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In a leakage channel fiber, the desired fundamental mode (FM) has negligible waveguide loss. Higher-order modes (HOM) are designed to have much higher waveguide losses so that they are practically eliminated during propagation. Coherent reflection at the fiber outer boundary can lead to additional confinement especially for highly leaky HOM, leading to lower HOM losses than what are predicted by conventional FEM mode solver considering infinite cladding. In this work, we conducted, for the first time, careful measurements of HOM losses in two leakage channel fibers (LCF) with circular and rounded hexagonal boundary shapes respectively. Impact on HOM losses from coiling, fiber boundary shapes and coating indexes were studied in comparison to simulations. This work, for the first time, demonstrates the limit of the simulation method commonly used in the large-mode-area fiber designs and the need for an improved approach. More importantly, this work also demonstrates that a deviation from circular fiber outer shape may be an effective method to mitigate HOM loss reduction from coherent reflection from fiber outer boundary, even in double-clad fibers, with HOM losses in excess of 20dB/m measured in the hexagonal LCF with ~50µm core diameter while keeping FM loss negligible.
© 2013 Optical Society of America
1. Introduction
Fiber lasers are increasingly becoming significant advanced manufacturing tools, in addition to successes in many other areas such as medical, scientific and defense. Higher powers are highly still desired for glass/ceramic processing, particle accelerations, many defense applications, in addition to high throughput in manufacturing. Power scaling of fiber lasers is limited by nonlinear effects, which can be effectively mitigated by mode area scaling.
One of the most effective methods for mode area scaling, especially for coiled fibers which are critical for high average powers, is to exploit mode-dependent losses in leaky waveguides. Conventional large mode area (LMA) fibers exploit mode-dependent bend losses [1]. Some recent designs such as leakage channel fibers (LCF) [2–5], chirally-coupled-core (CCC) [6,7] fibers, and all-solid photonic bandgap fibers (ASPBF) [8] have built-in mode-dependent losses in fiber designs. Recently, it has been reported that mode instability can develop in fiber amplifiers supporting few modes due to nonlinear interaction between mode interference and quantum defect heating [9–13]. One method to mitigate this is to significantly increase the waveguide losses of the higher-order modes. These highly leaky HOMs are no longer confined to the core and have, therefore, significant reduced overlap with active area of the fiber amplifier, minimizing the impact of quantum heating.
LCFs are particularly useful to generate high differential loss of modes. A typical geometric arrangement of LCF is shown in Fig. 1a. It is worth noting that these LCFs are made entirely of glass without any air holes. The discontinuity of core-cladding boundary makes all modes leaky, allowing the fiber to be engineered to have high transmission loss for all HOM while maintaining negligible loss of FM. Traditional LCF have identical cladding features placed periodically in the cladding, typically in a triangular matrix [2,3]. The features, however, do not have to be identical. In fact, both index and dimension of each cladding layers can be independently designed in order to cause resonance between the lowest-loss HOM and the 2D structured cladding. This resonance can pull the HOM further out into the cladding, leading to much improved HOM suppression of LCF. These LCFs are referred to as resonantly-enhanced leakage channel fibers (Re-LCF) [14]. Performance of Re-LCF with ~50µm core diameters was recently reported [14,15].
Fig. 1 Cross-section images of Re-LCFs used in this work, (a) circular Re-LCF and (b) hexagonal Re-LCF.
HOM losses are very important design parameters for the performance of fibers with large effective mode areas. They have, however, never been accurately measured in actual optical fibers. Using S2 technique, HOM content at the output of an optical fiber can be measured accurately [16]. This is typically done in a way that is hard to separate many possible contributors such as launching conditions, fiber layout configurations, and fiber designs.
Conventional design approach is often based on the assumption of infinite cladding. This is a good assumption for well guided modes where light is mostly in the core. It is no longer a good assumption for highly leaky modes where a significant amount of light is radiated away from the core into the cladding. In this case, the reflection from any material interface, e.g. glass/coating boundary in the fiber, can provide additional confinement of the mode, leading to lower waveguide losses for the modes. The effect of circular glass/coating boundary on waveguide losses has been theoretically studied previously [4], showing that the waveguide losses of modes are strongly dependent on the fiber diameter. This is not surprising, considering the coherent nature of reflection.
Another important question is regarding the impact of refractive index of coating on the waveguide losses of modes. Double-clad fibers used in fiber lasers are often coated with a low-index polymer coating in order to provide a multimode pump guide [17]. Total internal reflection can take place at such boundary, completely trapping optical power in the guided modes of the highly multimode pump guide. The radiated power from modes guided mostly in the core region is expected to satisfy the total internal reflection condition at such boundary. Does this mean waveguide losses of core modes will vanish? It was speculated in [4] that the leaky core modes will still lose power to modes in the multimode pump waveguide in this case. This is, however, never proven.
For the further progress of mode area scaling of optical fibers, it is very important to accurately know the losses of HOMs in optical fibers and how they relate to designs. It is also very important to understand how factors such as coiling, fiber shapes and index of coating impact the waveguide losses in relation to simulations. All these factors change the nature of reflection at material interfaces in fibers.
In an effort to answer some of these questions, we have accurately measured waveguide losses of modes using a cut-back technique in combination with a S2 technique and a fully spliced configuration to ensure constant launch conditions. The measured waveguide losses were then compared to simulations based on infinite cladding. The test was conducted for a variety of coil diameters to identify any impact from coiling. Two Re-LCFs with ~50µm core diameter were tested. The first fiber has a circular glass/coating boundary and is coated with standard coating with high refractive index. The second fiber has a rounded hexagonal glass/coating boundary and is coated with low-index acrylic coating with a refractive index of 1.375.
The results confirm that the simulation based on infinite cladding is accurate for well confined modes with low waveguide losses. But for the highly leaky modes, the measured losses can be significantly lower than what are predicted by conventional simulation method at large coil diameters in the circular LCF. The measured loss, however, start to approach the simulation results at smaller coil diameters. The measured losses of the highly leak modes in the hexagonal LCF, on the other hand, are consistent with the simulation even at large coil diameters.
The results show that tight coiling can mitigate the effect of coherent reflection at outer boundary in fibers, possibly due to phase walk-off from the coiled cylindrical surface. The results from the rounded hexagonal fiber are even more startling. It suggests that a deviation from circular boundary can be very effective in mitigating the impact of the coherent reflection from outer boundary in fibers. The low-index polymer coating on this fiber does not seem to matter at all. This is strong evidence that the radiated powers from the core are reflected into the guided modes in the multimode pump waveguide. This is also a strong proof that the design concept of exploiting strong leakage losses of HOMs works even in double-clad fibers with a suitable design of fiber boundary.
2. Experiments
The cross-section images of the two fibers used in this work are shown in Fig. 1. The dimensions of features for each of the cladding layers are slightly different for optimized HOM losses at the operating coiling condition and around the wavelength of 1050nm. The fiber is designed to operate at a coil diameter of ~40cm, which is advantageous for applications requiring compact packaging. For the circular Re-LCF, the core is 48µm at its smallest dimension (flat-to-flat) and 49.3µm at its largest dimension (corner-to-corner). The diameter of the circular Re-LCF is 392.7µm. For the hexagonal Re-LCF, the core is 50.9µm at its smallest dimension and 51.3µm at its largest dimension. The cladding is 426.1µm at its smallest dimension (flat-to-flat) and 449.3µm at its largest dimension (corner-to-corner). The two layers of features for both fibers are made from fluorine-doped silica glass, whose refractive index is 0.0155 below silica. For the circular Re-LCF, the average feature size of inside layer is 30.1µm and outside layer is 28.31µm. For the hexagonal Re-LCF, the average feature size of inside layer is 32.38µm and outside layer is 29.32µm. The circular Re-LCF is coated with a standard high-index coating and was fabricated at Nufern. The hexagonal Re-LCF was drawn at Clemson with features fabricated at Nufern and is coated with low-index polymer coating (n = 1.375). This fiber was drawn at a slightly lower temperature in order to maintain the hexagonal shape of the stack.
The feature boundaries shown in Fig. 2 were acquired from the cross-section images in Fig. 1 and were used in all the simulations. In a coiled fiber with a curvature radius R, the equivalent refractive index profile neq(x,y) is approximated as:
where ns(x,y) is the refractive index when fiber is straight [18]. A perfect matched layer (PML) is implemented to simulate the infinite cladding [19]. The FEM simulation obtains complex effective refractive indices and loss is then derived from the imaginary part.Fig. 2 Designs used for the simulation, (a) circular and (b) hexagonal Re-LCF. The designs are acquired from feature boundaries in the cross-section images.
In order to ensure launch stability during the measurements, the Re-LCF was spliced to a SM980nm fiber through a tapered mode adaptor to minimize the mode mismatch, which was fabricated by tapering the Re-LCF down to a core diameter of ~8µm over a length of ~6cm. The S2 technique used to measure HOM content was used previously for measuring 50µm core all-solid photonic bandgap fibers [8]. It has a tunable laser and CCD for imaging capture. The fiber was laid in a circular grove fabricated into an aluminum plate. The part of the fibers which was outside the circular grove is made to be as straight as possible. Circular groves with various diameters are fabricated into the same aluminum plate so that dependence on coil diameters can be tested.
Our S2 setup has a ~-40dB detection limit in ratio of HOM power to FM power. In all of our experiments, only LP11 mode was observed in the two Re-LCFs. A sample of S2 imaging is illustrated in Fig. 3. The sharp peaks followed by the LP11 mode are from multiple reflections from bulk optics in the system, which were carefully calibrated prior to the measurement. They can be easily identified due to their FM mode shape and always remain at the same location. The normal scan range was from 1026nm to 1076nm with a center wavelength of 1051nm. After power ratio of LP11 mode to LP01 modes was determined at varying coil diameters, the fiber was cut by approximately 1m. The measurements were repeated for varying coil diameters. The fibers were cut back several times during the measurements. Eventually, in order to obtain HOM loss, the measured and normalized LP11 mode contents on a dB scale were plotted against the lengths of coiled fibers for each coil diameter and a straight line was fitted (see Fig. 4 for data at few selected coil diameters). Since the measured LP11 mode in the S2 measurements always shows a well-defined narrow peak in delay, we have assumed that the coupling between LP01 and LP11 modes is minimal in our fibers. The fundamental mode loss is assumed to be negligible in arriving at the LP11 mode loss. This is largely true for the range of coil diameters used in the measurements. The slope of the straight line was regarded as the loss of the LP11 mode based on the two assumptions above. The error is estimated to be typically less than 10%. The FM loss was measured separately at fixed wavelength of 1050nm using a cut-back technique while ensuring fundamental mode at the output. The fiber lengths used in the experiment and related coil lengths at various coil diameters are summarized in Table 1 for the circular Re-LCF and hexagonal Re-LCF.
Fig. 3 Fourier transform of the spectrum versus differential group delay for circular LCF coil at diameter of 50cm. The insets are the resolved LP11 mode pattern and phase.
Fig. 4 Measured relative LP11 mode content (circles) versus coiled fiber length at various coil diameters for the circular Re-LCF and their linear fit (line).
Table 1. Fiber lengths of the circular Re-LCF used in the experiment
The measured LP11 mode content, i.e. power ratio of LP11 and LP01 modes, is summarized in Fig. 5 for the circular Re-LCF. The coil lengths for each fiber length are different depending on coil diameters (see Table 1). The LP11 mode content at the output is largely determined by the launch condition and LP11 mode loss over the coiled section of the fiber. The LP11 mode losses are determined, as described earlier, by the slope of linear fit to the measured LP11 mode content versus coil length data for each coil diameter. Due to the very high LP11 mode loss at 30cm coil diameter, much shorter fiber length had to be used in this case (see Fig. 5).
The simulated loss for the fundamental mode, second mode and third mode are shown in Fig. 6. The second mode and third mode are two different orientations of the LP11 mode (see insets in Fig. 6). The measured FM loss is also shown along with the measured LP11 mode loss. Two sets of FM measurement are shown, one with free space launch and one with spliced input. The fiber was designed for operation at a coil diameter of 40cm. At smaller coil diameters, the predicted FM loss can be very high (see Fig. 6 for diameters less than 0.35m). As it can be seen, the measured FM losses fit well with the simulation in the low loss regime. This is consistent with what we expected. The mode is well confined to the core region in the low loss regime. There is very little impact from what is going on far beyond the core. The measured FM losses are, however, lower than the simulation in the high loss regime when coil diameter is below 35cm.
The measured LP11 mode losses are, however, much lower than the simulation at large coil diameters. The difference between the measured LP11 mode losses and the simulation, however, converges at small coil diameters when coil diameter is below 0.35m. The lower measured losses of both the fundamental and LP11 modes in the predicted high loss regime can be explained by the reflection at the circular glass/coating boundary. The modes which are significantly radiated away from the core into the cladding are likely to be reflected back to the core due to the coherent reflection, leading to much lower waveguide loss than the simulated. The LP11 mode is designed to have high waveguide loss and consequently, is expected to experience larger impact from the coherent reflection at the fiber glass/coating boundary. The convergence of the measured LP11 mode losses and the simulation at smaller coil diameters is interesting. This may be an indication that phase walk-off in the reflection from the curved cylindrical boundary of the coiled fiber can mitigate the coherent reflection at small coil diameters. It is worth noting that, since we could not distinguish the LP11 mode with the two different orientations illustrated in the insets in Fig. 6, our measured data represent an average of the two orientations. Our tunable light was slightly polarized and there was no polarization control in the measurement.
To investigate further on how to mitigate the effect of the coherent reflection from fiber boundary, we conducted the same set of measurements on the hexagonal Re-LCF. This fiber is coated with low-index polymer coating (n = 1.375) to simulate the effect of double-clad fiber. In a double-clad fiber, optical powers can be trapped within the pump guide due to the total internal reflection at the interface between pump core and cladding, leading to potentially lower HOM losses than those with high index coating. Since this is the situation where most large mode area fibers are used, it is very important to understand the impact of pump cladding on the HOM losses in this case. The simulated mode losses for the fundamental mode, second mode and the third mode for this fiber are shown in Fig. 7. The simulation present similar loss pattern as those in Fig. 6. The minor differences of the loss curves between the circular and hexagonal Re-LCF are mainly caused by slightly different dimensions of the features. This fiber was also designed for operating at ~40cm coil diameter. The measured mode losses are also shown in the figure. It is interesting to see the LP11 mode losses fit reasonably well with the simulation even at large coil diameters. This is a dramatic improvement on HOM losses compared with those in the circular LCF. Since the radiated optical powers from the core modes are expected to be trapped by the pump cladding it is reasonable to assume that the loss of LP11 mode power is through reflection into modes of the multimode pump guide at the pump core and cladding interface [4]. The result is a strong indication that non-circular pump cladding can be very effective in mitigation of the coherent reflection at the pump core and cladding interface. This is significant and confirms the validity of the design approach based on suppression of HOM propagation for mode area scaling. The measured FM losses also fit reasonably well to the simulation (see Fig. 7).
Effective mode area of FM was also simulated for the hexagonal Re-LCF for various coil diameters in Fig. 8. The effective mode area is ~900µm2 at the operating coil diameter of 40cm.
The wavelength dependence of LP11 mode content can be measured by dividing the wavelength scan used in the S2 measurement into a number of smaller sub-scans with equal wavelength span. This was done in Fig. 9 for the LP11 mode content in the 4m hexagonal Re-LCF coiled in 35cm diameter coil. The sub-scan has a wavelength range of 10nm. Wavelengths at the center of each sub-scan are used for the plot. The flat wavelength dependence over this wavelength range is expected and consistent with the simulation. It is worth noting that ~-40dB HOM suppression can be achieved over such a short fiber length, especially considering the short length of the coiled section of ~1.4m (see Table1).
Fig. 9 Wavelength dependence of the measured LP11 mode content in the 4m hexagonal Re-LCF in 35cm coil. Coiled length is 1.37m.
Differential group delay between the LP01 and LP11 modes can also be measured by dividing the total wavelength scan in the S2 measurement into a number of sub-scans of equal wavelength span. The differential group delays were obtained from the S2 measurement of the circular Re-LCF and are plotted against the center wavelengths of each of the sub-scans in Fig. 10. The differential group delay was also simulated by a mutlipole mode solver using approximate circular features and is also plotted in Fig. 10. There is an excellent agreement between the measured differential GVD and the simulation. Same results were also observed on hexagonal Re-LCF.
Fig. 10 Simulated and measured differential group delay between LP01 and LP11 modes in the circular Re-LCF. The simulation was done for a straight fiber. The measurements were performed at a range of coil diameters.
3. Conclusion
In this work, we conducted careful measurements of HOM losses using a cut-back technique in combination with a S2 technique and a fully spliced configuration to ensure launch stability. Impact on HOM losses from coiling, fiber shapes and coating indexes were studied in comparison to simulations based on infinite cladding. It is found that the measured HOM losses can be significantly lower than the simulation in a circular fiber at large coil diameters. As the coil diameter decreases, the measured HOM losses approach the simulation in the circular fiber. Deviation from circular shape is found to be very effective in mitigating the problem, leading to the measured losses being very close to the simulation even at large coil diameters in low-index coated fibers. HOM losses in excess of 20dB/m were measured in the hexagonal Re-LCF with ~50µm core diameter.
Acknowledgments
This material is based upon work supported in part by the U. S. Army Research Laboratory and the U. S. Army Research Office under contract/grant number W911NF-12-1-0332 through a Joint Technology Office MRI program.
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