## Abstract

A monolithic diode laser array with 35 elements is operated as a coherent array through the use of a Self-Fourier cavity. By analyzing the far field interference pattern, the coherence was measured to be 0.57 with all 35 elements operating and was measured to be approximately constant for arrays with greater than 15 elements. These results are in rough agreement with previous analyses which predict a coherence equal to 0.65 for very large arrays of passively coupled laser elements and demonstrate how the use of regenerative feedback benefits the passive phasing of coherent laser arrays. These results demonstrate that it is possible to circumvent previous cold cavity theories that predict poor phasing properties for arrays with greater than ~10 elements.

© 2014 Optical Society of America

## 1. Introduction

Passive coherent beam combination remains an attractive technique to increase the brightness of laser systems due to its inherent simplicity and associated ruggedness and has been investigated for a long time [1]. However, the scalability of these arrays to larger numbers of elements still needs to be demonstrated and better understood. Previous cold cavity models of simple amplifier operation predict an upper limit somewhere between 8 and 10 elements for passive beam combination with good coherence. These models assume that for any given wavelength, the output phase of each laser element is linearly proportional to its cold-cavity optical path length, so that a random distribution in optical path lengths will result in a similar random distribution in the output phases between 0 and 2*π* [2–5]. Corcoran had developed a coincident mode model for passive beam combination that assumes that a coherent array will oscillate in a supermode where all laser cavities are in resonance simultaneously [2]. This assumption led to a predicted exponential decrease in the probability of this occurring with each added fiber laser and resulted in the prediction that a maximum of 10 elements could be combined with a guaranteed efficiency greater than 24%. Siegman developed a statistical model [3] predicting the coherence for passively coupled fiber lasers with lengths ~10m. This model predicts that there is a less than 50% chance of finding a mode with less than 10% loss for an array with only 8 fiber lasers with this probability dropping rapidly for larger arrays. The Kouznetsov model [4] predicts a maximum efficiency less than 60% for an array with only 12 fiber lasers with lengths ~30m and also dropping quickly above this number of elements. The Rothenberg model predicts a maximum coherence equal to about 32% for an array with 30 fiber lasers [5]. As pointed out in these analyses, the efficiency of these systems can be shown to increase with an increase in the nominal length of the laser cavities, so that shorter resonators are expected to perform with lower efficiencies. These models of laser operation are statistical in nature and do not take into account intrinsic laser mechanisms such as the resonant (gain dependent) phase shift, the Kerr nonlinearity, and/or design features such as the use of regenerative feedback [6] or phase-contrast spatial filtering [7]. In a properly designed system, these effects can be collectively utilized to injection lock each element to the fundamental supermode of the array, thus, providing a highly phased output. This paper describes the successful demonstration of a phase locked diode laser array with 35 elements in a Self-Fourier (SF) cavity with a coherence equal to 0.57.

The coherent diode laser array coupled to the SF cavity is presented in Fig. 1 [8,9]. The Fourier lens pair and output coupler reflect the spatial Fourier transform of the array output back onto itself, to provide globally coupled feedback to the array. With this configuration, the dominant eigenvalue of the fundamental supermode of the array is equal to ~0.98, while all higher order supermodes are completely extinguished upon each round trip.

The monolithic diode laser array used in the demonstration was obtained from Dilas specifically for this project. The laser diode was made from InP material and emitted at a wavelength of *λ* = 1465nm with a FWHM of approximately 8nm as shown in Fig. 2 below.

The output power was measured to be 20W at a current of 50A with a lasing threshold of 1.40A. The monolithic array had 35 elements nominally spaced at *d* = 270*μ*m, with a cavity length of 2.5mm and a ridge waveguide width equal to 5*μ*m, thus providing single spatial-mode operation. By measuring the far field of the complete (incoherent) laser array, as presented in Fig. 3, we determined that the near field of each laser emitter had a near Gaussian profile with radius equal to 2.9*μ*m.

The output facet of the array was antireflection (AR) coated which provided the regenerative reflectivity estimated at 0.1%. The laser array chip was mounted on an industry-standard CS-style copper substrate for heat sinking and the output facet placed at the entrance to the SF cavity. A fast axis collimating (FAC) lens with 900μm focal length was used to collimate the outputs of the laser array along the vertical axis. The lenses in the SF cavity provided an effective round-trip focal length of *F _{eff}* = 49.6mm as required to satisfy the Self-Fourier condition:

*d*

^{2}=

*F*and the total cavity length was 47.5mm. The output coupler (OC) was a multilayered dielectric mirror obtained from CVI with a reflectivity equal to 50%. In order to take into account the fact that the center element receives a higher level of feedback than the edge elements (as well as additional losses in the cavity), we choose this value of output coupler to result in an effective reflectivity to the laser elements with a range between 10% and 30%. A photograph of the prototype cavity is presented in Fig. 4.

_{eff}‧λWith the monolithic array bolted down to the heat sink, there were 4 degrees of freedom required for alignment of the external SF cavity: the longitudinal position of the Fourier lens, and the longitudinal position and the tip/tilt rotations of the common output coupler.

With the full diode laser array (35 elements) coupled into the standard SF cavity and operated at a current of 1.8A, the measured far field pattern is presented in Fig. 5. Our data was collected using an averaging of 20 samples taken at a rate of 200 samples per second. This averaging was selected in order to minimize the noise (in the frequency range of 100 Hz to 100 kHz) in our detection system that is believed to come from the electronic detector circuit. As a result, we found that the data was highly repeatable with less than 1% variation between any two different sets of data.

The measured far field pattern exhibits the typical fringes generated by the interference of the multiple coherent beams. We note however that there is a complex structure of sub-fringes in-between the main peaks. This structure is stable in time (for periods of up to 2 hours) and, as can be seen, exhibits a similar shape for each peak. As discussed by Nabors, the shape of the peaks in the far field and the presence of sub-fringes in the pattern result from a non-uniform, but fixed, phase distribution of the individual emitters in the array [10]. We believe that such non-uniform phase distribution resulted from aberrations in the Fourier lenses and are looking into this at the present time.

From this data, the coherence of the array was measured by taking the ratio of the power contained in the fringes relative to the total power. The total power was measured by numerically integrating the measured Far-Field intensity profile over the complete far-field area. The power contained in the fringes was obtained by subtracting a background envelope to the measured intensity profile. This background envelope was chosen as a wide Gaussian profile connecting the lowest intensity points (the “valleys”) of the pattern. This method includes the power in all interference fringes and is not dependent on the exact profile of the interference fringes. The coherence value obtained from this measurement is independent of the fill-factor of the interference fringes as it directly measures the total area of the interference fringes.

The coherence of the laser array was found to be equal to 0.57 +/− 0.01. We note that the estimated 0.1% regenerative feedback provided by the residual reflectivity of the output facet has not been optimized and is, in fact, far from the optimum value predicted by our compound resonator analysis. The optimum regenerative feedback level is a complex function of several variables, including the output coupler reflectivity, the gain-dependent phase shift, and the coupling matrix (scattering matrix) of the cavity. Based on our preliminary model of operation, we estimate that the optimum level of regenerative feedback would be somewhere between 1% and 5%.

The next set of experiments was performed to determine the coherence as a function of the number of elements in the array. By placing a variable aperture in the near field, we were able to select a desired subset of elements to participate in the lasing action. We then measured the coherence of the array as described above varying only the size of the aperture; all other parameters (including the alignment of the SF cavity) remaining unchanged. The results of this experiment are presented in Fig. 6, which shows the coherence of the array as a function of number of elements in the array. It should be noted that the design of the cavity (the fill factor, in particular) was optimized assuming all 35 elements participating in the coherent lasing.

The coherence of the array was measured to be 0.85 with only 3 elements operating in the array. As the number was increased from 3 up to 35 elements, the coherence initially decreased to 0.58 at about 15 elements, and then remained approximately constant up to the maximum array size of 35 elements.

In the SF cavity, the feedback to the laser array is created from its own far-field pattern. The SF cavity used for these experiments was designed so that the width of the interference fringes in the far-field pattern approximately matches the width of the individual emitters with all 35 elements operating, to provide optimum feedback coupling. As the number of selected elements decreases, the width of the near field of the array decreases, the width of the far field interference fringes increases, and thus, the amount of feedback coupled to the array decreases. We estimated that the effective feedback to the individual elements (taking into account the 50% reflectivity of the output coupler) was approximately 25% when all 35 elements were participating in the coherent lasing, and less than 1% with only 3 elements selected. With the reduced level of feedback, this could result in a reduction in the coherence of the array.

The results presented in Fig. 6 can be contrasted to the previous predictions obtained using cold cavity models. For instance, by adapting the Siegman analysis to our system with parameters appropriate to our laser array, this would predict that there is less than a 2% chance of achieving a coherence of even 10% for arrays with greater than 20 elements.

These experimental results are in good agreement, however, with theoretical analyses of large arrays that utilize the nonlinearities in the laser gain medium. In a previous paper, we predicted that the use of regenerative feedback in a coherent laser array could result in a coherence equal to ~0.65 for arrays with more than 20 elements [11].

This earlier prediction was obtained using an array of fiber lasers and assuming a completely random distribution of cold cavity phase shifts. Diode lasers have much shorter lengths and the distribution of the cold-cavity phase shifts are not necessarily completely random. A preliminary thermal analysis indicates that a temperature variation only 1K between the individual emitters will result in sufficient variation in the optical path lengths of the different emitters to model the spectral positioning of the longitudinal modes as being approximately random.

Napartovich has analyzed an array of fiber lasers using regenerative feedback both with and without the resonant nonlinearity [12, 13]. With the resonant nonlinearity and gain saturation included, these results predict a coherence up to ~0.70 for arrays of 20 elements and remains relatively constant for larger arrays. Jeux [7] has recently analyzed and demonstrated a passively combined coherent array with the use of a hybrid amplitude/phase spatial filter in the Fourier plane of the feedback to the array. This spatial filter converts phase changes in the array outputs into intensity changes in the feedback. The change in feedback intensity results in gain variations due to gain saturation. As the gain varies, the resonant nonlinearity induces a change in the output phase, which has been shown to substantially compensate for the original phase variations in the array output. Using this configuration, they have experimentally demonstrated the coherent operation of an array of fiber lasers with 20 elements with a coherence equal to 78% [14,15].

In summary, we have experimentally demonstrated the coherent operation of a 35-element diode laser array with a measured coherence equal to 0.57. These experimental results are in agreement with recent nonlinear analyses that predict that passively coupled coherent laser arrays can overcome previous cold-cavity predicted limitations if the resonator is designed appropriately.

## Acknowledgments

This material is based upon work supported by the Air Force Research Laboratory. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of AFRL. We gratefully acknowledge helpful technical discussions with Steve Patterson from DILAS.

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