We convert a linearly polarized Gaussian beam into a radially polarized doughnut beam with an eight-segment spirally varying retarder (SVR) at wavelength of 808 nm. The SVR is designed based on the linear birefringence of α-barium borate (α-BBO) crystal and fabricated using a dry etching process. Radially polarized light of high purity (>96% at far-field distribution) was generated experimentally using the segmented SVR positioned between two quarter waveplates with orthogonal slow axes. The emergent polarization can be switched between radially and azimuthally polarized cylindrical vector beams with a pair of half-wave plates.
©2008 Optical Society of America
Radially polarized light has cylindrical symmetry in polarization , and has proven its usefulness in many applications. Its ability to be focused tighter is desirable in optical data storage , optical trapping of metallic particles  and measurement probe optimization for localized surface plasmon microscopy . It can also be used to enhance laser machining  and for focus shaping . Many schemes, both intra-cavity [7–9] and extra-cavity [10–20, 22], have been proposed to generate radially polarized beams. Here we focus on an extra-cavity scheme so that laser dynamics are not tempered with, easing further manipulation. Some of the schemes demonstrated include interferometric arrangement [10–12], polarization manipulation , specially designed polarization elements based on liquid crystal gel , subwavelength gratings [15,16], electro-optic induced birefringence , stress-induced birefringence , and spiral phase plate in conjunction with radial-type linear analyzer . More recently, we demonstrated the generation of high power radially polarized light using a twelve-segment photonic crystal half-wave plate . Though it is capable of generating almost 99% of radial polarization purity, its high price tag is a drawback, caused mainly by expensive substrate material and fabrication technique .
We have proven the concept of radially polarized light generation using a custom designed spirally varying retarder (SVR) fabricated using a y-cut crystalline quartz, detailed analysis and results are presented in . However, the quality of the generated beam was still far from ideal, primarily due to the choice of fabrication technique. Here, we present an improved version of our SVR which generates light with high radial polarization purity. Previously, the SVR had a continuous spiral surface profile and was fabricated using laser-induced backside wet etching. In this work, we modified the continuous spiral profile into a segmented one and a new fabrication technique was adopted in order to improve the SVR’s surface roughness. This fabrication technique is described in the subsequent section.
2. Fabrication technique
The segmented SVR is fabricated on an α-BBO crystal in a multi-stage dry etching process using inductively coupled plasma of argon gas. α-BBO is a negative uniaxial crystal, and has large birefringence over broad transparent range from 189 nm to 3500 nm. (s-1) etching processes are needed for s segments SVR, since the original crystal thickness is considered as the first segment. We adopt uniform and equal etch depth for each segment. The etching depth is calculated as follows;
where λ is the operating wavelength, Δn the birefringence of the material, s the number of segment, Dseg the etch depth of each segment, and DTotal the total depth of the SVR. The total retardation is φ=(2π/λ)(ΔnDTotal)=4π(1-1/s). We define the error in phase retardation as the deviation in retardation change with respect to the number of segment, i.e. d 2 φ/ds 2. Therefore, the error in phase retardation relating to the number of segment is d 2φ/ds 2=-8π/s 3. For reasonable and practical assumptions, s is assumed to be more than four segments. To obtain a phase error of less than 5%, the least number of segments required is eight.
During each etching process, a mask was used to expose the desired area to be etched on the α-BBO crystal. These masks (M1 to M7) as shown in Fig. 1 were cut from 300 µm thick silicon wafer into the desired shapes using Q-switched diode pumped solid state (DPSS) 532 nm laser. With the help of custom-made mechanical parts, each mask was glued onto the α-BBO crystal using silicone high vacuum grease and was aligned to the crystal’s fast axis before each dry etching process. After the etching process, the silicon mask was removed and the grease left on the crystal was cleaned away using isopropyl alcohol.
To create the desired stepped spiral profile, the order in which the mask is used is important and there are two possible ways to do this. The first is to use the masks in an anticlockwise manner (refer to Fig. 2), M7 is used to cover S1 during the first etching process, M6 is used to cover S1 and S2 during the second etching process and so on and so forth until the final (seventh) etching process whereby M1 is used to cover S1 to S7. The second way is to use the masks in a clockwise manner, M1 covers S1 to S7 during the first etching process, M2 covers S1 to S6 during the second etching process and so on until the final (seventh) etching process whereby M7 covers S1 only. By adopting either methods, it can be deduced that after a total of 7 etching processes, S1 is not etched, S2 is etched once, S3 twice and so on and so forth, with S8 etched 7 times. The end result will be the stepped spiral profile as shown in Fig. 2(a). By adopting dry etching as the fabrication process, the surface roughness of the fabricated SVR is also greatly improved compared to that fabricated in . This is evident from Fig. 2(b).
The extraordinary and ordinary refractive indexes of α-BBO are calculated based on Sellmeier’s equations; and we obtain a birefringence of -0.1383 at a wavelength of 808 nm. Hence, the ideal etched depth for each segment of an 8-segment SVR is ~1.46 µm. As a result, the ideal total etched depth will be ~10.2 µm. Fig. 3 shows the actual 3D surface profile, as characterized by a surface profiler, at the central region of the fabricated SVR. The stepped spiral profile can be clearly seen and a total etched depth of ~11 µm was measured experimentally.
3. Experimental setup
The experimental setup is shown in Fig. 4. A CW Ti:sapphire laser operating at 808 nm with a linewidth of ~0.06 nm is used as the light source to the SVR. The beam is expanded to cover almost the whole area of the SVR, so as to maximize its conversion capability. The clear aperture of the SVR is about 22 mm. The SVR is sandwiched between two optically flat fused silica substrates with an optical index matching gel to eliminate most of the spiral wave front distortion induced by the SVR.
The SVR is then placed between the two orthogonally oriented quarter-wave plates (QWP1 and QWP2), and its slow axis is at 45° with respect to that of the first QWP. Subsequently, the emergent light from the SVR and QWPs passes through a pair of half-wave plates. They are used to rotate the emergent polarization state to the cylindrical vector beam  of interest such as radially or azimuthally polarized light .
4. Results and discussion
Figure 5 shows the near-field intensity distribution of the generated radially polarized light imaged using a CCD camera placed at the reduced 2f imaging distance of a lens. The actual SVR profile can be clearly seen when a polarizer is not used. When a polarizer is used to check the polarization state of the generated light, two bright lobes are seen rotating with the polarizer. The white arrows shown indicate the directions of the transmission axes of the polarizer and it can be deduced that the generated light is radially polarized. Looking at the intensity distribution of the emergent beam from the horizontal polarizer, one of the segments on the left appears darker than that on the right. This is due to a deviation in the fabricated height from the desired. Another supportive evidence can be seen from the intensity distribution of the emergent beam from the vertical polarizer. The same segment that appears dark previously is now bright which is undesirable. Using a 2D polarimeter, the radial polarization purity at the near field is measured and a value of ~94.6% is obtained.
Figure 6 shows the far-field intensity distribution of the generated radially polarized light imaged using a CCD camera placed at the focal plane of a lens. A clear doughnut shape is observed at the far field when a polarizer is not used. As in the near-field case, two bright lobes are seen when a polarizer is used and they rotate with the polarizer’s transmission axis. At the far-field region, the radial polarization purity obtained is ~96% with a M2 value of 2.39.
Despite the deviation of one of the segments from its desired height, the radial polarization purity obtained is close to the theoretical maximum possible for an 8-segment SVR. Thus, this scheme of radially polarized light generation is robust in the sense that it allows some deviations in step height. This eliminates the need for precise depth control and eases fabrication requirement. However, the demand for precise depth control becomes more stringent if a crystal with a higher birefringence is used. To further improve the polarization purity, one can modify the number of segments of the SVR. This can be easily deduced from the error in phase retardation shown earlier. With an increase in the number of segments, the error in phase retardation is reduced which will imply a higher theoretical polarization purity.
When the number of segments is increased, the total etching time remains the same as the total etched depth required is the same for a particular wavelength of light. Extra masks and finer mechanical aligners would be needed but these masks can be re-used and once fabricated, they will not add to the time required for fabricating the SVR. This can be a plus point from the fabrication view point.
Using silicon masks and mechanical aligners, the segmented SVR was successfully fabricated using a multi-stage dry etching process. The fabricated SVR has good surface roughness and a stepped spiral surface profile. To characterize the fabricated SVR, it was used to generate radially polarized light and then the radial polarization purity of the generated light is measured using a 2D polarimeter. The measured polarization purity is about 96%. By adopting dry etching as the fabrication method, fabricating a SVR with a large clear aperture becomes possible and this would facilitate the use of the SVR in high power laser applications. Also, fabrication costs would be cheaper than its photonic crystal counterpart. For the generation scheme, the main advantages include a simple setup and good robustness. Furthermore, the polarization purity can be enhanced by increasing the number of segments of the SVR.
This work was supported by Nanyang Technological University, DSO National Laboratories and Data Storage Institute, Agency for Science, Technology and Research, Singapore
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