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Higher-order mode fiber amplifiers have demonstrated effective areas as large as 6000 μm2, allowing for high pulse energy and peak power amplification. Long-period gratings are used to convert the fundamental mode to the higher-order mode at the entrance to the amplifier, and reconvert back to the fundamental at the exit, to achieve a diffraction limited beam. However, long period gratings are susceptible to nonlinearity at high peak power. In this work, we propose and demonstrate axicons for linear bulk-optic mode conversion at the output of higher order mode amplifiers. We achieve an M2 of less than 1.25 for 80% mode conversion efficiency. Experiments with pulsed amplifiers confirm that the mode conversion is free from nonlinearity. Furthermore, chirp pulse amplifier experiments confirm that HOM amplifiers plus axicon mode convertors provide energy scalability in femtosecond pulses, compared to smaller effective area, fundamental mode fiber amplifiers. We also propose and demonstrate a route towards fiber integration of the axicon mode convertor by fabricating axicons directly on the tip of the fiber amplifier end-cap.
© 2015 Optical Society of America
1. Introduction
The drive to higher output powers and pulse energies in high-power fiber lasers brings with it a corresponding need to mitigate nonlinearities such as self-phase modulation, Brillouin scattering, and Raman scattering. Consequently there have been a number of approaches to increasing the fiber effective area (Aeff) in order to achieve large-mode area (LMA) high power fiber lasers. These LMA fiber strategies include large-pitch, photonic crystal fibers [1], chirally coupled fibers [2], leakage channel fibers [3], helically coiled cores [4], multi-trench fibers [5], and large-mode area, solid core, photonic bandgap fibers [6].
All these approaches, however, operate on the fundamental mode. Coiling the fiber causes bend-induced changes to the refractive index profile, which in turn causes the fundamental mode to experience a significant reduction in effective area. Consequently, fiber amplifiers based on the fundamental mode experience increased nonlinearities with coiling, offsetting the advantage of LMA fiber designs. Furthermore, this effect becomes more pronounced as Aeff is increased [7,8].
One solution to impairments caused by bending, the rod-type fiber, is to simply make the fiber rigid and hold it straight [9]. Doing so however eliminates many of the advantages of the conventional fiber geometry, not the least of which is the ability to package the fiber laser in a compact format.
An alternate approach to operating with the inherently bend-sensitive fundamental mode is to intentionally operate in a single, large effective area, higher-order mode (HOM) of a specially designed, multi-mode fiber [10,11]. Higher-order modes are less susceptible than the fundamental mode to bend induced area reduction [12]. At the same time, compared to the fundamental mode, HOMs are more resistant to nearest neighbor mode coupling, which scatters the LPM,N mode into the LPM ± 1,N and is typically the dominant form of mode-coupling in multi-mode fibers [13]. The resistance to nearest neighbor coupling occurs because the difference in effective index between the LP0,N and LP1,N modes increases with increasing N.
A schematic of an Er-doped fiber amplifier based on higher order modes is shown in Fig. 1, along with the index profile of an HOM fiber. The pump, a single-mode, 1480 nm, Raman fiber laser [14], and signal are multiplexed together with a conventional fused fiber WDM and then launched into the higher order mode fiber. A center peak in the index of refraction of the HOM fiber, guides the fundamental mode, shown in red in Fig. 1(b). This center core of the HOM fiber is designed such that the LP01 of the HOM fiber is mode matched to the input SMF, allowing for low-loss fusion splicing and coupling of the SMF into the LP01 of the HOM fiber.
Fig. 1 (a) Schematic of an Er-doped higher-order mode fiber amplifier. (b) The index profile of a rare-earth doped, higher-order mode fiber. The LP0,1 mode (red) is guided in the central core whereas the LP0,N higher-order modes (blue) reside in the outer core. (c) Output power vs. pump power. (d) Output beam profile and M2 measurement at 50 W output power.
The higher order modes of interest in this work are the symmetric LP0,N modes, where N>1. The higher order mode, shown as a blue line in Fig. 1(b), resides in the large outer core region. The shaded area is doped with rare-earth ions (erbium, in this work), to provide gain.
A long-period grating (LPG) provides phase matched coupling between the fundamental mode and the higher-order mode [15]. In the case of an Er-doped higher order mode amplifier, both pump and signal are coupled into the same higher-order mode, providing a high degree of pump/signal overlap, and helping to suppress other unwanted modes. Amplification takes place in the higher order mode, and a second LPG, matched to the input LPG, reconverts the higher-order mode back to the fundamental, for a diffraction limited output [16].
Typical CW amplifier performance of a 4.5 m long Er-doped HOM amplifier operating in the LP0,14 mode is shown in Fig. 1(c). The effective area of the LP0,14 mode, with the fiber straight was approximately 6000 μm2, however, the amplifier results were obtained with the fiber coiled to approximately 25 cm diameter. At this coil diameter, the effective area is reduced due to bending effects to approximately 4250 μm2. In spite of the small bend diameter, the output mode (inset, Fig. 1(d)), reconverted back to the LP0,1 with the second LPG, still shows an M2 < 1.1 (Fig. 1(d)). To the best of our knowledge, higher order mode fibers are the only fiber technology currently demonstrated with such a large effective area that is capable of delivering a diffraction limited beam profile in a small coil diameter and a fusion spliced format.
When operated in a pulsed format, the ultra-large area of the HOM fiber enables the generation of record peak powers with low nonlinearity in all-fiber fusion spliced amplifiers when there is no output LPG and the beam exits in the higher-order mode [17]. However, the output LPG becomes problematic in high peak power systems, as LPGs are known to be sensitive to nonlinear impairment due to self-phase modulation [18]. Recent simulations also suggest that self-focusing can play a roll, even when operating far below the critical power for self-focusing [19]. In pulsed systems with low peak power, limited by SBS, for example, the output LPG does not limit the performance of the system and diffraction limited, high energy, single frequency pulses can be achieved [16]. In contrast, in high peak power pulsed systems, even if the fiber is terminated immediately after the LPG and the beam subsequently enters free space, requiring reconversion to the fundamental mode before exiting the fiber can add substantially to the nonlinearity in the amplifier [20]. Consequently, a low-nonlinearity, bulk-optic approach to beam conversion at the output of an HOM fiber amplifier would be advantageous for high peak power systems.
A number of devices have been proposed for mode conversion in few-mode fibers. Spatial light modulators are used in spatial division multiplexing experiments for communication applications in few-mode fibers [21], and for launching HOMs into LMA fibers [22–24]. While flexible, these devices are expensive and not well suited to high-power operation. Binary phase plates have also been proposed for mode conversion in HOM amplifiers [25].
In this work, we propose and demonstrate for the first time mode conversion at the output of an HOM fiber amplifier using a bulk-optic axicon. An axicon is a conical lens that is known to produce in its focus an approximate J0 Bessel beam [26] from an incident Gaussian beam. HOM fibers, on the other hand, have modes which are similar, but not identical to, Bessel beams, and have many of the same properties as Bessel beams, such as a non-diffracting, self-healing center spot [27]. Here we operate the axicon in the reverse of its typical direction, entering the axicon with a field that is approximately a Bessel beam to achieve nonlinearity-free conversion of an HOM amplifier to a diffraction limited output.
2. Higher-order mode conversion with axicons - simulations
Figure 2 illustrates the setup for mode conversion of an LP0,N mode using an axicon. The higher order mode (in this example, the LP0,14) exits the HOM fiber. A magnification lens then magnifies the HOM beam, so that it has the proper dimensions for conversion with an axicon of a certain apex angle. The axicon then imparts a linear radial phase to the beam. Finally, a second lens propagates the beam to the far field, where an aperture filters out residual high divergence light, providing a beam with low M2.
Given a particular LP0,N mode to convert, and an axicon with certain apex angle, we use a 1D propagation code to optimize the propagation distance and lens magnification for optimal mode conversion with the highest possible efficiency. We start by simulating the propagation of a Gaussian beam in the reverse direction through the system. A Gaussian beam with a certain beam diameter is incident on the axicon, and propagated backwards, through its focal point. At each point during the backward propagation after the axicon, the overlap integral between the input beam and the HOM field with a range of magnifications is calculated. This procedure provides the HOM magnification and image distance that yields the highest overlap between HOM field and Gaussian beam converted by an axicon. The starting Gaussian beam diameter is then adjusted and the entire procedure repeated, until the maximum possible overlap is determined, thus determining the optimal magnification and object distance to the axicon lens for a given LP0,N mode and axicon apex angle.
The results of this simulation procedure are shown in Fig. 3. The intensity obtained in the focus is shown in Fig. 3(a), for two different incident Gaussian beam diameters. The larger the incident beam, the more rings are generated in the focus. This result shows that an axicon can in general convert any incident LP0,N mode, as long as the beam size incident on the axicon is appropriate.
Fig. 3 Simulations of axicon mode conversion of a higher order mode. (a) The beam produced by a Gaussian focused by an axicon for 1 mm diameter beam, vs. a 2 mm diameter beam. (b) Optimal overlap of the LP0,14 mode with a Gaussian focused by an axicon, as a function of input beam width, for different axicon apex angles. (c) Required magnification of the LP0,14 for optimal conversion, as a function of axicon apex angle. (d) Axicon placement for optimal conversion of the LP0,14 mode, as a function of axicon apex angle.
Figure 3(b) shows the overlap obtained between a Gaussian beam focused by an axicon and an optimally magnified HOM beam, for different axicon apex angles. It can be seen that independent of axicon apex angle, the overlap is approximately 77%, but smaller apex angles require larger beam sizes. These results are collected in Fig. 3(c) and 3(d), plotting the required LP0,14 magnification and image distance for different apex angles. Given the axicon apex angle, these plots define the rest of the parameters required for the mode converter setup of Fig. 2.
Note that when the magnification lens is removed from the system (magnification of 1), optimal mode conversion for a given LP0,N mode is obtained for a single axicon apex and angle and image distance. These values were used in designing a fiber integrated axicon end-cap, discussed further in Section 3.2.
Depending on the details of the higher-order mode considered, the best overlap obtained for an LP0,N mode for a fiber with an index profile as shown Fig. 1(b) is between 75 and 80%. The difference between an HOM intensity profile, and a Gaussian beam focused by an axicon is illustrated in Fig. 4(a). The rings of the HOM are more intense than the axicon beam, and the spacing of the first few rings slightly different. These differences between HOM and axicon beams are what ultimately limit the conversion efficiency of the axicon mode convertor.
Fig. 4 (a) Intensity of the LP0,14 mode of a typical higher-order mode fiber, compared to the intensity produced by a Gaussian beam incident on an axicon. (b) M2 vs. aperture transmission for the axicon mode convertor, compared to that achieved with the binary phase plate proposed in Ref [25], N. Lindlein et. al.
Once the optimal optical setup is defined for a given axicon apex angle and LP0,N mode, we propagate the HOM field in the forward direction through the mode converter. At the plane of the spatial filter, an aperture is applied to the beam, and then M2 is calculated. The result of this calculation is shown in Fig. 4(b) for the axicon mode converter as well as the binary phase plate mode converter, proposed in [25].
For the axicon mode convertor, an optimum M2 of 1 is achieved for 77% aperture transmission, the same value as the overlap between the HOM and a Gaussian converted by an axicon. The binary phase plate also achieves an M2 of 1 for similar conversion efficiency. However the degradation of M2 for higher conversion efficiencies is much gentler for the axicon, compared to the binary phase plate. This slow degradation in M2, up to around 92% conversion efficiency, could have some benefit in applications that don’t necessarily require M2 of 1.
The considerations discussed in this section are independent of average power, so for high power lasers (i.e. kW class), conversion efficiency would be a concern for power scaling. However, for such high average power CW lasers where peak powers are not in the range of hundereds of kiloWatts, an LPG with better than 99% conversion efficiency would still be a viable option.
3. Higher-order mode conversion with axicons - experiments
3.1 Mode conversion with a bulk-optic axicon
The axicon mode conversion was then implemented experimentally. A commercially available, off-the-shelf, axicon with 1 degree apex angle and broadband anti-reflection coating was used (ThorLabs AX251-C). A high power Raman fiber laser at 1480 nm was used as a pump source [14]. The CW signal was 500 mW at 1560 nm. Pump and signal were multiplexed with a fused-fiber WDM and launched into the fundamental mode of the HOM fiber with a fusion splice. A single, broad-band LPG converted both pump and signal to the LP0,14 mode. Amplification took place in 4.5 m of propagation in the HOM. The output end of the amplifier was terminated with an 8 degree angle-polished end-cap. M2 and beam profile measurements were performed at a pump power of 80W and output power of approximately 45W. The magnification lens was an AR coated asphere with focal length of 11 mm and the lens for propagating to the far field, after the axicon, had a focal length of 30 cm.
An image of the beam profile (measured with a phosphor coated CCD camera) without, and with, the axicon in the optical system is shown in Fig. 5(a) and 5(b), respectively. With the axicon, the beam could be tightly focused to a single spot, at a point approximately 1.5 m away from the end tip of the HOM fiber. Without the axicon, such a tightly focused spot could not be achieved. Note that the camera images were not used for M2 measurements, but only for viewing the beam. Furthermore, although the output mode from the amplifier largely consists of the LP0,14 higher order mode, S2 measurements on HOM amplifier confirm the presence of small amounts of other HOM modes [17]. This small amount of residual unwanted mode content can be responsible for the slightly uneven power distribution seen in Fig. 5(a).
Fig. 5 Measured performance of axicon mode conversion of the LP0,14 mode. (a) Beam profile measured with lens 1 and lens 2, but without the axicon. (b) Beam profile measured when the axicon is in the system. (c) M2 vs. aperture transmission. (c) M2 measurement at 70% aperture transmission.
An aperture was then placed in the plane where the tightest focus was obtained, and M2 was measured as a function of aperture transmission. The M2 measurement was done using a commercial device from Photon Kinetics based on a detector head with a rotating slit which used a 4-sigma definition of beam width. Figure 5(c) shows the measurement result. For aperture transmissions less than 0.7, a diffraction limited beam with M2 < 1.1 was achieved. For aperture transmission of 0.8, M2 was less than 1.25. Higher aperture transmissions were difficult to measure as, due to space limitations, the M2 measurement device was several meters from the amplifier, and residual high divergence light diffracted too quickly to be captured by the aperture of the M2 device.
3.2 Mode conversion with a fiber integrated axicon
The fiber integrated nature of long-period gratings makes them extremely attractive as mode convertors. While a bulk axicon performs the mode conversion well, it would be advantageous to integrate an axicon onto the end-tip of a fiber amplifier. Fiber integration can be achieved by adding a coreless end-cap of the appropriate length to the output end of the amplifier, and terminating the end-cap with an axicon. Axicons can be fabricated on fiber end-tips via a variety of means, such as polishing the fiber while it is spinning [28], chemical etching [29,30], focused ion beam milling [31], or direct laser writing [32], for example.
The setup for an HOM amplifier with input mode conversion performed with LPG, and output mode conversion performed with fiber-integrated axicon end-cap, is illustrated in Fig. 6(a). In this case there is no magnification lens, so length of the end-cap and apex angle of the axicon are determined by the LP0,N mode being used, as shown in Fig. 3(c) and 3(d). For the LP0,14 mode, the end-cap length was simulated to be approximately 800 μm, and the required apex angle approximately 15 degrees.
Fig. 6 Mode conversion performance of a fiber-based axicon end-cap. (a) Schematic of the amplifier architecture. (b) Microscope images of the fabricated axicon end-cap. (c) Beam profile. (d) M2 vs. aperture transmission
To fabricate the end-cap, a 330μm OD core-less fiber was first spliced to the end of the HOM amplifier, and then cleaved to a length of 900 μm. The end-cap was then polished at a 15 degree angle, while the fiber was rotated at approximately 10 RPM. While polishing, 100 μm length was removed to achieve the desired 800 μm end-cap length. A four stage polish with grit sizes of 9 μm, 3 μm, 1 μm and 0.3 μm was used. Microscope images of the side view and top view of a typical fabricated end-cap are shown in Fig. 6(b).
The beam profile and measured M2 vs. aperture transmission are shown in Fig. 6(c) and 6(d). M2 varied between 2.7 and 4.5, depending on aperture transmission.
To better understand why the axicon end-cap did not provide as low an M2 as the bulk-optic axicon, we simulated the sensitivity of M2 to deviations from the ideal geometry. Figure 7(a) shows calculated M2 as a function of both end-cap length and apex angle at 77% transmission through the spatial filter. The tolerance on end-cap length for a low M2 is relatively loose with a length of ± 100 μm sufficient to achieve M2 less than 1.2. On the other hand, angle tolerance requirements are relatively tight, needing an apex angle of ± 0.25 degree from the optimal value to ensure a low M2. Furthermore, the radius of curvature of the end-tip of the axicon (Fig. 7(b)) also needs to be less than 1 μm, to prevent M2 from degrading rapidly.
Fig. 7 Fabrication tolerances in an axicon end-cap (a) M2 vs. apex angle and end-cap length for 77% transmission through the spatial filter. (b) M2 vs. end-cap length and end-tip radius of curvature for 77% transmission through the spatial filter.
A round, tightly focused beam was achieved, indicating that the axicon was well-centered on the HOM beam. However, the tolerance required on the apex angle is much tighter than the control we have currently in our rotating polishing system. Considering that M2 ≈14 in the case of an LP0,14 mode, the axicon end-cap did succeed in improving considerably the focusability of the output beam. We expect with further improvements in the geometry of the axicon end-cap, we can further improve the M2 provided by an axicon end-cap.
4. Pulsed HOM amplifier experiments with an axicon based mode convertor
To investigate the nonlinear properties of the axicon mode convertor, pulsed amplifier experiments were performed. A 1ns, 100 kHz pulse train was amplified in an HOM amplifier. Beam profile measurements were obtained using a scanning, knife-edge measurement.
Figure 8(a) shows beam profiles obtained when an LPG was used as an output mode converter. The beam profile obtained for a CW signal (black curve), shows a single peak in the profile. When 1 ns, 100 kHz pulses and MHz linewidth were amplified to a peak power of 13 kW, the beam profile obtained was essentially identical to the CW beam profile. However, at higher peak powers of 122 kW, or 165 kW, the nonlinearity that takes place in the output LPG degrades the mode conversion, causing power in the center peak to be lost to power in the wings of the beam profile. We estimate that at 165 kW of peak power, only 67% of the power in the output beam is contained in the center peak. These results illustrate the nonlinear limitation in output mode conversion with an LPG for pulses with peak powers on the order of 100 kW or more.
Fig. 8 Beam profiles measured with scanning knife edge for both CW and pulsed operation. (a) HOM amplifier with output LPG for mode conversion. (b) HOM amplifier with axicon for output mode conversion.
In contrast the beam profiles for axicon mode conversion are shown in Fig. 8(b). CW beam profiles at 0.7 W and 44 W output power are shown in black and red curves, whereas pulses with peak power of 4.3 kW and 270 kW are shown with green and blue curves. All beam profiles are essentially identical, and do not show the same degradation in mode conversion at high peak power as the LPG mode convertor. On the other hand no significant differences were observed in temporal pulse profiles for axicon mode conversion compared to LPG mode conversion. These results confirm that the degradation in beam profile was caused by nonlinearity in the output LPG and that the axicon mode conversion is effectively free from nonlinear degradation at the power levels tested.
Finally, we also performed a femtosecond chirp-pulse amplifier experiment, comparing amplification in a fundamental mode, very-large mode area (VLMA) amplifier with approximately 1,000 μm2 effective area (when straight) [33], to the HOM amplifier with an axicon mode convertor.
A femtosecond polarization-maintaining Fig. 8 laser [34] operating at 33 MHz was used as a seed source. The pulses from the oscillator were stretched to 348 ps in a fiber-based stretcher, and amplified. The repetition frequency of the pulse train was then reduced with a combination of acousto-optic and electro-optic modulators to 100 kHz. The pulse train was then amplified again before entering the final VLMA or HOM power amplifier. After the amplifier the pulses were recompressed using a diffraction grating pair with groove density of 1200 l/mm. At low powers, the pulses could be recompressed to 491 fs, approximately 1.3 times the bandwidth limit.
Both amplifiers were coiled to approximately 25 cm coil diameter. Spectra and auto-correlations as a function of pulse energy out of the compressor for the VLMA amplifier, compared to the HOM amplifier are shown in Fig. 9.
Fig. 9 Femtosecond chirped-pulse amplifier results comparing an LP01 VLMA amplifier spectrum, (a), and autocorrelation, (b), to an HOM-Er amplifier with axicon mode conversion (c) and (d).
Single grating diffraction efficiency was ~92%, and the VLMA amplifier showed approximately 70% compressor throughput, as expected. On the other hand for the HOM amplifier we found that the output power after the compressor was approximately the same whether an aperture with 85% throughput was placed before the compressor, or there was no aperture in the system. With the aperture in the system before the compressor, the compressor throughput was 70%, identical to the throughput measured for the VLMA amplifier. Without the aperture in the system, the unreconverted, high-divergence light, was effectively lost through the system as it propagated through the compressor, due to the long path length. Without the axicon in the system, the HOM beam diffracted too quickly to propagate any significant power through the compressor.
To measure the pulse width, a small fraction of the beam was picked off using an uncoated 10 degree wedge, decreased in average power using neutral density filters, and measured with a home-made autocorrelator using a silicon photo-diode as a two-photon detector. For low pulse energy, both amplifiers achieved approximately 490 fs pulse width. As the pulse energy was increased, spectral broadening due to nonlinearity was observed, and at the same time satellite pulses developed in the autocorrelations (Fig. 9). However, the pulse energy at which this was observed in the HOM amplifier was significantly higher than in the VLMA amplifier. For example a 5.7 μJ pulse in the VLMA amplifier showed similar levels of distortion in the correlation as a 41 μJ pulse in the HOM amplifier, showing the benefit of the ultra-large HOM area together with the low-nonlinearity axicon mode conversion.
Recently a high pulse energy CPA system using an HOM fiber with output LPG for mode conversion achieved 300 μJ/pulse [20]. However that work used 1.7 ns stretched pulses, (5 times longer than here), a much shorter fiber length (2.65 m compared to 4.5 m), and active phase and amplitude shaping. We expect that with such system advances, an HOM CPA amplifier with an axicon could produce mJ class pulses.
5. Conclusions
In summary, we have proposed and demonstrated for the first time bulk-optic mode conversion of the output beam from a higher-order mode fiber amplifier using an axicon. With a bulk-optic axicon, we demonstrated an M2 of < 1.25 for 80% conversion efficiency.
A fiber integrated axicon on an end-cap was also tested. Although the M2 was not as low as the bulk-optic axicon, the M2 of 4 still showed a considerable reduction from the M2 of 14 for an un-reconverted LP0,14 mode. Simulations of design tolerances in the axicon end-cap suggest tight, but achievable tolerances required in the axicon apex angle and tip roundedness.
Experiments amplifying 1 ns, 100 kHz pulse trains confirmed that mode conversion with an output LPG is susceptible to nonlinearity, with the output beam profile degrading for peak powers approaching 100 kW. In contrast, mode conversion with an axicon showed no dependence on either peak power or average power, confirming that the axicon mode conversion was free from nonlinearity at the tested power levels.
Finally, we compared chirp-pulse amplification in a conventional LP01 VLMA amplifier to amplification in HOM amplifier with axicon mode convertor. The results showed that the combination of ultra-large area in the HOM amplifier plus nonlinearity free mode conversion directly enabled the energy scaling in comparison to the VLMA amplifier.
In conclusion, we expect mode conversion with axicons to further enable applications of ultra-large area higher-order mode fiber amplifiers.
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