1. Introduction

Optical waveguides are far more than merely connecting elements between integrated optical components. Benefiting from their flexible geometries and good optical confinement, dielectric waveguides are full of possibilities for optical functions such as beam steering, optical modulation, lasing, and nonlinear frequency conversion [1–4]. One- (1D) and two-dimensional (2D) lattices of coupled channel waveguides provide a versatile platform for manipulating the flow of light [5]. Such arrays played a significant role in recent studies on optical analogs of many fundamental quantum mechanical effects such as Bloch oscillations [6,7], Zener tunneling [8,9], continuous-time quantum random walks [10,11], Anderson localization [12,13], and other processes [14–19].

For fabrication of coupled channel waveguide arrays, femtosecond-laser direct writing (FsLDW) is becoming one of the most practical technique due to its flexibility in defining waveguide geometries and dimensions in various of transparent dielectrics [4,20–30]. In contrast to that in amorphous glasses (usually Δn > 0 at the irradiated focal volume, namely “single-line” configuration), FsLDW in optical crystals usually causes negative refractive-index change (Δn < 0) at the directly irradiated region, resulting in guiding cores (usually with “double-line” and “depressed-cladding” geometries) located at the neighboring region of laser tracks [4,20]. Since such a modification in crystals generally requires high laser fluences and thus massive damage to the local crystalline lattice structure, the negative refractive-index change at laser-induced tracks acts as high optical barrier, limiting the overlapping between adjacent waveguide modes. Therefore, it is not surprising that almost all the previous reports on FsLDW coupled waveguide arrays are based on amorphous glasses (with “single-line” configuration where guiding core is eventually located at the damaged region) [20–24], while little attention has been paid on FsLDW of crystalline photonic lattices [25,26]. Besides, in comparison to the “depressed cladding” geometries, e.g. the single- and multi-cladding waveguides in Refs. [29,30], which are usually consist of more than 50 laser tracks, FsLDW of “double-line” structures are more suitable due to their ease of fabrication [25,26].

One of the most important features of coupled waveguide arrays is their relatively flexible discrete diffraction patterns (modal distributions) achieved via optical excitation of different waveguide channels [26], which can be very interesting for various applications such as optical communication, integrated optics and nonlinear optics. Up to now, such a discrete optical effect has been reported in passive waveguides [26]. But none of the previously reported studies focuses on fabrication of active waveguide arrays, e.g. waveguide laser arrays.

In this work, we report on, for the first time to the best of our knowledge, fabrication of 1D active waveguide laser array in Nd:YAG crystals based on “double-line” geometry defined by FsLDW. Relying on the evanescent coupling between adjacent waveguide modes, discrete diffraction patterns with different laser intensity distribution can be realized via adjusting coupling condition. The experimental results are well supported by the simulation.

2. Waveguide array fabrication

The raw Nd:YAG (1 at.% Nd³⁺ ions) crystal wafer used in this work has dimensions of 4 × 10 × 2 mm³. All the crystal facets have been well polished to an optical grade before further processing and characterization. A Ti:Sapphire regenerative amplifier (Spitfire, Spectra Physics), which delivers 795-nm pulses with a temporal duration of 120 fs and a maximum pulse energy of 1 mJ at a repetition rate of 1 kHz, was employed for FsLDW. In the laser-writing process, the incident laser beam was focused through the largest crystal facet (4 × 8 mm²) at a fixed depth of 250 µm by a 10× microscope objective (N.A. = 0.3). The average laser power was attenuated to milliwatts level. The crystal wafer was placed on a motorized XYZ micro-positioning stage which allows for precise translation of the sample at a constant velocity (50 µm/s in this work) with respect to the incident laser beam. A pulse energy of 6.3 µJ (on sample) was identified as the optimal value in order to produce laser-damage tracks while avoiding crystal cracking. Under our experimental conditions, a damage track with a vertical length of 30 µm and a lateral width of 1.5 µm can be produced via a single scan. Subsequently, 16 parallel scans were performed, with a constant lateral separation of 15 µm, at the same depth beneath the crystal surface to define the desired 1D waveguide array. As a result, 15 “dual-line” waveguides (marked as WG_m with m = −7 to + 7 in which WG₀ refers to the central one) line up and distribute uniformly with a fixed separation, as shown in the cross-sectional microscopic image in the inset in Fig. 1. All the laser-induced tracks were written along the long-axis (i.e. waveguide array length of 10 mm) of the crystal wafer. The main intention of choosing this FsLDW parameter combination is to achieve efficient guiding via the stress-field induced refractive index modification and evanescent coupling between adjacent waveguide modes.

 

Fig. 1. Schematic diagram of the end-face coupling arrangement for waveguide array characterization. The inset is the cross-sectional microscopic image of the fabricated waveguide array. Scale bar denotes 30 µm.

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3. Waveguide array characterization

3.1 Waveguide laser array: discrete diffraction pattern

To investigate the guiding and lasing properties of the fabricated waveguide array, a standard end-face coupling arrangement was employed, as schematically shown in Fig. 1. The polarized 808-nm pump light was provided by a tunable continuous-wave (CW) Ti:Sapphire laser (Coherent MBR 110). We used a plano-convex lens (f = 25 mm) and a microscope objective (20×/0.40) for in- and out-coupling, respectively. The waveguide sample, the lens and the objective were placed on separate manual 3D-translation optical stages, enabling flexible adjustment of coupling condition as well as optical excitation of different waveguides by simply translating the sample or the lens laterally/vertically. Two dielectric mirrors were butt-adhered to the in- (reflectivity of >99% at 1.06 µm and high transmittance of 98% at 808 nm) and out-coupling (reflectivity of approximately 60% at 1.06 µm and reflectivity of >99% at 808 nm) end facets of the sample, forming a compact Fabry-Perot cavity.

Laser emission from the waveguide array was confirmed by a spectrometer with a minimum resolution of 0.2 nm, resulting in a central lasing wavelength of 1065 nm with the full wave at half maximum (FWHM) value of 0.3 nm, corresponding to the transition band ⁴F_3/2 → ⁴I_11/2 of Nd³⁺. By laterally moving the position of focal spot within the waveguide array area, no shift of the lasing spectrum can be identified. By rotating the polarization of pump light via a half-wave plate, we found that efficient optical guiding can be obtained only along TM polarization (incident pump light), which is a typical feature for FsLDW “dual-line” waveguides in optically isotropic crystals like Nd:YAG [20]. The generated waveguide laser intensity profile was imaged by a CCD camera, as shown in Fig. 2 in case of locating the pump focal spot at WG₀ (Fig. 2(c)) and WG₊₇ (Fig. 2(e)), respectively. It is clear that the fabricated array allows the evanescent field of individual waveguide mode to extend through and beyond the laser damage regions (optical barrier), offering the necessary overlap between adjacent waveguide modes via evanescent coupling. To simulate this process, the FsLDW-induced refractive index modification information is required.

 

Fig. 2. (a) Reconstructed refractive index profile of the fabricated 1D waveguide array. (b, d) Simulated and (c, e) experimental results of the intensity distribution at 1.06 µm of the waveguide array (using focal lens with f = 25 mm). White dotted lines and circles denote the laser-induced tracks position and the focal spot location of the incident light, respectively. Scale bar denotes 30 µm.

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The maximum refractive index change (Δn) in the waveguide core is estimated to be 2.8 × 10⁻³ according to the formula Δn = sin²θ_m/2n (n = 1.815 is the refractive index of the Nd:YAG bulk at 1064 nm) by determining the angular aperture θ_m of the guided mode in the far-field and assuming a step-index profile [31]. Based on the estimated Δn, the refractive index profile of the waveguide array can be reconstructed according to the analysis in [32], as shown in Fig. 2(a). Then we used the finite-difference beam propagation method (FD-BPM) based BeamPROP^TM software to simulate the optical propagation and the far-field intensity distribution of the waveguide array [33]. It is worth noting that the optical simulation here considers only 1.06-µm light beam evolution in the waveguide array under passive regime. In the simulation, the incident 1.06-µm light beam was set to be 20-µm diameter (confirmed experimentally) with Gaussian intensity distribution, which is in fairly good agreement with that in the experiment when using the incoulping lens with f = 25 mm. Scattering losses from the laser induced-tracks are ignored in the simulation. The waveguide lengths are fixed at 10 mm (the same as that in the real case) in the simulation.

When locating the incident light beam (focal spot) at WG₀, a far-field discrete diffraction pattern due to the evanescent coupling between neighboring waveguides is clearly shown in the simulation (Fig. 2(b)). Interestingly, in the laser operation experiment (active regime), this diffraction pattern can be well preserved as shown in Fig. 2(c). This phenomenon can be further confirmed in case of placing the focal spot at WG₊₇ (mirror-symmetrically identical to that at WG₋₇), as shown in Figs. 2(d) and 2(e). Please note that the experimentally observed intensity patterns for passive (non-lasing) regime at 1.06 µm are found to be identical to the results in simulation as well as in active (lasing) regime. To get a better understanding of the formation mechanism of this phenomenon, we studied the optical losses of the waveguide array. When locating the focal spot of the incident light at WG₀, the maximum total waveguide loss is determined to be 3.7 dB (by comparing the input and output optical power). We attribute this loss to a sum of the incoupling loss at the end facet and the propagation loss due to scattering of waveguide boundaries. As a reference, we also studied an individual “double-line” waveguide fabricated by using the same FsLDW parameters, giving a total loss of 3.4 dB at 1064 nm, which is very close to that of the waveguide array. According to the coupling efficiency formula ${\eta _c} = \frac{{4w_1^2w_2^2}}{{{{({w_1^2 + w_2^2} )}^2}}}$ (with w₁ and w₂ are the radii of the incident spot size and guided modes) for single-mode waveguide, the coupling loss of an individual “double-line” waveguide is calculated to be around 0.4 dB, resulting in a propagation loss of around 3 dB/cm (corresponding to a single-pass transmission of 50%). And because of such a relatively “high” propagation loss, the lasing performance as well as the discrete diffraction pattern in the active regime are mainly provided by the single-pass optical excitation in the coupled waveguide array. By further considering the reflectivity (approximately 60% at 1.06 µm and >99% at 808 nm) of the outcoupling cavity mirror, the contribution of the second-order light transmission on the ultimate 1.06-µm light field is only 15% (60% × 50% × 50%) compared to the first-order one. The second- and higher-order transmission therefore have very limited impacts on the lasing performance and the discrete diffraction patterns of the whole waveguide array device. Besides, the pump (808nm) and lasing wavelengths (1.06 µm) are close to each other, thus exhibiting similar modal profiles and effective index as well as very close coupling constants. As a consequence, it is not surprising that identical intensity patterns for both active and passive regimes are observed in experiments and simulation (as shown in Fig. 2). In addition, in such a mixture process of light propagation (optical guiding), beam evolution (evanescent coupling, as shown in Figs. 3(a) and 3(b)), as well as laser generation (lasing), only slight disturbance on the intensity distribution can be identified by comparing the simulated and experimental results, suggesting good quality of the FsLDW waveguide array and good alignment of the optical setup. In fact, even with 3° tilting (laterally) of the incident light, the guided light is very much scattered and attenuated, as illustrated in Fig. 3(c). The modal disturbance is mainly caused by imperfect waveguide boundaries, i.e. laser-induced tracks, and gain-guiding effect in the waveguide array.

 

Fig. 3. Discrete diffraction of 1.06-µm light propagation in the waveguide array when placing the incident beam at (a) WG₀, (b) WG₊₇, and (c) again at WG₀ but with 3° tilting (laterally). The white frame area in (c) is already outside the waveguide array region.

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Furthermore, to investigate how the coupling condition impact the far-field discrete diffraction pattern, we replaced the incoupling lens by an f = 50 mm one (focal spot size of 40 µm approximately) and located the focal spot again at WG₀. In this case, the intensity profile (simulation result in Fig. 4(a) and experimental in Fig. 4(b)) is very much dissimilar to that in Figs. 2(b) and 2(c), exhibiting waveguide laser emission with modal distribution in a more continuous manner. Further tuning of the modal distribution under passive regime by using larger focal spot sizes is also possible according to the simulation (not shown here), but the laser performance of the waveguide array is seriously deteriorated in experiments because of the inefficient optical coupling.

 

Fig. 4. (a) Simulation and (b) experimental results of discrete diffraction of 1.06-µm light propagation in the waveguide array when using incoupling lens with f = 50 mm (placing the incident focal spot at WG₀). White dotted lines and circles denote the laser-induced tracks position and the focal spot location of the incident light, respectively. Scale bar denotes 30 µm.

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3.2 Waveguide laser array: lasing performance

The laser performance of the waveguide array was studied when pumping at WG₀ and WG_±7 with incoupling lens of f = 25 mm, the alignment was separately optimized for reaching maximum output power for each measurement. The input-output dependences are summarized in Fig. 5. The exact lasing thresholds P_th and slope efficiencies η are also indicated separately for each measurement. When pumping at WG₀, the lasing threshold and slope efficiency are determined to be P_th = 70.7 mW and η = 37%, exhibiting a better lasing performance than pumping at WG_±7 (P_th = 108.3 and 110.5 mW, η = 27% and 26.7%). This is because in the latter cases, a portion of light is scattered away from the waveguide array area (as illustrated in Fig. 3(b)), resulting in higher scattering losses and thus higher lasing threshold and lower lasing slope efficiency according to the modified Caird analysis [34]. The maximum output power, in case of pumping at WG₀, reaches 226.4 mW at an incident pump power of 705.7 mW, giving an optical-to-optical conversion efficiency of 32%. During measurements, no much changes on the laser modal distribution of waveguide array can be identified by increasing/decreasing the pump power, suggesting negligible thermal loading and good lasing stability of FsLDW arrayed structures. By comparison, the lasing performance of previously reported single “double-line” Nd:YAG waveguide [35] is better than that of arrayed “double-line” waveguides in this work in terms of lasing threshold and slope efficiency, which is because of the lower waveguide losses (1.6 dB/cm) therein [35].

 

Fig. 5. Output power as a function of incident power obtained from fabricated waveguide array with pump beam located at WG₀ (red), WG₊₇ (olive) and WG₋₇ (blue). Solid and dashed lines represent linear fit of the experimental data.

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4. Conclusion

In summary, we have fabricated and characterized FsLDW channel waveguide laser array in Nd:YAG. Evanescent coupling under passive regime is proved to be also valid at active regime, giving identical discrete diffraction patterns of intensity distribution in both regimes. The discrete diffraction patterns can be further tuned by adjusting the optical coupling condition. The experimental results in this work are well supported by the simulation based on FD-BPM. Future work may, on one hand, focus on further optimization of the fabrication recipe and reduction of scattering losses caused by the imperfect waveguide boundaries and, on the other, explore disordered photonic lattices with more complex geometries at active regime for exotic effects, e.g., Anderson localization [12,13].