Nonlinearities enhance combining of coherent beams

Passive techniques for coherent coupling (i.e., combining) of lasers represent an attractively simple, all-optical means of generating high-brightness laser beams for uses that include free-space communications, manufacturing, and defense.^1–9 Many configurations have been investigated that yield coherent summation of the optical power available from separate fiber amplifiers. In most cases, the best solution for high-power operation is an array of fiber amplifiers inserted into a common laser cavity that delivers an array of phase-locked beams. However, research has shown that passive coherent coupling becomes less efficient as the size of the laser array increases.^10–13 For this reason, research in the field has focused on ways of overcoming the efficiency threshold of about 10 lasers. All the approaches published thus far (e.g., phase conjugation, coupled cavity) exploit an optical nonlinearity. Here, we describe a new cavity design that combines optical nonlinearity with a specific spatial filter (see Figure 1).¹⁴

Figure 1. Coupled-fiber-amplifiers array in a ring cavity with a specific spatial filter. N: Number.

The nonlinearity we consider results from the effect of rare-earth ions on the refractive index in the fiber amplifiers and is significantly larger than the so-called nonresonant Kerr nonlinearity of silica. It is usually assumed that the nonlinear phase shift evolves linearly with the gain. However, we have carried out experiments using an ytterbium-doped fiber amplifier that confirm a nearly linear relationship whatever the pump level. Accordingly, the basic idea behind our new cavity design is the following. Self-organization of a laser in standard design relies solely on selecting the lowest-loss mode after iterative linear filtering. Assuming many lasers of different lengths, longitudinal modes common to all the cavity arms do not exist. The laser beams are not perfectly in phase, and phase deviations are observed in the array outputs. We suggest transforming the phase deviations into power deviations so that the gain can vary from one channel to another. In this way, a gain-dependent phase introduced during amplification can compensate for the linear phase delay between the different laser fields. In one implementation of this principle, we proposed using Zernike's setup for phase-contrast microscopy.¹⁵

We assessed the potential of the new passive coherent coupling scheme—which uses only four 10W amplifiers—by numerically simulating the laser operation (see Figure 2). Our model takes into account the linear properties of the cavity as well as the gain bandwidth, saturation, and added phase in each amplifier. Starting from noise, the model computes the laser mode build-up, giving the final laser frequencies and spatial pattern.

Figure 2. Combining efficiency as a function of number of lasers according to coupling scheme. γ: Gain-dependent phase coefficient.

Figure 3. Experimental setup including phase-contrast filtering function. P.C.: Polarization control. Iso: Isolator. L: Lens. Inset graph: Experimental recording of the laser 2D far-field pattern together with a horizontal cross-section.

Figure 4. (a) Normalized spectrum observed with a standard passive coupling technique. (b) Normalized spectrum observed with the new passive coupling technique. a.u.: Arbitrary units.

To demonstrate the scheme, we adjusted the path length difference between the four arms to less than 1cm. In this configuration, we can simulate the unstable spectral behavior of a large array of lasers using only four of them (see Figure 3). Next, we replaced the phase contrast filter by a simple pinhole. The laser configuration is thus similar to a standard passive one without phase-to-amplitude conversion. In this case, as expected, the scarcity of common frequencies in the gain bandwidth of the four lasers is very high: see Figure 4(a). As a result, the instability of the power as well as the far-field pattern is also very high. This behavior is the same as we observed for many lasers with a large path-length difference.

In a second step, we replaced the pinhole by a phase-contrast filter. In this configuration, the output power and the far-field pattern become very stable over time. Moreover, the observed spectrum shows a higher number of resonant frequencies generated in the gain bandwidth—see Figure 4(b)—despite the very low path-length difference applied between the amplifying arms. This highlights the substantial effect of the new degree of freedom given by the phase-to-amplitude conversion of the beam array and the exploitation of the resonant nonlinearities in the fiber amplifiers. In a final step, we modified our experimental setup to accommodate nine amplifiers. We obtained behavior very similar to that with four beams.

In summary, we proposed a new cavity design for passive phase-locking of laser arrays with the goal of coherently combining their power in the far field. The new scheme involves a coupling device, performing a phase-to-amplitude transform, and a gain-dependent phase shift introduced by amplifiers. We have experimentally demonstrated the potential of this new scheme with only four and then nine lasers, but with a sub-cavity length distribution that normally would produce inferior phase-locking performance. In contrast to a standard passive configuration, this new scheme enables very stable emission and far-field patterns. In the coming months we plan to carry out a new demonstration with up to 20 lasers.