radially polarized laser beam (generation)
Generation of radially polarized laser beams
Radially polarized laser beams are known to have a unique polarization distribution and related focusing characteristics that only the electric component parallel to the optical axis exists on the optical axis near the focal point. This implies that energy flow vanishes around the focus. While several attempts to generate the beam with radial polarization have been reported, stable and reliable laser sources has not been realized. We designed and fabricated a novel optical element which satisfies the Brewster condition for the radial direction. This conical Brewster prism1 was applied to a diode pumped Nd:YAG laser. As a result, a radially polarized laser beam was generated. This optical element is very simple.
In addition, we utilized the birefringence of a laser material itself to generate a radially polarized beam achieving an ultimately simple structure of laser cavity and hence extremely stable laser operation3-5. In this case, the generation mechanism is based on the difference of the refractive index between the ordinary and extraordinary rays in the crystal. Because the laser crystal is a c-cut YVO4 crystal that has positive birefringence, the stability limit for the extraordinary ray is longer than that for the ordinary ray. As a result, only the extraordinary ray, namely the radially polarized light, can stably oscillate by properly adjusting the cavity length. The longer the crystal length is, the easier the alignment of the cavity length is. This is because the stable region of the laser cavity only for the radial polarization is roughly proportional to the crystal length. Because the the laser consists of a laser crystal and two cavity mirrors, the configuration for the generation of a radially polarized beam is very simple resulting in the stable operation.
This technique is also applicable to isotropic laser media if a c-cut birefringent material is inserted into a laser cavity. This idea was realized for Nd:YAG and Ti:sapphire laser with a c-cut non-doped YVO4 crystal.6,11 The output power over 1W was observed bringing out nearly maximum ability of the laser cavity used in the experiment. Accordingly, drastic increase of the output power is expected if the pumping power is increased without any change of basic configuration.
An axially symmetric, polarized laser beam with narrow linewidth and fine tunability was developed by using a two-mode optical fiber.7 The principle of the generation was based on the fact that radially and azimuthally polarized mode beams are degenerated in a LP11 mode propagating in a multi-mode optical fiber as shown in Fig. 4. A stress on the optical fiber can be used for selecting a mode we want. Firstly, we generated a TEM01 mode beam with narrow linewidth and fine tunability from an external cavity diode laser (ECDL). A phase adjustment plate made by a thin transparent material was inserted in the external cavity. By adjusting the position and the angle of the plate, a TEM01 or TEM10 mode beam can be generated from an ECDL. Then the beam was passed in a two-mode optical fiber that was properly stressed. A desired mode such as TE01, TM01 or hybrid mode beam can be selected. We believe that the generations of TEM01 or TEM10 mode beam from an ECDL and wavelength tunable axially symmetric, polarized beams were reported for the first time to our best knowledge.
Photonic crystals fabricated by an auto-cloning technique are known to have the birefringence due to its directional structure. This feature can be used as polarization optical elements such as polarization selective mirror and wave plate with spatially arbitrary pattern of polarization. We demonstrated generation of axially symmetric, polarized beams and helical beams by using photonic crystal polarization elements.
Radially and azimuthally polarized beams were generated by using polarization selective photonic crystal mirrors8 with concentric polarization pattern. Nd:YAG laser beams with radial and azimuthal polarization were generated by simply replacing a output coupler with a photonic crystal mirror. The laser performance are not affected by the replacement of the mirror8.
Single higher-order transverse mode operation of radially polarized Nd:YAG laser was demonstrated by using a photonic crystal mirror that has an annulus with low reflectivity of radial polarization. Because this annulus with low reflectivity provides a cavity loss, the transverse mode of the output beam will be higher-order corresponding to a radius of the annulus. Although a single TM02 mode operation has been demonstrated in the paper12, this method will be applied for higher-order transverse modes.
Helical beam is related to the spiral phase shift resulting in an orbital angular moment. We demonstrated simultaneous generation of helical beams with linear and radial polarization9 (linearly and radially polarized Laguerre-Gaussian beams with an orbital angular momentum) by using a segmented half-wave plate placed inside a Ti:sapphire laser cavity. The radially polarized Laguerre-Gaussian beam changed the transverse intensity profile as the beam propagation. At the far field, the pattern is not doughnut-shaped but almost a fundamental Gaussian beam. The polarization is nearly circular indicating that the an orbital angular momentum of the radially polarized Laguerre-Gaussian beam changed to an spin angular momentum. (Because the quality of Figs. 2 to 4 in the paper9 are not good, higher quality images are shown below.)
The amplification of a radially polarized beam13 is an important issue for laser processing to obtain sufficient laser power maintaining the beam quality. The double-clad fiber laser amplifier is an attractive means for this purpose. We demonstrated the amplification of a radially polarized laser beam, which was generated by using birefringence of a Nd:YVO4 rod3, by a Yb-doped double-clad fiber laser with larger core diameter13. when the input power of the radially polarized laser beam was 100 mW, the output power was more than 1 W. The intensity and polarization distributions were mostly maintained. When the input power was smaller than 100 mW, the amplified spontaneous emission (ASE) became stronger. The intensity distribution of the ASE was very close to the Gaussian function indicating that the gain produced in the fiber core was partly consumed for the ASE. However, the ASE can be suppressed by sufficient input power even if conventional Yb-doped double-clad fiber laser. If the structure or gain distribution of the core is suitably modified, further improvement and higher performance will be expected.
A simple cavity is expected to offer a reliable and robust generation method of cylindrical vector beams. Thermal birefringence of the laser medium can be used to separate ordinary and extraordinary rays, namely azimuthally and radially polarized beams. Thermal lensing is also helpful to make a laser cavity with flat mirrors stable. We demonstrated that selective oscillation of cylindrical vector beams by thermal effects14 can be qualitatively elucidated based on the stability diagram of a laser cavity. Further, the cavity configuration to extract higher output power for radially or azimuthally polarized laser beam can be easily predicted owing to the analysis of the stability diagram. The output power more than 40 W in a single transverse mode was obtained without an aperture for both radially and azimuthally polarized beams. Note that the pumping module used in this experiment is capable of generating the output power of 100 W in multi-transverse mode. Thus, the generation of the output power of 40 W in a single transverse mode is quite efficient.
An annular beam with radial polarization is intensively expected to provide an extremely small spot size down to 0.36 l / NA. An easy way to produce such a beam is to convert a Gaussian beam with linear polarization to a radially polarized beam and to block the central area by a circular mask. We have demonstrated an alternative way by using a second harmonic generation process15. The beam generated has a very narrow width, 1/40th of the radius of the annulus. This narrowing is based on the phase matching of the second harmonic generation, where an angle between the c-axis of a nonlinear crystal and the input beam is strictly determined.
Detection of a longitudinal electric field generated by strong focusing of a radially polarized beam using second harmonic generation10
It is well known that a strong longitudinal electric field is generated near the focus when a radially polarized beam is tightly focused. In order to detect the longitudinal electric field without disturbing the electric field near the focus, we developed a new scheme for non-invasive detection of the field by second harmonic generation8. In this technique, second harmonic generation of higher order transverse mode beams are discussed because lowest order radially and azimuthally polarized beams used in the experiment are considered to be a superposition of two first-order Hermite-Gaussian beams with orthogonal polarizations and beam patterns. We carefully selected a (110) zinc selenide crystal as a non-linear crystal suitable for the experiment, which has only three equivalent non-linear tensor components and higher non-linear susceptibility than conventional, birefringent non-linear bulk crystals used for the generation of second harmonic wave. Furthermore, this crystal is transparent in the wavelength region of the second harmonic wave for a fundamental Nd:YAG laser beam.
The second harmonic wave generated with a HG01 mode beam is a superposition of HG02 and HG00 mode beams. Consequently, the intensity pattern depends on the phase shift between the two modes. The calculation predicted that the beam is three-lobe pattern. Based on this indication, the total second harmonic pattern is expected to be figure of "eight" as shown in the figure below. Note that the z component of nonlinear polarization, Pz, induced by a longitudinal electric field has a phase shift of p compared to that induced by a transverse electric field. As a result, the intensity in the beam center is lower than that by a azimuthally polarized beam due to the destructive interference. This discrepancy of intensities in the center between radially and azimuthally polarized beams is the contribution of the longitudinal electric field. In the paper, interesting mode conversion is also described observed when another cylindrically polarized beam (alternating mode) is used. The alternating mode is expressed as a superposition of HG01 and HG10 modes with orthogonal polarizations and the phase shift of p/2.
References
1) Y. Kozawa and S. Sato, Generation of a radially polarized laser beam by use of a conical Brewster prism, Optics Letters 30, 3063 (2005). link
This research was introduced in Photonics Spectra, December 2005. (http://www.photonics.com/spectra/research/XQ/ASP/preaid.272/placement.HomeIndex/QX/read.htm)
2) Y. Kozawa and S. Sato, Focusing property of a double-ring-shaped radially polarized beam, Optics Letters 31, 820 (2006). link
3) K. Yonezawa, Y. Kozawa and S. Sato, Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal, Optics Letters 31, 2151 (2006). link
4) Y. Yonezawa, Y. Kozawa and S. Sato, A compact laser with radial polarization by using a birefringent laser medium, Jpn. J. Appl. Phys.. 46, 5160 (2007). link
5) Y. Yonezawa, Y. Kozawa and S. Sato, Focusing of radially and azimuthally polarized beams through a uniaxial crystal, Journal of Optical Society of America A 25, 469 (2008). link
6) Y. Kozawa, K. Yonezawa and S. Sato, Radially polarized laser beam from a Nd:YAG laser cavity with a c-cut YVO4 crystal, Appl. Phys. B 88, 43 (2007). link
7) T. Hirayama, Y. Kozawa, T. Nakamura and S. Sato, Generation of a cylindrically symmetric, polarized laser beam with narrow linewidth and fine tunability, Optics Express 14, 12839 (2006). link
8) Y. Kozawa, S. Sato, T. Sato, Y. Inoue, Y. Ohtera and S. Kawakami, Cylindrical vector laser beam generated by the use of a photonic crystal mirror, Appl. Phys. Express 1, 022008 (2008). link
9) H. Kawauchi, Y. Kozawa, S. Sato, T. Sato and S. Kawakami, Simultaneous generation of helical beams with linear and radial polarization by use of a segmented half-wave plate, Optics Letters 33, 399 (2008). link
10) Y. Kozawa and S. Sato, Observation of longitudinal field of focused laser beam by second harmonic generation, Journal of Optical Society of America B 25, 175 (2008). link
11) H. Kawauchi, Y. Kozawa and S. Sato, Generation of radially polarized Ti:sapphire laser beam using a c-cut crystal, Optics Letters 33, 1984 (2008). link
12) Y. Kozawa and S. Sato, Single higher-order transverse mode operation of a radially polarized Nd:YAG laser using an annularly reflectivity-modulated photonic crystal coupler, Optics Letters 33, 2278 (2008). link
13) T. Chubachi, Y. Kozawa and S. Sato, Amplification of a radially polarized laser beam using an Yb-doped double-clad fiber,” Optics Letters 34, 716 (2009). link
14) A. Ito, Y. Kozawa and S. Sato, Selective oscillation of radially and azimuthally polarized laser beam induced by thermal birefringence and lensing, Journal of Optical Society of America B 26, 708 (2009). link
15) S. Sato and Y. Kozawa, Radially polarized annular beam generated through a second-harmonic-generation process, Optics Letters 34, 3166 (2009). link
16) A. Ohtsu, Y. Kozawa and S. Sato, Calculation of second-harmonic wave pattern generated by focused cylindrical vector beams, Appl. Phys. B 98, 851 (2010). link
17) Y. Kozawa and S. Sato, Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams, Optics Express, 18 10828 (2010). link
18) Y. Kozawa and S. Sato, Demonstration and selection of a single-transverse higher-order-mode beam with radial polarization, Journal of Optical Society of America A, 27, 399 (2010). link
19) A. Ito, Y. Kozawa, S. Sato, Generation of hollow scalar and vector beams using a spot-defect mirror, Journal of Optical Society of America A, 27, 2072 (2010). link
20) K. Kano, Y. Kozawa, S. Sato, Generation of a Purely Single TransverseMode Vortex Beam from a He-Ne Laser Cavity with a Spot-Defect Mirror, International Journal of Optics, 2012, 359141 (2012). link
21) Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, S. Sato, Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam, Optics Express, 19(17), 15947 (2011) link
22) K. Shimohira, Y. Kozawa, S. Sato, Transverse mode control by manipulating gain distribution in a Yb:YAG ceramic thin disk, Optics Letters, 36(21), 4137 (2011) link
23) R. Takeuchi, Y. kozawa, and S. Sato, Polarization coupling of vector Bessel-Gaussian beams, J. Opt., 15(7), 075710 (2013), link, selected as a "Highlights of 2013"
24) S. Ipponjima, T. Hibi, Y. kozawa, H. Horanai, H. Yokoyama, S. Sato, T. Nemoto, Improvement of lateral resolution and extension of depth of field in two-photon microscopy by a higher-order radially polarized beam, Microscopy, 63(1) 23 (2014) link
25) S. Vyas, Y. Kozawa, S. Sato, Generation of radially polarized Bessel-Gaussian beams from c-cut Nd:YVO4 laser, Opt. Lett., 39(4), 1101 (2014) link
26) S. Vyas, Y. Kozawa, S. Sato, Generation of a vector doughnut beam from internal mirror He-Ne laser, Opt. Lett., 39(7), 2080 (2014) link
27) S. Kanazawa, Y. Kozawa, S. Sato, High power and highly efficient amplification of radially polarized beam using Yb doped double-clad fiber, Opt. Lett., 39(10), 2857 (2014) link
28) S. Segawa, Y. Kozawa, S. Sato, Demonstration of subtraction imaging in confocal microscopy with vector beams, Opt. Lett., 39(15), 4529 (2014) link
