1. Introduction

Owing to their high electro-optical conversion efficiency, compactness, and long life time, high power broad-area laser diode arrays (LDAs) have extensive applications in material processing, illumination, spin-exchange optical pumping (SEOP), and solid state and fiber lasers pumping. In broad area laser arrays, each laser emitter has multi-transverse and multi-longitudinal modes. The free-running spectrum is 2~3 nm width, and the beam divergence is around 120 mrad along the slow-axis. Poor beam quality and broaden spectrum significantly limit high power LDA applications. Therefore, achieving coherent emission with excellent beam quality and narrowing the linewidth is a major challenge for the development of novel and innovative technologies.

According to the application objectives, one may classify semiconductor laser arrays into three categories: (1) linewidth-narrowed laser source [1–7]; (2) high beam-quality laser source [8–12]; and (3) coherent laser source with narrow linewidth and high spatial beam quality.

In SEOP application [1], spectral linewidth narrowing is important in increasing the optical pumping efficiency. There are two different external cavity approaches to narrow the linewidth. One is external cavity with plane diffraction grating [2–4]. The other is the external cavity comprised of volume Bragg grating (VBG) and beam-transform optics [5–7]. Normally the plane diffraction grating external cavity provides wider wavelength tunable range while the VGB external cavity generates narrower linewidth. On the other hand, in the applications such as material processing, illumination and solid state, fiber laser pumping, the beam quality is the critical factor for effective energy delivery. Spectral beam combination technology provides good beam quality with around more than 10 nm-broad spectrums [8, 9]. Excellent beam quality (near diffraction-limited beam) is achieved by using a 100-element, 100-micron pitch array of slab-coupled optical waveguide laser [10, 11]. Spectral beam combining technology is also applicable for beam combining in fiber lasers [12].

Coherent beam combination is a very promising methodology to simultaneously achieve excellent beam quality (near diffraction-limited beam) and narrow-spectral-linewidth. Potential application fields for high power coherent beam could be directed energy, space and underwater communication, and others. High power coherent beam can be used for variety of nonlinear optics process, such as high-efficiency second harmonic and terahertz generation.

A variety of optics designs have been considered to achieve a coherent beam addition. The MOPA (master optical power oscillators) architecture companied with fast electronic phase control loop is used in the active coherent beam combination. In MOPA design, a stable master laser is used to injection lock the slave lasers. MOPA design requires fast response phase control loop over all the lasers and this requirement introduces a significant challenge, in particular when very large laser arrays are being considered [13–15].

Alternatively, passive coherent beam combination schemes require much less external control. Such designs are relatively simple and have been extensively studied. The evanescent wave coupling and external Talbot cavity are two popular approaches to achieve passive coherent beam addition [16–22]. The external Talbot cavity technology has been successfully used for single-mode laser diode array coherent addition [19–22]. Optical coupler provides the diffraction feedback which is normal to the front-facet of laser diode. This configuration has been successfully applied to single-mode laser diode arrays. However feedback normal to the front-facet of broad-area laser diodes may excite multi-transverse modes that consequently impair coherent addition of laser diode array. In order to avoid multi-transverse mode excitation, the laser diode array with external cavity feedback is limited to operations at low injection levels. Recently, single-lobe coherent addition at low power level from a broad-area laser diode array with carefully designed amplitude mask external Talbot cavity was demonstrated [23].

In the past two decades, single-transverse mode operation has been demonstrated for both single broad-area laser diode and multi-stripe laser diode array based on off-axis external cavity technology [24–30]. The off-axis feedback, generated by a stripe-mirror (aperture-limited mirror) provides angle-sensitive feedback which allows only radiation travelling at a specific angle within the broad-area laser diode to oscillate in the external cavity. A plane diffraction grating replaced the stripe mirror and provided angle-sensitive and spectral-sensitive feedback to a broad-area laser diode. A broad-area laser diode generated single-transverse mode, narrow linewidth coherent radiation by grating feedback [28–30]. Recently, the above off-axis feedback scheme was studied in broad-area laser diode array. The stripe mirror array provided each broad-area laser diode off-axis feedback. Therefore the entire array beam divergence angle was reduced to 26 mrad at high power level without controlling laser spectral linewidth [31]. For more convenient design, the volume Bragg grating or aperture-limited mirror were used to provide angle-sensitive off-axis feedback. The beam quality of entire array was improved [32–34] and spectral linewidth was reduced to 0.3 nm by volume Bragg grating feedback [33]. However, there was no evidence for a coherent addition in these systems [31–34]. Achieving high power and narrow linewidth coherent beam combination from broad-area laser diode array still remains a major challenge.

 

Fig. 1. (Color online) Schematic of V-shape external cavity. The V-shape external cavity is shown in top view (slow-axis). LDA is laser diode array, CL1~CL4 are cylindrical lenses. GRIN lens and CL2 collimate laser beam along fast-axis and the con-focal lens pair CL1, CL3 image laser diodes on CL3 focal plane. There is an angle θ between two reflection surfaces of prism mirrors. The two prism mirrors separate the laser beam into two paths: one for feedback and the other for output. Feedback path consists of CL1~CL3, and grating. D is the distance between grating and CL3. In output path, cylindrical lens CL4 projects laser diode array far-field profile on its focal plane. A CCD camera images the far-field profile and spectrometer measures the spectrum while a power-meter monitors the output power. Inset 1: each broad-area laser diode V-shape external cavity. Inset 2: effective external cavity. The effective cavity length is the distance between grating and laser diodes image (CL3 focal plane).

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In this paper, we propose, implement, and demonstrate external cavity which provides transverse mode control and carries out a coherent addition of the entire laser diode array. The newly designed external cavity forces each broad-area laser diode to oscillate at single transverse mode and generates mutual coherence among broad-area laser diodes. The two laser beams generated by the off-axis external cavity are spatially separated by two prism mirrors. Therefore there is enough space to build up external Talbot cavity. The two prism mirrors, laser diode array, transform optics and diffraction grating form the external cavity. We call such an external cavity scheme as a V-shape external cavity since two prism mirror reflection surface forms a V-shape geometry. Our experiments demonstrate coherent beam addition from high-power broad-area laser diode array subject to the V-shape external cavity. When shifting the grating position, we observed a transition from incoherent to coherent addition. The angle of the center lobe of the array far-field profile is around 1.0 mrad and spectral linewidth is about 0.1 nm. The output power reaches 9.0 Watts with high current injection and the coherent addition far-field profile maintains high-visibility. The interference profile generated by a phase-locked array coherent addition is confirmed by the numerical calculations.

2. Experiment

The experimental scheme is shown in Fig. 1. Laser diode array was manufactured by Lasertel. It comprises of 49 emitters with 100 µm emitter size with a center wavelength around 770 nm and separation between the emitters is 200 µm. The front facet of the array is anti-reflection (AR) coated with reflectivity R≈1% and rear facet is high-reflection coated.

A pair of prism mirrors separates the laser beam into two paths. One is the feedback path (top half of Fig. 1). The other one is the output path (bottom half of Fig. 1). Each prism mirror is mounted on a precision rotation stage. An angle (θ=92.86°) between two reflection planes is carefully set in order to achieve a high power output and a clear far-field interference profile. The two prism mirrors steer two laser beams parallel to laser diode facet along slow-axis direction.

In the feedback path, a telescope comprised of a gradient index (GRIN) lens (f_g=1.3 mm, NA=0.5) and a cylindrical lens CL2 (f₂=200 mm) collimate the laser beam along the fast axis. The vertical position of laser diodes on linear array has a curved distribution due to non-perfect manufacture process. As a result, the image of laser diodes shows a “smile” pattern. With external grating feedback, the vertical position “smile” distribution of laser diodes generates lasing wavelength “smile” distribution. It is called “smile” effect. By using telescope in external cavity, the “smile” effect can be reduced [2]. Our feedback branch telescope is comprised of cylindrical lenses. This design is slightly different from round lens telescope in [2]. Following the ray-tracking calculation procedure in [2], the “smile” effect of the laser array is reduced by f₂/(d₂-f₂-f_g) in our external cavity configuration, where d₂ is the distance between CL2 and laser diode array (d ₂ is not shown in Fig. 1). The “smile” effect is reduced by a factor of eight in our external cavity configuration. A con-focal cylindrical lens pair CL1 and CL3 (f ₁=f ₃=200 mm) transfer laser diodes image to the surface of the diffraction grating (830-line/mm, gold-coating) which is arranged in a Littrow configuration. The grating blaze angle is about 18 degrees and the first-order diffraction efficiency is more than 85%. The locked center wavelength is determined by grating title angle. The grating is mounted on a linear stage and its position is continuously tunable between the image plane (CL3 focal plane, D=f ₃) and the half Talbot plane at D=f ₃+Z _t/2 where Z_t=2d ²/λ is the Talbot distance, λ is the laser wavelength, and d is the array pitch. Since cylindrical lenses transfer laser diode image on CL3 focal plane, the cavity round-trip is calculated by formula L=2(D-f ₃). In the output path, the laser diodes far-field profile is imaged on the focal plane of the cylindrical lens CL4 (f ₄=300 mm) and is recorded by a CCD camera. The spectrometer with a fiber-collection tip is used to measure the spectrum while the power-meter behind the beam-splitter monitors the output power.

The inset 1 of Fig. 1 shows the resonant cavity for each broad-area laser diode. The cavity is composed of front-facet, rear-facet, and diffraction grating (considering the diffraction grating reflectivity is higher than the front facet reflectivity of laser diode with AR-coating). The diffraction grating serves as an end mirror and a spectral selector; meanwhile rear facet and front facet serve as the beam folding mirror and the output coupler, respectively. The folding cavity doubles the gain medium length and provides higher power gain to support laser diode lasing even with the low AR-coating front facet. Fig. 1 also shows that the feedback beam from the V-shape external cavity enters the laser cavity at a certain incidence angle. Such an off-axis feedback will change the effective emission mode size of each laser emitter as discussed in the next section.

3. Results and discussions

Figure 2(a) shows the far-field profile generated from the phase-locked laser diode array when the grating is positioned around the half-Talbot plane (round-trip of external cavity is Talbot distance. The profile clearly demonstrates a coherent addition and the visibility of the profile is larger than 80%. The full width at half maximum (FWHM) of the center lobe far-field angle is about 1.0 mrad. The angle between two adjacent peaks is 3.85 mrad that is consistent with the theoretical angle spacing between the different diffraction orders of a 200 µm-periodic source (λ/D=0.77 µm/200 µm=3.85 mrad). The spectral linewidth is about 0.1 nm. The output power is 5.3 Watts at 30 A. We find that the energy ratio (center lobe/total) in the far-field profile does not match the calculation with the filling factor 0.5 of the laser diode array (100 µm emitter mode size and 200 µm emitter separation). This is because the off-axis feedback in our V-shape external cavity changes the effective emission mode size as observed in single broad-area laser diode external cavity [27]. In our cavity, each broad-area laser emitter in the array is forced to the single transverse mode operation. The actual emission mode size was estimated to be around 40 µm. To further verify the effective emission mode size, we have numerically calculated the center energy ratio as a function of the filling-factor for the phased locked array and results are plotted in Fig. 2(b). The experimental measurements of the center energy ratio in both 30 A and 50 A cases are shown in solid and dashed line, respectively. This result confirms that the observed far-field coherent interference pattern is generated by a phase locked laser diode array with a filling factor ~ 0.2, i.e., 40 µm mode size with a 200 µm emitter separation. Due to the inhomogeneous AR-coating, intensity fluctuations of individual laser diodes in the array are of the order of 20%. Such intensity fluctuation broadens the far-field angle of each lobe and reduces the interference pattern visibility. It is important to note that no spatial filter is needed in our V-shape external cavity since the V-shape external cavity provides sufficient mode discrimination [22].

 

Fig. 2. (Color online) (a) Experimental results of far-field profile of phase-locked laser array at 30 Amps current injection and (b) center energy ratio (center lobe energy/total energy) of the far-field profile versus the phase locked laser diode array filling factor. In (b) the hollow-dot line is the numerical simulation of far-field energy ratio for different filling factor phase locked laser diode array while the solid line and dashed line are the experimental measurements at 30 A (corresponding to Fig. 3 (a)) and 50 A (corresponding to Fig. 4 (a)), respectively.

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In order to elucidate the effect of laser coupling on coherent addition we studied far-field patterns as the grating position was shifted. Figure 3 shows two far-field profiles corresponding to different cavity round-trip lengths. According to our V-shape external cavity configuration, the con-focal cylindrical lenses pair (CL1 and CL3) image laser diode array on CL3 focal plane. The effective external cavity of feedback branch is shown in the inset 2 of Fig. 1, which is similar to Fig. 3 in [20]. The effective external cavity is consisted of the image of laser diodes and the grating. The effective cavity round trip is 2(D-f₃). When grating is shifted close to the image plane (D≈f₃), the effective cavity round trip is close zero (L≈0). The emission of each laser diode is directly feed back to laser diode itself. Such an image does not contain sufficient diffraction coupling among lasers and therefore is not able to lock the phase of entire laser array [21]. Accordingly the far-field profile shows a single broad peak generated by incoherent addition of individual laser beams. When grating is shifted close to the second plane (D≈f ₃+Z_t/2, L≈Z_t), the self-image formed by the Talbot cavity creates a strong diffraction coupling among lasers and the entire array is phase-locked as shown in Fig. 3(b). The transition between incoherent addition and coherent addition shown in Fig. 3 is similar to the result of single-mode laser diode array in a Talbot cavity [21].

 

Fig. 3. Transition between incoherent addition and coherent addition. (a) Grating position is around the image plane (D=f ₃) and the far-field profile shows a single broaden peak. (b) Grating position is shifted to the half-Talbot plane (D=f ₃+d²/λ) and the far-field profile shows a multi-lobe interference pattern. Both intensities are normalized by the highest peak intensity in Fig. 3(b).

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To examine our V-shape external Talbot cavity design at high power levels, the driving current of the array was increased to 50 A and the output power of the array was 9 W. At high power high-order modes are usually being excited and consequently the coherence of LDA is deteriorating. Therefore high power operation is usually challenging for LDA coherent addition external cavity designs. Nevertheless, in our experiment, we observed high visibility interference far-field profile as shown in Fig. 4(a). A narrow spectral linewidth (FWHM=0.1 nm) is demonstrated in Fig. 4(b). The multi-lobe far-field profile indicates that our V-shape external Talbot cavity provides a robust mode discrimination and strong coupling for coherent beam addition at high power levels.

The robust mode discrimination is primarily based on off-axis external cavity design. Previously, off-axis external feedback has been proved to increase the mode selection capability of single broad-area emitter [24–30] as well as broad-area laser diode arrays [31–34]. The V-shape Talbot external cavity described in this work provides a spectrum-resolved, diffraction coupled, off-axis external feedback. It also reduces the effective emission mode size that helps to further increase the mode-discrimination [22].

 

Fig. 4. Experimental results of (a) far-field profile and (b) spectrum of a phase-locked laser array at 50 A with a V-shape external Talbot cavity.

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4. Conclusion

In conclusion, we have implemented high-power coherent addition of LDA with a narrow linewidth by using a novel V-shape external cavity design. The off-axis optical feedback induced in the V-shape external cavity forces each broad-area laser diode to operate at single-transverse mode and the Talbot configuration external cavity results in coherent addition of laser beams. In our V-shape cavity scheme, the folding cavity doubles the gain media length and compensates the cavity loss induced by the low-reflectivity AR coating on the front facet. The far-field profile of phase-locked laser diode array is consistent with our numerical simulation. The V-shape external cavity design is robust and provides the high-power operation capability.

The multi-lobe far-field profile is generated by the low-filling factor of the phase-locked array. There are two possible solutions to increase the beam combining efficiency. One is to increase the filling-factor by customizing higher-filling-factor laser diode arrays. The other is to use two phase masks to compensate the non-uniform phase distribution along array due to the low-filling factor and therefore to concentrate the energy in the center lobe [35, 36].