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/2 retardation 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

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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

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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. (a) The pattern formation from unstable to stable region. (b) The range of each polarization. AP notes azimuthally polarized, RP notes radially polarized, and UnP notes unpolarized.

Figure 3. Intensity distributions of ring patterns at the various z2 values：(a) z2 = 12.200 cm (azimuthal polarization), (b) z2 = 12.290 cm (radial polarization), and (c) z2 = 12.360 cm (azimuthal polarization). Each red arrow shows the direction of the polarizer and “N” represents the ring pattern without adding polarizer. 2.3 The quality of polarization state To measure the purity of the polarization, the spatial distribution at the specific angles were selected with a 300-μm-wide slit. After using the slit to determine the measured portion of the pattern, the beam passed through the polarizer, and the power was measured by using the power meter. The slit and polarizer were mounted on a rotation stages to alter different

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/03/2014 Terms of Use: http://spiedl.org/terms angles, and the horizontal direction was set to be 0°. When the orientation of the slit being -30° for z2=12.200 cm, the typically transmitted power results are plotted in Fig. 4(a). It shows the measured power dependence of the orientation of the polarizer. By using the sine-squared function to fit the experimental data, the curve of red line demonstrates the polarization direction and degree of polarization. The degree of polarization by the following definition can be given (Imax - Imin)/(Imax + Imin), where Imax and Imin are the intensity of maximum and minimum of the fitting curve, respectively. The polarization direction and degree of polarization determined by rotating the orientation of the slit, the results are presented in Fig. 4(b). A slope of 0.999 ± 0.006 with a shift of 90° was observed from the red linear fitting curve for the case of azimuthally polarized laser. A degree of polarization is greater than 96.3% ± 0.9% for various orientations of the slit.

Linear fit of the experiment data 120 1.0 180:(b) 100 0.8 150 o 120 0.6 80 no 90 o 0.4 60 60N 0.2 30 40 0.0 0 ,-...... -20.., 0 50 100150 200 250 300 350 -90 -60 -30 0 306090 Polarizer angle (degree) Orientation of slit (degree) Figure 4. (a) Dependence of the measured output power for the ring pattern on the polarizer angle with the slit angle of -30° and z2=12.200 cm. (b) Polarization direction and degree of polarization as a function of the slit angle. Further changing the position of output coupler toward stable region, the beam polarization transferred from azimuthal to radial polarization such as z2=12.290 cm. The degree of polarization and the polarization direction at different position was also measured and computed in the abovementioned way. Figure 5(a) shows the transmitted power as a function of the polarization angle with a slit angle of 60°. The slope for z2=12.290 cm was 1.019 ± 0.005, and 92.2% ± 2.0% in degree of polarization, respectively, as shown in Fig. 5(b). A shift of 90° between polarization direction and slit angles disappear especially for radial polarization. For z2=12.360 cm, the characteristics of polarization were the same as the case with z2=12.200 cm. The degree of polarization is 93.7% ± 1.5%. By way of contrast, the degree of polarization is lower than that of z2=12.200 cm.

0.1 Linear fit of the experiment data 1.2 120G 90 1.0 (b) 100m 60 to 0.8 o ° 30 80 0.6 o 0 sÿ 0.4 60 N 0-30 0.2 ó -60 40 á 0.0 N-90 20 0 50 100 150 200 250 300 350óos -90 -60 -300 306090 Polarizer angle (degree) Orientation of slit (degree) Figure 5. (a) Dependence of the measured output power for the ring pattern on the polarizer angle with the slit angle of 90° and z2=12.290 cm. (b) Polarization direction and degree of polarization as a function of the slit angle.

3. ANALYSIS AND DISCUSSIONS The mechanism of the transformation of the polarization could be resulted from the different extracting efficiency between the e- and o-rays. The self-consistence of q-parameter based on the round-trip ABCD transfer matrices was employed to analyze the behavior of o-ray and e-ray in the three-element cavity configuration. In the previous work [26], the spot size of the e-ray and o-ray at M1 could be calculated by the abovementioned method, as shown in Fig. 6(a) with

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/03/2014 Terms of Use: http://spiedl.org/terms z1=20.0 cm. When z2 is less than the boundary of stable region for the e-ray, z2 = 12.1620 cm in Fig. 6(a), the intrinsic oscillation of o-ray existed which corresponds to azimuthally polarized beam in this region. However, a radially polarized beam can be obtained in the region around zA, which could be considered from the extracting efficiency of the cavity mode. Figure 6(b) displays the spot-size distributions of the o- and e-rays in the gain medium at z2 = 12.1267 cm. Because the cavity configuration for e-ray is close to the boundary of the stable region, a short Rayleigh range leads to the larger divergent angle and spot-size distribution in the gain medium than those of o-ray. It is expected that the extracting efficiency of e-ray is greater than that of o-ray. Thus, a radially polarized laser beam can be generated. When z2 decreases to that the cavity configurations for both of the e- and o-rays are stable, such as Fig. 6(c) at z2 = 12.200 cm, the spot size had a higher average-value for the o-ray and the azimuthally polarized beam was preferably generated again. Thus, a sequence of azimuthal, radial, and azimuthal polarizations again could be observed in experiments as decreasing z2. The region associated with the polarization transform represents that the extracting efficiencies of the o- and e-rays are close to lase both rays. An unpolarized light was generated. (a) o-ray e-ray (b) zZ zp 12.1627 cm ,-. 0.20 0.12 0.16 E 0.12 E 0.08 0.08 y 0 2 4 6 8 .N. (e) z2= zR 12.2000 cm .iì ó0.093 °o. 0.04 0.090 0.087:------12.15 12.20 12.25 12.30 0 2 4 6 8 The distance between L and OC, z2 (cm) The position in the gain medium (mm)

Figure 6. (a) Spot size versus z2 at z1=20 cm was calculated by ABCD law involving extraordinary ray (red short-dash line) and ordinary ray (blue solid line), respectively. (b) Spot size at various position within the range of gain medium for z2=12.1627 cm and z2=12.2000 cm.

4. CONCLUSION In conclusion, the variations of CV polarizations around the boundary of the stable region were observed in a diode- pumped Nd:GdVO4 laser with a three-element cavity. We offer a simple analysis by considering the extraction efficiencies of e- and o-rays to clarify the transformation of polarization states when the cavity length was increased. Cylindrical vector lasers were performed with excellent slope efficiencies being greater than 36.7% and the degree of polarization being greater than 92.2% ± 2.0%. Moreover, we would like to emphasize that cylindrical vector beams can be simply produced by using a generalized cavity without inserting any intra-cavity elements and significantly potentially applied in various fields.

ACKNOWLEDGMENTS

The authors would like to thank the National Science Council of the Republic of China for financially supporting this research under Contracts No. NSC 101-2112-M-006-014-MY3.

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