Laser expander design of highly efficient Blu-ray disc pickup head

Laser expander design of highly efficient Blu-ray disc pickup head Wen-Shing Sun, 1,* Kun-Di Liu, 1 Jui-Wen Pan, 1 Chuen-Lin Tien, 2 and Min-Sheng Hsieh 1 1 Department of Optics and Photonics, National Central University, 32001 Chung-Li, Taiwan(R.O.C) 2 Department of Electrical Engineering, Feng Chia University, Taichung, Taiwan( R.O.C.) * Corresponding author: wssun@dop.ncu.edu.tw Abstract: We present a collimator design with a horizontal beam expander for a Blu-ray Disc pickup head. The design transforms the shape of a laser diode beam from an elliptical into circular which achieves higher efficiency in the pickup head system. In this research, we suggest two ways to do the beam expander. One way is to use two cylindrical lenses, and the other is to use two prisms. 2009 Optical Society of America OCIS codes: (080.0080) Geometric optics; (220.4830) Systems design; (110.2945) Illumination design; (210.0210) Optical data storage; (210.4590) Optical disks References and links 1. W. S. Sun, T. X. Lee, C. C. Sun, C. H. Lin, and C. Y. Chen, Design of miniature HD-DVD optical pick-up head using a Penta prism, J. Mod. Opt. 52, 775-789 (2005). 2. W. S. Sun, C. C. Sun, J. T. Chang, C. L. Tien, and S. H. Ma, Triple-wavelength optical pickup head designs for compact disk, digital versatile disk and high-density digital versatile disk devices, J. Mod. Opt. 52, 2523-2547 (2005). 3. N. Murao, H. Koyanagi, K. Koike, and S. Ohtaki, Photo-Polymer objective lens for red blue lasers, Jpn. J. Appl. Phys. 39, 906-907 (2000). 4. Y. Tanaka, T. Watanabe, M. Shinoda, T. Shimouma, Y. Murakami, and A. Takahashi, Applying an objective lens of 0.7-numerical aperture to a center-aperture-detection type of magnetically induced superresolution disk, Jpn. J. Appl. Phys. 39, 719-724 (2000). 5. R. Liang, J. Carriere, and M. Mansuripur, Intensity, polarization, and phase information in optical disk systems, Appl. Opt. 41, 1565-1573 (2002). 6. W. H. Lee, Holographic optical head for compact disk applications, Opt. Eng. 28, 650-653 (1989). 7. Y. Komma, S. Kadowaki, Y. Hori, and M. Kato, Holographic Optical element for an optical disk head with spot-size detection sevo optics, Appl. Opt. 29, 5127-5130 (1990). 8. I. Ichimura, F. Maeda, K Osato, K. Yamamoto, and Y. Kasamiet, Optical Disk Recording Using a GaN Blu-Violet Laser Diode, Jpn. J. Appl. Phy. 39, 037-942 (2000). 9. W. H. Sun, U.S. Parent 20060209293 (Sep. 21, 2006). 10. W. H. Sun, U.S. Parent 20060215530 (Sep. 28, 2006). 11. W. H. Sun, U.S. Parent 7355798 (Apr. 8, 2008). 12. M. Lakin, Lens Design (Marcel Dekker, New York, 1995) p. 148. 13. R. Kingslake, Optical System Design (Academic Press, New York, 1983) p. 225. 14. LightTools Core Module User s Guide, Version 6.1, Optical Research Associates, 2008. 15. Code V Reference Manual, Version 9.8, Optical Research Associates, 2007. 1. Introduction Generally, the traditional optical pickup head has such a low efficiency, that its power must be increased by the use of a laser diode as shown in Fig. 1 [1,2]. This leads to high cost, and induces thermal management and shorter light time problems. The typical optical pickup head consists of a laser diode, beam splitter, collimating lens, objective lens and photo detector integrated circuit (PDIC). The laser diode has two emissive angles in the horizontal and vertical directions. The design angle of the pickup head in relation to the horizontal intensity is defined as 1/e 2. In the typical pickup head design, a collimating lens is used to collimate the light with the design angle, so most of the vertical beam is cut-off by the collimating lens. This leads to large energy loss as shown in Fig. 2. The design angle is 7.161 degrees and the (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2235

optical efficiency of this design is only 45.46%. There is 50% reflectance loss after passing through the beam splitter. The light source is focused on the optical disk by the objective lens. The light after being reflected by the optical disk goes to the objective lens, collimating lens, beam splitter and photo detector. The final total optical efficiency is 8.89%. Fig. 1. Layout of the traditional optical pickup head. The light from the laser diode is approximately 90% polarized. In order to enhance the efficiency, we first replaced the beam splitter with a polarizing beam splitter (PBS) then added a 1/4λ wave plate [3-5]. The polarizing beam splitter has P polarization transmittance and S polarization reflectance. After passing forward and backward through a 1/4λ wave plate, the polarization state of the light is altered from the P state to the S state. The optical efficiency of the PBS and 1/4λ wave plate optical system increases to 31.82%. Lee [6] and Komma et al. [7] replaced the beam splitter and cylindrical lens in the traditional optical pickup head with a hologram. The diffractive efficiency of the holographic optical element was 40% and 20% for zero diffractive order and first diffractive order, respectively. The beam passing through the hologram to the disc use the first order when reflected by disc resulting in a total optical efficiency of only 2.85 %. Ichimura [8] et al. reported on an anamorphic-prism design. The beam expansion caused deviation of the optical axis in the horizontal direction. It is time consuming to align the optical axis of the collimator lens and the optical axis of the objective lens simultaneously. The enhancement of the efficiency of the collimator lens is the main goal of this work. We used the horizontal beam expander to increase the optical efficiency from 45.5% to 82.54%.[9-11] 2. Theory The Blu-ray disc optical design consists of an objective lens and a collimating lens. In order to enhance the optical efficiency, we use a horizontal beam expander to transform the elliptical beam into a circular beam without any loss of the vertical laser beam. 2.1 Objective lens design Table 1 shows the specification of the Blu-ray disc. According to the specifications, the numerical aperture (NA o ) of the objective lens is 0.85. The numerical aperture is a characteristic parameter of an optical system defined by Do NAo = no sin θo =, (1) 2 f where n o is the refractive index of the disc; θ o is half the focus angle; D 0 is the clear aperture; and f o is the effective focal length (EFL) of the objective lens [1,2]. o (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2236

Table 1. Specifications of the HD-DVD system. HD-DVD Source wavelength 405 nm NA of objective lens 0.85 Disk thickness of transparent layer 0.1 mm 2.2 Collimating lens design We use the laser vertical intensity at 1/e 2 as the design angle for the emissive beam. According to Fig. 2, the design angle of collimating lens is 19.372 degrees. The numerical aperture of the collimating lens can thus be defined as Dc NAc = sin19.372 = = 0.332, (2) 2 fc where D c is the aperture of the collimating lens; f c is the EFL of the collimating lens. The tracking error of the objective lens should be kept within ±0.3 mm, meaning that the aperture size of the collimating lens will be D c = D o + 0.6 mm [1,2]. We found intensity in the horizontal direction decrease to be zero when the emissive angle was larger than 17. The elliptical beam passing through the collimating lens leads to a big disadvantage for data reading on the disc. We used a horizontal beam expander to transform an elliptical beam into a circular beam, so that the aperture size would be the same in the horizontal direction as in vertical direction. Fig. 2. Relative intensity distribution of the laser diode for the traditional optical pickup head. 2.3 Horizontal beam expander with cylindrical lens Based in the design principle of the Galilean telescope [12], we utilized two cylindrical lenses to finish the horizontal beam expander as shown in Fig. 3. We set f 1 and f 2 to be the focal lengths of the first and the second cylindrical lens, respectively. This makes the first cylindrical lens a negative lens (f 1 <0), and the second cylindrical lens a positive lens (f 2 >0). The distance between the two cylindrical lenses is the sum of two effective focal lengths. The beam expander magnification (m) is defined as angular magnification f2 D2 m= =, (3) f1 D1 where D 1 and D 2 are the beam diameters of the first and the second cylindrical lenses, respectively. This is the ratio of positive focal length to the negative focal length of the two cylindrical lenses. (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2237

2.4 Horizontal beam expander with prisms We also used two prisms as the horizontal beam expander [13]. Fig. 4 shows the beam expander in the prism system. α represents the vertex angle of the prisms, α 1 is the tilt angle of first prism, d 1 is the diameter of incident beam, θ 1 = α + α 1 indicates the incident angle of the first surface of the first prism and θ 1 = α indicates the refractive angle of the first surface of the first prism. We find that both the incident angle θ 2 and the refractive angle θ 2 of the second surface of the first prism are zero. The diameter of the beam after passing through the first prism is d 2, so the magnification after passing through the first prism can be shown as follows: d2 cosθ 1 cosθ2 cosα m1 = = =. (4) d cosθ cosθ cos α+ α ( ) 1 1 2 1 The deviation of the first prism is thus δ 1 = -α 1. In the same way, we define the incident angle of the first surface in the second prism by θ 1 = - α - α 1 and the refractive angle of the first surface of the second prism to be θ 3 = -α. We find that both the incident angle θ 4 and the refractive angle θ 4 of the second surface of the second prism are zero. The diameter of the beam after passing through the second prism is d 3. We can obtain the magnification after passing through the second prism by d3 cosθ 3 cosθ4 cosα m2 = = =. (5) d 2 cosθ3 cosθ 4 cos( α+ α1) Thus the total magnification of the prism system can be shown as follows: 2 d3 cos α m= m1m 2 = =. (6) 2 d cos α+ α ( ) 1 1 The angle of deviation δ is now equal to zero. δ = δ1+ δ2 = 0. (7) Fig. 3. Horizontal beam expander with two cylindrical lenses. Fig. 4. Horizontal beam expander with two prisms. (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2238

2.5 S-Curve In order to validate the optical efficiency of the returning path of the optical pickup head, the variation of the beam profile which varied as an S-curve was monitored by a PDIC after which the system efficiency analysis was perform. A plano-concave cylindrical lens with its axis oriented at 45 along the returned path was added. This system was reconstructed by using the LightTools software [14]. The position of disk varied by ±10 µm, the observations obtain from a quadrant photo detector were used to calculate the energy distribution as shown in Fig. 5. When the reflected light beam impinges on A, B, C and D of the quadrant detector, a focus error signal (FES) is output based on distribution of the beam spot among A, B, C and D. As can be seen in Fig. 6, if the combination A+C-B-D < 0 the Blu-ray Disc position is in front of the focal point of the objective lens, and if A+C-B-D=0 it means that the Blu-ray Disc is locate on the focal point of the objective lens. If the diagonal signal A+C-B-D>0 it indicates that the Blu-ray Disc position is behind the focal point of the objective lens. FES is the value of A+C-B-D corresponding to the different focus errors. The relationship between both of them is indicated by the plot of the S-curve shown in Fig. 7. Fig. 5. Layout of quadrant photo detector. (a) (b) (c) Fig. 6. Beam shape measurements by astigmatism method (a) the Blu-ray Disc in front of the focal point. (b) the Blu-ray Disc on the focal point. (c) the Blu-ray Disc in behind of the focal point. Fig. 7. Plot of the S-Curve. (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2239

3. High efficiency optical pickup head design In order to increase the optical efficiency of a laser diode, we find the intensity at 1/e 2 when the design angle for the vertical direction is 19.372 degrees and for the horizontal direction is 7.161 degrees. If we use both these angles, the optical efficiency would increase to 93.79%, as shown in Fig. 8. The effective focal length of the collimating lens is 5.312 mm. We found the clear aperture of the intensity at 1/e 2 for the vertical direction to be 3.524 mm and that for the horizontal direction to be 1.324 mm, so the expander magnification is 2.662. Fig. 8. Relative intensity distribution of the horizontal beam expander for an optical pickup head. 3.1 Horizontal beam expander for an optical pickup head using two cylindrical lenses Figure 9 shows the beam expander for the optical pickup head using two cylindrical lenses. Two cylindrical lenses with an effective focal length of -2 mm and 5.323 mm to match the expander magnification of 2.662 are used to expand the horizontal beam equal to vertical bream. The distance between the two cylindrical lenses is represented by d. d = f1+ f2 = 3.323 mm. (8) Fig. 9. Layout of the horizontal beam expander with two cylindrical lenses. Figure 10 shows the efficiency of the un-polarized optical pickup head system with two cylindrical lenses. The optical efficiency of the laser beam after passing through the collimating lens was 93.79%. After passing through the horizontal beam expander system with two cylindrical lenses, the efficiency decreased to 82.36%. After passing through the beam splitter the optical efficiency decreased to 41.23%. Owing to tracking error loss, the (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2240

optical efficiency on the disc was 33.93%. After the ray was reflected and passed through the system, the optical efficiency on the photo detector was 16.72%. However we used a PBS and inserted a 1/4λ wave plate. The optical efficiency increased to 60.12% as shown in Fig. 11. Fig. 10. Optical efficiency of the un-polarized horizontal beam expander with two cylindrical lenses. Fig. 11. Optical efficiency of the polarized horizontal beam expander with two cylindrical lenses, a PBS and a 1/4λ wave plate. 3.2 Horizontal beam expander using two prisms of the optical pickup head The magnification of the horizontal beam expander can be used with Eq. (6). In this system, we used a plastic material of ZEONEX Z480R with an index of 1.5476. We set the horizontal beam expander magnification to be 2.66. We can now calculate the vertex angle α and the tilt angle α 1 using Eqs. (9) and (10) sin α+ α = nsin α, (9) ( ) 2 m 1 sin α =, (10) 2 mn 1 We now have α = 33.781 and α 1 = 25.591. The two prisms of un-polarized horizontal beam expander are shown in Fig. 12. We can see that light passes first through the beam splitter, then the collimating lens and is focused on the disc by the objective lens. The optical efficiency on the photo detector was 16.67% as shown in Fig. 13. If we used a PBS and inserted a 1/4λ wave plate, the optical efficiency increased to 59.71% as shown in Fig. 14. 1 (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2241

Fig. 12. Layout of the horizontal beam expander with two prisms. Fig. 13. Optical efficiency of the un-polarized horizontal beam expander with two prisms. Fig. 14. Optical efficiency of the polarized horizontal beam expander with two prisms, a PBS and a 1/4λ wave plate. 4. Tolerance analysis An example of the horizontal beam expander system with two cylindrical lenses is shown in Fig. 9. The Code V [15] program is used to simulate the tolerance analysis of this design as shown in Fig. 15. The root mean square value (RMS) of the wavefront error is 0.0323λ for (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2242

97.7% cumulative probability [2]. There are two adjustments for the tolerance analysis. One is to use an actuator to adjust the tilt and/or to defocus the objective lens. The other is to adjust the collimating lens. 5. Comparison Fig. 15. Tolerance analysis of the horizontal beam expander system with two cylindrical lenses. Figure 16 presents a round-trip light efficiency distribution for different pickup head designs. There are two traditional designs with un-polarization and polarization, two horizontal expander designs with un-polarization and polarization. 70% Efficiency Summary 60% 60.12% 59.71% 50% Efficiency 40% 30% 31.82% 20% 16.72% 16.67% 10% 8.89% 0% Typical Cylindrical Prism Typical Cylindrical Prism pickup head expander expander pickup expander expander pickup head pickup head head(pol.) pickup pickup head(pol.) head(pol.) Fig. 16. Comparison of optical efficiency for different optical pickup head designs. The traditional Blu-ray Disc system with un-polarization is shown in Fig. 1. The laser beam spot impinges on the disc reflecting the light beam at different focusing positions on the PIDC. The variation in the beam profile is shown in Fig. 17. The basic structure of the unpolarized horizontal beam expander for the Blu-ray Disc system is shown in Fig. 10. The laser beam spot impinges on the disc then reflects the light beam to different focusing positions on the PIDC. The variation in the beam profile is shown in Fig. 18. (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2243

On focus Defocus +2.0 µ m Defocus -2.0 µ m Defocus +4.0 µ m Defocus -4.0 µ m Defocus +6.0 µ m Defocus -6.0 µ m Fig. 17. Traditional design with un-polarization by the beam shape changes at different focusing position on the photo detector. (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2244

On focus Defocus +4.0 µ m Defocus -4.0 µ m Defocus +8.0 µ m Defocus -8.0 µ m Defocus +12.0 µ m Defocus -12.0 µ m Fig. 18. Horizontal beam expander design with un-polarization by the beam shape changes at different focusing position on the photo detector. (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2245

6. Conclusions A horizontal beam expander collimator can increase the optical efficiency of a laser diode. The efficiency can be enhanced to triple that of the traditional optical pickup head. Thus the power of the laser diode can be decreased and the life time of the laser diode increased. This would lead to the power saving and the achieving of a more compact system. Acknowledgments This study was sponsored by the National Science Council of Republic of China, Taiwan, under contract number NSC 95-3114-P-001-008-MY3. (C) 2009 OSA 16 February 2009 / Vol. 17, No. 4 / OPTICS EXPRESS 2246