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We demonstrate adaptive-spatial mode control (ASMC) in few-moded double-clad large mode area (LMA) fiber amplifiers by using an all-fiber-based photonic lantern. Three single-mode fiber inputs are used to adaptively inject the appropriate superposition of input modes in a multimode gain fiber to achieve the desired mode at the output. By actively adjusting the relative phase of the single-mode inputs, near-unity coherent combination resulting in a single fundamental mode at the output is achieved.
© 2016 Optical Society of America
1. Introduction
Fiber amplifier power scaling has shown significant progress as evidenced by the commercial availability of kW-class amplifiers [1]. Power scaling beyond the kW-class has been achieved by coherently combining several fiber amplifiers [2]. One of the benefits of coherent beam combination (CBC) arises from aperture synthesis. A larger aperture, with less power per unit area, is achieved through synthesis of several subapertures. Scaling the modal area of an individual fiber amplifier similarly serves to reduce the intensity. The lowering of the intensity through modal-area scaling by utilization of large mode area (LMA) fibers has suppressed a number of nonlinearities, which has resulted, in part, in the successful power scaling of today’s fiber amplifiers. However, advances achieved by scaling the modal area of an individual fiber amplifier have been hampered by the onset of transverse-mode instability (TMI) [3–5]. Specifically even with the highly effective conventional method of coiling LMA fiber to maintain single-mode operation, fiber laser amplifier power scaling has been limited by the thermally induced nonlinearities that drive modal power coupling, despite the relatively large higher-order mode losses that are achieved. Moreover, fibers cannot be bent arbitrarily due to mode distortion, shrinking, and bend loss. The larger the core, the more critical these parameters become.
Here an alternative approach to spatial-mode control using active feedback is described. Our results demonstrate the ability of active feedback to stabilize the fundamental mode output of a multimode fiber by appropriately launching the correct superposition of input modes in both phase and amplitude to achieve the desired mode on the output. In effect, an all-fiber based adaptive-optic system is demonstrated that preconditions the input to achieve a nearly diffraction-limited, single-mode beam on the output.
We call this adaptive spatial mode control (ASMC). This all-fiber based adaptive optic approach makes use of photonic lantern technology, which has found applications in astrophotonics [6–8] and spatial-division multiplexing for communications [9]. Below the salient features of the photonic lantern relevant to fiber power scaling is described.
The operation of the combiner is perhaps best described by considering the problem in reverse. Consider launching the fundamental LP01 mode in reverse, labeled u1 in Fig. 1, into the output of a three-moded photonic lantern. The output fiber illustrated in red in Fig. 1 is referred to as the delivery fiber and may be passive, active, or both (i.e. a passive splice onto an active fiber). For an ideal lossless lantern, properly mode-matched to the delivery fiber, all of the power would be distributed among the input fibers with amplitude vi and phase θi irrespective of the mode-coupling dynamics in the delivery fiber. In order to faithfully reproduce the desired output mode u1 in the forward direction, the control system must launch the same amplitudes vi and conjugate phases θi on the input. This closed-loop control could therefore faithfully reproduce the desired output mode in the presence of imperfections and thermal perturbations that may be present in the delivery fiber which could not be compensated for by static (open-loop) approaches including a single-mode fiber taper to the LMA fiber.
Fig. 1 Instructional schematic of a photonic lantern operating in reverse. The fundamental LP01 mode is launched into the output generating an amplitude and phase distribution among the input fibers. Time-reversal symmetry allows launching the conjugate inputs to reproduce the output.
To gain further insight into the operation of the photonic lantern, one may consider launching a single mode into an individual input fiber as illustrated in Fig. 2. As the input fiber undergoes an adiabatic taper the output emerges as a superposition of output modes u1, u2, and u3 representing the LP01, LP11o, and LP11e modes respectively where the additional LP11 subscripts {o,e} have been used to describe the orientation of the lobes with respect to their odd or even symmetry about the x-axis using a coordinate frame illustrated in Fig. 3. Mathematically, we observe that this input basis [v1, 0, 0] vector is not the appropriate basis vector to launch on the input to achieve the desired output mode [u1, 0, 0]. Since the photonic lantern performs a unitary operation, there exists an appropriate set of orthogonal input vectors, which will map onto a desired orthogonal set of output vectors.
Fig. 2 Launching a single input on one of the input channels in a three-mode lantern results in a superposition of the three modes supported by the delivery fiber. The input and output relation may be described by a transfer matrix.
Fig. 3 Input supermodes and the output modes of a lossless three-channel lantern where the input fibers lie in an equilateral triangle pattern. This ideal lossless lantern performs a unitary transformation mapping an orthogonal set of input vectors to an orthogonal set of output vectors.
Moreover, since the photonic lantern is a linear-optical device, it may be considered a mode converter that maps input orthogonal sets to output orthogonal sets [10]. In particular, a transfer matrix may describe the relation between the input and output in a photonic lantern. This relationship between the input and output superposition of modes in an ideal lantern, defined here as a lossless lantern, may be compactly expressed as Avi = ui, where the transfer matrix A may be derived from symmetry considerations [9,10] and is expressed below for a three-channel lantern with the input fibers arranged in an equilateral triangle configuration as illustrated in Fig. 3
For this ideal lantern transfer matrix, we observe that launching [1, 1, 1]/(31/2) on the input would result in exciting the pure LP01 fundamental mode u1. An orthogonal input vector [1, 1, −2]/(61/2) would excite the u2 (LP11o) mode, and a third orthogonal input vector [1, −1, 0]/(21/2) would excite the u3 (LP11e) mode.
In practice, fabrication tolerances of a photonic lantern and mode mismatch in the splicing of the lantern to an output fiber, along with any static or dynamic mode coupling in the delivery fiber, would result in a different transfer matrix from the ideal. In addition, loss may result from mode-mismatch between the lantern and the delivery fiber. Nonetheless, in general there is still a suitable input vector to completely excite the desired output mode albeit with some loss [11]. In the most general case, the transfer matrix may then be decomposed using singular value decomposition into the form Avi = σi ui, where σi represents the transmission loss in exciting mode ui [9]. For the ideal lossless lantern σi = 1.
2. Photonic-lantern-based beam combining
In many respects, a photonic lantern may be viewed as an all-fiber-based approach to achieve CBC. For illustration, we compare a diffractive-optical element (DOE) based combining approach [12,13] to a photonic-lantern combiner in Fig. 4. On the left, we observe that sending in a single beam on the input to a DOE results in 3 non-overlapping (orthogonal) beams on the output. Similarly, sending in a single fiber on the input to a lantern results in three orthogonal beams on the output. It is possible to reverse the DOE operation by sending in three appropriately phase-adjusted beams on the input to achieve a single beam on the output [12]. Similarly, sending in the appropriately phased modes on the input to a photonic lantern results in a fundamental mode on the output.
Fig. 4 Comparison of DOE-based CBC with a photonic-lantern-based beam combining approach. (Upper left) a single beam incident on a 3-channel DOE generates three output beams. (Lower left) a single channel on a photonic lantern generates three modes. (Upper right) three appropriately phased beams incident on a DOE generate a single output beam. (Lower right) three appropriately phased beams incident on a lantern generate a single mode.
This correspondence between the photonic lantern and conventional CBC allows application of the CBC formalism to estimate the impact of various errors on combining efficiency [14,15]. In particular, one can determine the impact of phase, amplitude, and polarization errors on the combining efficiency. The combining efficiency is defined here as the fraction of power in the desired fundamental mode over the total power.
It should be noted that while general CBC principles apply, the photonic lantern also allows for compensation of both static and dynamic mode coupling in the delivery fiber. In this regard, the photonic lantern is analogous to tiled-aperture phased-array CBC in which the input phase and amplitude may be adjusted dynamically to compensate for atmospheric disturbances. The lantern has the advantage in that the number of guided modes in the delivery fiber is finite and known a priori. In this respect, the number of input channels must match the number of modes in the delivery fiber for complete compensation.
For the three-channel photonic lantern with input fibers arranged as shown in Fig. 3, it is clear from the matrix description that all three channels are required to purely excite the fundamental mode. In the most general case, N input fibers are needed to efficiently excite the fundamental mode in an N channel fiber [5–9]. Assuming for simplicity the three-channel transfer matrix, which requires equal amplitudes on the input to excite the fundamental mode, the impact of the amplitude variation on combining efficiency η is
where Pm is the power in channel m, and N = 3 for the three-channel lantern [14]. In the limit of small amplitude errors, the combining efficiency loss (1-η) is given by ¼(σP2)/P2 where P is the nominal power per channel and σP is the power standard deviation on the input channels. Similarly, the RMS phase-variation impact on combining efficiency may be expressed as (1- η)~σθ2 for small phase errors where σθ is the RMS phase error.While the photonic lantern is similar in many respects to other CBC approaches, it offers a number of unique benefits when used in a fiber amplifier. First, the photonic lantern may be integrated (spliced) onto the front-end of a fiber amplifier. Since the photonic lantern is used at the seeding stage, the efficiency of a high-power fiber amplifier is minimally impacted by the insertion loss of the photonic lantern, and, therefore is more forgiving than the insertion loss of a combiner used on the output of a high-power system. Furthermore, the photonic lantern provides a possible path to modal-area scaling. The scaling recipe requires that the number of input fibers match the number of modes in the delivery fiber. A few additional comments regarding modal area scaling are warranted. As the number of channels of the photonic lantern increase, the ideal transfer matrix may in general require non-uniform channel excitation on the input to excite the fundamental mode. In these circumstances, amplitude adjustment of the input is required in order to maximize the power in the fundamental mode.
Modal-area scaling in turn may allow one to suppress intensity-dependent nonlinearities. Lastly, mode control offers the promise of combating TMI and serves as an alternative to or can be used in conjunction with coiling a fiber to provide modal discrimination.
It is worth noting that other active-mitigation strategies to combat TMI have been successfully applied [18]. These alternate approaches have utilized acousto-optic deflection of an incident beam on a fiber. By laterally offsetting the input launch, a different superposition of modes is launched into the gain fiber. Our photonic-lantern ASMC approach differs from the acousto-optic modulator approach in three main aspects: (a) the input is all fiber-based and no free-space optics are needed, (b) the intrinsic mode matching allows one to selectively excite any desired mode with high efficiency, and (c) scaling to large number of modes can be done by increasing the number of input fibers with appropriate phase and amplitude adjustment in principle.
As we will describe in the next section, our hill-climbing algorithm seeks to maximize the LP01 mode by measuring the on-axis intensity while adaptively adjusting the phase input to the photonic lantern. For the three-moded lantern, LP01 is the only mode that has an on-axis intensity component. In concluding our modal-area scaling remarks it is worth noting that as the number of modes increases beyond 5, the circularly symmetric LP0m modes starting with LP02 begin to contribute to the on-axis intensity. In these circumstances, a suitable correlation filter or other approach may need to be used to discriminate between the LP01 and higher-order LP0m contributions on-axis [19].
3. Experimental results
A proof of concept experiment is illustrated in Fig. 5. A seed laser is split into three fibers using a polarization-maintaining fiber splitter. The three output fibers from the splitter are then sent to individually addressable lithium niobate phase modulators. The fiber outputs of the phase modulators are then spliced into a photonic lantern that is mode matched and fusion spliced to a delivery fiber consisting of a passive Nufern 25/400 fiber spliced onto an active Yb-doped Nufern 25/400 double-clad fiber. The active fiber is diode pumped using a Dilas 30 W pump module (not shown) that is co-pumped using a 6x1 + 1 combiner, which serves to combine the seed signal and the pump light to the double-clad gain fiber.
Fig. 5 Photonic lantern coherent combining schematic. The seed laser output is sent to a 1x3 splitter. The output of the splitter feeds an array of phase modulators. The output of the modulator array is input to a three-channel photonic lantern. The photonic lantern is mode matched to a three-moded gain fiber. The on-axis component of the output beam is sampled by a SPGD detector. The SPGD controller iteratively adjusts the input phases to maximize the on-axis intensity.
The individual input amplitudes in the photonic lantern were set to be equal. The output of the photonic lantern contribution to the fundamental mode in the passive section of the delivery fiber was observed prior to splicing onto the gain fiber. Based on the observed on-axis amplitude variations of the output for an equal amplitude excitation on the input obtained from sequential on-axis measurements with only a single input channel on at a time we estimate a combining loss (1-η) of ~3% consistent with a variance of (σP2)/P2~12%. For an ideal delivery fiber, absent mode-coupling dynamics, dynamic amplitude control is not required, as the delivery fiber would have a static identity transfer matrix. In the presence of mode-coupling dynamics, leading to a temporally varying transfer matrix, amplitude control would generally be required for high efficiency as the overall system transfer matrix would be a product of the lantern transfer matrix with that of the delivery fiber. The impact of amplitude errors on the combining efficiency may be estimated through Eq. (2) based on the particular time-varying disturbance. For example, the impact of non-uniform coefficients in the first row of the transfer matrix of Eq. (1) may be modeled equivalently as being similar to having uniform coefficients with unequal inputs allowing application of Eq. (2). The reason that amplitudes can be set to be near equal and that no dynamic control is needed in this experiment implies that the lantern is near ideal and mode coupling in the delivery fiber is minimal.
The three-channel photonic lantern was fabricated using a similar tapering process to that described in detail elsewhere [7–9]; we briefly review the fabrication process. Three single-mode fibers are placed into a capillary tube. The input fibers are tapered until the fiber modes become guided by their cladding which adiabatically becomes the core of the output fiber, and the capillary tube becomes the new cladding of the output fiber. The index of the capillary tube and the individual fiber claddings determine the index contrast of the output waveguide and are choosen to match the numerical aperture NA of the delivery fiber. The final core size is also designed to mode-match the delivery fiber, which consists of a 0.065 NA, 25-micron core. The measured insertion loss of each individual fiber into the core of the delivery fiber was less than 3 dB.
A stochastic parallel gradient descent (SPGD) algorithm [16] was used to adaptively determine the appropriate phase to be applied to the input fibers to maximize the on-axis intensity of the output beam. SPGD has been successfully applied to a number of CBC demonstrations [2,12,17]. For completeness, we briefly summarize the operation of the algorithm. The desired fundamental mode is the only mode that contains an on-axis component while the LP11e and LP11o modes have an on-axis null. A pinhole is placed before the SPGD detector in order to sample the on-axis (or LP01) component of the output beam. The SPGD controller applies a dither vector across the three phase modulators, although only two phase modulators are actually needed, as the common phase need not be controlled. The same dither vector is then applied with the opposite sign. Based on the response to the applied dithers, a correction is applied to maximize the signal on-axis. A new orthonormal dither is then applied, and the algorithm iteratively applies a correction until the on-axis signal is maximized. The convergence time of the SPGD algorithm is proportional to the number of input fibers and inversely proportional to the dither frequency. For these experiments, frequency dithers of up to 100 kHz were used.
The SPGD signal along with a representative mode before and after the SPGD is turned on is shown in Fig. 6 below. When SPGD is turned off, the output of the fiber is generally a superposition of the LP01 and both LP11 modes. Shown on the top left of Fig. 6 is a single-frame image of the output of the fiber with SPGD off; the output beam resembles the LP11 modes with reduced on-axis intensity. When SPGD is turned on, the on-axis intensity is maximized, and the SPGD signal rapidly increases. The gain in the fiber was set to produce 0.5 W of output power. A low gain value was used in order to maintain a low level of backward emission so as to prevent damage to the phase-modulators and connectorized fiber connections. We anticipate that inserting isolators after the phase modulators and splicing all fiber components will allow increased output power. The output beam is observed to converge to the LP01 mode as shown in the upper right of Fig. 6. Furthermore, since the SPGD signal increases, CBC increases the brightness of the output as anticipated.
Fig. 6 Top (Left): Representative mode profile with SPGD off. Top (Right): Output mode with SPGD on. Bottom: SPGD detector signal measuring the on-axis intensity. An increase in the on-axis intensity occurs when SPGD is turned on at time equals zero.
In order to further quantify the performance of the photonic-lantern ASMC we performed modal analysis of the output with a spatial light modulator (SLM) using a correlation filter method [18–21]. The desired mode to be analyzed was projected onto the SLM. The multiplication of the incident field with the SLM pattern results in a correlation in the far field. The on-axis component of the far field provides the appropriate modal weighting intensity. The resulting modal decomposition from these measurements is shown in Fig. 7. This modal decomposition was taken from the photonic lantern output that was spliced into a passive 25/400 fiber prior to being spliced into the gain fiber.
Fig. 7 Modal decomposition of the output of the photonic lantern spliced to a passive 25/400 fiber before and after SPGD is turned on. SPGD combines the power in the fiber into the LP01 mode.
As shown in Fig. 7 a random time-varying phase of the individual inputs to the photonic lantern result in a time-varying superposition of incident modes before SPGD is turned on. Once SPGD is turned on, the on-axis component rapidly increases with the end result of achieving a 97% combining efficiency into the fundamental mode. This result is consistent with our expected combining efficiency loss resulting from applying a phase-only correction.
This experiment was repeated after the photonic lantern was spliced into the gain fiber. At output power levels of 0.5 W, the modal decomposition resulted in all of the power being delivered to the fundamental mode within the accuracy of our modal decomposition (estimated to be about ~1%). We attribute the slight increase in performance due to the improved modal overlap of the fundamental mode with the doped core, which provides additional modal discrimination. In these experiments, polarization did not play a role as the photonic lantern is effectively non-birefringent.
4. Conclusions
We have demonstrated ASMC with a photonic lantern using SPGD. In this respect, the photonic lantern functions as an all-fiber-based adaptive optic. Namely, it enables coherent combination of input fibers at the seeding stage of an amplifier to achieve a diffraction-limited beam on the output.
Our results based on a few-mode (N = 3) fiber are potentially scalable to N>3. Scaling requires that the number input modes on the photonic lantern match the number of modes in the delivery fiber. Coiling may serve to further reduce the number of modes, and photonic lanterns with over 120 channels have been developed offering promise toward even larger modal-area scaling [22].
Since the SPGD algorithm is a control algorithm that does not require a priori knowledge of the desired phase distribution, the particular disturbances that describe the mode coupling within the delivery fiber are irrelevant to the operation of the controller. This approach shows promise and has implications toward combating TMI arising from mode coupling at kHz rates. By implementing a control algorithm that works faster than the disturbance time-scale, it may be possible to eliminate the instability ultimately allowing continued scaling of the modal area and power of an individual fiber amplifier.
Acknowledgments
This work is sponsored by the HEL-JTO under Air Force Contract #FA8721-05-C-0002. Opinions, interpretations, conclusions and recommendations are those of the author and are not necessarily endorsed by the United States Government.
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