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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 7 — Apr. 7, 2014
  • pp: 8420–8425
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Passive coherent combination of a diode laser array with 35 elements

Christopher J. Corcoran and Frederic Durville  »View Author Affiliations


Optics Express, Vol. 22, Issue 7, pp. 8420-8425 (2014)
http://dx.doi.org/10.1364/OE.22.008420


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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

The coherent diode laser array coupled to the SF cavity is presented in Fig. 1
Fig. 1 Coherent diode laser array in self-Fourier cavity.
[8

8. C. J. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86(20), 201118 (2005).

,9

9. C. J. Corcoran and F. M. Durville, “Passive phasing in a coherent laser array,” IEEE J. Sel. Top. Quantum Electron. 15(2), 294–300 (2009). [CrossRef]

]. 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
Fig. 2 Spectrum of diode laser array.
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 = 270μm, with a cavity length of 2.5mm and a ridge waveguide width equal to 5μm, thus providing single spatial-mode operation. By measuring the far field of the complete (incoherent) laser array, as presented in Fig. 3
Fig. 3 Far field of incoherent laser diode array.
, we determined that the near field of each laser emitter had a near Gaussian profile with radius equal to 2.9μm.

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 Feff = 49.6mm as required to satisfy the Self-Fourier condition: d2 = Feff ‧λ 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
Fig. 4 Prototype SF cavity with monolithic diode laser array in upper left.
.

With 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
Fig. 5 Far field interference fringes of coherent laser array with 35 elements. Left - Complete far field. Right - Detail of two fringes.
. 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

10. C. D. Nabors, “Effects of phase errors on coherent emitter arrays,” Appl. Opt. 33(12), 2284–2289 (1994). [CrossRef] [PubMed]

]. 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 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.

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

12. D. V. Vysotsky, N. N. Elkin, and A. P. Napartovich, “Radiation phase locking in an array of globally coupled fiber lasers,” Quantum Electron. 40(10), 861–867 (2010). [CrossRef]

, 13

13. A. P. Napartovich, N. N. Elkin, and D. V. Vysotsky, “Influence of non-linear index on coherent passive beam combining of fiber lasers,” Proc. of SPIE, Fiber Lasers VIII: Technology, Systems, and Applications 7914, 791428–1 - 791428–10, (2011). [CrossRef]

]. 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

7. F. Jeux, A. Desfarges-Berthelemot, V. Kermène, J. Guillot, and A. Barthelemy, “Passive coherent combining of lasers with phase-contrast filtering for enhanced efficiency,” Appl. Phys. B 108(1), 81–87 (2012). [CrossRef]

] 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

14. F. Jeux, A. Desfarges-Berthelemot, V. Kermène, and A. Barthelemy, “Experimental demonstration of passive coherent combining of fiber lasers by phase contrast filtering,” Opt. Express 20(27), 28941–28946 (2012). [CrossRef] [PubMed]

,15

15. F. Jeux, A. Desfarges-Berthelemot, V. Kermène, A. Barthelemy, “Passive coherent combining of 15 fiber lasers by phase contrast filtering,” CLEO, CJ-4.5, pp. 792, Munich, May (2013).

].

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.

References and links

1.

L. Goldberg and J. F. Weller, “Single lobe operation of a 40-element laser array in an external ring laser cavity,” Appl. Phys. Lett. 51(12), 871–873 (1987). [CrossRef]

2.

C. J. Corcoran and R. H. Rediker, “The dependence of the output of an external-cavity laser on the relative phases of inputs from the five gain elements,” IEEE Photon. Technol. Lett. 4(11), 1197–1200 (1992). [CrossRef]

3.

A. E. Siegman, “Resonant Modes of linearly coupled multiple fiber laser structures,” [Unpublished Manuscript], Stanford Univ., (2004).

4.

D. Kouznetsov, J. Bisson, A. Shirakawa, and K. Ueda, “Limits of coherent addition of lasers: simple estimate,” Opt. Rev. 12(6), 445–447 (2005). [CrossRef]

5.

J. E. Rothenberg, “Passive coherent phasing of fiber laser arrays,” Fiber Lasers V: Technology, Systems, and Applications, Proc. of SPIE 6873, 687315 (2008).

6.

C. J. Corcoran, F. Durville, and W. Ray, “Regenerative phase shift and its effect on coherent laser arrays,” IEEE J. Quantum Electron. 47(7), 1043–1048 (2011). [CrossRef]

7.

F. Jeux, A. Desfarges-Berthelemot, V. Kermène, J. Guillot, and A. Barthelemy, “Passive coherent combining of lasers with phase-contrast filtering for enhanced efficiency,” Appl. Phys. B 108(1), 81–87 (2012). [CrossRef]

8.

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86(20), 201118 (2005).

9.

C. J. Corcoran and F. M. Durville, “Passive phasing in a coherent laser array,” IEEE J. Sel. Top. Quantum Electron. 15(2), 294–300 (2009). [CrossRef]

10.

C. D. Nabors, “Effects of phase errors on coherent emitter arrays,” Appl. Opt. 33(12), 2284–2289 (1994). [CrossRef] [PubMed]

11.

C. J. Corcoran, F. Durville, and K. A. Pasch, “Coherent array of nonlinear regenerative fiber amplifiers,” IEEE J. Quantum Electron. 44(3), 275–282 (2008). [CrossRef]

12.

D. V. Vysotsky, N. N. Elkin, and A. P. Napartovich, “Radiation phase locking in an array of globally coupled fiber lasers,” Quantum Electron. 40(10), 861–867 (2010). [CrossRef]

13.

A. P. Napartovich, N. N. Elkin, and D. V. Vysotsky, “Influence of non-linear index on coherent passive beam combining of fiber lasers,” Proc. of SPIE, Fiber Lasers VIII: Technology, Systems, and Applications 7914, 791428–1 - 791428–10, (2011). [CrossRef]

14.

F. Jeux, A. Desfarges-Berthelemot, V. Kermène, and A. Barthelemy, “Experimental demonstration of passive coherent combining of fiber lasers by phase contrast filtering,” Opt. Express 20(27), 28941–28946 (2012). [CrossRef] [PubMed]

15.

F. Jeux, A. Desfarges-Berthelemot, V. Kermène, A. Barthelemy, “Passive coherent combining of 15 fiber lasers by phase contrast filtering,” CLEO, CJ-4.5, pp. 792, Munich, May (2013).

OCIS Codes
(140.2010) Lasers and laser optics : Diode laser arrays
(140.3290) Lasers and laser optics : Laser arrays
(140.3520) Lasers and laser optics : Lasers, injection-locked
(140.3298) Lasers and laser optics : Laser beam combining

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: February 28, 2014
Revised Manuscript: March 24, 2014
Manuscript Accepted: March 24, 2014
Published: April 1, 2014

Citation
Christopher J. Corcoran and Frederic Durville, "Passive coherent combination of a diode laser array with 35 elements," Opt. Express 22, 8420-8425 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-7-8420


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References

  1. L. Goldberg, J. F. Weller, “Single lobe operation of a 40-element laser array in an external ring laser cavity,” Appl. Phys. Lett. 51(12), 871–873 (1987). [CrossRef]
  2. C. J. Corcoran, R. H. Rediker, “The dependence of the output of an external-cavity laser on the relative phases of inputs from the five gain elements,” IEEE Photon. Technol. Lett. 4(11), 1197–1200 (1992). [CrossRef]
  3. A. E. Siegman, “Resonant Modes of linearly coupled multiple fiber laser structures,” [Unpublished Manuscript], Stanford Univ., (2004).
  4. D. Kouznetsov, J. Bisson, A. Shirakawa, K. Ueda, “Limits of coherent addition of lasers: simple estimate,” Opt. Rev. 12(6), 445–447 (2005). [CrossRef]
  5. J. E. Rothenberg, “Passive coherent phasing of fiber laser arrays,” Fiber Lasers V: Technology, Systems, and Applications, Proc. of SPIE 6873, 687315 (2008).
  6. C. J. Corcoran, F. Durville, W. Ray, “Regenerative phase shift and its effect on coherent laser arrays,” IEEE J. Quantum Electron. 47(7), 1043–1048 (2011). [CrossRef]
  7. F. Jeux, A. Desfarges-Berthelemot, V. Kermène, J. Guillot, A. Barthelemy, “Passive coherent combining of lasers with phase-contrast filtering for enhanced efficiency,” Appl. Phys. B 108(1), 81–87 (2012). [CrossRef]
  8. C. J. Corcoran, F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86(20), 201118 (2005).
  9. C. J. Corcoran, F. M. Durville, “Passive phasing in a coherent laser array,” IEEE J. Sel. Top. Quantum Electron. 15(2), 294–300 (2009). [CrossRef]
  10. C. D. Nabors, “Effects of phase errors on coherent emitter arrays,” Appl. Opt. 33(12), 2284–2289 (1994). [CrossRef] [PubMed]
  11. C. J. Corcoran, F. Durville, K. A. Pasch, “Coherent array of nonlinear regenerative fiber amplifiers,” IEEE J. Quantum Electron. 44(3), 275–282 (2008). [CrossRef]
  12. D. V. Vysotsky, N. N. Elkin, A. P. Napartovich, “Radiation phase locking in an array of globally coupled fiber lasers,” Quantum Electron. 40(10), 861–867 (2010). [CrossRef]
  13. A. P. Napartovich, N. N. Elkin, and D. V. Vysotsky, “Influence of non-linear index on coherent passive beam combining of fiber lasers,” Proc. of SPIE, Fiber Lasers VIII: Technology, Systems, and Applications 7914, 791428–1 - 791428–10, (2011). [CrossRef]
  14. F. Jeux, A. Desfarges-Berthelemot, V. Kermène, A. Barthelemy, “Experimental demonstration of passive coherent combining of fiber lasers by phase contrast filtering,” Opt. Express 20(27), 28941–28946 (2012). [CrossRef] [PubMed]
  15. F. Jeux, A. Desfarges-Berthelemot, V. Kermène, A. Barthelemy, “Passive coherent combining of 15 fiber lasers by phase contrast filtering,” CLEO, CJ-4.5, pp. 792, Munich, May (2013).

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