May 15, 2003 / Vol. 28, No. 10 / OPTICS LETTERS 807

Production of radially or azimuthally polarized beams insolid-state lasers and the elimination

of thermally induced birefringence effects

Inon Moshe, Steven Jackel, and Avi Meir

Non-linear Optics Group, Soreq Nuclear Research Center, Yavne 81800, Israel

Received December 2, 2002

Production and amplification of radially and azimuthally (tangentially) polarized laser beams are demonstrated.Based on the different focusing between radially and tangentially polarized light in thermally stressed isotropiclaser rods, Nd:YAG laser oscillators were developed to produce low-loss stable oscillation in a single polariza-tion. Pure radially polarized light at 70 W with M 2 � 2 and on-axis impure radially polarized light at 150 Wwith M2 � 2.5 were achieved. The radially polarized beams were then amplified while good beam qualityand polarization purity were retained. Complete elimination of thermal-birefringence-induced aberrationswas demonstrated. This should allow much better beam quality from rod-based high-power lasers. © 2003Optical Society of America

OCIS codes: 140.0140, 140.3410, 140.6830.

Tangentially or radially polarized laser light isimportant in many fields, such as material process-ing,1 particle trapping or acceleration,2 and focusingthrough high-numerical-aperture lenses.3 An addi-tional application treated here utilizes the uniquecylindrical symmetry of these polarizations to by-pass thermal-birefringence-induced aberrations inrod-based solid-state lasers and thus to avoid the needfor complex birefringence compensators.

Various methods of producing radially polarizedbeams in laser oscillators have been suggested. Po-larization discrimination was implemented by useof conical elements4 and complex Brewster win-dows5 but found to be complicated and involvedpractical diff iculties. In CO2 lasers, polarization-sensitive diffractive mirrors were used to form radi-ally or tangentially polarized beams.6 This methodis practical and suitable in CO2 lasers but provideslow polarization extinction ratios and may be diff i-cult to implement at shorter wavelengths. Radialpolarization oscillations were obtained from reso-nators by use of an intracavity calcite telescope todiscriminate between polarizations.7 This methodgave pure radial or tangential polarization but maynot be compatible with high-power applications. Anadditional method used in an apertured resonatoroscillated only on TEM01 modes.8 The TEM01 modeswere separated by a calcite beam displacer, and theTEM00 mode in each branch was eliminated by useof binary phase plates. Coherent combining of thetwo orthogonal modes was done with a tilted plate.Although that resonator worked in the stable region,coherent mode combining is very sensitive. Also,calcite has high power limitations.

In this Letter we present a method that enablesoscillators to operate in various levels of polarizationpurity and output power, without special components.This approach is based on the fact that radially andtangentially polarized beams focused differently inuniformly pumped isotropic solid-state rods (suchas Nd:YAG). When rods are volume pumped andperiphery cooled, thermal lensing and thermally

0146-9592/03/100807-03$15.00/0 ©

induced birefringence arise.9 Combined thermallensing and birefringence results in bipolar lensing,where the radial and tangential polarization compo-nents focus differently. Although this effect stronglyaberrates linear, circular, or unpolarized beams, it isextremely useful for tangential and radial polarizationdiscrimination for two reasons: (1) Mode stabilityis strongly dependent on thermal focusing insideresonators, and it is thus feasible to design a resonatorto be stable and have low diffraction loss for onepolarization and unstable with high diffraction lossfor the orthogonal polarization. (2) Apertures can beused at the desired polarization focal plane to increasethe diffraction loss of only the undesired polarization.The purest polarization is achieved with an aperturesized to maximize the polarization extinction ratio.In unstable resonators, which have thermal-lensing-dependent magnif ication, bipolar lensing can be usedto produce different magnif ication losses for radiallyand tangentially polarized beams.

We have experimentally combined both polariza-tion discrimination factors in half-symmetric andsymmetric oscillators. All oscillators were basedon diode-side-pumped, 0.635 cm 3 14.6 cm Nd:YAGrods in f lat–f lat or f lat–convex resonators. In thehalf-symmetric configuration (Fig. 1), the resonatorlength was 50 cm, and the rod was located 0.5 cmfrom the rear high-ref lectivity mirror. The aperturewas located 0.5 cm from the front mirror (ref lectivityR � 0.7). Pump-power-dependent thermal bipolarfocusing together with aperture size determined thepolarization extinction ratio. At the limit of lasingstability the beam was thermally focused onto thefront mirror, and higher diffraction losses occurredin the more strongly focused radial polarization. A

Fig. 1. Half-symmetric resonator schematic.

2003 Optical Society of America

808 OPTICS LETTERS / Vol. 28, No. 10 / May 15, 2003

tangentially polarized beam was them produced.Flipping tangential and radial polarization was easilyaccomplished with an extracavity 90± quartz rotator.Two methods were used to analyze beam polarization.First, the desired beam plane was imaged onto aCCD camera after transmittance through a rotatingcube polarizer oriented at several angles (a staticpolarizer plus a rotatable 1/2l waveplate were alsoused). Image processing gave the two-dimensionalpolarization orientation. In the second method, thebeam was imaged onto a narrow rotating slit pluspolarizer and then measured by a CCD camera orpowermeter. In this way the beam cross section wasdivided into radial slices, and the extinction ratio wascalculated for each slice as the intensity ratio with thepolarizer parallel and perpendicular to the slit.

Measurement results for the output power andextinction ratio are presented in Fig. 2. No apertureat the front mirror resulted in the highest outputpower with pure tangential polarization but at anoperation point sensitive to variations in pump power.The beam diameter at the output mirror was 1.5 mm.The pump power was 3.07 kW (highest extinction ra-tio). As the aperture size decreased, pure tangentialpolarization appeared deeper inside the stable oper-ation zone. Beam qualities at the highest extinctionratios were M2 � 4.5, 10, and 17 for aperture sizesof 1 mm, 2 mm, and fully open, respectively. Beamprofiles at the rod aperture and at the mirror waist areshown in Fig. 3. This resonator allowed oscillation ofseveral high-order helical modes10 rather than a singlelow-order helical mode �TEM01

��. This promoteda ringlike intensity distribution and a disorderedfar-field polarization. Whereas a single coherentradially (or tangentially) polarized mode destructivelyinterferes on axis and thus preserves polarization,multiple modes are not necessarily coherent with oneanother and thus may permit an unpolarized on-axisfar-field peak. The beam profiles were taken atpump power of 3.06 kW and with a 2-mm aperture.Lasing eff iciency was low ��8% of electrical power tolaser light). We attribute this to the helical modes’size and shape, which did not utilize the full apertureof the rod.

In the symmetric scheme (Fig. 4) the laser rod wasplaced at the resonator center. The distances be-tween the mirrors and the rod were 40 cm. A 1.1-mm-diameter aperture was placed next to the outputmirror. Pump power was adjusted so that the laserrod thermally focused the radially polarized beam ontothe mirrors. Calculated beam diameters �M2 � 2� atthe output mirror were 20.5 mm for the infocus radialmode and �1.4 mm for the out-of-focus tangentialmode, whereas the radial polarization was well fo-cused through the aperture, the tangentially polarizedmodes suffered higher diffraction losses. To increasethe unfocused tangential mode losses, we used a 0.5-mradius-of-curvature convex mirror as the rear mirror.The unfocused tangentially polarized mode size thenincreased at the aperture plane (in comparison with aplano–plano scheme). Pure radially polarized beamswere achieved in the near and far fields by use ofplano or convex rear mirrors at output powers of 25 W

and 70 W, respectively. The beam diameter at themirror aperture was 0.55 mm.

At higher pump powers, a multimode beam withmultiple polarization states was produced. Underthese conditions, 150 W of power was produced in anearly top-hat beam composed of a radially polarizedring plus a linear polarized on-axis disk with theplano–plano mirrors. Measurement results for bothresonator schemes are depicted in Fig. 5. The resultsshow that radial polarization was maintained in thenear and far fields. This means that beam polariza-tion did not vary with propagation. Note that despitethe presence of an on-axis polarization impurity sucha hybrid polarization state would still bypass birefrin-gence-induced aberrations, because such aberrationsare negligible on axis. As can be seen from Fig. 5,the beam size in the rod was quite small comparedwith the rod aperture, and thus reduced availablelasing eff iciency. An enhanced resonator design that

Fig. 2. Output power and extinction ratio (tangentialpolarization/radial polarization) results from the half-symmetric resonator for various apertures.

Fig. 3. Tangentially polarized intensity distributionsat the rod aperture (a) without the analyzing polarizer,(b) for vertical polarization, (c), for horizontal polarization,and (d) at the front-mirror waist (nonpolarized).

Fig. 4. Symmetric resonator scheme.

May 15, 2003 / Vol. 28, No. 10 / OPTICS LETTERS 809

Fig. 5. Images of near- and far-f ield intensity distributionfrom the symmetric plano–plano and plano–convex reso-nators after passage of the beam through a horizontal, ver-tical, or 45±-oriented polarizer.

Fig. 6. Comparison of beam-quality degradation in asingle-pass laser amplif ier by use of radially polarizedor unpolarized probe beams. TEM00 and TEM01 beam-quality comparison reference’s also included.

enlarges the mode size inside the rod should improvelasing eff iciency. Moreover, a master oscillator poweramplifier design that uses high-gain amplifiers suffersless from oscillator inefficiency.

High polarization purity was maintained for thepure radial mode over pump-power variations of upto 62%. The hybrid mode polarization structurewas found to tolerate pump-power variations of upto 65%. Greater pump-power instability could becontrolled with adaptive-optics elements such as avariable radius mirror.11

The attractiveness of radially and tangentiallypolarized beams in bypassing thermal-birefringence-induced aberrations will now be shown. Thermalbirefringence usually aberrates linearly, circularly,or unpolarized beams. The aberration is bipolar

focusing, which focuses radial and tangential polar-ization components differently, and manifests itselfin beam-quality degradation. A pure tangentiallyor pure radially polarized beam will not accumulatebipolar lensing-induced aberrations, because the po-larization axis is always parallel to one of the bipolarlens axes. A beam profile with impure central polar-ization may also maintain good beam quality, becausethe optical aberration strength increases with radiusand tends to be negligible on axis. We quantifiedbeam quality by the M2 propagation factor after singlepassing a Nd:YAG amplifier and performing themeasurements while varying amplif ier pump power(birefringence strength). In these measurements, theinput beams were the pure or hybrid radially polarizedbeams shown in Fig. 5, or an unpolarized beam wasobtained from the plano–plano symmetric resonator atlow pump power. Measurement results are presentedin Fig. 6. The results demonstrate good beam-qualitypreservation during amplification of the radiallypolarized beams, in contrast to strong degradationwith the unpolarized beam. Good performance wasalso achieved with the hybrid radially polarized beam.This last result is important because such a beam hasa top-hat profile and is attractive for amplif ication.

In summary, we developed a method of producingradially or tangentially polarized beams in solid-statelasers, based on thermal bipolar lensing. Radiallyor tangentially polarized lasing was demonstrated inhalf-symmetric and symmetric laser oscillators withpowers up to 250 W. The best beam quality achievedin a pure radially polarized beam was M2 � 2 (70 W),and in an on-axis impure/off-axis pure radially polar-ized beam it was M2 � 2.5 (150 W). Amplificationof a radially polarized beam in a strongly pumpedNd:YAG rod allowed us to bypass thermal bire-fringence-induced aberrations and to improve beamquality. Amplified beam quality was M2 � 3 asopposed to M2 � 9 for an unpolarized beam.

I. Moshe’s e-mail address is inon@soreq.gov.il.

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