum. The same peaks have been observed previously in cylindrically symmetric Bragg fibers [14], and they are known to be caused by the coupling between the core mode and the cladding modes localized in the high-index rings [14]. In our case, there is only one high-index ring and only a few cladding modes (see Fig. 5 (a)). This configuration leads to a significant spectral distance (approximately 100 nm) between the loss peaks. A small change of the OD allows one to shift the position of the peaks outside the operational spectral range.

To examine the fabricated hybrid fiber, we used it to compress chirped ultrashort pulses. To produce positively chirped pulses, we used 5-ps, bandwidth-limited (~1 nm) pulses from a commercially available (Fianium) master oscillator (MO) at a repetition rate of 20 MHz. The signal from the MO was amplified up to 70 mW in a step-index 6/125 μm Yb-doped fiber. After amplification, the pulse duration increased up to 8 ps and the spectrum was broadened up to 10 nm due to self-phase modulation. Thus, the resulting pulses had become chirped and could be decompressed by a pair of diffraction gratings down to a sub-ps duration. Next, the average pulse power was decreased down to 1 mW to avoid nonlinear effects, and the pulses were launched into a piece of the fabricated hybrid fiber with OD = 110 μm. A passive SMF was spliced at the output end of the hybrid fiber to further suppress modes located in the high-index ring (including the fundamental LP₀₁ mode). Measurements of the autocorrelation function at the output were performed with an FR-103 mn autocorrelator (Femtochrome Research Inc). The dependence of the pulse duration on the length of the hybrid fiber is shown in Fig. 6. It can be seen that the anomalous dispersion of the hybrid fiber compressed the pulses down to a duration of 330 fs. Autocorrelation traces of the initial pulses (before entering the hybrid fiber) and the compressed pulses (after propagating in 69 m of the hybrid fiber) are shown in the inset of Fig. 6. The appearance of side wings in the autocorrelation function may be due to a nonlinear chirp of the pulses and a non-zero dispersion slope.

 

Fig. 6 Dependence of the pulse duration on the length of the hybrid fiber; inset – autocorrelation traces measured with and without 69 m of hybrid fiber.

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4. Conclusion

In conclusion, we propose a novel fiber design with hybrid modes that are guided by TIR but formed by coherent Fresnel reflection. The proposed fiber design consists of only four layers (including the outer pure silica cladding) and could be easily fabricated by the conventional MCVD techniques. The hybrid mode (LP₀₂) was easily excited by typical splicing with conventional single-mode step-index fibers with a splicing loss of less than 1.5 dB. Anomalous dispersion of approximately 13 ps/nm/km and optical loss of approximately 6 dB/km were measured at 1064 nm for this mode. The fabricated hybrid fiber was successfully utilized to compress chirped 8 ps pulses down to 330 fs.