Placing a Brewster-angle axicon inside a laser resonator makes it possible to produce a radially-polarized (RP) oscillation pattern distributed on a thin ring or a portion of a ring. Laser-diode end-pumped, Nd:Y3Al5O12 and Nd:YVO4 lasers were studied. Spatially coherent RP beams distributed on circular arcs were obtained with a polarization contrast ratio up to 80:1. Incoherent RP outputs on a full ring were also produced with a polarization contrast ratio of about 5:1. Applications of these beams to increase absorption efficiency in laser-matter interaction are discussed.
©2006 Optical Society of America
There is considerable interest to develop solid-state lasers with a radially polarized (RP) output. [1–5]. Besides the fact that thermal birefringence can be cancelled in lasers with isotropic active element [2,4], RP beams have found use also for several applications, such as drilling and cutting [6,7], achievement of tighter focusing compared to linearly polarized beams , particle trapping , mapping of dipole moment  and particle acceleration .
One simple way to produce RP beams consists in placing a Brewster-angle axicon inside the resonator. Using parallel conical surfaces, obtained either by combining complementary concave and convex axicons , by using a hollow axicon  or an immersed axicon , ensures that beam trajectories inside a resonator remain paraxial. This provides laser operation with a “classical” axially symmetrical Laguerre-Gaussian TEM01* mode output. Multilayer coating of the conical surface of the axicon was used to enhance the selectivity of the radial polarization [5,13].
In contrast to previous works, we used a Brewster-angle axicon with only one conical surface in a cw end-pumped neodymium laser. We produced off-axis, RP, thin ring- and arclike laser beams. Both cases of spatially coherent and incoherent RP outputs were observed with different polarization contrast ratios. Unlike the RP TEM01* mode, we obtained RP beams distributed on a thinner ring or portion of a ring. The intensity distributions and the polarization contrast ratio of the output beams were studied. The possibility to achieve increased absorption efficiency by a target with such type of radiation is discussed.
2. Neodymium laser with an intra-cavity axicon
The experimental scheme is shown in Fig. 1. A 2-mm-thick, 1% at. Nd:Y3Al5O12 (YAG) ceramics or a 3-mm-thick, c-cut, 1% at. Nd:YVO4 plates were used as active materials. The resonator was formed by the high-reflection-coated (HR) planar surface of the plate, and the plane output coupler. The pump radiation from a fiber-coupled laser diode (λ=808 nm) was focused by a pair of lenses in the sample along the resonator axis to a circular spot of about 400 μm diameter. A glass axicon with a diameter of 30 mm and an apex angle of 118° was placed inside the resonator in front of the sample and provided the refraction of the laser radiation at 1.064 μm close to the Brewster angle. The spacing between the Nd-doped sample and the axicon was such that the focal line of the axicon passed through the pumped region and reached the HR-coated face. At about 3 W pumping power, the neodymium laser emitted one or two ring-like (or arc-like) beams at a power up to 300 mW. Beams like thin rings or arcs (<0.5mm-thick) were produced by off-axis oscillations going through a narrow annulus region of the axicon.
Two distinct oscillation patterns were observed. One of these beams (type 1) was a diverging conical beam, while the other (type 2) emerged almost parallel to the optical axis. The ray tracing of these two types of oscillations is shown in Fig. 1, together with a picture of the Nd:YAG laser output obtained with a digital camera. The type-1 off-axis modes correspond to self-reproduction in one round trip inside the resonator while the type-2 modes correspond to self-reproduction in 2 round trips. The beam trajectory inside the gain medium was inclined by about 10 degrees for the type-2 beam, slightly more than for the type-1 beam. The output beam diameter of both types and divergence angle of type-1 oscillation (reaching up to 10°) could be controlled either by changing the length of the resonator (7-50 cm) or the distance of the axicon to the active material. Since both type-1 and type-2 modes overlapped significantly in the gain medium, it was generally difficult to obtain simultaneous oscillation of both types of modes: type-2 mode generally appeared first. A circular diaphragm placed inside the cavity enabled to suppress oscillations of type-2 beam. When type-2 oscillation was suppressed, type-1 oscillation generally appeared.
The spatial distribution of the output radiation intensity was captured with a CCD camera. The output beam intensity was distributed either throughout 360°, Fig. 2(a), or on one or two pairs of opposite arcs of limited angular extent, Fig. 3(a), or contained arcs overlapped with a ring, Fig. 4. Ring-like output was achieved by careful alignment of the axicon axis with the axis of the pumping spot and observed mainly for type-2 oscillation. The type-2 ring beam with the diameter of 20 mm at the output mirror shows a chaotic intensity distribution, Fig. 2(a). On the other hand, pure arc-like output predominated for type 1 oscillation. The type-1 arc-like beam, Fig. 3(a), has a well contrasted, multilobe structure. Enlarged portion of one arc is shown at the right image of Fig. 3(a). The thickness of rings and arcs at the laser output was about 200 μm (type 1) and 350 μm (type 2). For a type-2 output, the full angle divergence of ring- or arc-like beams was about 10-3 rad. The divergence of the same order was observed for type 1 beams after collimation. For type-1 beams, opposite arcs correspond to independent off-axis oscillations of the clock-wise and counter clock-wise arc-like modes.
Figure 2(b) and Fig. 3(b) show the far field intensity distributions for ring-like and arc-like beams respectively. The far field image of the ring beam shows a smoothed intensity distribution with a central peak, Fig. 2(b). On the other hand, there is a distinct multilobe structure in the far field image of the arcs beam, Fig. 3(b). For type-1, arc-like beams, the intensity distribution, the angular extent and the beam divergence of 2 opposite arcs may differ because they correspond to different, counter-propagating modes, in accordance with the Fig. 1 ray tracing scheme.
Ring- and arc-like off-axis (type 1 and 2) oscillations in neodymium lasers were also observed with intra-cavity axicons having larger (160°) or smaller (78°) apex angles. The output patterns were made of rings or several high-order arc-like modes with the total number of lobes ranging from less than 10, for larger apex angle, up to several hundred for smaller apex angle.
3. Polarization state in the near- and the far-field.
Figure 5 shows pictures of near-field patterns for type 1 arc-like laser beams after passing through an analyzer of polarization, mounted on a rotation stage. As the analyzer was rotated, portions of arcs that were orthogonal to the transmission axis of the analyzer were extinguished. The relative angular position of the analyzer is shown on the top of each picture. These pictures show (in a qualitative form) the radial character of the output beam polarization. Using an analyzer of polarization, we observed similar pictures for other type 1 and 2 ring and arc beams. The far field pattern for the arc beam was linearly polarized, Fig. 3(b), while the far-field pattern of ring, Fig. 2(b), did not show any preferred polarization.
The spatial distribution of polarization directions of output beams and the polarization purity of the output for different angular sectors along the ring were measured using a 300-μm-wide slit and the analyzer of polarization, both mounted on graduated rotation stages . Radial slices of the beam were selected by the slit, then transmitted through an analyzer and sent to the powermeter. For each position of the slit, and at angular positions of the analyzer corresponding to the minimum and maximum of the transmission, laser radiation transmitted through the analyzer was measured and the ratio of the maximum to the minimum of transmitted power was estimated. This polarization contrast ratio was used as the measure for the level of the RP at the output of the laser. Measurements along the circumference of the ring-like output, Fig. 6(a), or along part of the circumference in the case of an arc-like oscillation, Fig. 7(a), showed that the polarization vector for each slice points towards the center, which confirms the RP nature of the beam.
The polarization ratio was measured also for ring- and arc-like beams. In the case of the Nd:YAG laser for the ring-like output, the polarization ratio was 3-7, Fig. 6(b). For arc-like beams the ratio up to 60 was registered. For beams of the Nd:YVO4 laser, slightly larger polarization ratios were obtained and the polarization ratio up to 80 was observed for the case of an arc like output, Fig. 7(b). The error bars in Fig. 7 represent the reproducibility over several realizations of the arc-like, type-1 oscillation. The actual measurement error is estimated to be smaller than ±5; this error mainly arises from the noise of the detector and the need to subtract residual background signal from the pump. The improved polarization ratio for Nd:YVO4 laser may be ascribed to the large difference in the stimulated emission cross-sections, σs (a axis) and σπ(c-axis), σπ being several times greater than σs . The non-zero projection of the electric field of the laser radiation on the c-axis for the RP light may give an advantage to the latter.
In the case of ring beams, Fig. 2, the comparison of the near- and far-field indicates that the RP ring-like beam is a spatially incoherent beam composed of a large number of modes. This is already apparent from the fast intensity fluctuations along the ring and it is confirmed by the fact that on-axis peak intensity is observed in the far field, Fig. 2(b). Moreover, the far field was found unpolarized because of the incoherent contribution of different portions of the beam with different polarization states. Hence, the RP ring beams can be considered quasi-RP, i.e., made from independent “beamlets” with linear polarizations directed toward the center. Such beams can be concentrated on a target as a p-polarized beam.
On the other hand, in the case of arc beams, Fig. 3–4, the multilobe structure with a good contrast in the near and far field suggests the generation of a spatially coherent output. Note that opposite arcs are not mutually coherent, as they correspond to counter-propagating beams inside the resonator. As to the polarization state of the arc beam in the far field, we observed the transformation of the RP near field arc-like laser output to a linearly polarized output in the far field, Fig. 3(b). The fact that the radial polarization in the near field becomes linear at the far field substantiates the spatial coherence of our beam, because it indicates that different parts of the beam interfere together at the focus to alter the direction of polarization. In the case of RP coherent arc, the vectorial addition of electrical field from opposite parts of the beams at the focus cancels the transverse component of the field to a large extent.
Intensity distributions of type-1 and type-2 beams differ markedly from the eigenmodes of axially-symmetric laser resonators in the paraxial approximation [15,16]. The trajectories of our beams are significantly inclined with respect to the optical axis. Hence, the observed ring-and arc-like output may be classified as cases of off-axis oscillation [17–20]. The angular aperture of the beam inside the active medium is too large to produce the coherent generation of a single mode Bessel-like output, which has nevertheless been realized by using intra-cavity axicon with very small apex angles .
Note that off-axis beam propagation scheme with an axicon enabled us to produce RP beams without axial symmetry with a high purity of polarization (up to 99% or 80:1). Coherent RP beam was even found on a portion of a ring. This results contrasts with conventional paraxial beams, which must be axially symmetrical in order to be radially polarized .
The obtained 300-mW power level is not a fundamental limitation of our scheme. Much higher power could probably be obtained by scaling up the pumping power while decreasing the resonator losses, optimizing the pumping conditions, by using an amplifier stage or by using other types of gain media. It could also work in pulsed regime and eventually opening new possibilities for laser-matter interaction. Thin RP ring and arc beams could be concentrated onto targets using lenses or axicons as a p-polarized radiation. It is well known that absorption peaks at some specific incident angle for the p polarization, for plasmas, in the case of resonant absorption, and by metals [6,7,22–25]. Hence, the generation of RP beams in the form of a narrow ring, such as those produced in this work, could be useful to irradiate targets with p polarized light near these maxima of absorption, providing higher energy transfer to metals and more efficient plasma heating. In particular, improved efficiency of metal cutting  and improved conversion of laser radiation to soft X-ray in a plasma for EUV lithography  can be seriously considered. Other proposals for the usage of conical laser beams, p- and RP- polarized beams in different aspects of laser technology [27–29] have been reported.
A rather simple scheme to produce RP laser beams using an intra-cavity Brewster-angle axicon was presented. Unlike previous reports, RP beams with the laser radiation distributed along a thin ring or portions of a ring were produced. Polarization ratio up to 80:1 has been measured for the coherent arcs and in the order of 5:1 for the full incoherent ring beams with optical-optical conversion efficiency of 10%. The power-scaled and pulsed type of such laser appears feasible and can seriously be considered for improving the absorption efficiency in some laser-matter interaction experiments. For practical applications, the study of lasers with axicons, methods of generation and amplification of RP radiation and methods of concentration of this radiation onto the targets should be studied.
The authors thank A. Stepanov and D. Kartashov for granting one of the axicons used in experiments and V. Niziev, D. Kouznetsov and M. Kurdoglyan for helpful discussions. This work was supported by the 21st Century COE program of the Ministry of Education, Science and Culture of Japan.
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