1. Introduction

Coherent combining techniques have been widely studied these last years to increase the brightness of fiber lasers. This kind of laser source is based on the use of several parallel amplifiers. The multiple output beams from these amplifiers have to be locked in phase so that their coherent summation occurs in the far field where all the beams overlap. The coherent control of the laser outputs provides high peak power, evolving with the square of the number of amplifying channels, on the propagation axis. The coherent combining techniques are based either on active or on passive phase-locking methods depending on whether the phase control is made in a MOPA architecture or inside a compound cavity. The main interest of passive techniques is their capability to self-adjust the laser array operation to maintain in phase relationships in an unprotected environment. This kind of laser sources consists in a single cavity including several parallel arms with amplifiers. Intra cavity coupling and filtering select the inphase emission while the laser spectrum self-adjusts to minimize losses. Different laser architectures, which are simple to implement, operate on this principle and have achieved coherent power combining [1–10]. Unfortunately, it is difficult to efficiently lock a large array of lasers. Considering fiber lasers, the decrease of combining efficiency becomes sensitive beyond 10 lasers [10–13]. It can be explained by the fact that the elementary fiber lasers cannot be built and maintained with identical lengths. So common resonance frequencies become scarce in the gain bandwidth when the number of sub-cavities increases, up to the case where there is not even a single frequency compatible with an inphase emission. Numerical and theoretical approaches have been shown to reproduce the observed decrease in efficiency. The limitation applies to almost all the known passive techniques.

A large number of passive techniques for fiber lasers are based on couplings leading to a uniform feedback in the different amplifying channels. As the feedback seeds all the parallel amplifiers with the same amplitude and phase information, the wavelength is the only degree of freedom of the laser to ensure the delivery of phase-locked fields despite the differences in sub-cavity lengths. We have recently proposed a new architecture exploiting nonlinear phase contributions and individual feedbacks to the parallel amplifying sections [14]. It increases the degrees of freedom of the compound laser. The working principle can be summarized as follow. Let us assume first that the parameters of the multi-branch laser are such that there is no resonance frequency shared by the different sub-cavities of the resonator. For the frequency of lowest loss, the laser delivers an array of beams which are not perfectly synchronized. Considering approximately identical intensity for the exiting elementary fields, their phase deviations are mapped into amplitude deviations before they are returned for a new round in the cavity. The resulting inhomogeneous distribution of feedbacks creates differences in gain among the amplifiers. Saturation of the amplification is therefore not identical in all the laser arms. The resonant contribution to the refractive index due to the gain adds a phase-shift which mitigates to some extent the linear phase deviation. After iteration of the process at each cavity round trip in the compound cavity, the multiple output beams converge to a steady state inphase emission at the expense of slight intensity modulation in the array cross-section. We numerically demonstrated, in reference [14], the capability of this new scheme of cavity to improve combining efficiency for large number of parallel amplifying channels. It was suggested to perform the phase to intensity mapping by means of a phase contrast imaging set-up.

We report here preliminary experiments on the implementation of the phase-contrast technique for the synchronization of four fiber lasers together with comparison with the architecture based on uniform feedback. It was predicted that the new phase-locking process increases the number of oscillating frequencies in the gain bandwidth, fitted to the emission of the in-phase mode. In this paper, we present an experimental setup that highlights this phenomenon. Spectral filling improvement of multi-amplifier lasers is an essential point to overcome limitation on the number of lasers that can be synchronized by passive techniques.

2. Phase contrast laser cavity

We have designed a ring cavity with four parallel amplifiers so that the beam array can be phase locked either by standard passive technique or by the new method we proposed in the previous paper [14]. Thus, we can compare the spectral behaviors of the compound lasers that depend on the combining technique implemented. As the number of amplifiers involved is low, the laser architecture was specifically designed to minimize the number of common resonant frequencies between the four amplifying sub-cavities. Our goal is potentially to observe the increase of laser frequencies when the new combining approach is chosen. To do this, the lengths of these four parallel arms were adjusted to be very close to each other. The principle scheme of the laser architecture is depicted in Fig. 1(a) . The laser is made up of four parallel Ytterbium doped fiber amplifiers. At the output of the amplifiers, the four collinear beams distributed at the vertices of a square were collimated by a matrix of micro-lenses. A common output coupler extracted a part of the energy out of the cavity while the other part was reflected to feed the amplifiers array after filtering. These beams were focused in the focal plane of a positive lens L where a spatial filter ensured coupling between the four cavities. Then, each of the four beams was launched in their own amplifying fiber through a symmetric optical system. Four isolators (Iso) forced the laser oscillation in the counterclockwise direction. Some polarization controllers were adjusted to obtain an identical polarization state from each laser arm in the free space part of the cavity. Without filtering, the four cavities oscillated independently.

 

Fig. 1 (a) Scheme of the 4 amplifier laser cavity using the hybrid amplitude/phase plate (APP). µl microlens array, L positive lens, PC polarization controller, Iso. isolator, YDFA Ytterbium doped fiber amplifier, P1 and P2 image plans. (b) APP filter. Tc transmission of the central part, Ts transmission of the outer part corresponding to the high spatial frequency of the far field pattern.

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Consider first a spatial filter like a pinhole introduced in the central part of the far-field. Phase-locking is obtained in that case by standard filtering rules of passive combining techniques. The laser architecture is then very similar to the all feedback loop laser or to the interferometer laser for which the pinhole is replaced by the input end of a single mode fiber [2,3,6,7]. In such kind of compound resonators, the same amplitude and phase information is back-seeded to all the amplifying arms after filtering. Only the central part of the inner cavity far field is feedback to the whole amplifying arms. The inphase mode exhibiting the highest on axis intensity is best fitted to this filter giving thus the lowest intracavity losses. The laser therefore generates the inphase mode if the gain bandwidth contains the appropriate set of frequencies common to all its sub-cavities.

The novel coherent combining technique requires a different filtering process. The pinhole of the previous standard technique is replaced by a hybrid amplitude/phase plate APP (Fig. 1(b)). The 1:1 imaging telescope equipped with the APP coupled the fields from the different emitters in the array in a way which can be represented in a simplified form by the following coupling matrix:

Previously known passive coherent combining techniques are already efficient to phase-lock a small number of lasers with an appropriate design. We have specifically chosen the lengths of the laser amplifying arms to depart from a good design. So, the configuration of Fig. 1 with a pinhole should have a spectral behavior similar to the one of a well designed laser array of larger size. In that case, common resonant frequencies are becoming scarcer in the compound laser. It is possible to observe such behavior with a four amplifiers laser by adjusting the four sub-cavity lengths close to each other. The number of common resonant frequencies indeed depends on the product of the root mean square length difference δL with the useful spectral bandwidth Δλ of the laser [12]. The maximum length difference ΔL between the four sub-cavities was fixed around 1mm instead of few meters usually, leading to an average spectral envelop structuring δλ greater than 1nm at λ_o = 1085nm (δλ ~λ_o²/ ΔL).

3. Phase contrast laser behavior

After adjustment of the cavity the laser system including the APP component has operated on an inphase mode as expected. That was obtained despite the improper choice of fiber amplifiers lengths.

We can see on Fig. 2 , the far field recorded at the laser output, made of a main central lobe and four side lobes in a square distribution, which is typically due to the identical phase of the four output beams. The observation confirmed experimentally that the new filtering process converge to the generation of the inphase mode as it was numerically predicted [14]. The phase-locking performance of the array was estimated to be better than λ/10 after time averaging. In that first experiment on the phase contrast approach, the fiber amplifiers were of low power and the efficiency of the cavity was not optimized. The delivered power was at maximum of 1.5W.

 

Fig. 2 (a) Far field pattern of the 4 output beams from the laser using the APP component. (b) Far field cross section.

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We also observed the spectral behavior and stability of this laser so as to compare it with that of standard configuration based on a uniform feedback (pinhole filter). As shown Fig. 3(a) , spectra from the four individual lasers did not overlap perfectly, spreading over less than 5nm from 1087.5nm to 1091.5nm. These spectra were recorded when no filter was included within the cavity, the four lasers oscillating independently. The standard combining technique with a pinhole filter leaded to a scarce spectrum spreading over a large 11nm bandwidth. Only few peaks appeared simultaneously (Fig. 3(b)) most of the time at the edges of the spectrum. Low loss modes related to quasi inphase beams were rare inside the laser bandwidth leading to phase change between the four output beams over time. In contrast, the laser including the APP filter generated a large number of peaks inside a smaller spectral domain (Fig. 3(c)). It indicated that with the new combining technique more modes are free to oscillate which are compatible with the same output field pattern. That is connected with the fact that linear phase deviations in the array can be compensated by nonlinear contributions to the refractive index, thanks to the phase intensity mapping.

 

Fig. 3 Normalized spectra recorded at a similar output power (a) from each 4 independent lasers, (b) from the standard laser architecture using pinhole, (c) and from the new laser architecture with APP component.

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In order to compare the four beam phase relationships over time at the outputs of both laser architectures, we measured the power at the center of the far field pattern during a short time period (Fig. 4 ). Notice that peak power fluctuated with the standard laser configuration as shown on Fig. 4(a). It was due to unintentional environmental perturbations (acoustic, thermal…) which induced path length changes in the cavity. Strong phase alteration appeared in the four output beams that the self-adaptation of frequency, single degree of freedom of this scheme, could not totally compensate. Consequently, the far field pattern changed over time, its lobes shifted and the peak power on the propagation axis fluctuated by about twenty percent around its average value (Fig. 4(a)). In the same environmental conditions, the laser architecture including the APP filter provided more stable far field pattern. Standard deviation of the on-axis peak power fluctuation is three times less than the one obtained with the previous configuration (Fig. 4(b)). These stability features can be related to the spectra of the two phase-locked lasers. For simplicity, let consider the generic case of a standard two-element array. When the length difference between the two arms of the laser varies, the periodic modulations in the laser spectrum drift on the frequency axis. When there is a large number of a resonance inside the gain bandwidth, there is an impact neither on the power stability nor on the phase-locking. On the contrary when there is only one or two lines only in the laser spectrum, path length fluctuations in the system cause significant variation in the combined power and in the phase relationship of the output fields. The same general behaviors are expected here. Since the laser array with uniform feedback gave fewer laser lines than the phase contrast configuration it is consistent with the fact that the stability is improved in the latter situation.

 

Fig. 4 Evolution of the peak power collected on the propagation axis in the far field (a) at the output of the standard laser architecture using a pinhole as filter (b) and at the output of the new laser configuration using the APP filter.

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4. Conclusion

We experimentally demonstrated passive coherent combining of a two-dimensional laser array by use of two complementary optical transformations inside the cavity. The laser cavity is designed so that, firstly, linear phase deviations due to path length differences are changed in intensity modulations at the input of the array of amplifiers. Secondly, the phase/gain coupling occurring during the amplification step is used to compensate the initial phase deviations. The recorded laser pattern showed that the cavity including the phase contrast filtering forced the laser array to oscillate with in-phase emissions. As it was numerically predicted, we observed the capability of this new architecture to enrich the laser frequency spectrum in comparison with the passive techniques based on uniform feedback. The demonstration was made with 4 ytterbium doped fiber lasers. Their lengths were chosen to obtain a spectral behavior similar to the one of a laser array with large number of arms. Unlike standard configuration, the laser based on the new approach was significantly more robust with respect to the environmental perturbations and featured a stable peak power in the far field. This experimental demonstration is a first step towards passive coherent combining of a large number of lasers with an enhanced efficiency.