Simple Coherent Polarization Manipulation Scheme for Generating High Power Radially Polarized Beam

We present a simple novel scheme that converts a Gaussian beam into an approximated radially polarized beam using coherent polarization manipulation together with Poynting walk-off in birefringent crystals. Our scheme alleviates the interferometric stability required by previous schemes that implemented this coherent mode summation using Mach-Zehnder-like interferometers. A symmetrical arrangement of two walk-off crystals with a half-wave plate, allows coherence control even when the laser has short temporal coherence length. We generated 14 watts of radially polarized beam from an Ytterbium fiber laser, only limited by the available fiber laser power.

Radially polarized beam has gained much interest recently [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], due to its ability to be focussed tighter than a diffraction-limited beam [1]. This can improve applications such as particle-trapping, optical data storage, laser machining and micro-lithography. In addition, the presence of high intense longitudinal electric field in the vicinity of the focal point of a laser beam can also enhance nonlinear effects for applications such as tip-enhanced Raman spectroscopy [2]. This longitudinal electric field can also be used for laser particle acceleration without a plasma wave. Most reported methods generate radially polarized beam by placing specially designed optical elements [4][5][6][7][8][9][10] inside the laser cavity. However, this introduces additional intra-cavity loss, and may make the optimal design of the laser difficult. Moreover, for high power fiber lasers, UV lasers used in lithography, semiconductor lasers, it is not always viable to add such optical elements inside the laser resonator. Thus, an external radially polarization conversion is an attractive and flexible alternative [1,[11][12][13][14][15][16]. Previous reported external polarization conversion schemes based on a liquid crystal array [11] and diffractive phase element [12], tend to have low power handling while schemes that use segmented half wave-plates scheme [1] can only approximate the radially polarized beam. While the spirally varying retarder proposed recently in [14] has high laser power handling capability, it requires specialized fabrication technique for its spiral profile.
Radially polarized beam is a coherent summation of a horizontal polarized TEM 10 with a vertical polarized TEM 01 Hermite-Gaussian mode [6,13,15,16]. Previous interesting schemes [6,13,15,16] implemented this coherent summation of modes using Mach-Zehnder-like interferometric arrangements, in the effort of converting Gaussian beam into a radially polarized beam. Most recently, Ref. [17] proposed the coherent mode transformation in the reverse manner, from a radially polarized beam to an approximated Gaussian mode. The main limitation of these interferometric methods is they require interferometric stability. This may limit its practical usefulness. In addition, they also require specially designed optics such as spiral phase plate and binary diffractive optical element, which may not be widely available as they require special fabrication techniques.
In this paper, we propose a simple and stable coherent polarization manipulation scheme to convert a Gaussian mode to an approximated radially polarized beam. The scheme makes use of Poynting walk-off effect in birefringent crystals together with coherent polarization manipulation accomplished using standard off-the-shelf polarization wave-plates.
In this scheme, we not only manipulate the polarizations of the various parts of the beam, we also maintain certain phase relationship between them, so that they interfere appropriately to generate an approximated radially polarized beam. For this reason, we call it a coherent polarization manipulation scheme. This manipulation, being carried out inside birefringent crystals instead of free-space interferometers, offers the compactness, mechanical stability and robustness demanded by practical applications. We have generated 14 Watts of approximated radially polarized beam from a Ytterbium (Yb) fiber laser. The demonstrated power is only limited by the available power from our fiber laser. However, since all optical components used in our scheme are standard off-the-shelf components that have power handling capability of more than kilowatts of laser power, the scheme will be a promising radial polarization converter for high power fiber laser.  [18], these modes can superimpose coherently in far-field to approximate the radially polarized beam.
We first use a continuous-wave, single longitudinal mode, 1064nm laser to demonstrate this scheme. This highly coherent laser source has power only up to a few milli-watts. With a spatial filter that allows ~75% power throughput, we generated a nearly radially polarized beam as shown in Figure 2, with a beam quality of 2 M~2.2. Without a polarizer, the output was a doughnut-shaped light beam as shown in Figure 2(a). When the polarizer was inserted prior to the camera, two spots were clearly seen, and they rotated with the transmitting axis of the polarizer, as seen in Figure 2(b)-(e) which clearly illustrated the radially polarized profile.
The mode conversion is stable and it lasts many hours to several days without any tweeking. This is expected since all polarization and phase manipulations occur inside the crystals and waveplates. Such stability is much better than that of free-space interferometric methods suggested in [6,13,15,16,17].
To scale up the power level ( >10 Watts) of the radially polarized light, we changed the laser source to a Ytterbium (Yb) doped fiber laser that can produce 15 Watts of polarized 1064 nm. This fiber laser has a broad bandwidth of 2 nm and our initial attempt to perform radial polarization conversion using the three-element scheme shown in Figure 1, was unsuccessful. This is because the coherent length of this laser is shorter than the optical path difference (i.e In conclusion, we have presented a novel scheme that starts with a Gaussian mode, and using Poynting walk-off effect in birefringent crystals together with coherent polarization manipulation, the scheme converts it to an approximated set of orthogonally polarized and coherently in-phase TEM 10 and TEM 01 modes. These modes superimpose at far field to generate a near radially polarized beam. Since the manipulation is accomplished inside the crystals, it alleviates the high interferometric sensitivity of previous interferometric arrangements and offers a much compact, stable, and robust scheme to convert a Gaussian mode into a radially polarized beam. We demonstrated 14 watts of radially polarized beam but the scheme has potential to produce much higher power of radially polarized beam. In addition, we have shown a symmetrical arrangement of two walk-off crystals with a half-wave plate so that the temporal coherence length of the laser will not pose a problem to the coherent manipulation of the beam. The authors would like to acknowledge Lim Yuan Liang, Lai Kin Seng, Tan Beng Sing for their helpful discussion, and Teo Kien Boon for his support and encouragement in this work.    .