1. Introduction

Cylindrical-vector beam (CVB) exhibits axially symmetry both in field-amplitude and polarization with polarization singularity in beam axis, and is characterized by doughnut-shaped intensity pattern. Generation of the CVB with radial or azimuthal polarization directly from an active resonator has attained much attention^1-4, based on their many significant applications as in particle physics⁵, optical tweezers⁶, high-resolution microscopy⁷ and material processing⁸, etc. And now, various techniques are developed to form such beams inside a laser including the utilization of coherent summation² or polarization-selective components (for example, axis symmetrically grating⁹ and Brewster axicon^{4, 10, 11}) etc. However, as indicted in [2], big challenges are encountered in improving the laser efficiency, beam’s cylindrical symmetry and polarization purity simultaneously.

Recently the three-dimensional subwavelength grating, referred to as photonic crystal grating (PCG) and fabricated by autocloned technique^12-15, appeared as a candidate of intracavity polarization selector based on its polarization-dependent band structure. The PCG is composed of high- and low-refractive-index layers alternately, and its each layer is shaped into concentric corrugations (groove), and exhibits artificial birefringence and also the different reflectance (transmittance) to the transverse electric (TE, polarization orthogonal to grating groove) and transverse magnetic (TM, polarization parallel to grating groove) waves. The interference effects of the multilayer stack enhance the polarization extinction ratio (PER) and wavelength passband feature of this component.

Furthermore, previously, the solid-state laser that emitted CVBs was side-pumped with the multiples LDs or lamp^{2, 4, 16}. Therein the lasing mode easily deviated from cylindrical symmetry due to the complication in arranging pump symmetry, and the laser efficiency was limited by the low overlap ratio between the lasing and pumping areas in lasant rod. Meanwhile an extra aperture was required to suppress the high-order transverse mode. Comparably, the LD end-pumped microchip laser configuration could be extend to generate CVBs with significant advantages in achieving efficient oscillation and controlling modal symmetry, based on the near unity overlap between the pump area and lasing mode (including the radial- or azimuthal-polarization mode) and intrinsic gain-aperture effect.

In this paper, by use of two PCGs as the radial- and azimuthal-polarization-selective output couplers respectively, we presented the efficient excitations of the CVBs from an LD end-pumped Nd:YAG ceramic microchip laser with high polarization purity and cylindrical symmetry. The details are given as follows.

2. Experimental setup

Figure 1 shows the experimental setup for the end-pumped Nd:YAG microchip laser to produce the CVBs. The gain medium was 0.45 at. % neodymium-doped yttrium aluminum garnet (Nd:YAG) ceramic microchip with 1.9-mm thickness and 15-mm diameter. Its planar front surface was coated for high transmission at 808nm and total reflection at 1064nm, while its planar rear surface was antireflection-coated at 1064nm. This microchip was sandwiched in between two flat copper plates, and both copper plates had the 2-mm-diameter light tunnel drilled along the cavity axis. The copper plate clingy to the rear surface of Nd:YAG microchip was connected to the 20°C water cooling. A fiber-coupled 808-nm laser diode with 400-µm core diameter and 0.4 numerical aperture was used as the pump source. The coupling optics consisting of two focus lens with 8.5mm focal length was used to focus the pump light into ~400µm spot size onto the front surface of ceramic gain medium. A planar and patterned PCG was deployed as an output coupler. The total length of laser cavity was 6.5cm. The laser power and beam profile were monitored with a powermeter and CCD camera, respectively.

 

Fig. 1. Experiment setup of an end-pumped microchip laser with a PCG as the output coupler. The gain microchip is water-cooled on its rear surface.

Download Full Size | PDF

 

Fig. 2. The paradigmatic images of PCG mirror obtained by use of scanning electron microscope (SEM): (a) cross section and (b) surface view. The pitch of concentric corrugations in (b) is 466 nm.

Download Full Size | PDF

Figure 2 plots the paradigmatic illustrations of a PCG output coupler fabricated by autocloned technique. The multilayer triangle corrugations in Fig. 2(a) were composed of high- and low-refractive-index layers (Nb₂O₅/SiO₂) alternately with subwavelength layer thickness. The surface view in Fig. 2(b) revealed concentric pattern in single layer with a subwavelength pitch of 466 nm. This grating is fabricated by stacking Nb₂O₅ and SiO₂ alternately onto a concentric grooved glass substrate by RF bias sputtering. By setting deposition parameter such as gas pressure, main and bias RF power and bias voltage schedule for appropriate etching, the effects of sputter-deposition and sputter-etching are balanced, and the triangular wave shape is reproduced and duplicated stably. The detailed descriptions on the autocloned fabrication method could be found in Ref. 12-15.

The polarization-dependent bandpass structure of subwavelength multilayer grating is based on combining the form-birefringence effect of subwavelength grating with the resonant interference of a multilayer structure, which has been widely investigated with the term “high-spatial- frequency grating”^17-19. As a result, the multilayer concentric pattern exhibits anisotropic spectra bandpass characteristics to TE (radial polarization) and TM (radial polarization) waves. Thus it is reasonable subwavelength multilayer concentric grating is expected to act as axisymmetric-polarization output coupler. To realize such component, a finite-difference time-domain (FDTD) calculation¹⁴ can be performed, with the desired transmittances (or reflectances) to different polarization components (TE wave and TM wave), as well as the PER would be determined by choosing the period and incline angle of the triangle corrugation, layer’s thickness and numbers. In our experiment, for TE-wave PCG output coupler, the pitch of triangle groove was 500 nm, the thick of each Nb₂O₅/SiO₂ layer was 634 nm and total stack thickness was 5072 nm (corresponding to 8 pairs of Nb₂O₅/SiO₂ layers); for TM-wave PCG, the pitch of triangle groove was 500 nm, the thick of each Nb₂O₅/SiO₂ layer was 585 nm and total stack thickness was 2925 nm (corresponding to 5 pairs of Nb₂O₅/SiO₂ layers). Figure 3 shows the measured reflectivity of both PCGs for TE and TM wave respectively. As seen, the TE-wave PCG had the reflectivity of about 83% for radial polarization with high transmission for azimuthal polarization at 1064nm, while the TM-wave PCG had the reflectivity of about 85% for azimuthal polarization with high transmission for radial polarization at 1064nm.

 

Fig. 3. The measured reflectances of (a) TE-and (b) TM-wave PCGs for different polarizations.

Download Full Size | PDF

3. Experiment results and discussions

When the center of PCG was located to the cavity axis, the laser emitted the annular beam at 1064nm, and the annular shape persisted within full range of pumping level above the lasing threshold. Figure 4 depicts the beam power as a function of absorbed pump power. When TE-wave PCG output coupler was applied, the threshold pump power for the lasing, in the name of absorbed pump power (P_abs), was 2.2W, corresponding to 4.6W of incident pump power. Above the threshold, the beam power increased linearly with P_abs in a slope efficiency of 68.2%. With further increase of P_abs, the beam power began to saturate, and then reached a maximum value of 610mW at P_abs=3.7W, thereafter decrease when P_abs>3.7W. In the case of that TM-wave PCG output coupler was applied, the laser power showed similar variation with P_abs. With the increase of P_abs above the lasing threshold of 1.8W absorbed pump, the laser power increased linearly with 47.7% slope efficiency, and then tended to saturate, gradually reached a maximum value of 626mW at P_abs=3.78W before decreasing. The measured laser spectrum at P_abs=3.7W when applying TE-wave PCG output coupler is shown in Fig. 5, where the multi-peak structure revealed the laser oscillated in multi longitudinal modes.

The reduction of laser power at higher pumping in Fig. 4 was attributed to the thermal lensing effect of the Nd:YAG microchip, which based on the following experimental tests. It was observed, without water cooling, the laser output power was less than the power as that shown in Fig.4. When we used a metal plate to block the pump beam, with single-surface cooling, the temperature of gain microchip was cooled to 20°C in the absence of pump irradiation. When pump beam with the power corresponding 3.7-W absorbed pump power was illuminated on the gain medium suddenly by removing the blocking plate quickly, the laser gave an instantaneous output power much more than 940 mW. Within minutes the power quickly decreased and finally stabilized at the level of around 610 mW or 626 mW in the case of TE- and TM-wave PCG output couplers applied respectively. The observed transition in output power was an evidence of the appearance of thermal lensing effect, and it reflected the buildup of equilibrium between the temperature rise induced by pump absorption and insufficient cooling. As only rear surface of Nd:YAG microchip is connected to water cooling, the heat accumulation on its front surface side at higher pumping could not be removed efficiently and thereafter caused large temperature gradient inside the microchip. Consequently the thermal lensing becomes seriously and degraded the output power. Provided the gain microchip could be cooled much more efficiently, for example by applying the efficient water-cooling to both surfaces of microchip gain medium after redesigning the copper heat sink, the laser power could be scaled up with high pumping.

 

Fig. 4. Output power of the laser as a function of the absorbed pump power.

Download Full Size | PDF

 

Fig. 5. Measured laser spectrum at P_abs=3.7W when TE-wave PCG output coupler was used.

Download Full Size | PDF

The laser beams profile was monitored by use of a CCD camera with a 45-mm-focal-length lens placed at the optical path in front of camera. The near- and far-field intensity distributions of the beam are measured by moving the CCD camera fore and aft the focus spot respectively. Figure 6(a) and (b) represent the measured beam profile at P_abs=3.7 W when TE-wave PCG output coupler was applied, where the doughnut-shaped cross sections with dark center were discerned clearly. To measure the polarization state of laser beam, a linear polarizer was inserted perpendicularly into the optical path behind the output coupler. The beam profile of the transmitted light through the polarizer was monitor by CCD camera. Figure 6(c)-(f) showed the measured variations of the far-field intensity distributions of the transmitted beam profile when the polarizer axis was rotated at different directions respectively. A seen, in these images, the two-lobe structures were parallel to the polarizer axis’s directions respectively. This means that, the local polarization state of the off-axis lobe was parallel to direction of corresponding polarizer axis, namely, identical to the axial direction of itself. Therefore the laser beam was radially polarized.

 

Fig. 6. (a) Far-field and (b) near-field intensity distributions of the laser beam profile, and (c)-(f) variations of far-field intensity distributions of the passage beam through the polarizer analyzer with different orientations of the polarizer (White arrows indict the directions of polarizer analyzer’s axis).

Download Full Size | PDF

 

Fig. 7. (a) Far-field and (b) near-field intensity distributions of the laser beam profile, and (c)-(f) variations of far-field intensity distributions of the passage beam through the polarizer analyzer with different orientations of the polarizer (White arrows indict the directions of polarizer analyzer’s axis).

Download Full Size | PDF

Similarly the images in Fig. 7(a) and (b) depict the far- and near-field intensity distributions of the beam profile at P_abs=3.78W when applying TM-wave PCG output coupler, in which both profiles have the doughnut-like shape with a dark center. The polarization state of this beam was also checked with a linear polarizer analyzer by use of the same method described above. Figure 7(c)-(d) show the far-field intensity distributions of the transmitted beam profile through the linear polarizer analyzer. As seen, the two-lobe structure in each image was orthogonal to the polarizer’s axis. This revealed that, the local polarization state of each off-axis lobe was parallel to the direction of corresponding polarizer axis, namely, orthogonal to the axial direction of each lobe. Thus it was concluded the laser beam was azimuthally polarized beam when applying TM-wave PCG output coupler.

Herein it is emphasized that the transverse profiles of obtained radial- and azimuthal-polarization beams didn’t show substaintial change at whatever the available pump power above the lasing threshold. Therefore there was no need to insert an aperture into laser cavity to suppress high-order mode oscillation at high pump power, and this made the laser system simple and robust. Instead of an additional intracavity aperture, the end-pumped microchip laser configuration imposed an intrinsic gain aperture to the oscillating mode via the near unity overlap between the pump absorption area and emission area in the gain medium.

The polarization purity of the obtained CVBs was determined by following method. Firstly a 300-µm-diameter aperture was placed into the optical path at a distance of 68cm behind PCG, where the diameter of full beam was about 3.9mm and much larger than the aperture size. The leakage power through the aperture was maximized by lateral adjustment to the aperture’s position. This selected light fragment was considered to be lineally polarized, and its PER was measured to be 61:1 at P_abs=3.7 W for radial-polarization beam, and 58:1 for azimuthal-polarization beam at P_abs=3.78W, demonstrating high polarization purities of the emitted beams provided by respective PCG output couplers.

Physically both radially and azimuthally polarized beam, so called R-TEM_01* mode and A-TEM_01* mode, can be considered as synthesis of different polarization configurations from two linearly polarized TEM₀₁ mode if their planes of polarization are perpendicular^{9, 20}. The propagation factor - M square (M ²) of such beam is equal to 2 theoretically. The M squares of CVBs obtained in our experiment were also measured respectively by the following way. Firstly a lens with 45mm focal length was placed into optical path at a distance of 40 cm behind the output coupler. It was assumed the laser beam propagated along z axis of Cartesian coordinates. The beam waist (ω₀, half of focus spot size) and its location of focused beam were found and measured by moving the CCD camera along z-axis direction. Thereafter the Rayleigh range (Z _R), where spot size is 1.414 times the measured focus spot size, was determined by moving camera toward either side of the focus spot. The measured ω₀, as well as Z _R, had two components at transverse directions (x and y) of beam profile. Correspondingly both the components of M² could be calculated by the equation on M ²=πω ² ₀(Z_Rλ), where λ was lasing wavelength of the laser and equal to 1064 nm. At P_abs=3.7W, for radial polarized laser output, we measured x- and y-direction components of 2ω₀ and Z _R equal to 0.100 mm and 3.55 mm respectively, so it was determined that M ² _x=M ² _y=2.08. In the case of azimuthally polarized laser output, at P_abs=3.78W, it was measured 2ω₀=0.099 mm and Z _R=3.43 mm for their respective x-direction components; and 2ω₀=0.099 mm and Z _R=3.41 mm for their y-direction components, correspondingly M ² _x=2.11 and M ² _y=2.12 respectively. These measurements indicted the obtained CVBs had near-diffraction limited quality.

4. Conclusions

In summary, the excitations of cylindrical-vector beams with radial and azimuthal polarization were obtained from LD end-pumped microchip laser, by use of PCGs as the axisymmetric-polarization- dependent output coupler. Both laser beams showed the high polarization purity and diffraction-limited beam quality, as well as improved laser efficiency when compared with that in previous investigations^{2-4, 16}. With end-pumped microchip configuration, the laser is simple and robust, and there is no need to insert an additional aperture into laser cavity to suppress the high-order mode oscillation. Provided the cooling problem is solved in future, the laser powers could be scaled up with higher pump power. These result manifested that, the end-pump microchip laser configuration, in conjunction with the subwavelength multilayer concentric grating as polarization mirror, could offer an important way to achieve cylindrical vector laser beams with high laser efficiency and excellent beam quality. The progresses made in this research are important for various kinds of applications.