Simple coherent polarization manipulation scheme for generating high power radially polarized beam
P. B. Phua1,* and W. J. Lai2
1 DSO National Laboratories, 20, Science Park Drive, S118230, Republic of Singapore, Nanyang Technological University, 50, Nanyang Avenue, S 639798, Republic of Singapore 2 Temak Laboratory, Nanyang Technological University, 50, Nanyang Avenue, S 639798, Republic of Singapore * Corresponding Author: ppohboon@alum.mit.edu鹤望兰花
Abstract: We prent 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 lar has short temporal coherence length. We generated 14 watts of radially polarized beam from an Ytterbium fiber lar, only limited by the available fiber lar power.
©2007 Optical Society of America
OCIS codes: (140.0140) Lars; (260.1440) Birefringence.
References and links
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15 16 R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Review Lett. 91, 233901 (2003). N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tipenhanced Raman spectroscopy,” Appl. Phys. Lett. 85, 6239 – 6241 (2004). T. Mor, H. Glur, P. Peier, M. Meier, E. Wyss, V. Ramano, M. Abdou Ahmed, O. Parriaux, U. Roth and Th. Graf, “Generation of radial polarization in Nd:YAG and CO2 lars and its applications,” Proc. SPIE, 5708, 112-123 (2005). I. Moshe, S. Jackel, and A. Meir, “Production of radially or azimuthally polarized beams in solid state lars and the elimination of thermally induced birefringence effects,” Opt. Lett. 28, 807 (2003). J. F. Bisson, J. Li, K. Ueda, and Yu. Senatsky, “Radially polarized ring and arc beams of a neodymium lar with an intra-cavity axicon”, Opt. Express 14, 3304 – 3311 (2006). R. Oron, S. Blit, N. Davidson, A. A. Friem, Z. Bomzon and E. Hasman, “The formation of lar beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322 (2000). D. Pohl, “Operation of a ruby lar in the purely transver electric mode,” Appl. Phys. Lett. 20, 266 (1972). K. Yonezawa¸ Y. Kozawa, and S. Sato, “Generation of a radially polarized lar beam by u of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett. 31, 2151 (2006). A. V. Nesterov, V G Niziev and V P Yakunin, “Ge
neration of high-power radially polarized beam,” J. Phys. D 32, 2871-2875 (1999). Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant subwavelength metal strip grating,” Opt. Lett. 27, 285-287 (2002). M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid crystal,” Opt. Lett. 21, 1948-1950 (1996). C. H. Niu, B. Y. Gu, B. Z. Dong, and Y. Zhang, “A new method for generating axially-symmetric and radially-polarized beams,” J. Phys. D, 38, 827-832 (2005). S. C. Tidwell, D. H. Ford, and W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2234-2239 (1990). P. B. Phua, W. J. Lai, Yuan Liang Lim, K. S. Tiaw, B. C. Lim, H. H. Teo, M. H. Hong, “Mimicking optical activity for generating radially polarized light,” Opt. Lett. 32, 376 – 378 (2007). S. C. Tidwell, G. H. Kim, and Wayne D. Kimura, “Efficient radially polarized lar beam generation with a double interferometer,” Appl. Opt. 32, 5222-5229 (1993). N. Passilly, R. d. S. Denis, K. Ait-Ameur, F. Treussart, R. Hierle, and J. F. Roch, “Simple interferometric technique for generation of a radially polarized light beam,” J. Opt. Soc. Am. A 22, 984-991 (2005).
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Received 4 Sep 2007; revid 8 Oct 2007; accepted 8 Oct 2007; published 12 Oct 2007
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G. Machavariani, Y. Lumer, I. Moshe, S. Jackel, and N. Davidson, “Efficient conversion of a radially– polarized beam to a nearly-Gaussian beam,” Opt. Lett. 32, 924-926 (2007.) J. Li, K. Ueda, M. Musha, A. Shirakawa, and Z. Zhang, “Converging-axicon-bad radially polarized ytterbium fiber lar and evidence on the mode profile inside the gain fiber,” Opt. Lett. 32, 1360-1362 (2007). H. Kogelnik and T. Li, “Lar beams and resonator,” Appl. Opt. 5, 1550-1567 (1966).
Radially polarized beam has gained much interest recently [1-18], due to its ability to be focusd tighter than a diffraction-limited beam [1]. This can improve applications such as particle-trapping, optical data storage, lar machining and micro-lithography. In addition, the prence of high inten longitudinal electric field in the vicinity of the focal point of a lar beam can also enhance nonlinear effects for applications such as tip-enhanced Raman spectroscopy [2]. This longitudinal electric field can also be ud for lar particle acceleration without a plasma wave. Most reported methods generate radially polarized beam by placing specially designed optical elements [4-10] inside the lar cavity. However, this introduces additional intra-cavity loss, and may make the optimal design o
f the lar difficult. Moreover, for high power fiber lars, UV lars ud in lithography, miconductor lars, it is not always viable to add such optical elements inside the lar resonator. Thus, an external radially polarization conversion is an attractive and flexible alternative [1, 11-16]. Previous reported external polarization conversion schemes bad on a liquid crystal array [11] and diffractive pha element [12], tend to have low power handling while schemes that u gmented half wave-plates scheme [1] can only approximate the radially polarized beam. While the spirally varying retarder propod recently in [14] has high lar power handling capability, it requires specialized fabrication technique for its spiral profile. Radially polarized beam is a coherent summation of a horizontal polarized TEM10 with a vertical polarized TEM01 Hermite-Gaussian mode [6, 13, 15, 16]. Previous interesting schemes [6, 13, 15, 16] implemented this coherent summation of modes using Mach-Zehnderlike interferometric arrangements, in the effort of converting Gaussian beam into a radially polarized beam. Most recently, Ref. [17] propod the coherent mode transformation in the rever manner, from a radially polarized beam to an approximated Gaussian mode. The main limitation of the interferometric methods is they require interferometric stability. This may limit its practical ufulness. In addition, they also require specially designed optics such as spiral pha plate and binary diffractive optical element, which may not be widely available as they require special fabrication techniques. In this paper, we propo a simple and stable coherent p
olarization manipulation scheme to convert a Gaussian mode to an approximated radially polarized beam. The scheme makes u 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 pha 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 lar. The demonstrated power is only limited by the available power from our fiber lar. However, since all optical components ud in our scheme are standard off-the-shelf components that have power handling capability of more than kilowatts of lar power, the scheme will be a promising radial polarization converter for high power fiber lar. Our simple scheme, in principle, requires only three optical components: a Poynting walkoff crystal, a thin half-wave plate and a 45o quartz rotator, as shown in Fig. 1. The lar
#87143 - $15.00 USD
Received 4 Sep 2007; revid 8 Oct 2007; accepted 8 Oct 2007; published 12 Oct 2007
(C) 2007 OSA
17 October 2007 / Vol. 15, No. 21 / OPTICS EXPRESS 14252
Elliptical Gaussian Beam
Optics Axis
Walk-Off Crystal
HWP数学名言大全
Quartz Rotator
Fig. 1. Schematic of our simple coherent polarization manipulation scheme which comprid of a walk-off crystal, a thin Half-Wave Plate (HWP) and a 45o quartz rotator. Their lar beam cross-ctions and their associated polarizations after each component are also shown.
beam cross-ction after each stage of the scheme, and their associated polarizations are also show
n in Fig. 1. An input elliptical Gaussian beam with a 45o linear polarization is being splitted by a Poynting walk-off crystal into two equal power beams with a beam paration that determined by the crystal’s walk-off length. The polarizations of the top and bottom beam are orthogonal and their fields are controlled to be in pha by slight tilting the walk-off crystal. A thin half-wave plate (HWP), with slow axis of 45o with respect to the horizontal direction, is then ud to rotate the polarization of the right half of both the top and bottom elliptical beams by 90o. By tilting HWP about the vertical direction, as shown in Fig. 1, we control the pha difference between the left and the right lobes of the beams to be 180o out of pha. A subquent 45o optical activity quartz rotator then rotates the polarizations of the four lobes globally by 45o. The generated 4-lobes beam, and their respective polarizations (as shown in Fig. 1) form a t of approximated Hermite-Gaussian TEM10 and TEM01 modes in a 45o rotated frame. The TEM10 and TEM01 modes are of orthogonal polarizations and are coherently in-pha. As suggested by Kogelnik and Li back in 1966 [19], the modes can superimpo coherently in far-field to approximate the radially polarized beam. We first u a continuous-wave, single longitudinal mode, 1064nm lar to demonstrate this scheme. This highly coherent lar 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 Fig. 2, with a beam quality of M 2 ~2.2. Without a polarizer, the output was a doughnut-shaped light beam as shown in F运动会发言稿
ig. 2(a). When the polarizer was inrted prior to the camera, two spots were clearly en, and they rotated with the transmitting axis of the polarizer, as en in Figs. 2(b)-2(e) which clearly illustrated the radially polarized profile. The mode conversion is stable and it lasts many hours to veral days without any tweeking. This is expected since all polarization and pha 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 lar source to a Ytterbium (Yb) doped fiber lar that can produce 15 Watts of polarized 1064 nm. This fiber lar has a broad bandwidth of 2 nm and our initial attempt to perform radial polarization conversion using the three-element scheme shown in Fig. 1, was unsuccessful. This is becau the coherent length of this lar is shorter than the optical path difference (i.e (n e −no ) l ) traverd by the two orthogonally polarized beams in the walk-off
#87143 - $15.00 USD
Received 4 Sep 2007; revid 8 Oct 2007; accepted 8 Oct 2007; published 12 Oct 2007
(C) 2007 OSA
17 October 2007 / Vol. 15, No. 21 / OPTICS EXPRESS 14253
(b) 0
o
(c) 90
o
(a) No Polarizer
(d) 45
o
(e) 135
o伊斯兰卡
Fig. 2. Radially polarized beam converted from a highly coherent, single longitudinal mode 1064 nm lar: (a) obrved without polarizer, and obrved with polarizer who transmitting axis is (b) 0o, (c) 90o (d) 45o, and (e) 135o.
crystal. Noted that no and n e are the respective refractive indices of the ordinary and extraordinary polarization of the crystals. This inhibits any coherent mode superposition for the generating radially polaried light. To circumvent this issue, we ud two identical birefringent crystals (Walk-Off Crystal 1 and Walk-Off Crystal 2) with a half-wave plate (HWP2) placed between the two crystals, as shown in Fig. 3, to perform the beam paration. The crystallographic optics axis of Walk-Off Crystal 1 is 45o with respect to the lar propagation direction while that of Walk-Off Crystal 2 is 135o. Each crystal has length l and has a Poynting walk-off distance of d w for their extra-ordinary polarization. Figures 3(b) – 3(h) show the lar beam cross-ctions and their associated polarizations after each stage of the scheme. Upon entering the Walk-Off Crystal 1, the extra-ordinary polarization component (i.e. vertical polarization) walk-off vertically upward with respect to the ordinary polarization component (i.e. horizontal polarization). With the slow axis of HWP2 being 45o with respect to the horizontal direction, the top elliptical beam after passing though HWP2, becomes the ordinary polarization while the bottom becomes the extra-ordinary polarization of Walk-Off Crystal 2. The bottom elliptical beam therefore walks a distance of d w vertically downward after passing through Walk-Off Crystal 2. The total paration between the two elliptical beams after passing through the two crystals is 2d w . It is worthwhile to note that, with such two-crystal arrangement, both top and bottom elliptical beam have traverd the same optical length of (no + n e ) l . Thus, constant coherent pha relation
ship can be maintained between the top and bottom elliptical beam even when the lar has short temporal coherence length. Thus this allows coherent superposition of modes even for the broadband Yb fiber lar. In addition, in this particular experiment, instead of rotating the Walk-off crystal, as shown in Fig. 1, to maintain same pha for the top and bottom elliptical beams, we u a polarization controller comprising of a half-wave plate (HWP1) followed by a quarter-wave plate (QWP) to accomplish the same effect. The input polarization of the elliptical beam, in
#87143 - $15.00 USD
Received 4 Sep 2007; revid 8 Oct 2007; accepted 8 Oct 2007; published 12 Oct 2007
(C) 2007 OSA
17 October 2007 / Vol. 15, No. 21 / OPTICS EXPRESS 14254
(a)
Elliptical Gaussian Beam
(b)
ωy ωx
HWP1 QWP
Walk-Off Crystal 1 Optics Axis
HWP2
Walk-Off Crystal 2 Optics Axis
开罗会议Quartz Rotator
HWP3
(g) (h)
(c)
(d)
(e)
(f)
2d w
西游记人物Fig. 3. Schematic of our coherent polarization manipulation scheme for low coherent broadband Yb fiber lar. Lar beam cross-ctions and their associated polarizations of (b) input elliptical Gaussian beam, (c) after QWP, (d) after Walk-Off Crystal 1, (e) after HWP2, (f) after Walk-Off Crystal 2, (g) after HWP3, (h) after quartz rotator.
this ca, is vertically linear. The slow axis of QWP is fixed at 45o with respect to the horizontal direction while the slow axis of the half-wave plate is adjustable. By rotating the slow axis of HWP1, we adjust the ellipticity of the 45o oriented input polarization that enters Walk-Off crystal 1, so that the top and bottom elliptical beam exiting from Walk-Off Crystal 2, have equal power and pha. This accomplishes the same effect as rotating the Walk-off crystal in Fig. 1. In this experiment, the 1-micron Ytterbium (Yb) doped fiber lar beam was shaped using a pair of cylindrical lens into an elliptical Gaussian profile of ω x of 2.7 mm and ω y of 1.35 mm. The two crystals ud were identical Alpha-BBO crystals (45o-cut) of length 11.4 mm. Each crystal contributes a walk-off distance of 1 mm and their orientations were accordingly to Fig. 3. For HWP3, we ud a 60.8 microns thick cryst
alline quartz waveplate which is a true zero-order half-wave plate, and its slow axis is 45o with respect to the horizontal direction. The small thickness of HWP3 gives robust angular tolerance in controlling the pha difference between the left and right lobes of the beams. We obtained 14 watts of average power of approximated radially polarized beam, only limited by the maximum power available from our fiber lar. Without any thermal management for the walk-off crystals and polarization wave-plates, we did not obrve any thermal fluctuation at this operating power. This endors the fact that the alpha-BBO crystals and the crystalline quartz wave-plates have negligible lar absorption and high power handling capability. Thus, we are optimistic that the scheme has good potential to produce more than hundreds of watts of radially polarized light. The approximated radially polarized 2 2 beam, has the measured beam quality was M x ~ 3.6 and M y ~ 2.1. Fig. 4 shows the radially polarized beam (obrved with and without polarizer) after a spatial filtering of power 2 2 throughput of 73%. The measured beam quality after filtering was M x ~ 2.43 and M y ~ 2.28. In conclusion, we have prented 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 t of orthogonally polarized and coherently in-pha TEM10 and TEM01 modes. The modes superimpo at far field to generate a near radially polarized beam. Since the manipulation is accomplished inside the crystals, it alleviates the high interferometric nsitivity of previous interferometric
#87143 - $15.00 USD
Received 4 Sep 2007; revid 8 Oct 2007; accepted 8 Oct 2007; published 12 Oct 2007
(C) 2007 OSA
17 October 2007 / Vol. 15, No. 21 / OPTICS EXPRESS 14255
(b) 0= 0 deg Polarizer
驳组词语
o
(c) 90 Polarizer = 90 deg
o
(a) No Polarizer
No Polarizer
(d) 45 Polarizer = 45 deg
o
(e) 135 Polarizer = 135 deg
o
吉祥结怎么编
Fig. 4. Radially polarized beam converted from a low coherent, broadband 1064 nm Yb fiber lar: (a) obrved without polarizer, and obrved with polarizer who transmitting axis is (b) 0o, (c) 90o (d) 45o, and (e) 135o.
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 halfwave plate so that the temporal coherence length of the lar will not po a problem to the coherent manipulation of the beam. Acknowledgments 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.
#87143 - $15.00 USD
Received 4 Sep 2007; revid 8 Oct 2007; accepted 8 Oct 2007; published 12 Oct 2007
(C) 2007 OSA
17 October 2007 / Vol. 15, No. 21 / OPTICS EXPRESS 14256
