Effects of thermally induced aberrations on radially and azimuthally polarized beams Yaakov Lumer, Inon Moshe, Steven Jackel Non-linear Optics Group, Soreq Nuclear Research Center, Yavne 81800, Israel
[email protected]
Abstract: Radial polarization maintenance in cw multi-kW rod based lasers has been theoretically and experimentally investigated. Non-radially symmetric wave-front aberrations were found to significantly degrade beam polarization. Meanings for pump design and amplifier architecture are discussed.
The subject of radially polarized beams and their unique features has seen a lot of attention. Obtaining high-power, radially polarized beams is advantageous in fields like material processing [1,2] and highpower, good beam-quality lasers [3,4]. In order to achieve such high-power radially polarized beams, it is needed to pass them through high-power amplifiers. Such high-power amplifiers induce thermal aberrations, which affect the properties of the beam [4]. The focus of this work is the degradation of radial polarization caused by non-radially symmetric thermally induced aberrations. This affects most applications of radially polarized beams. Material processing requires the radially polarized beam to be focused, where the special polarization properties of the radial polarization are exploited. Thus, the degree of radial polarization of an aberrated beam near a focus is of importance and needs to be fully understood. High-power lasers use radially polarized beams to bypass the thermally induced bi-focusing. In such systems, the degree of polarization is important as it is a major factor in determining the beam quality of the system. Thus, a way to calculate and optimize the beam propagation through the system in terms of polarization is needed. Radially polarized beams are defined as optical beams in which the polarization vector points in the radial direction across the entire cross-section of the beam. The lowest order mode describing a radially polarized beam is a combination of Hermite-Gaussian modes TEM 01 and TEM 10 in orthogonal polarizations. In this case, the electric field has the form:
r 2 E (r , ϕ ) = 2 E0 e − r
w2
(r cos(ϕ )xˆ + r sin (ϕ ) yˆ ) =
2 E0 e − r
2
w2
rrˆ
(1)
where r and φ are the cylindrical coordinates, E0 is the magnitude of the field, w is the waist parameter of the Gaussian beam and xˆ , yˆ and rˆ are unit vectors in the horizontal, vertical and radial directions, respectively. When examining the propagation properties of a radially polarized beam, it is straightforward to see that a radially polarized beam such as described in equation (1) remains radially polarized when propagated through free space and to the far-field. A general non-radially polarized beam has the form:
r E (r , ϕ ) = E ( r ) (r , ϕ )rˆ + E (ϕ ) (r , ϕ )ϕˆ
(2)
The degree of radial polarization for such a beam is defined as the ratio of energy of the beam directed in the radial polarization to the total energy of the beam. When examining the propagation properties of a non-radially polarized beam, it is possible to deduce analytically that the degree of radial polarization is not a conserved quantity. The degree of radial polarization can change drastically when the beam is propagated through free space and to the far-field. Non-radially symmetric wave-front aberrations were found to have a significant impact on radially polarized beams. Such aberrations do not affect the degree of radial polarization in the near field. However at the far-field such aberrations affect the degree of radial polarization in a significant matter, which eliminates the possibility of exploiting the unique properties of the radially polarized beams. Experimental as well as simulation results were obtained in order to investigate and quantify the degradation of radial polarization caused by wave-front aberrations. In order to generate a radially polarized beam, we used the rod's thermally induced bi-focusing to build a resonator which has different parameters for radially and azimuthally polarized beams [5], thus obtaining a high-quality radially polarized beam (M²=2.3, 99% radially polarized), shown in figure 1.
Figure 1. Intensity profiles of the radially polarized beam with and without a linear polarizer. Arrows indicate polarizer orientation. Measured degree of radial polarization is 99%.
The amplifiers used in the experiments were Soreq manufactured STAR (Stripe Through Apertured Reflector) 2KW pump-chambers [6]. The working point was set at 3100W of diode light. The amount of heat was estimated to be 1100 W and the thermal focusing was measured to be 10cm. The pump profile and induced wave-front aberrations were measured, and shown in figure 2.
Figure 2. Pump profile and wave-front distortion of the used STAR pump-chambers.
The experimental setup was designed so that the beam symmetrically propagates the rod, thus obtaining a high fill-factor. The beam was measured at the thermal focus of the laser rod, and far-field images and degree of radial polarization measurements were made. The beam at the thermal focus shows the distinctive 5-fold symmetry of the wave-front aberrations, as well as a drastic decrease in degree of radial polarization – from 99% to 59%. The results can be seen in figure 3.
Figure 3. Intensity profiles of the radially polarized beam after passing through high-pump-power pump chamber, with and without a linear polarizer. Arrows indicate polarizer orientation. Measured degree of radial polarization is 59%.
The beam starts as a very pure radially polarized mode. Such mode is characterized by total radial symmetry in intensity, phase and polarization. When radially symmetric aberrations are introduced, the radial symmetry is conserved, and there is no degradation in radial polarization, in any plane. However, when non-radially symmetric wave-front aberrations are introduced (such as those shown in figure 1) the total radial symmetry is broken and the beam is no longer purely radially polarized. Such wavefront aberrations affect the intensity profile and thus the degree of radial polarization when the beam is propagated to the thermal focus (or the far-field). Thus at the rod's exit face the beam still has a high degree of radial polarization, however at the thermal focus the beam no longer has its radial symmetry, and the radial polarization degrades rapidly. Figure 4 shows measurement and simulation results of the degree of radial polarization after the rod's exit face and through the thermal focus.
Figure 4. Experimental and simulation results of degree of radial polarization of a radially polarized beam after passing a high-pump-power laser rod. Thermal focus is at 14cm.
The degree of radial polarization near the thermal focus reaches a value of 59% (69% in the simulations). Such a low value means that the unique properties of radially polarized beams cannot be exploited at the focus. Thus, wave-front compensation methods are needed in order to maintain the radial polarization, after passage through high-pump-power laser rod amplifiers. One compensation method is to specifically design the pump-chamber to induce minimal wavefront aberrations. This can be accomplished by using ray-tracing and thermal simulations, to estimate the pump-profile and induced thermal aberrations. Specific attention should be paid to misalignment sensitivity, as it was found that low-order azimuthal aberrations (such as astigmatism) arising from misalignments have a significant impact on radial polarization degradation. Another compensation method is to use two similar, rotated pump-chambers. This method has been successfully demonstrated in the past [4], and shown partial compensation of azimuthal aberrations. An important requirement for this method of compensation is high similarity of the two pump-chambers. A third compensation method is by using direct wave-front correction methods. One such method is the use of specially designed phase-plates that compensate for the induced wave-front aberrations. Such compensation method is optimal for a specific working point. Another direct compensation method is the use of an adaptive mirror that has sufficient dynamic range and power handling to work in the high-power regime. References [1] V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser beam cutting efficiency", J. Phys. D 32, 14551461, 1999 [2] Matthias Meier, Hansjuerg Glur, Eduard Wyss, Thomas Feurer, Valerio Romano, "Laser microhole drilling using Q-switched radially and tangentially polarized beams", Proceedings of, SPIE, International Conference on Lasers, Applications, and Technologies, 2005, 605312-1 – 605312-2 [3] I. Moshe and S. Jackel, "Influence of birefringence-induced bifocusing on optical beams" J. Opt. Soc. Am. B 22, 1228, 2005. [4] I. Moshe, S. Jackel and A. Meir, "Correction of spherical and azimuthal aberrations in radially polarized beams from strongly pumped laser rods", Applied Optics 44, 7823, 2005 [5] I. Moshe, S. Jackel and A. Meir, "Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects", Opt. Lett. 28, 807, 2003 [6] E. Leibush, S. Jackel, S. Goldring, I. Moshe, Y. Tsuk and A. Meir, "Elimination of spherical aberration in multi-kW, Nd:YAG, rod pump-chambers by pump distribution control," in Advanced Solid-State Photonics Conference 2005, OSA Trends in Optics and Photonics Series (Optical society of America, 2005)
