Generation and Transformation of Azimuthal and Radial Polarization in a Typically Three-Element Nd:Gdvo4 Laser

Generation and transformation of azimuthal and radial polarization in a typically three-element Nd:GdVO4 laser Ken-Chia Chang, and Ming-Dar Wei* Department of Photonics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan *E-mail: [email protected] ABSTRACT Based on the birefringence of the laser crystal and cavity design, a simple method directly generate radially and azimuthally polarized laser beams with a c-cut Nd:GdVO4 in a three-element cavity. The experimental results reveal that the transformations of polarization are observed by tuning cavity length with hundreds of micrometer. The slope efficiency is maintained up to 36.7% and output power reaches up to 1.34 W with the pump power of 5 W. The degree of polarizations can be greater than 92.2% for both of azimuthally and radially polarized beams. By considering the extraction efficiency from pump energy with the condition of changing the cavity length for o-ray and e-ray, mechanism of polarization transformation in the laser is discussed. Keywords: vector beam, solid-state laser, diode-pumped 1. INTRODUCTION Cylindrical vector (CV) beams have attracted much interest in the past decade because of the spatial-dependent polarization. The radial and azimuthal polarizations with axial symmetry are the famous cases because of the practical importance in the various applications of particle acceleration [1], optical trapping [2], high resolution microscopy [3], and material processing [4,5]. Various methods for the passive or active mechanisms have been developed to generate radially and azimuthally polarized beams, which were significantly completely reviewed by Zhan [6]. The passive method was used to vary the polarization outside the laser cavity that incorporated into employing a process of interference [7], liquid crystal spatial light modulator (LC SLM) [8], and λ/2retardation plate with spatially variable of the directions of fast axis [9]. However, the disadvantages of most of passive methods had a problem with beam stability or needed precise alignment of discrete optical elements. On the contrary, the active methods can directly generate the CV beams inside the laser cavity by using intra-cavity elements, including birefringent elements [10-12], an intra-cavity axicon [13–15], and thermally induced birefringence to the isotropic laser rods [16-17], as well as polarization-selective elements such as photonic crystal grating and diffraction mirror [18-19]. Recently, a gain distribution method by the shape of pump profile was utilized for the direct generation of radial polarization in microchip Nd:YVO4 laser [20]. By the same way, radially or azimuthally polarized Bessel–Gaussian beams for the lowest-order or higher-order transverse mode were demonstrated [21-22]. Apparently, the effect of birefringence plays an important role in producing CV beams. The index difference of ordinary ray (o-ray) and extraordinary ray (e-ray) will induce distinguishing stable regions for the e-ray and the o-ray. Thus, the edges of the stable region can survive one of these rays only. For a hemispherical cavity configuration, the inherent birefringence of the c-cut Nd:YVO4 or Nd:GdVO4 crystal was used to oscillate radially polarized beam that enabled the e-ray to become stable near the boundary of stable region [23-24]. A radially polarized beam was generated by inserting an undoped c-cut YVO4 crystal to offer birefringence with an isotropic Nd:YAG laser in hemispherical cavity [12]. Unfortunately, only radial polarization can be generated for a simple cavity with hemispherical configuration. Using the characteristics of thermally induced birefringence of an isotropic Nd:YAG can generate radially or azimuthally polarized beam [16-17], but the strong pumping condition is required. Moreover, designed the cavity which consists of uniaxial birefringent crystal and intra-cavity lens to realize radially or azimuthal polarized laser beam, was demonstrated in a cw Yb:YAG laser [11]. In fiber laser system, a method was reported to generate CV beams with a combination of the c-cut calcite crystal and three-lens telescope [25]. Both of the mentioned case, the polarization state of laser output could be easily switched by properly adjusting an intra-cavity Laser Beam Shaping XV, edited by Andrew Forbes, Todd E. Lizotte, Proc. of SPIE Vol. 9194, 919415 © 2014 SPIE · CCC code: 0277-786X/14/$18 · doi: 10.1117/12.2061489 Proc. of SPIE Vol. 9194 919415-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/03/2014 Terms of Use: http://spiedl.org/terms lens in their schemes. However, it needed inserting an intra-cavity birefringent medium or setting more optical components. In this work, a simple three-element cavity configuration can be demonstrated the transform of laser beam between radial and azimuthal polarization by only slightly adjusting the cavity length in Nd:GdVO4 laser. Although the similar phenomenon was observed for the method of shaping the pump profile in Ref. 21, the purity of polarization remained to be further improved, and the mechanism of inducing the transform of the polarization was different. Moreover, a three-element cavity with a general diode pump can sustain the radial and azimuthal polarization without inserting an intra-cavity element or an intra-cavity aperture stop. 2. EXPERIMENTS 2.1 Experimental setup The schematic of experimental setup is depicted in Fig. 1. A fiber-coupled laser diode (LD) with the wavelength of 808- nm was employed as the pump source. A collimation element of optical imaging accessory (OIA) was used to focus the pump beam of LD onto the laser crystal, resulting in an approximately 450 μm beam diameter. The three-element laser resonator consisted of a concave mirror M1, an intracavity lens L, and an output coupler OC. The concave mirror M1 with a radius of curvature of Rc=100 mm, an anti-reflection coating for 808 nm and a high-reflection coating for 1064 nm 3+ acted as one of the end mirror. The gain medium was a c-cut, 1 at. % Nd doping, Nd:GdVO4 crystal with dimensions of 3 mm × 3 mm × 8 mm, and both end faces of crystal were anti-reflection broadband coating from 800 to 1350 nm. The laser crystal was mounted in a copper block, which was connected the 18°C cooling water to reduce the thermal lens effect. The planar mirror M2 was used as an output coupler of 91% reflectivity. An intra-cavity lens had the focal length f=75 mm and an anti-reflection coating for 1064 nm. The lens was located between the Nd:GdVO4 crystal, and the distance from L to M1 and from L to OC were z1 and z2, respectively. The output power and beam pattern could be measured by using a power meter and a charge-coupled device (CCD) camera, respectively. The output coupler M2 was posited on the translation stage and could be shifted along the optical axis. R=100mm f = 75 mm R= ci Zt Z2 808 nm LD OIA Nd:GdVO, M1 L M2(OC) Laser cavity Figure 1. The experimental setup, where z1 labels the distance between M1 and L, and z2 labels the distance between L and OC. 2.2 Polarization transformation results In the experiment, the symmetry pattern of the laser could be achieved by the precision alignment of the cavity. When the cavity configuration operated around the boundary of the stable region, the intensity distribution of the ring patterns were obtained from the various positions of z2, as shown in Fig. 2(a) with z1=20 cm and the pump power of 4 W. The size of ring patterns decreased as increasing z2, which indicates the decrease of the divergent angle as tuning the cavity configuration from the unstable to stable region. In the region with the ring pattern, not only the size of the pattern but also the polarization was varied and was dependent on the cavity length. When z2 increased, the polarizations of the laser were obtained in a sequence of azimuthal polarization, unpolarization, radial polarization, unpolarization and finally retransferring to azimuthal polarization, as shown in Fig. 2(b). As z2 > 12.385 cm, the polarization keeps unpolarization and the pattern gradually transform toward Gaussian mode. Figure 3 displays the various patterns with and without adding a polarizer to verify the polarization characteristics. The beam patterns in Fig. 3 were captured by a CCD after passing them through a linear polarizer, in which the red arrow indicated the direction of the polarizer and “N” represented the original pattern without adding the polarizer. Figure 3(a) with z2 = 12.200 cm shows that adding the polarizer caused the part of the pattern corresponding to the parallel direction of the polarization angle to disappear. An azimuthally polarized beam was formed. On the contrary, the radial polarization has that the portion of the pattern, which is perpendicular to the direction of the polarizer, disappeared, as shown in Fig. 3(b) as z2 = 12.290 cm. When z2 increased, the azimuthal polarization occurred, as shown Proc. of SPIE Vol. 9194 919415-2 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/03/2014 Terms of Use: http://spiedl.org/terms in Fig. 3(c) with z2 = 12.360 cm. Although the laser cavity was operated around the boundary of stable region, the slope efficiencies in the various z2 were near the typically stable laser systems in the range from 36.7% to 39.0% and a lasing threshold powers were approximately in the range from 1.3 W to 1.6 W. The higher of lasing threshold near the boundary of stable region, which may be attributed to the effects of the high-order transverse mode oscillation. z:=12.200 cmz2 =12.255 cmz:=12.204cmz-2 =12.320 cm z:=12.360 cm I I z2 (cm) 12.175 12.235 12.280 12.300 12.335 12.385 instable region stab Figure 2.

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