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We propose and demonstrate amplification of a single high-order mode in an optical fiber having an elongated, ribbon-like core having an effective mode area of area of 600 µm2 and an aspect ratio of 13:1. When operated as an amplifier, the double-clad, ytterbium doped, photonic crystal fiber produced 50% slope efficiency and a seed-limited power of 10.5 W, corresponding to a gain of 24 dB. The high order mode remained pure through 20 dB of gain without intervention or realignment.
©2013 Optical Society of America
1. Introduction
Extremely high power diffraction-limited lasers are needed for projected research, defense, and manufacturing applications. The power generated from conventional fiber lasers – those based on fibers having cores with circular cross-sections - has risen significantly over the last decade [1]. Today 10 kW fiber lasers are commercially available, but these may be approaching fundamental limits; tradeoffs between thermal lensing [inversely proportional to area] and either stimulated Brillouin scattering (SBS) or stimulated Raman scattering (SRS) [proportional to area] are expected to limit the power to 2 kW for narrowband, SBS-limited sources or 36 kW for broadband, SRS-limited sources. In addition to these limits, bending induced mode distortion limits large circular-core fibers to mode field diameters of roughly 50 µm [2], and at that size, SRS will likely limit broadband fiber laser amplifiers to powers of roughly 10 kW.
Beam combining techniques sidestep the limits of individual fiber lasers and amplifiers by combining many lasers into a single, brighter beam [3–8]. Higher power unit cells benefit all such approaches by reducing the number of cells required to reach a target combined output power.
We present here a novel method for scaling the power of single emitters beyond their current limits. The method involves transitioning away from traditional circular-core fiber amplifiers to rectangular-core fiber amplifiers. A rectangular (hereafter, ribbon) core has a larger surface area than a circular core for the same enclosed volume, and thus radiates heat more efficiently. The geometry also raises the nonlinear thermal lensing limit because the thermal gradient in the wide dimension has a nearly flat top profile, leaving the thermal lensing to be limited by the width and numerical aperture of the single mode narrow dimension. A ribbon core also sidesteps bending limits, provided the fiber is selectively bent about its narrow axis. A ribbon core thus can be made large enough to significantly raise its SBS and SRS limits without making it thermal-lensing or bending limited.
Larger cores generally allow additional propagation modes. Though these can be problematic, they have an important advantage: compared to the fundamental, high order modes are more stable (there is a larger separation between their propagation constants and those of their neighboring modes [9]). Unlike the high order modes of a circular core, all lobes of all modes of a ribbon core have the same peak intensity. Thus, ribbon-core fibers can propagate and amplify power in a high-order mode without suffering from hotspot-precipitated nonlinearities or damage. The high order modes of a ribbon-core fiber are consequently preferred, provided they can be cleanly excited from the TEM00 mode of a seed laser, amplified without distortion, and efficiently converted back to a TEM00 beam – spatially analogous to chirped pulse amplification, where a pulse is stretched in time, amplified, and then recompressed.
Others have investigated ribbon core fibers but have either taken a multi-core approach [10] (in that reference, incoherent cores) or have focused on fibers that propagate the fundamental mode but with weakly-guided high order modes [11–13]. An active ribbon fiber operating in a high order mode has been previously demonstrated [14], but refractive index non-uniformity across the core created modal impurities, and its relatively absorptive, low melting-temperature phosphate-based glass limited its power to less than 1 W. Selective mode excitation in ribbon-core fibers [15] and efficient conversion from a high-order ribbon mode to a TEM00 beam [16] has already been demonstrated. Single binary phase plates have been shown to convert from circularly symmetric high order modes to the TEM00 mode in free space with lossy filtering [17], but this technique has not yet been reported to excite a high order ribbon fiber mode from a TEM00 mode. In contrast to the previous work, this work is based on silica photonic crystal fibers. Two fibers were fabricated by our group: a passive version to validate our mode excitation techniques and an Yb-doped active version to demonstrate power scaling. The excitation technique reported here differs from past work in that it uses a one dimensional binary phase plate, a more flexible approach that achieves higher modal purity; we further demonstrate high modal stability through 20 dB of gain.
In this paper, we first discuss a novel technique for excitation of a single high order mode in a ribbon fiber (§2.1-2.2) followed by a short description of how mode purity is calculated (§2.3). Next we demonstrate this technique in an un-doped PCF ribbon fiber (§2.4). Then we report excitation of a single high-order mode in an Yb-doped, double-clad, PCF ribbon fiber (§2.5). The core in the un-doped fiber is guided in a silica core by air holes that lower the average index in the region surrounding the core, while the core in the Yb-doped fiber is guided by the raised index of its Yb-doped core rods. Finally, we present the use of the Yb-doped fiber as a single high-order mode amplifier and describe its performance (§3).
2. Excitation of high order ribbon fiber modes
2.1 Method
Large mode-area ribbon core fibers will likely support modes with many lobes in the wide dimension. Figure 1 illustrates the calculated near-field intensity pattern of a four lobed mode of a hypothetical ribbon fiber (NA = 0.05, core 10 × 100 µm). Figure 2 illustrates the far field of this mode; the near field peaks alternate in phase between 0 and π. The far field has two primary lobes, holding roughly 90% of the power, and a series of less-intense lobes between them; the number of less-intense lobes depends on the mode’s order.
Fig. 1 Calculated near field intensity plot for a four lobed ribbon fiber mode, (a) 2D intensity plot, and (b) 1D intensity plot.
Fig. 2 Calculated far field intensity plot for a four lobed ribbon fiber mode, (a) 2D intensity plot, and (b) 1D intensity plot.
We have previously shown that a pair of spatial light modulators – in essence, programmable phase plates – can convert a TEM00 beam to a multi-lobed ribbon mode with high efficiency [16]. Spatial light modulators are typically only suitable for use with a few milliwatts of power. Custom, static, phase plates can also convert the beam and are suitable for high power applications [18,19], but inconvenient at this stage of our research. A third alternative, which we use here, is to convert the TEM00 beam to a single high-order-mode with a simple, and relatively inexpensive, binary phase plate and a cylindrical lens. In this approach, the conversion efficiency is not as high as it can be with SLMs or custom phase plates, but the purity of the illuminated mode can still reach 99%.
Laser beam quality is typically quantified by the M2 parameter or power in the bucket; however, both metrics compare the beam under test to an ideal TEM00 beam and are inappropriate for high order modes. Here, we compare the amplitude and phase of the field of the excited mode to those of the target mode, and define the purity as the overlap integral of the two fields. In a finished laser system, M2 can be used if the high order mode is converted back to a TEM00 mode [16], though we do not take that step here.
2.2 Experimental setup and alignment procedure
Figure 3 shows the experimental setup for illuminating a high order ribbon fiber mode using a simple binary phase plate. First, a cylindrical lens focuses a collimated TEM00 beam in the axis perpendicular to the optical table (it remains collimated in the axis parallel to the table) and a binary phase is placed at the focal plane of the cylindrical lens. The phase plate used in this work has a half period of 250 µm, and is 25 mm in width which gives it 100 half periods; in general, the plate should have at least as many half periods as lobes in the desired ribbon mode. The period of the phase plate can be chosen arbitrarily since the image of the light exiting the plate will be de-magnified to match the size of the mode on the fiber end face.
Fig. 3 Single high order ribbon fiber mode illumination experimental setup. FFD = front focal distance, d = distance between effective focal length lens pair, BFD = back focal distance.
The lobes of an ideal high-order ribbon-mode are of nearly equal peak intensity. In order to illuminate a mode properly, it is necessary to illuminate the correct number of periods on the phase plate with a nearly flat top beam. A simple way to accomplish this is to overfill the phase plate illumination (in this case by a factor of three) and clip off the power outside the central region with a one dimensional spatial filter; this yields a reasonably flat illumination, though at the expense of efficiency. Thus, the spatial filter which sits immediately after the binary phase plate serves two purposes; to form a flat top beam out of a Gaussian input beam in the absence of a refractive beam shaper, and to illuminate the correct number of phase half periods to match the lobes of the desired HOM.
The mode exiting the phase plate-spatial filter portion of the setup is a nearly flat top beam with a series of 0 to π phase shifts across it, shown in Fig. 4(a). The far field intensity pattern of this beam, shown in Fig. 4(b), has two bright primary lobes (which are matched to corresponding lobes in the far field pattern of the target mode) and a series of additional undesired lobes at progressively higher angles of diminishing intensity as a result of the square shape of the lobes exiting the phase plate. Since the latter cannot be launched into the target mode, shown as dashed lines in Fig. 4(c) and (d), we clip them with a spatial filter in the far field plane (as shown). The clipped far field profile is shown in Fig. 4(c) (solid) with the far field of the target five-lobed mode (dashed). Figure 4(d) shows the final de-magnified beam profile at the fiber facet (solid) with the near field of the target five-lobed mode (dashed).
Fig. 4 Calculated 1D beam cross-section at various planes in the mode excitation setup. The near field plots (left) are given as amplitudes so the phase of each lobe can be seen while the far field plots (right) are kept as intensities. (a) Amplitude just after the phase plate and spatial filter in the near field plane. (b) Intensity just before the spatial filter in the far field plane, and Fourier transform of (a) for lens pair f = 240 mm. (c) Intensity just after the spatial filter in the far field plane (solid), and intensity of the calculated far field of the target five-lobed ribbon fiber mode (dashed). (d) Amplitude just before the fiber facet, and Fourier transform of (c) for FC-L1 = 15 mm (solid), and intensity of the calculated target near field of the five-lobed ribbon fiber mode (dashed).
A full 2D overlap integral between the two profiles shows that up to 99% purity with 80% efficiency is possible using this method. The power not coupled into the desired mode leaves the fiber and thus does not couple into unwanted modes. This is analogous to the conversion from a HOM to the TEM00 mode in which the power outside the far field central lobe after conversion is clipped, leaving only a high purity central lobe with up to 80% efficiency. Similar purity and efficiency results have been reported for conversion from circularly symmetric HOMs to the TEM00 mode with far field mode filtering [17].
Before coupling into the fiber, the near field of the input beam must be de-magnified to match the target mode. In our setup (Fig. 3), the fiber coupling lens is an aspheric lens having a focal length of 15 mm. The effective focal length lens pair, however, can be adjusted to achieve the correct magnification. Equation (1) gives the effective focal length of the lens pair, measured from the lens pair’s principal planes. Equations (2) and (3) give the front and back focal distances (measured from the principal planes); they assume the lenses in the pair are thin compared to their respective focal lengths,
where n is the refractive index of the medium between the lens pair, in this case air, d is the distance between the two lenses, and f1 and f2 are the focal lengths of lenses 1 and 2, respectively.To form an initial guess for the correct demagnification factor, we assume that the lobes of the target mode match the de-magnified phase plate, or N half-periods fit the fiber core width. An initial solution can be arrived at by dividing the product of the half period of the phase plate and the number of lobes in the desired mode by the ribbon core width. Once the demagnification factor is determined, an effective focal length for the lens pair can be calculated by multiplying the fiber coupling lens focal length by the demagnification factor. Then, an appropriate lens pair and spacing is chosen to create the desired effective focal length, and therefore to achieve the desired demagnification.
These steps yield an approximate spacing between the lenses. The spacing can be checked experimentally by reverse-propagating a beam through the fiber. The reverse beam projects an image of the core onto the phase plate, which is then imaged onto a camera. The spacing between the lens pair, and the consequent changes in front and back focal distances, can then be fine-tuned until the transitions in the phase plate fall at the appropriate positions of the core (as determined by modeling); see Fig. 5(b).
Fig. 5 (a) Photonic crystal ribbon fiber with a rectangular core cross-section, (b) An image of a ribbon fiber end face with overlaid illustrated binary phase plate transitions and target mode profile..
With the demagnification properly set and forward propagation resumed, the vertical tip angle can be aligned easily by maximizing the coupled power in the forward direction. Aligning the horizontal tilt angle is not as simple and requires an additional step, one that calls for diagnostic images of the near and far field of the output in order to determine the launched modal content. In this step, the tilt of the fiber is adjusted until only two peaks are visible in the far field of the fiber output, and the desired number of lobes is visible in the near field. If the horizontal translation is inadvertently displaced during horizontal tilt alignment, the reverse propagating diagnostic can be used to realign it.
2.3 High order mode excitation in a passive photonic crystal ribbon fiber
Here we report a passive photonic crystal ribbon fiber and excitation of a single higher order mode with 90% purity and a mode area of 650 µm2. Figure 5(a) shows an image of the end face of an air guided, passive, ribbon fiber. In this fiber, guiding is achieved by a set of air holes that lower the average index of the region around the core; we estimate that the fiber supports 14 modes. In a high power ribbon fiber, the outer cladding might also be rectangular to allow selective bending and better thermal control, though the fibers described in this paper all have round outer claddings.
Using the method described in the above section, a high order five-lobed mode was illuminated with 90% purity. The purity is defined by the overlap integral of the excitation field (determined from the measured intensity distribution and the inferred phase, found via the Gerchberg-Saxton algorithm) and the expected field of the target mode [20]. Equation (4) gives the overlap integral between a particular mode, m, and the normalized measured field,
whereEquation (5) is the normalized electric field of the measured beam, and Eq. (6) is the electric field of a fiber mode, m, extracted from an image of the fiber cross-section and the known index(s) of the fiber. The modes used for the overlap calculation are derived from the geometry of the specific fiber as fabricated.
An overlap integral performed between the measured mode and each of the known modes shows that 94% of the total measured power overlaps with the 14 known modes, and that 95% of this power overlaps only with the desired 5 lobed mode. The measured power which does not overlap any of the known modes could be the result of a combination of many factors such as error in the phase retrieval, potential leaky modes, cladding modes or scattered light which is non-guiding, or a variation in the expected modes vs. the actual modes of the fiber. Considering the portion of power that has not been attributed to any mode, the modal purity in the primary five-lobed mode is in the range of 90% to 95%.
Figure 6 shows good agreement between the intensity cross-sections of the measured and expected mode for both the near and far fields.
Fig. 6 Normalized intensity cross-section of the measured (dashes), and calculated (solid) five-lobed mode a) near field in Watts per square µm per kW, b) far field in arbitrary units.
Figure 7(a) and (b) show, respectively, the near- and far-field 2D intensity distributions of expected and measured five-lobed mode of the fiber of Fig. 5. We chose to excite a middle mode because those modes have better modal isolation than the lowest-order modes (as discussed in the introduction) and are less lossy than the highest order modes. In this case, a middle order mode is a good balance between modal isolation and high confinement.
Fig. 7 The near- and far-field intensity profiles of a single five lobed mode of the photonic crystal ribbon fiber of Fig. 5, calculated (a), and measured (b).
Although our experimental result shows 90% modal purity, even this might present a problem in some applications. Theory suggests, however, that higher purity can be achieved. Additionally, BPM simulations suggest that the ratio of impurities does not necessarily grow with amplification, so an amplifier could operate with a 90% pure mode launch, and the impurities could be filtered at the output.
2.4 High order mode excitation in an active ribbon fiber
Figure 8(a) shows the cross-section of an air-clad, ytterbium doped ribbon fiber, the first reported. The fiber was fabricated by the photonic crystal, stack-and-draw method. The core consists of 13 Yb-doped silica rods having a nominal doping level of 0.05 molar% Yb2O3 and 1.0 molar% Al2O3; the dopants raised the refractive index by 2.53 × 10−3 relative to the index of silica, creating an numerical aperture of 0.086 (custom glass supplied by Heraeus Tenvo, Inc). The core was surrounded by pure silica rods, a silica tube, silica capillaries (to form the pump cladding), and a second tube. All silica rods and capillaries, and all but the outermost tube were made of Heraeus F300 glass (< 1ppm OH); the outermost tube was made of silica supplied by Momentive, Inc (GE 214 silica, water content unknown). The fiber’s core was 8.3 × 107.8 µm and supports only a single mode along its narrow dimension. Its pump cladding consists of a ring of 57 holes having an inner diameter of 167 µm and an outer diameter of 245 µm; we measure a numerical aperture of 0.3. Though the numerical aperture of this fiber’s pump-cladding is modest, others have shown that the air-cladding technique can achieve numerical apertures greater than 0.45 [21], which would ultimately allow for higher pump powers (this was not a limitation for this work).
Fig. 8 (a) The rare-earth doped ribbon fiber drawn via a stack and draw technique having an air-cladding and inner guiding structure. (b) The near field (top), and far field (bottom) of the high order mode illuminated in the ytterbium doped ribbon fiber at low power
A high order mode of the ribbon fiber was excited by the binary phase plate method described above. Figure 8(b) shows the near and far field profiles of the mode, which has an effective area of approximately 600 µm2. This is comparable to the area of the modes supported by some of the largest commercially-available fibers, and can clearly be increased by making the core wider (still restricting the narrow dimension to allow only a single mode) or by reducing the core’s numerical aperture and increasing its size in both dimensions.
The far-field of the excited mode (Fig. 8(b)) appears much like a standard ribbon fiber mode in that the power is mostly confined to a pair of lobes symmetric about the center, suggesting a pure mode. The near-field, despite the discrete lobe locations, has an unusual envelope across the mode with each lobe displaying variations in intensity. However, because the shape is stable with amplification (presented below) and the excitation method was successful with the passive ribbon fiber (presented above), we believe that we have indeed excited a mode of the fiber – a mode that differs from an ideal ribbon mode. We initially thought that rod-to-rod shape variations in the final fiber created the near-field envelope, but our models suggest that this is not the case. We now attribute the envelope to variations in the index of the doped core rods, an issue which has also been identified for circular high order mode results [9]. A separate multiple-core ytterbium ribbon fiber effort demonstrated similar behavior of the individual power content in each particular near field lobe [10].
A major drawback of the method we employ to calculate modal purity is that it requires knowledge of the modes being measured to make an accurate calculation, and relies on precise measurements of the near field and far field intensities at their respective Fourier planes. The method works especially well when the cross-sectional index profile of a fiber is known with high precision such as in the passive fiber case in §2.3 where the entire fiber is pure silica. The necessity to have known modes only becomes a problem in the active fiber case of §2.4 in which we believe there are refractive index differences between each doped rod which forms the core. In this case, the modes are not known and this method cannot be employed with confidence.
Fabrication of active ribbon fibers is ongoing research and we anticipate the fabrication of fibers with greater core uniformity and selectively-doped cores (for mode selectivity) in the future, and to implement mode imaging techniques such as the C2 method to validate the modal properties of future fibers [22].
3. Ribbon fiber amplifier results
Figure 9 shows the experimental setup for the single high-order-mode ribbon-fiber amplifier. The field distribution that matches the target mode (described above) is coupled into the ytterbium doped ribbon fiber of Fig. 8. The pump laser diode (Jenoptik JOLD-75-FC-11, 915 nm, NA = 0.15) is focused to NA = 0.3 and launched into the amplifier’s output end – that is, the signal and pump counter-propagate – filling the fiber’s pump cladding. A band pass filter eliminates any ASE that might pollute the power measurements or the output intensity distribution, though the spectra shown below are not filtered. The dichroic beam splitters were Semrock FF875-Di01 long pass filters, angle tuned to match the signal wavelength. The seed beam was produced by a single transverse mode ytterbium-doped fiber oscillator with a diffraction grating in the Littrow configuration which produced a 2 nm bandwidth seed beam. The ribbon amplifier fiber was 6 m long which was optimized for length by a cut back while oscillating in multiple modes. The coupled pump power was determined by optimizing the pump launch optics into a short, 10 cm, piece of ribbon fiber. The pump power exiting the short 10 cm piece was measured and adjusted up to account for the small quantity of expected absorption. This coupled pump power value was determined to be repeatable as a result of the spot size and NA of the pump beam both being smaller than the size and NA of the fiber cladding.
Figure 10(a) shows the signal output power vs. coupled pump power, and Fig. 10(b) shows signal gain vs. coupled pump power. The amplifier reached a signal output power of 10.5 W, corresponding to a gain of 24 dB. The slope efficiency of 50% is slightly lower than sometimes reported by others [23]. The amplifier length was optimized during multimode oscillation. Therefore, we suspect that this amplifier’s slope efficiency might be improved by optimizing the fiber’s length for single mode amplifier operation. Additionally, the mode does not have a 100% overlap with the Yb-doped region which causes an inversion profile which is not fully sampled by the high order mode. This may also affect the amplifier slope efficiency. This mode overlap with the doped core region can be improved by selectively doping the core region for a specific mode [14].
Figure 11 shows the spectrum of the amplifier output at the highest gain measurement. Note that though only 38 mW of seed power was coupled into the fiber, the amplifier generated little ASE. Due to its large mode size, this fiber is capable of generating much more power than 10.5 W while still operating below nonlinear and damage limits. Higher powers were not explored, though, because we were interested only in the single high order mode regime, and the mode began to show distortions above 20 dB of gain.
Figure 12 shows the near field and far field profiles of the output field at various gain values. The modal purity as evidenced by the far field profile remains unchanged through 90% of the amplification curve (through 20 dB of gain), although far-field impurities that are insignificant at lower gain appear to grow as saturation is approached. Even though the near field pattern differs significantly from that of an ideal ribbon mode, we believe that it is indeed a pure mode of the fiber, for three reasons: our excitation technique works well with a more ideal ribbon fiber (see §2.3), the near and far-field patterns are stable with amplification, and the far-field pattern has the distinct single high-order mode shape expected and seen with the more ideal fiber (Fig. 7). We do not yet know the reason for the degradation of modal purity at high gain. We speculate that it may be caused by thermal stresses on the pump side of the fiber causing light from the primary mode to leak into nearby modes. Alternatively, it could be a result of amplification of existing modal impurities or spontaneous emission once saturation of the primary mode is reached. Analogous efforts to combine arrays of diodes into a single coherent beam have faced similar issues of a non-ideal near field shape and degradation of modal purity which they attribute to fabrication non-uniformity and multiple longitudinal modes respectively [24]. We are currently investigating mode-selective gain structures, which should mitigate the mode degradation seen here at high pump power [14].
Fig. 12 Near field (top row) and far field (bottom row) images of the signal output at four different gain values.
This result shows that a single high-order ribbon fiber mode can be launched into an amplifier, and the mode can be amplified to high gain levels without degradation until the highest gain values.
4. Summary and conclusions
Ribbon fiber lasers and amplifiers show great promise in sidestepping the power limits of conventional, circular-core fiber lasers and amplifiers. In this paper, we report two custom-fabricated photonic crystal ribbon fibers – one having an air-guiding silica core (a passive ribbon fiber), the other having a rare earth-doped, index-guiding core (an active ribbon fiber). We demonstrate a novel technique for exciting a single high-order-mode in these fibers that, in the passive fiber, achieves 90% mode purity. In the active fiber, we also demonstrate single-mode excitation, though the modes of that fiber appear to be non-ideal. Configured as an amplifier, the active fiber achieves a slope efficiency of 50%, 10.5 W of output power, and greater than 24 dB of gain. High purity excitation was maintained through approximately 20 dB of gain with no adjustment of the launch conditions.
The active ribbon fiber might be improved by reducing rod-to-rod variations in the index of the Yb-doped core rods, to which we attribute the slightly distorted shapes of the fibers modes. A bigger improvement might result by doping the core to selectively amplify a target high-order-mode; that is, by alternating doped and un-doped core rods across the preform’s core, a previously suggested approach [14,25].
The active fiber’s pump cladding, a ring of 57 air holes, was somewhat disappointing; its numerical aperture was modest (NA = 0.3) and the relatively large holes made the fiber sensitive to thermal shock – if the pump power was not introduced and removed gradually, the holes tended to shatter. Reassuringly, others regularly fabricate air-claddings with NA > 0.45 that are robust, demonstrating that these issues can be overcome.
Ribbon core fibers may ultimately provide the capability to produce laser amplifiers with 100 kW of diffraction-limited output power by mitigating the nonlinear effects that currently limit circular core fibers. In order to scale the proof of concept reported in this paper to higher output power, additional research is needed to improve the mode uniformity, increase the width of the fiber, as well as the incorporation of mode selective gain.
Acknowledgments
The authors would like to acknowledge the assistance of Sham Dixit, as well as Jerry Britten and his team, for the fabrication of the binary phase plates. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. (IM release # LLNL-JRNL-610152).
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