July 15, 2006 / Vol. 31, No. 14 / OPTICS LETTERS 2151

Generation of a radially polarized laser beam byuse of the birefringence ofa c-cut Nd:YVO4 crystal

Kazuhiro Yonezawa, Yuichi Kozawa, and Shunichi SatoInstitute of Multidisciplinary Research for Advanced Materials, Tohoku University, Katahira 2-1-1, Aoba-ku,

Sendai 980-8577, Japan

Received April 13, 2006; revised May 2, 2006; accepted May 4, 2006; posted May 8, 2006 (Doc. ID 69968)

We demonstrated the generation of a radially polarized laser beam from an extremely simple laser resonatorincluding a c-cut Nd:YVO4 crystal as a laser medium. The oscillation in the radial polarization was based onthe optical path difference between an extraordinary ray and an ordinary ray induced by the birefringenceof the crystal. By simply adjusting the distance between two cavity mirrors, only the extraordinary ray be-came stable for the oscillation, resulting in the generation of a radially polarized beam. The beam was verystable even at low power output and is expected to be a promising radially polarized laser source because ofits excellent simplicity. © 2006 Optical Society of America

OCIS codes: 140.3410, 140.3580, 260.1440, 260.5430.

Radially polarized laser beams are attracting muchattention due to their unique properties1,2 in manyresearch fields, such as optical trapping,3,4 materialprocessing,5,6 particle acceleration,7 and high-resolution microscopy.8 There are many reports onthe generation of radially polarized beams, for ex-ample, an interferometric superposition of linearlypolarized beams,7,9 a partial superposition of severalbeams in a complex laser resonator,10 and a coherentsuperposition of higher-order transverse modes withpolarization elements and phase adjusters.11 Thesemethods using superposition techniques, however,have a peculiar problem with beam stability, becausethe position of each optical element should be alignedwith a precision of the order of the wavelength. Incontrast, a simple laser structure has the advantageof improved stability. A conical Brewster prism12 wasdeveloped and applied for direct generation of a radi-ally polarized laser beam from a laser cavity based onthe difference of polarization selectivity between theradial and azimuthal polarization components. Bire-fringence of a calcite crystal incorporated into a lasercavity was utilized for the generation of an azimuth-ally polarized, pulsed ruby laser beam.13 The diverg-ing beam produced by a pair of lenses in the cavitywas used to spatially separate ordinary rays (azi-muthal polarization) from extraordinary rays (radialpolarization). A similar effect based on thermally in-duced birefringence was reported for a Nd:YAGlaser,14 while thermal birefringence can be achievedunder a strong pumping condition.

In this Letter, we demonstrate an ultimatelysimple method for the generation of a radially polar-ized laser beam. A c-cut Nd:YVO4 crystal was em-ployed as a laser medium with cylindrically symmet-ric birefringence that distinguishes a radiallypolarized beam from an azimuthally polarized one.By simply adjusting the length of the two-mirror cav-ity, a radially polarized beam that was stable andpump-power independent was obtained without anyadditional optical element or superposition tech-

nique.

0146-9592/06/142151-3/$15.00 ©

Figure 1 shows a schematic of a laser cavity for thegeneration of a radially polarized beam. In general,a-cut Nd:YVO4 crystal is commonly used because ab-sorption and emission cross sections for �-polarizedlight are higher than for �-polarized light.15 Conse-quently, the polarization of the output laser beam islinear, and its direction is parallel to the c-axis of thecrystal (� polarization). However, we adopted a c-cutNd:YVO4 crystal at the cost of lower laser efficiencyto ultimately achieve simple cavity configuration forgeneration of a radially polarized beam. TheNd:YVO4 crystal has positive birefringence, and therefractive indices for ordinary and extraordinary raysare no=1.9573 and nex=2.1652 at 1.064 �m, respec-tively. When the beam passing the birefringent crys-tal is diverging or converging, the ordinary and ex-traordinary rays will take different paths because ofthe different refractive indices. Suppose that the cav-ity consists of flat and concave mirrors and the sepa-ration of the mirrors is almost the same as the radiusof the concave mirror. Because the extraordinary raywill be largely refracted at the crystal surfaces com-pared with the ordinary ray, as shown in Fig. 1, thelimit of the stable cavity length for the extraordinary

Fig. 1. Schematic of a laser resonator for generation of aradially polarized beam. It is shown that the ordinary andextraordinary rays take different optical paths in theNd:YVO4 rod because of the different refractive indices.

HR, high reflection.

2006 Optical Society of America

2152 OPTICS LETTERS / Vol. 31, No. 14 / July 15, 2006

ray becomes longer than that for the ordinary ray.Thus, a cavity length range in which the extraordi-nary ray is stable but the ordinary ray is unstablewill be generated. In this cavity, only the extraordi-nary ray can oscillate at a cavity length slightlylonger than the radius of the concave mirror. Becausethe extraordinary ray corresponds to the radially po-larized light, a radially polarized beam will be gener-ated in this way.

According to this concept, we designed the lasercavity shown in Fig. 1. A c-cut Nd:YVO4 rod of 2 mmdiameter was used. Although the typical length of aNd:YVO4 crystal is nearly 1 mm in conventional la-sers, a 15 mm long rod was used in this experimentbecause the separation of the ordinary ray from theextraordinary ray becomes large with increasing rodlength. A 98% reflection flat mirror and a high-reflection concave mirror of 250 mm radius were usedas an output coupler and a rear mirror, respectively.In this case, the limit of the stable cavity length wasslightly longer than 250 mm. An aperture was in-serted between the rear mirror and the rod to sup-press higher-order transverse modes.

Figure 2 shows a pumping scheme for the c-cutNd:YVO4 laser rod. Five laser diodes at 808 nm wereused for pumping the Nd:YVO4 rod. The output ofeach laser diode was 2 W. These laser diodes emit theTM-mode beam, the polarization of which is parallelto the c-axis of the rod, enabling us to increase thepumping efficiency by �-polarization pumping. Thelaser diodes were arranged around the rod at thesame angle to one another to achieve cylindricallysymmetric gain distribution, where possible, which ispreferable for a ring-shaped radially polarized beam.

At a cavity length shorter than 250 mm, this cavityproduced a nonpolarized TEM00-mode beam as ex-pected. When the cavity length was gradually in-creased beyond 250 mm, the transverse mode pat-tern suddenly changed, indicating that the TEM00mode was unstable and had switched to another cav-ity mode. Figure 3 shows intensity distributionswhen the cavity length was over 250 mm. Figure 3(a)is a total intensity distribution of the laser beam.There was a dark spot at the center of the laser

Fig. 2. Pumping scheme for the c-cut Nd:YVO4 crystal. (a)Directions of the c-axis of the Nd:YVO4 crystal and the po-larization of the pump beam from a laser diode. (b) Cross-sectional view of the arrangement of the laser rod and di-ode lasers for pumping.

beam, and the beam shape was like a doughnut. The

output power of this beam was 75 mW. The intensitydistributions of the beam after it passed through alinear polarizer are shown in Figs. 3(b)–3(e). The ar-rows indicate the direction of the linear polarizer.Two-lobe-shaped intensity distributions along the di-rection of the polarizer were obtained, indicating thatthis beam from the cavity was radially polarized. Asis well known, a linearly polarized Laguerre–Gaussian mode beam and a superposition ofHermite–Gaussian TEM01 and TEM10 modes withouta fixed phase relation will show the doughnut-shapedintensity distribution seen in Fig. 3(a). However, theformer is linearly polarized, and the latter will showdifferent features from Figs. 3(b)–3(e). The variationof the intensity distribution with the change of thelinear polarizer as shown in Figs. 3(b)–3(e) is aunique feature of the so-called R-TEM01

* mode,12,16

which is also expressed as a superposition of theHermite–Gaussian TEM01 and TEM10 modes with or-thogonal polarizations and zero phase shift. In fact,the intensity profile along the line crossing the cen-ters of these lobes showed good agreement with thetheoretical profile of the Hermite–Gaussian TEM01mode, as shown in Fig. 3(f). The polarization contrastratio estimated from these image data, for example,Figs. 3(b) and 3(d), was approximately 20, indicatinga good polarization property of the obtained laserbeam.

It should be emphasized that the mode stability ofthe radially polarized beam obtained in this experi-ment was very high. For achieving the oscillation, aprecision tool such as a micrometer-based stage wasnot needed. Even though the pumping power of thelaser diodes was changed, the oscillation in the radialpolarization was maintained in the whole pumpingrange. In addition, the oscillation was not disturbedby the mechanical noise commonly generated in labo-ratories. It was possible to achieve the oscillationwithout an aperture, but careful alignment wasneeded to obtain and maintain the oscillation. There-fore, it is better to insert an aperture for high-order

Fig. 3. Intensity distributions of the laser beam. (a) Totalintensity distribution. (b)–(e) Intensity distributions afterthe beam passes through a linear polarizer. The arrows in-dicate the directions of the polarizer. (f) Intensity profile(gray circles) along the vertical line intersecting the centerof (a) and the result of fitting to the TEM01 mode profile(solid curve).

July 15, 2006 / Vol. 31, No. 14 / OPTICS LETTERS 2153

mode suppression and stabilization of the beam oscil-lation. The oscillation was not affected by the posi-tion of the aperture. Similar radially polarized laserbeam oscillation with improved thermal conductivityis expected by use of a Nd:GdVO4 laser crystal.17 It isnoted that direct generation of an azimuthally polar-ized laser beam will be possible by using negative bi-refringence crystal. Finally, note that this experi-ment is to our knowledge the first demonstration ofgeneration of a radially polarized beam solely by us-ing the birefringence of the laser crystal, althoughgeneration of a radially polarized ring and arc beamsby use of an a c-cut Nd:YVO4 crystal in conjunctionwith a Brewster-angled intracavity axicon was re-ported very recently.18 The energy efficiency will begreatly improved by optimizing such parameters ascrystal length, doping level, pumping scheme, andcavity configuration.

In conclusion, we have demonstrated generation ofa radially polarized beam by use of a c-cut Nd:YVO4crystal. The structure of the laser was ultimatelysimple and consisted of the laser medium and twomirrors. By adjusting the separation between themirrors, the birefringence of the c-cut Nd:YVO4 crys-tal inherently enforced the oscillation in the radialpolarization. The oscillation was independent ofpumping power and very stable even in the low out-put power range.

K. Yonezawa’s e-mail address is k�yone@mail.tagen.tohoku.ac.jp.

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