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We produced a high power radially-polarized output directly from a diode-pumped Nd:YVO4 bounce amplifier, using an autocloned photonic crystal mirror as an output coupler, with a simple cavity configuration. The radially-polarized output power of ~6 W was achieved, and a corresponding slope efficiency was estimated to be ~17 %. The output was characterized to be an ideal radially-polarized beam from its polarization distribution profiles. The output mode was not an eigenmode in the resonator. We discussed and clarified intra-cavity mode dynamics in terms of polarization distribution in the wavefront.
©2008 Optical Society of America
1. Introduction
A radially-polarized beam shows an annular spatial shape owing to polarization singularity. Under a tightly focusing condition, a longitudinal electric field along the propagation direction is generated [1,2]. Moreover, a spot size of the longitudinal electric field is expected smaller than those of transversely-polarized beams [3-5]. Thus, a radially-polarized beam has been attracting much attention for high resolution microscopy, material processing, optical trapping, particle acceleration, and plasma physics [3-13].
Several methods to obtain radially-polarized beams, using superposition techniques and special optical elements, have been demonstrated [14-21]. Since these techniques require rigorous optical alignment, obtained beams were sensitive to experimental conditions. Certainly diffraction techniques and mode conversion techniques using a fiber are not sensitive. However, their conversion efficiencies and damage thresholds are not high enough for high-power region. In contrast, a direct production of the beam inside a laser cavity is highly stable and it can give an ideal radially-polarized output. Thus, direct generation technique of a radially-polarized output is the most favorable for the practical applications.
Several direct generation techniques using Nd:YAG have been demonstrated [22-24]. One of them has achieved an output power over hundred watts in a flat-convex resonator using a thermally induced birefringence effect [23]. However, this method is not a stable generation technique owing to low regulatory alignment. Crystals of Nd:YVO4 were employed as laser materials to obtain a high-power beam. It has several advantages as an laser amplifier in comparison with Nd:YAG crystal, that is, higher absorption, larger absorption band width, larger emission cross section as well as strong birefringence [25]. Therefore, it has been investigated intensively as a promising candidate for a direct generation technique of an ideal radially-polarized output with high conversion efficiency.
Recently, two types of direct production of a radially-polarized output based on Nd:YVO4 laser resonator have been demonstrated [26, 27]. One is based on an end-pumped laser resonator placing a Brewster-angle axicon inside [26]. An output power of 300 mW and an optical-optical conversion efficiency of 10 % were reported. These values were not high enough, as in their discussion. The other is based on side-pumped cylindrically symmetric gain using c-cut Nd:YVO4 as well as a birefringence of the laser crystal [27]. This technique requires a careful cavity alignment to maintain the laser oscillation and distinguish a radially-polarized mode from an azimuthally-polarized mode. And thus, the output power is limited to be as much as 75 mW. As another scheme, a diode-side-pumped bounce amplifier based on Nd:YVO4 slabs can surpass the two schemes mentioned above. This configuration, in which extremely high inversion density is produced below the pump face of the amplifier, is a promising solution for producing high power outputs at ultrahigh efficiency with a simple cavity design [28].
In this paper, we present an extension of the bounce lasers to produce a high power radially-polarized output, for the first time. A maximum output power of ~6 W and its slope efficiency of 17 % were achieved. This is the highest value, to the best of our knowledge, obtained in direct production of radially-polarized output from a Nd:YVO4 laser resonator.
2. Experiments
2.1 Experimental setups
Figure 1 shows a schematic diagram of the laser cavity setup. An amplifier used in this experiment was a 1 at. % Nd3+ doped a-cut YVO4 slab with dimensions of 2 mm×5 mm×20 mm. It was transversely-pumped by a TM-polarized 808 nm CW laser diode array. The pump diode output was line-focused onto the pump face of the amplifier, where maximum pump power was 44 W. The laser cavity was composed of a high-reflection flat mirror, EM, for 1064 nm, an output coupler, OC, a quarter-wave plate, QP, a beam expander (×4.5), BE, and two cylindrical lenses, CL1 and CL2 (f=50 mm) in the vertical direction. The BE was used to match spatially the laser mode with the effective aperture of the OC. The cavity length was extended to be 800 mm, so that the effective Fresnel’s number of the cavity was ~2. The OC was an autocloned photonic crystal mirror (Photonic Lattice Inc., LMR-1064) containing an aperture with a diameter of 5 mm [29]. Usually, photonic crystals are composed of periodic structures having a photonic band gap that forbids propagation to a certain frequency of light. This property enables us to control light. The photonic crystal mirror employed here has a concentric structure, as shown in the inset of Fig. 1. Propagation of electric field parallel to the pattern (azimuthally-polarized component) is forbidden at a wavelength of 1064 nm, owing to the photonic band gap, resulting in almost perfect reflection by the mirror. In good contrast, propagation of electric field normal to the structure (radially-polarized component) is allowed, giving almost perfect transmission. The details of the photonic crystal mirror have been described in Ref. [29]. We measured transmittivities of the photonic crystal mirror for azimuthally- and radially-polarized components to be 10 % and 90 %, respectively.
Fig. 1. Experimental setup of laser cavity (top view). EM is a high-reflection flat mirror, OC is an output coupler formed by an autocloned photonic crystal mirror, QP is a quarter waveplate, L1, L2, and L3 are spherical lenses, and CL1 and CL2 are cylindrical lenses, respectively. M is a high-reflection flat mirror and SF is a spatial filter. Transversely-pumping laser diode is TM- polarized (vertically-polarized).
Figures 2(a) and 2(b) show an optical property of the OC, which are transmission and reflection profiles of a linearly and a circularly polarized incident beams. For a vertically-polarized incident beam, the transmitted beam becomes radially-polarized beam. Its intensity profile is not doughnut-like, but similar to the TEM01 profile, as marked “T” in Fig. 2(a). This is because the OC was designed so that vertically-polarized component was not transmitted on its central region in the vertical direction. In good contrast, the reflected beam becomes azimuthally-polarized. Its intensity profile is as the TEM10 profile, as marked “R” in Fig. 2(a). Note that the OC around the center region reflects the incident beam almost 100 % thanks to the polarization singularity. For a circularly-polarized incident beam, the transmitted beam becomes radially-polarized, as shown in Fig. 2(b). Therefore, we inserted the QP inside the cavity to circularly-polarized incident beam to the OC and thus produce the radially-polarized output efficiently from the system. The effective OC reflectivity of 50 % was measured for a circularly-polarized incidence.
Fig. 2. Transmission and reflection properties of the OC (side view), for (a) a linearly incident beam and (b) a circularly polarized incident beam. I, T, and R denote an incident beam, a transmitted beam, and a reflected beam, respectively.
2.2 Experimental results
Figure 3(a) shows the experimental output power as a function of the pump power. A maximum output power of 10 W was measured at the pump power of 44 W. Figure 4(a) shows the near-field pattern of the output beam. Not only a doughnuts profile but also extra outputs in left- and right-hand sides were observed. Essentially, an output from bounce laser cavity had horizontally-long and elliptic intensity profile, whose aspect ratio was estimated to be ~1:2. The beam was expanded by the BE, so that the beam size on the OC became wider than the aperture size of the OC in the horizontal direction. Thus, the output from the system somewhat included unconverted circularly-polarized component together with the radially-polarized output. Using a SF formed by an aperture with a diameter of 3 mm after focusing by a lens L3 with a focal length of f=300 mm, we removed unconverted circularly-polarized mode. Figure 4(b) shows the far-field pattern of the output beam with a spatial filter. It exhibits an annular spatial form due to the diffraction from the aperture of the OC. The maximum power of the radially-polarized output was measured to be ~6 W. The power ratio of the unconverted component to the output was evaluated to be <0.4. Red circles in Fig. 3 show the radially-polarized output power as a function of pump power. Its corresponding slope efficiency and threshold pump power were evaluated to be 17 % and 7.0 W, respectively. These values were the highest, to the best of our knowledge, for a radially-polarized output produced directly from Nd:YVO4 lasers. Hereafter, we call this configuration “case A”. To clarify mode evolution processes in the cavity, we monitored the beam leaked from the EM as shown in Fig. 4(c). The leaked beam was almost vertically polarized (its purity to be >95 %) and its profile was the elliptic fundamental TEM00 mode. It means that the radially-polarized mode is not an eigenmode in the cavity.
We also investigated the polarization of the output by using a rotational polarizer. Figures 5(a)-5(c) show the experimental vertically-, 45°-, and horizontally-polarized intensity profiles of the output, respectively, indicating that the output was radially-polarized.
Fig. 4. (a). Near-field pattern of the output without spatial filter. (b) Far-field pattern with spatial filter. (c) Spatial form of the leaked beam from the EM. The leaked beam is almost vertically-polarized (its purity to be >95 %).
Fig. 5. Spatial shapes of the radially-polarized output. Intensity profiles of (a) vertically-polarized component, (b) 45°-polarized component, and (c) horizontally-polarized component.
To clarify effects of the photonic-crystal output coupler on laser performance, we also investigated slope efficiency in other case, which is the same cavity configuration except replacing the photonic-crystal OC with a normal flat OC (case B). Reflectivity of the flat OC to be 50 %, being similar to the effective reflectivity of the photonic-crystal OC. Solid green circles in Fig. 6(a) show its output powers as a function of pump power. Here, the solid black line denotes the radially-polarized output power in case A. The slope efficiency and the threshold power were measured to be ~17 % and ~2.5 W for case B, respectively. It was clear that the slope efficiency in case B was comparable to that in case A.
Furthermore, to estimate an internal loss ratio within the round trip in the cavity, we measured output powers using flat OCs with reflectivities of 20, 50, 70, and 90 % in the case B. Figure 6(a) shows output power as a function of pump power. Their slope efficiencies are plotted in Fig. 6(b). The slope efficiency is proportional to T/(L i+T), where T and L i are the output coupling and internal loss ratios within the round trip in the cavity. The ratio T is given by T=-ln R with the reflectivity R of OC. Hence, from slope efficiencies as functions of R, loss ratios L i were evaluated to be ~1.2.
Fig. 6. (a). Output powers as a function of pump power using flat-OC with various reflectivity in the case B. A solid black line denotes the radially-polarized output power. (b) The estimated slope efficiency as a function of reflectivity in case B. The red line is a fitting curve.
3. Discussion
First, we discuss the round-trip polarization evolution or dynamics in our laser cavity. In spite of radially-polarized beam output from the OC in our laser, the radially-polarized mode is not an eigenmode inside the cavity. We consider the round-trip polarization evolution or dynamics as follows. Laser beam emitted from the a-cut Nd:YVO4 slab amplifier is vertically polarized, as shown in Fig. 7(a). After passing through the QP, the beam was transformed to be right-circularly polarized (Fig. 7(b)). Then, it is reflected back by the OC and comes to be azimuthally-polarized (Fig. 7(c)), while the transmitted beam is radially-polarized simultaneously (Fig. 7(c’)). After passing back through the QP, the reflected beam keeps uniformity of vertical polarization components (Fig. 7(d)). The beam comes back to the Nd:YVO4 amplifier, where only vertical polarization components are amplified, making the beam traveling toward the EM almost vertically-polarized (Fig. 7(e) and (a), respectively). This polarization evolution or dynamics during a cavity round-trip is supported by facts that a leaked beam from the EM was almost vertically-polarized and it exhibited near-TEM00 mode profile, as shown in Fig. 4(c). This polarization evolution during cavity round-trip suggests the spatial phase distribution may be as same as that of the Laguerre-Gaussian mode [17, 30], rather than fundamental Gaussian. In this round-trip polarization evolution process, polarization states in the wavefront, depending on the azimuthal angles, draw closed paths on Poincaré sphere. Thus, the polarization evolution in our cavity can be explained by Pancharatnam-Berry phase [31].
Next, we will discuss the slope efficiency of our laser. The slope efficiency is one of the important factors to estimate how optimal the cavity is. It is essentially determined by the product of the pump absorption efficiency, the ratio of pump and laser photon energy, the quantum efficiency of the gain medium, the mode matching efficiency, and the output coupling efficiency of the laser cavity. The slope efficiency in the case A, corresponding to radially-polarized output, was as same as that in the case B, corresponding to circularly-polarized output, as shown in Fig. 6(a). This was caused by the same effective reflectivity of both OCs. Therefore, an optimized condition in case A will be similar to that in case B. Thus, the slope efficiency will be improved by using a photonic OC with lower effective reflectivity. The slope efficiency of up to 30 % is expected.
Furthermore, we also mention that the conversion efficiency of the radially-polarized output will be improved by utilizing an anamorphic beam expansion configuration and optimizing the Fresnel’s number of the laser cavity to yield a circularly-symmetric mode with aspect ratio of unity in the cavity.
4. Conclusion
To summarize, we demonstrated a direct generation of 6 W radially-polarized output from a diode-pumped Nd:YVO4 bounce laser. We measured the slope efficiency to be 17 %. We discussed intra-cavity mode evolution from the viewpoint of polarization distribution in the wavefront. Moreover, we clarified the effect of the photonic-crystal output coupler on laser performance, giving guidelines to optimize of the cavity. Further power scaling of the system is possible by optimizing the Fresnel’s number of the cavity and also by optimizing the polarization evolution inside the cavity. The system can be also extended to produce highly intense, radially-polarized pulses by the Q-switching as well as mode-locking techniques based on intra-cavity controllable loss elements, such as an electro-optic device or an acousto-optic modulator.
Acknowledgment
This work was partially supported by Grant-in-Aid for the 21st Century COE program on “Topological Science and Technology” and Grant-in-Aid for Exploratory Research, 2007-2009, No. 19656014, from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
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