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Abstract
In this work, we fabricate a hybrid waveguide-grating vortex laser in Nd:YSAG by using femtosecond laser direct writing (FsLDW). The detailed parameters of the hybrid structure are fixed by optical simulation. In experiments, an efficient vortex beam is produced in the passive operation at 1064 nm. Under optical pumping at 808 nm, a dual-wavelength waveguide laser at 1060/1062 nm as well as a waveguide-grating vortex laser at 1060 nm are obtained. The laser performance and diffraction properties of the generated vortex laser are detailed, studied, and discussed, providing meaningful reference results toward the practical applications of FsLDW and waveguide-grating structures in integrated photonics.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Light carrying orbital angular momentum (OAM), also known as vortex beam, possesses the helical phase front. The intensity distribution of the vortex beam presents annular-shape and the phase singularity is located at the center of the beam. Vortex beam has a spiral phase factor ∼exp(ilφ), where l is the topological charge (TC), theoretically infinite, and φ is the azimuthal angle [1–3]. These properties make vortex beam very promising in a variety of applications including optical communication [4,5], optical manipulation [6,7], super-resolution imaging [8,9], sensing [10,11], etc. Therefore, researchers are intrigued by vortex beam and there are an increasing number of methods to generate vortex beam in recent years, such as spiral phase plate [12,13], spatial light modulator [14,15], q-plate [16,17], metasurface [18,19], etc. However, the disadvantages of either complicated preparation or laser footprint limit their applications in integrated photonic circuits. In contrast, fork gratings are receiving increasingly more attention due to their simple structures and easy fabrication as well as efficient generation of vortex beams. Meanwhile, reducing the total footprint of the fork grating also provides a solution for the miniaturization of optical devices. In recent years, a number of excellent works have reported on generating vortex beams using the fork gratings [20–24]. For example, Miao et al. employed a microring cavity realizing vortex laser output with large OAM and introduced complex refractive index modulation to form an exceptional point [25]. Zhang et al. used a dual-polarization microchip laser simultaneously generating vortex laser of TEM00 and LG modes with different polarizations in the cavity [26]. Hayenga et al. fabricated the first tunable OAM microring cavity laser which is composed of an active microring resonator and an S-shaped waveguide and achieved tunable OAM laser on fully integrated semiconductor platform [27]. The demonstrated vortex beam lasers show great potential in applications of optical manipulation and communication [28,29].
Femtosecond laser direct writing (FsLDW) is one of the most powerful approaches for micro-/nano- fabrication of miniaturized photonic devices, such as gratings [30] and waveguides in transparent dielectrics [31–34], due to its unique advantage of non-contact and maskless fabrication with an ultra-high resolution [35,36]. As a compact solution to laser sources, waveguide lasers feature characteristics of reduced laser threshold, enhanced laser efficiency, and small footprint, rendering them promising for integrated photonics applications [37]. Furthermore, waveguide laser architecture offers great flexibility in terms of waveguide layout and gain medium, thereby providing rich possibilities in the aspect of incorporating additional optical functionalities, such as gratings, into the cavity [37–39]. The combination of waveguide and fork gratings is therefore a promising strategy for integrated vortex beam generation. The vortex beam laser plays an important role in optical fiber sensor [40] and waveguide sensor fabrication [41].
As a commonly used laser gain medium, Nd:YAG crystal has the characteristics of high gain, high efficiency, low laser threshold, and high optical quality [42]. However, the cross relaxation between ions will reduce the laser efficiency when the ions are mixed at a higher concentration, and its fluorescence line is narrow, which is difficult to achieve ultrafast laser output [43]. In case of Nd:YSAG, the Sc3+ in YSAG will preferentially replace the position of Al3+ that is originally doped in YAG. Since the diameter of Sc3+ is larger than that of the Al3+, the spacing of Nd3+ and the YAG unit cell will increase. These will weaken the quenching effect of Nd3+ and broaden the fluorescence spectrum line width while maintain the original advantages of Nd:YAG for laser generation [43,44]. These features make Nd:YSAG crystal a promising gain medium. However, experimental demonstration of Nd:YSAG waveguide laser has not yet been reported.
In this letter, we demonstrate a waveguide-grating vortex beam generator directly fabricated in the Nd:YSAG crystal by FsLDW. The confocal micro-photoluminescence (µ-PL) measurement is employed to analyze the refractive index modulation of grating and waveguide. The guiding and diffraction properties have been studied by end-face coupling system at 1064 nm. Under 808-nm optical pumping, a vortex beam array at 1.06 µm has been achieved.
2. Design and fabrication
2.1 Design of the waveguide-grating vortex generator
The Nd:YSAG crystal used in this work has a dimension of 10(x) × 5.68(y) × 2(z) mm3 with the x-y and x-z surfaces optically polished. The schematic diagram the waveguide-grating structure is shown in Fig. 1. The integrated waveguide-grating structure is composed of three segments: a cladding straight waveguide, a cone waveguide, and a fork grating. The cladding straight waveguide is beneficial for achieving single-mode laser oscillation in the Fabry-Pérot cavity, and the cone waveguide with a gradually increasing diameter extends the Gaussian beam from the straight waveguide output to cover the fork grating area to achieve high diffraction efficiency. Here, the mode mismatch between the straight and the cone waveguides introduce additional losses to the whole device. In order to optimize the dimension of each section of the hybrid structure and thus to minimize the mode mismatching, here, we use the commercial software BeamPROP, Rsoft, based on the finite-difference beam propagation method (FD-BPM) for optical simulation. In the simulation, Radial Calculation in 2D model is employed. The cross sections of the straight and cone waveguides define the waveguide geometries, namely rectangle and trapezoid shapes. As the stating parametric conditions, the diameters and lengths of the straight/cone waveguides are set to be 30/30-50 µm and 3/2.61 mm, respectively. The refractive indices of waveguide core section and the substrate are set to be 1.86, and the refractive index modification at the laser-modified track region is set to be -2.7 × 10−3, as discussed in the following, with a Gaussian-type profile. In the simulation, a combination of triangular and rectangle meshes are used with an average grid size of 50 × 50 nm2. The simulation results are shown in Fig. 2. Firstly, we determine the length of the cone waveguide. Before the calculation, a monitor is added to detect the output power in the simulation. Henceforth, the Launch MOST Optimizer/Scanner is used to perform parametric scanning. After the calculation, the relationship between cone waveguide length and output power can be obtained. The transmittance is obtained by dividing the output power by the input power. Figure 2(a) displays the length-dependent optical transmission of the cone waveguide. It is clear that the optical transmission increases with the length of the cone waveguide. However, if the cone waveguide is too long, stable single-mode laser oscillation cannot be formed in the straight waveguide, resulting in unstable mode of the output vortex beam. After balancing the stable single-mode laser oscillation and high optical transmittance, the cone waveguide length is determined to be 4 mm.
Fig. 1. Schematic illustration of the vortex laser generator processed in the Nd:YSAG crystal. (a) The input end-face of the straight cladding waveguide. (b) The top view of the straight cladding waveguide. (c) The top view of the cone waveguide. (d) The end-facet image of the fork grating.
Fig. 2. (a) Simulated optical transmission as a function of the cone waveguide length. (b) Simulated optical transmission as a function of the diameter of the cone waveguide output-face.
The diameter of the cladding straight waveguide is set to be 30 µm in order to maintain single-mode operation with low-loss waveguiding properties. Correspondingly, the diameter of the cone waveguide input end-face is also 30 µm. The diameter of the cone waveguide output end-face is determined by the optical simulation as well. Similarly, we use parametric scanning in the simulation. It can be seen from Fig. 2(b) that the optical transmittance is the highest when the diameter of the output end-face is about 50 µm. Thus, the diameter of cone waveguide output end-face is determined to be 50 µm. In order to match the fork grating area better, the laser spot from the cone waveguide output need be further enlarged. Based on the numerical aperture (N.A.) of the cone waveguide, the distance between the output facet of the waveguide and the fork grating can be determined. The maximum incidence angle θ can be calculated by the following formula:
where Δn ≈ 2.7 × 10−3 is the difference in refractive index between the waveguide region and the filament region. The n ≈ 1.86 is the refractive index of the crystal at 1.06 µm. When the distance between the output end-face of the cone waveguide and the fork grating is about 70 µm, the diameter of the laser spot is calculated to be approximately 55 µm, which is sufficiently large to cover the effective grating area.2.2 Fabrication of the hybrid waveguide-grating structure
The well-designed waveguide-grating structure is prepared by a femtosecond laser system (Astralla, Conherent Inc., USA) at 808 nm. For waveguide fabrication, we use single pulse power of 92.6 µW with a pulse width of 100 fs, the laser pulses are focused by an objective lens (50×, N.A. = 0.55) inside the crystal. The waveguide structures are written along the y-axis and the focused laser spot moves at a velocity of 0.5 mm/s. For reference, a pure cladding straight waveguide (with a diameter of 30 µm) and a pure cone waveguide (with a diameter gradually increasing from 30 to 50 µm) are fabricated.
The fork grating with a period of 3.9 µm is fabricated beneath the crystal surface near 70 µm away from the waveguide output end-face. The laser pulses with the power of 32 µW are focused by the same objective lens. The scanning speed is 0.02 mm/s. The fork grating is designed as a two-dimensional (2D) structure. Compared with the one-dimensional fork grating, 2D structure is able to extend the diffraction orders, so as to achieve the generation of a vortex laser array.
3. Results and discussion
3.1 Confocal µ-PL characterization of Nd:YSAG crystal
The refractive index modulation of the Nd:YSAG crystal processed by FsLDW is analyzed employing a confocal µ-PL spectroscopy system. Figure 3(a) displays the µ-PL spectra of different regions around the waveguide area. The µ-PL intensity of waveguide and substrate are nearly identical, indicating the good preservation of luminescence properties within the waveguide volume. It is observed that the µ-PL intensity of the laser-induced filament is weaker than the other two regions. This result manifests that the localized crystalline lattices are damaged in processed regions by FsLDW. To further investigate the mechanism of the refractive index modulation, the intensity and frequency shift mapping are measured, as illustrated in Figs. 3(c)-(d). The signal frequency of the laser-induced filament appears remarkably blue-shifted at 868 cm-1 (see Fig. 3(d)), indicating the localize lattice expansion. The lattice damage and extension are considered to be the causes of the refractive index reduction.
Fig. 3. (a) The Raman spectra of the substrate, guiding and waveguide filament region. (b) The Raman spectra of the substrate and grating filament. (c), (d) The Raman mapping of the waveguide input surface with the intensity and frequency shift of the peak at 868 cm-1. (e), (f) The Raman mapping of the fork grating with the intensity and frequency of the peak at 868 cm-1.
The µ-PL signals of the fork grating region are illustrated in Fig. 3(b). The intensity mapping of the fork grating is measured as illustrated in Fig. 3(e). The µ-PL intensity of the laser-induced filament is less than that in the substrate. This indicates that the lattice in the processed region is damaged. However, the frequency shift of the fork grating does not appear as shown in Fig. 3(f), indicating that the damage of the fork grating is weaker than the waveguide.
3.2 Nd:YSAG waveguide laser
To investigate the laser performance of Nd:YSAG cladding waveguide (without grating structure), a typical end-face coupling arrangement is employed. In the experimental setup, a tunable CW Ti:Sapphire laser (Coherent MBR) with a central waveguide at 808 nm is used as the pump source to excite the CW laser. A plano-convex lens (f = 25 mm) is utilized for coupling the pump laser into the input end-face of the waveguide. The polarization of the incident laser is adjusted by a half-wave plate. The waveguide laser cavity is consisting of a waveguide, a pump mirror (M1 with a transmittance of 99.8% at 808 nm and a reflectivity of >99.9% at 1064 nm), and an output mirror (M2 a reflectivity of about 60% at 1064 nm). The used two mirrors are butt-adhered to the end-facets of the Nd:YSAG waveguide to provide optical feedback. The output laser from the cladding waveguide is collected by an objective lens (20×, N.A. = 0.40) and detected by a power meter sensor.
The characteristics of the Nd:YSAG waveguide laser are summarized in Fig. 4. When using the pump power of 0.804 W, the maximum output laser power is measured to be 133.8 mW (with a slope efficiency of 28.3%) under TE-polarization pumping, and 58.5 mW (with a slope efficiency of 12.3%) under TM-polarization pumping, as shown in Fig. 4(a). By adjusting the half-wave plate, the output power of the Nd:YSAG cladding waveguide for all-angle polarization is measured (see Fig. 4(b)). It is clear that the output power is polarization-dependent. This is caused by the asymmetry of the waveguide structure, resulting in polarization-dependent optical gains. The output laser is a dual-wavelength waveguide laser with generated wavelengths of 1060 nm and 1062 nm, which cannot be achieved in Nd:YAG. The dual-wavelength laser performance is determined to be almost polarization-independent, which shows only slight difference while adjusting the pump polarization (see Fig. 4(c)). The inset of Fig. 4 is the near-field mode profile of the output waveguide laser with TE and TM polarizations, respectively. The experiment result shows that the laser mode profile is a good single-mode operation. It is worth noting that, this is the first, to the best of our knowledge, experimental demonstration of Nd:YSAG waveguide laser.
Fig. 4. (a) The output power as a function of the pump power obtained from Nd:YSAG cladding waveguide. (b) The output power of the Nd:YSAG cladding waveguide for all-angle polarization. (c) The laser emission spectrum of the output laser under TE and TM polarizations. The insets are the modal profiles of output laser under TE and TM polarizations.
3.3 Waveguide-grating vortex laser generation
Next, we measure the optical guiding properties of the waveguide and the optical diffraction properties of the fork grating at 1064 nm (i.e., in the passive regime). Here, we use a solid-state 1064-nm laser for optical excitation. An objective lens (10×, N.A. = 0.25) is used for coupling the laser into the input end-face of the waveguide-grating structure. The generated vortex beam modes are captured by the CCD camera as show in Fig. 5(a) to Fig. 5(i). The annular intensity distribution with a dark spot in the center is clearly seen, which is a symbol of the vortex beam generation. These experimental results indicate that our designed waveguide-grating structure is suitable for vortex beam generation at 1064 nm in the passive regime. In particular, a cylindrical lens is employed for determining the topological charge (TC) of the vortex beam. In this way, a vortex beam with TC of N (absolute value of TC) will be focused into the N + 1 bright lines. And this method is also capable of determining the positive and negative values of TC. If TC is positive, the focused spot of the vortex beam is orientation along the counter diagonal; otherwise, its orientation is along the main diagonal.
Fig. 5. (a)-(i) The intensity profiles of the far field output laser and the TC obtained be the cylindrical lens.
Furthermore, in the active regime, we then investigate the vortex laser performance of the waveguide-grating structure. The experimental setup is similar to that used in Section 3.2. Since the objective lens cannot collect all vortex laser modes, it is replaced by a plano-convex lens with a focal length of f = 50 mm. The pump laser is coupled into the waveguide to excite the 0-order Gaussian mode. The 0-order Gaussian mode travels to the fork grating area and is reflected by the cavity mirror M2. Thus, the laser oscillation is strongly affected by the fork grating structure.
The experimental results of the waveguide-grating vortex laser are summarized in Fig. 6 to Fig. 7. The central wavelength of pump laser and vortex laser are 808 nm and 1060 nm, as illustrated in Fig. 6(a). Compared with the pure waveguide laser, as discussed in Section 3.2, only the 1060-nm laser can be excited in the waveguide-grating structure. This can be due to the additional scattering loss introduced by the presence of fork grating structure, reducing the laser gain at 1062 nm. The output power of vortex laser in the (0, 0) diffraction order is also polarization-dependent (see Fig. 6(b)), which is similar to the results in Fig. 4(b). Due to the high loss of the fork grating, the generated laser powers of the vortex at high diffraction orders are relatively weak. Thus, CCD camera almost cannot capture the patterns of the vortex beam clearly. The patterns of the vortex lasers that are capable of being captured clearly are displayed in the insets of Fig. 6(a). According to the insets of Fig (6), the intensity distribution of (+1, 0) diffraction order vortex laser is asymmetrical, which is mainly due to gain-oriented effects.
Fig. 6. (a) The spectra of the pump laser and the output vortex laser. The inset is the intensity profile of (0, 0), (+1, 0) order output vortex laser mode. (b) The output power of the (0, 0) order vortex laser for all-angle polarization.
The output power of the generated vortex laser array at different diffraction orders is measured to further analyze the laser properties, and the results are shown in Fig. 7. It is clear that the output power of the (0, 0) order vortex laser is much higher than the other diffraction orders, and the maximum output power of the (0, 0) order vortex laser is determined to be 96.24 mW. Compared with the output power (which is 133.8 mW) of pure waveguide structure, the output power of the (0, 0) order vortex laser decreases by 28.1%. The laser slope efficiency of pure waveguide and waveguide-grating structure is 28.3% and 18.1%, respectively. The slope efficiency falls by 36%. Under 808-nm pumping, i.e., in case of active operation, the power ratio of the vortex laser in high order mode is 1.33%. In contrast, this value is 3.3% in the passive operation at 1064 nm. The above results indicate that, the grating structure introduces additional losses that reduce the total output laser power by around 28.1% and the power ratio of diffracted high-order modes by around 60%. By comparison, we believe the reduction in optical diffraction properties during active operation is the main cause for the relatively weak intensity in the high-order modes. The slope efficiency and relative diffraction efficiency of the hybrid waveguide-grating generator are listed in Table 1. It is observed that the relative diffraction efficiencies are relatively low. The main cause may be that the center of the waveguide is slightly misaligned to the center of the grating. This also leads to the difference in the output power of, e.g., the (-1, 0) order and the (+1, 0) order. We believe the laser performance and diffraction properties of the hybrid waveguide-grating structure can be improved further by optimizing the FsLDW processing parameters. Furthermore, we believe the nonuniformity of the fabricated grating tracks, in terms of locations and dimensions as shown in Fig. 3(e), also have an impact on the generated vortex lasers in terms of laser efficiency and beam quality. We will further optimize the fabrication parameters and try to improve the fabricated grating uniformity and thus the generated vortex laser efficiency and beam quality in future work.
Table 1. Slope efficiency (η), relative diffraction efficiency (η1) of the output vortex laser
4. Conclusion
In this work, a waveguide-grating vortex laser generator has been fabricated by FsLDW in Nd:YSAG crystal. The design scheme of the hybrid structure is discussed. The guiding performance of the waveguide and the diffraction properties of the grating are demonstrated at 1064 nm. A vortex laser array at a wavelength of 1060 nm is obtained by 808-nm pumping. The output power and diffraction efficiency are relatively weakened in comparison to that in passive operation, partly due to the slight misalignment of waveguide and grating structures and the additional losses introduced by the grating structures. In future work, we will focus on improve the diffraction efficiency via optimizing the FsLDW processing parameters. Our results suggest that the FsLDW is a promising technique for definition of hybrid waveguide device and the well-designed waveguide-grating configuration has great potential for optical-field steering applications in integrated photonics.
Funding
National Natural Science Foundation of China (12074223); Natural Science Foundation of Shandong Province (2022HWYQ-047, ZR2021ZD02); Taishan Scholar Foundation of Shandong Province (tspd20210303, tsqn201909041); Shandong University.
Acknowledgments
The authors gratefully acknowledge Mr. Q. Lu from Shandong University for his kind help on crystal processing.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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