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Photonic crystal changes coherent laser to incoherent laser with random phase
Optics Communications 283 (2010) 1394–1396
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Photonic crystal changes coherent laser to incoherent laser with random phase Hong-Zhao Zheng, Wen-Yao Liang, Zhen Li, Jian-Wen Dong, He-Zhou Wang * State Key Laboratory of Optoelectronic Materials and Technologies, Zhongshan (Sun Yat-Sen) University, Guangzhou 510275, China
a r t i c l e
i n f o
Article history: Received 19 September 2009 Received in revised form 25 November 2009 Accepted 25 November 2009
Keywords: Incoherent laser Photonic crystal Phase Polarization
a b s t r a c t It is revealed that the phase-shift and polarization properties of laser beam reflected from a photonic crystal (PC) are sensitive to the surface-layer thickness of the PC. A continuous variation of k/4 in surface-layer thickness produces a continuous change of p in the phase-shift. Besides, in the case of an asymmetric coupled-defect PC, various polarization patterns including linearly polarization in different directions, circular polarization, and different elliptical polarizations, will appear simultaneously within one laser beam. In this paper, a PC with modified surface-layer thickness is designed to induce incoherent laser irradiation with random phase at the focus point of the reflected field. This scheme will satisfy the increasing requirements for incoherent laser irradiation. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Lasers are one of the most significant inventions of the 20th century. A variety of applications of laser in optical communication, computer engineering, industry, medicine, military and scientific research were introduced in the past few decades. Since it first appeared in 1960, broad attention was attracted to the high coherence property of the output wave, which makes many applications possible. However, it is also shown that some of the laser applications do not necessarily relate to coherence. Recently, it is found that many emerging applications which highlight other laser properties, like high directionality, high intensity and monochromaticity, could be disturbed by laser’s coherence property [1–14]. Here, we give two representative examples: (1) coherence property makes the energy distribution at the focus point of laser inertial constraint nuclear fusion not uniform enough [1]. (2) The speckle noise, which results from coherence property of laser, increases the noise of laser radar, and seriously reduces the articulation of laser display (laser projection imaging or laser TV) [12,13]. Therefore, method to fully or partially eliminate the laser coherence is in urgent need. So far, three methods have been proposed for laser decoherence in certain applications: (1) for only two coherent laser beams, perpendicular polarizations can avoid coherence [10]. (2) In some experiments [4,8], incoherent laser condition is realized by employing different wavelength, multi-wavelength or broadband lasers. (3) Let the laser pass a two-level phase plate, in which the phase-shift is either 0 or p, to reduce the coherency of laser [1].
* Corresponding author. E-mail address: [email protected] (H.-Z. Wang). 0030-4018/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2009.11.070
On the other hand, investigation into ordinary radiation shows that waves with random phase are intrinsically incoherent. Therefore, generation of incoherent laser radiation with random phase is of great significance, which still lacks for study. Furthermore, it has been revealed that phases play an important role in many phenomena and applications of PC. The representative examples of phenomena related to phases of PC are superluminal (faster-than-light) or slow light [15–17] and micro-cavity [18]. Recently, some measurements of PC phase have been reported [19,20]; and some photonic crystal phase devices have appeared [21,22]. The phase properties of PC above demonstrate that it is possible to use PC to modify the phase of laser. In this letter, we find that the phase and polarization of the laser beam reflected from a 1D PC are sensitively dependent on the thickness of the surface-layer of the PC. Based on these properties, we develop a simple method for the generation of incoherent laser with random phase and random polarization to satisfy the increasing requirements. 2. Surface-layer thickness-dependent phase and polarization Firstly, let us discuss the dependency of the phase-shift of a laser beam on the varying surface-layer thickness of a 1D PC that reflects the beam. In this work, our calculation is carried out by using the transfer matrix method [23]. To reveal the basic idea of this modulation effect, we firstly evaluate the simplest structure of Hs(LH)7, in which, ns = nH = 2.45, nL = 1.38; and the optical thickness of periodic structure ndH = ndL = k0/4, and Hs refers to the surface-layer. The results of calculation are as follows. The reflectance of the PC almost does not change with the thickness of the surface-layer, i.e., the band gap structures are
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H.-Z. Zheng et al. / Optics Communications 283 (2010) 1394–1396
1.0
1.0
0.5
0.5
(a)
0.5
0.5 0.0 -0.5
(b)
0.0
(a)
0.0 1.0
θ (π)
θ (π)
0.0 1.0
(b)
-1.0 1.5
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independent on the surface-layer thickness. However, the phaseshift is sensitively dependent on the thickness of the surface-layer. Fig. 1 shows the relationship between the surface-layer thickness (nSdS) and the phase-shift (h) of a laser beam reflected from a 1D PC at normal incidence, and at an incident angle of 30° for S wave and P wave, respectively. The results demonstrate that the phaseshift changes by one p when the optical thickness of the surfacelayer of the PC increases from 0 to k0/4, while the reflectance of the PC almost does not change with the thickness of the surfacelayer. Our results also show that, at oblique incidence, the phaseshifts of S and P waves differ at different thickness of surface-layer, so the phase difference (Dh) between S and P waves is dependent on the thickness of surface-layer as well. Since the polarization of light is determined by Dh, the above results imply that the polarization of the reflected wave is also dependent on the thickness of surface-layer. However, Fig. 1 also shows that Dh is very small at the incident angle of 30°, and such a simple structure will not produce significant change in the polarization of the wave. Many 1D PC structures can be used to modify the phase-shift and the polarization of laser beam. Here we give a sensitive example, an asymmetric 1D PC with five coupled defects [22]. The structure of this asymmetric 1D PC with five coupled defects is HsL(HL)2D(LH)3L(HL)3D(LH)3L(HL)3D(LH)3L(HL)3D(LH)3L(HL)3D(LH)7, where nDdD = k0/2 and the other parameters are the same as above. For this asymmetric coupled-defects PC, the relationship between the surface-layer thickness (nDdD) and the phase-shift (h) of laser beam that reflect from a 1D PC is investigated, at normal incidence and the incident angle of 30°, respectively. As is shown in Fig. 2, at normalized frequency of 1.02608, Dh becomes very large, which indicates that this structure can produce a change large enough in the polarization of the wave. For different frequency, the relationship between Dh and the optical thickness of the surface-layer, at the incidence angle of 30°, are different. For the most frequencies around the defects modes, Dh covers a wide range from 0 to 1.2p. For example, Figs. 3a–c show the relationships between Dh and nSdS at the incidence angle of 30° for normalized frequency (x/x0) 1.02608, 1.02556, and 1.02513, respectively. Obviously, Dh covers a wide range from 0 to 1.2p. The results in Figs. 2 and 3 imply that after
0.15
0.20
0.25
Fig. 2. The phase-shift of laser beam that reflect from a 1D PC as a function of the optical thickness of the surface-layer. The structure of the coupled-defect asymmetric PC is HsL(HL)2D(LH)3L(HL)3D(LH)3L(HL)3D(LH)3L(HL)3D(LH)3L(HL)3D(LH)7. The normalized frequency (x/x0) is 1.02513. (a) normal incidence, (b) the incident angle of 30° for S wave, and (c) the incident angle of 30° for P wave.
(a)
1.5 1.0 0.5
Δθ (π)
Fig. 1. The phase-shift (h) of laser beam that reflect from a 1D PC as a function of the optical thickness (nSdS) of the surface-layer at (a) normal incidence, (b) the incident angle of 30° for S wave, and (c) the incident angle of 30° for P wave. The normalized frequency is x/x0 = 1. The structure is Hs(LH)7 (nS = nH = 2.45, nL = 1.38). The optical thicknesses of the periodic layers are nHdH = nLdL = k0/4.
0.10
nSdS/λ0
nSdS/ λ 0
0.0
(b)
-0.5
-1.0
(c)
1.5 1.0 0.5 0.00
0.05
0.10
0.15
0.20
0.25
nSdS/λ0 Fig. 3. The relationship between Dh and the optical thickness of the surface-layer, at the incidence angle of 30°, in which the normalized frequency (x/x0) are (a) 1.02513, (b) 1.02556, and (c) 1.02608. The Dh covers a wide range from 0 to 1.2p.
the laser beam reflects from this PC mirror, the polarizations change significantly with the optical thickness of the surface-layer; i.e., different polarizations, including linearly polarization in different directions, circular polarization, and various elliptical polarizations, will appear for different optical thickness of the surfacelayer. Some special polarizations corresponding to their optical thicknesses of the surface-layer are shown in Table 1. 3. Surface-layer modified PC According to the surface-layer-thickness-dependent phase and polarization properties stated above, and considering the structure easy to fabricate, we firstly coats a 1D PC on a glass substrate, then a k0/4 surface-layer, which has a periodic change of 0 to k0/4, as shown in Fig. 4. To fabricate this periodically changing surface-layer,
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H.-Z. Zheng et al. / Optics Communications 283 (2010) 1394–1396
Table 1 Some special polarizations for different optical thicknesses of surface-layer at x/ x0 = 1.02513. The coupled-defect PC is HsL(HL)2D(LH)3L(HL)3D(LH)3L(HL)3D(LH)3 L(HL)3D(LH)3L(HL)3D(LH)7.
Dh nSdS/k0
0.5p, 1.5p 0.211, 0.091
0.75p, 1.25p 0.157, 0.117
p
lasers into incoherent lasers with random phase. Another application example is in some spectroscopy experiments, in which incoherent laser is required only at the focal point on the measured samples. Thus, our scheme for incoherent laser at the focal point can satisfy all these requirements. 5. Conclusions
0.136
Fig. 4. The structure of surface-layer modified 1D PC for generation of incoherent laser beam with random phase and random polarization.
we only need to insert a mask as the surface-layer of PC is coating. The structure of the mask is a 2D structure, which makes the thickness of the surface-layer of PC change from 0 to k0/4 with the same period as the mask. During the coating of surface-layer, the mask should be placed a distance apart from the PC to ensure that not only the surface-layer has period structure but also each period unit of surface-layer continuously changes from 0 to k0/4. The periodic constant can be dozens to hundreds microns according to the requirement of applications, but not to be too small in order to avoid grating scattering loss. The period mask also can be substituted by a mask with other structures. 4. Results and discussion As described above, when a laser beam is reflected by this 1D PC with surface-layer modification, the phases and the polarizations of every point within the laser beam becomes different; while the intensity does not change because the high reflectance almost is the same for every point of the asymmetric PC within the band gap, including the defect modes. In other words, when a laser beam reflects from an asymmetric coupled-defects 1D PC with surfacelayer modification as shown in Fig. 4, different phase-shift (0–p) at different points within the beam will appear; and various polarizations, including linear polarization in different directions, circular polarization, and different elliptical polarizations will also appear. When this laser beam with different phases and different polarizations in different point within the beam is focused, at the focal point, the phase and the polarization of the laser are random. In fact, many applications requires incoherent laser irradiation only at the focal point. As an example of application, in the research of inertial constraint nuclear fusion, when coherent laser beams are focused and overlap on the surface of the target, the coherent property makes the irradiation intensity not uniform enough on the target. To insure the uniform irradiation on the target, this surface-modified 1D PCs can be used to change the coherent
In conclusion, it is revealed that the phase and polarization of the laser beam reflected from a 1D PC will change with the thickness of its surface-layer. As the thickness of its surface-layer changes from 0 to k/4, the phase will shift in a range of 0–p. Meanwhile, when an asymmetric 1D PC with five coupled defects is used, various polarizations, including linear polarization in different directions, circular polarization, and different elliptical polarizations will appear according to different thickness of the surface-layer of the PC. Base on this, we design a special 1D PC, in which the thickness of the surface-layer is modified as a 2D structure. After reflected from this special 1D PC, the laser beam will present a distribution of phases and polarizations relate to the modified surface-layer; and when this reflected laser is focused by a lens, a coherent polarized laser with narrow band and equiphase will become incoherent with random phases and random polarizations at the focal point. As more and more experiments and applications require incoherent laser at the focal point, this method is likely to satisfy the increasing requirements in these experiments and applications. Acknowledgments This work was supported by the National Natural Science Foundation of China (NNSFC) Grants 10874250 and 10674183, National 973 Project of China Grant 2004CB719804, Ph.D. Degrees Foundation of Ministry of Education of China Grant 20060558068. References [1] Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, Phys. Rev. Lett. 53 (1984) 1057. [2] T. Afshar-rad, L.A. Gizzi, M. Desselberger, F. Khattak, O. Willi, A. Giulietti, Phys. Rev. Lett. 68 (7) (1992) 942. [3] P.M. Lushnikov, H.A. Rose, Phys. Rev. Lett. 92 (25) (2004) 255003. [4] P. Fischer, C.T.A. Brown, J.E. Morris, C. López-Mariscal, E.M. Wright, W. Sibbett, K. Dholakia, Opt. Express 13 (17) (2005) 6657. [5] V. Peet, S. Shchemeljov, Phys. Rev. A 68 (2003) 043411. [6] D.N. Rao, S.V. Rao, F.J. Aranda, D.V.G.L.N. Rao, M. Nakashima, J.A. Akkara, J. Opt. Soc. Am. B 14 (10) (1997) 2710. [7] M. Fujiwara, R. Kuroda, H. Nakatsuka, J. Opt. Soc. Am. B 2 (10) (1985) 1634. [8] M.J. Stimson, D.J. Ulness, A.C. Albrecht, Chem. Phys. Lett. 263 (1996) 185. [9] M. Pfeiffer, A. Lau, J. Chem. Phys. 108 (10) (1998) 4159 (and 4173–4182). [10] A.A. Al-ghamdi, Appl. Opt. 40 (15) (2001) 2485. [11] S.A. Kandjani, R. Barille, S. Dabos-Seignon, J.-M. Nunzi, E. Ortyl, S. Kucharski, Opt. Lett. 30 (23) (2005) 3177. [12] T. Iwai, T. Asakura, Proc. IEEE 84 (5) (2002) 765. [13] L.L. Wang, T. Tschudi, T. Halldo´rsson, P.R. Pe´tursson, Appl. Opt. 37 (10) (1998) 1770. [14] S. Pitois, C. Finot, L. Provost, D.J. Richardson, J. Opt. Soc. Am. B 25 (9) (2008) 1537. [15] T. Baba, Nat. Photon. 2 (2008) 465. [16] Herbert G. Winful, Phys. Rev. Lett. 90 (2003) 023901. [17] M. Soljacic, S.G. Johnson, S.H. Fan, M. Ibanesca, E. Ippen, J.D. Joannopoulos, J. Opt. Soc. Am. B 19 (2002) 2052. [18] X.D. Yang, M.B. Yu, D.L. Kwong, C.W. Wong, Phys. Rev. Lett. 102 (2009) 173902. [19] Emanuel Istrate, Edward H. Sargent, Appl. Phys. Lett. 86 (2005) 151112. [20] Emanuel Istrate, Alexander A. Green, Edward H. Sargent, Phys. Rev. B 71 (2005) 195122. [21] Q.F. Dai, Y.W. Li, H.Z. Wang, Appl. Phys. Lett. 89 (2006) 061121. [22] K.S. Wu, J.W. Dong, H.Z. Wang, Appl. Phys. B 91 (2008) 145. [23] P.M. Bell, J.B. Pendry, L. Martin Moreno, A.J. Ward, Comput. Phys. Commun. 85 (1995) 306.
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Photonic crystal changes coherent laser to incoherent laser with random phase Hong-Zhao Zheng, Wen-Yao Liang, Zhen Li, Jian-Wen Dong, He-Zhou Wang * State Key Laboratory of Optoelectronic Materials and Technologies, Zhongshan (Sun Yat-Sen) University, Guangzhou 510275, China
a r t i c l e
i n f o
Article history: Received 19 September 2009 Received in revised form 25 November 2009 Accepted 25 November 2009
Keywords: Incoherent laser Photonic crystal Phase Polarization
a b s t r a c t It is revealed that the phase-shift and polarization properties of laser beam reflected from a photonic crystal (PC) are sensitive to the surface-layer thickness of the PC. A continuous variation of k/4 in surface-layer thickness produces a continuous change of p in the phase-shift. Besides, in the case of an asymmetric coupled-defect PC, various polarization patterns including linearly polarization in different directions, circular polarization, and different elliptical polarizations, will appear simultaneously within one laser beam. In this paper, a PC with modified surface-layer thickness is designed to induce incoherent laser irradiation with random phase at the focus point of the reflected field. This scheme will satisfy the increasing requirements for incoherent laser irradiation. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Lasers are one of the most significant inventions of the 20th century. A variety of applications of laser in optical communication, computer engineering, industry, medicine, military and scientific research were introduced in the past few decades. Since it first appeared in 1960, broad attention was attracted to the high coherence property of the output wave, which makes many applications possible. However, it is also shown that some of the laser applications do not necessarily relate to coherence. Recently, it is found that many emerging applications which highlight other laser properties, like high directionality, high intensity and monochromaticity, could be disturbed by laser’s coherence property [1–14]. Here, we give two representative examples: (1) coherence property makes the energy distribution at the focus point of laser inertial constraint nuclear fusion not uniform enough [1]. (2) The speckle noise, which results from coherence property of laser, increases the noise of laser radar, and seriously reduces the articulation of laser display (laser projection imaging or laser TV) [12,13]. Therefore, method to fully or partially eliminate the laser coherence is in urgent need. So far, three methods have been proposed for laser decoherence in certain applications: (1) for only two coherent laser beams, perpendicular polarizations can avoid coherence [10]. (2) In some experiments [4,8], incoherent laser condition is realized by employing different wavelength, multi-wavelength or broadband lasers. (3) Let the laser pass a two-level phase plate, in which the phase-shift is either 0 or p, to reduce the coherency of laser [1].
* Corresponding author. E-mail address: [email protected] (H.-Z. Wang). 0030-4018/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2009.11.070
On the other hand, investigation into ordinary radiation shows that waves with random phase are intrinsically incoherent. Therefore, generation of incoherent laser radiation with random phase is of great significance, which still lacks for study. Furthermore, it has been revealed that phases play an important role in many phenomena and applications of PC. The representative examples of phenomena related to phases of PC are superluminal (faster-than-light) or slow light [15–17] and micro-cavity [18]. Recently, some measurements of PC phase have been reported [19,20]; and some photonic crystal phase devices have appeared [21,22]. The phase properties of PC above demonstrate that it is possible to use PC to modify the phase of laser. In this letter, we find that the phase and polarization of the laser beam reflected from a 1D PC are sensitively dependent on the thickness of the surface-layer of the PC. Based on these properties, we develop a simple method for the generation of incoherent laser with random phase and random polarization to satisfy the increasing requirements. 2. Surface-layer thickness-dependent phase and polarization Firstly, let us discuss the dependency of the phase-shift of a laser beam on the varying surface-layer thickness of a 1D PC that reflects the beam. In this work, our calculation is carried out by using the transfer matrix method [23]. To reveal the basic idea of this modulation effect, we firstly evaluate the simplest structure of Hs(LH)7, in which, ns = nH = 2.45, nL = 1.38; and the optical thickness of periodic structure ndH = ndL = k0/4, and Hs refers to the surface-layer. The results of calculation are as follows. The reflectance of the PC almost does not change with the thickness of the surface-layer, i.e., the band gap structures are
1395
H.-Z. Zheng et al. / Optics Communications 283 (2010) 1394–1396
1.0
1.0
0.5
0.5
(a)
0.5
0.5 0.0 -0.5
(b)
0.0
(a)
0.0 1.0
θ (π)
θ (π)
0.0 1.0
(b)
-1.0 1.5
1.0 0.5
1.0
0.0 -0.5 0.00
(c)
(c) 0.05
0.10
0.15
0.20
0.5 0.00
0.25
0.05
independent on the surface-layer thickness. However, the phaseshift is sensitively dependent on the thickness of the surface-layer. Fig. 1 shows the relationship between the surface-layer thickness (nSdS) and the phase-shift (h) of a laser beam reflected from a 1D PC at normal incidence, and at an incident angle of 30° for S wave and P wave, respectively. The results demonstrate that the phaseshift changes by one p when the optical thickness of the surfacelayer of the PC increases from 0 to k0/4, while the reflectance of the PC almost does not change with the thickness of the surfacelayer. Our results also show that, at oblique incidence, the phaseshifts of S and P waves differ at different thickness of surface-layer, so the phase difference (Dh) between S and P waves is dependent on the thickness of surface-layer as well. Since the polarization of light is determined by Dh, the above results imply that the polarization of the reflected wave is also dependent on the thickness of surface-layer. However, Fig. 1 also shows that Dh is very small at the incident angle of 30°, and such a simple structure will not produce significant change in the polarization of the wave. Many 1D PC structures can be used to modify the phase-shift and the polarization of laser beam. Here we give a sensitive example, an asymmetric 1D PC with five coupled defects [22]. The structure of this asymmetric 1D PC with five coupled defects is HsL(HL)2D(LH)3L(HL)3D(LH)3L(HL)3D(LH)3L(HL)3D(LH)3L(HL)3D(LH)7, where nDdD = k0/2 and the other parameters are the same as above. For this asymmetric coupled-defects PC, the relationship between the surface-layer thickness (nDdD) and the phase-shift (h) of laser beam that reflect from a 1D PC is investigated, at normal incidence and the incident angle of 30°, respectively. As is shown in Fig. 2, at normalized frequency of 1.02608, Dh becomes very large, which indicates that this structure can produce a change large enough in the polarization of the wave. For different frequency, the relationship between Dh and the optical thickness of the surface-layer, at the incidence angle of 30°, are different. For the most frequencies around the defects modes, Dh covers a wide range from 0 to 1.2p. For example, Figs. 3a–c show the relationships between Dh and nSdS at the incidence angle of 30° for normalized frequency (x/x0) 1.02608, 1.02556, and 1.02513, respectively. Obviously, Dh covers a wide range from 0 to 1.2p. The results in Figs. 2 and 3 imply that after
0.15
0.20
0.25
Fig. 2. The phase-shift of laser beam that reflect from a 1D PC as a function of the optical thickness of the surface-layer. The structure of the coupled-defect asymmetric PC is HsL(HL)2D(LH)3L(HL)3D(LH)3L(HL)3D(LH)3L(HL)3D(LH)3L(HL)3D(LH)7. The normalized frequency (x/x0) is 1.02513. (a) normal incidence, (b) the incident angle of 30° for S wave, and (c) the incident angle of 30° for P wave.
(a)
1.5 1.0 0.5
Δθ (π)
Fig. 1. The phase-shift (h) of laser beam that reflect from a 1D PC as a function of the optical thickness (nSdS) of the surface-layer at (a) normal incidence, (b) the incident angle of 30° for S wave, and (c) the incident angle of 30° for P wave. The normalized frequency is x/x0 = 1. The structure is Hs(LH)7 (nS = nH = 2.45, nL = 1.38). The optical thicknesses of the periodic layers are nHdH = nLdL = k0/4.
0.10
nSdS/λ0
nSdS/ λ 0
0.0
(b)
-0.5
-1.0
(c)
1.5 1.0 0.5 0.00
0.05
0.10
0.15
0.20
0.25
nSdS/λ0 Fig. 3. The relationship between Dh and the optical thickness of the surface-layer, at the incidence angle of 30°, in which the normalized frequency (x/x0) are (a) 1.02513, (b) 1.02556, and (c) 1.02608. The Dh covers a wide range from 0 to 1.2p.
the laser beam reflects from this PC mirror, the polarizations change significantly with the optical thickness of the surface-layer; i.e., different polarizations, including linearly polarization in different directions, circular polarization, and various elliptical polarizations, will appear for different optical thickness of the surfacelayer. Some special polarizations corresponding to their optical thicknesses of the surface-layer are shown in Table 1. 3. Surface-layer modified PC According to the surface-layer-thickness-dependent phase and polarization properties stated above, and considering the structure easy to fabricate, we firstly coats a 1D PC on a glass substrate, then a k0/4 surface-layer, which has a periodic change of 0 to k0/4, as shown in Fig. 4. To fabricate this periodically changing surface-layer,
1396
H.-Z. Zheng et al. / Optics Communications 283 (2010) 1394–1396
Table 1 Some special polarizations for different optical thicknesses of surface-layer at x/ x0 = 1.02513. The coupled-defect PC is HsL(HL)2D(LH)3L(HL)3D(LH)3L(HL)3D(LH)3 L(HL)3D(LH)3L(HL)3D(LH)7.
Dh nSdS/k0
0.5p, 1.5p 0.211, 0.091
0.75p, 1.25p 0.157, 0.117
p
lasers into incoherent lasers with random phase. Another application example is in some spectroscopy experiments, in which incoherent laser is required only at the focal point on the measured samples. Thus, our scheme for incoherent laser at the focal point can satisfy all these requirements. 5. Conclusions
0.136
Fig. 4. The structure of surface-layer modified 1D PC for generation of incoherent laser beam with random phase and random polarization.
we only need to insert a mask as the surface-layer of PC is coating. The structure of the mask is a 2D structure, which makes the thickness of the surface-layer of PC change from 0 to k0/4 with the same period as the mask. During the coating of surface-layer, the mask should be placed a distance apart from the PC to ensure that not only the surface-layer has period structure but also each period unit of surface-layer continuously changes from 0 to k0/4. The periodic constant can be dozens to hundreds microns according to the requirement of applications, but not to be too small in order to avoid grating scattering loss. The period mask also can be substituted by a mask with other structures. 4. Results and discussion As described above, when a laser beam is reflected by this 1D PC with surface-layer modification, the phases and the polarizations of every point within the laser beam becomes different; while the intensity does not change because the high reflectance almost is the same for every point of the asymmetric PC within the band gap, including the defect modes. In other words, when a laser beam reflects from an asymmetric coupled-defects 1D PC with surfacelayer modification as shown in Fig. 4, different phase-shift (0–p) at different points within the beam will appear; and various polarizations, including linear polarization in different directions, circular polarization, and different elliptical polarizations will also appear. When this laser beam with different phases and different polarizations in different point within the beam is focused, at the focal point, the phase and the polarization of the laser are random. In fact, many applications requires incoherent laser irradiation only at the focal point. As an example of application, in the research of inertial constraint nuclear fusion, when coherent laser beams are focused and overlap on the surface of the target, the coherent property makes the irradiation intensity not uniform enough on the target. To insure the uniform irradiation on the target, this surface-modified 1D PCs can be used to change the coherent
In conclusion, it is revealed that the phase and polarization of the laser beam reflected from a 1D PC will change with the thickness of its surface-layer. As the thickness of its surface-layer changes from 0 to k/4, the phase will shift in a range of 0–p. Meanwhile, when an asymmetric 1D PC with five coupled defects is used, various polarizations, including linear polarization in different directions, circular polarization, and different elliptical polarizations will appear according to different thickness of the surface-layer of the PC. Base on this, we design a special 1D PC, in which the thickness of the surface-layer is modified as a 2D structure. After reflected from this special 1D PC, the laser beam will present a distribution of phases and polarizations relate to the modified surface-layer; and when this reflected laser is focused by a lens, a coherent polarized laser with narrow band and equiphase will become incoherent with random phases and random polarizations at the focal point. As more and more experiments and applications require incoherent laser at the focal point, this method is likely to satisfy the increasing requirements in these experiments and applications. Acknowledgments This work was supported by the National Natural Science Foundation of China (NNSFC) Grants 10874250 and 10674183, National 973 Project of China Grant 2004CB719804, Ph.D. Degrees Foundation of Ministry of Education of China Grant 20060558068. References [1] Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, Phys. Rev. Lett. 53 (1984) 1057. [2] T. Afshar-rad, L.A. Gizzi, M. Desselberger, F. Khattak, O. Willi, A. Giulietti, Phys. Rev. Lett. 68 (7) (1992) 942. [3] P.M. Lushnikov, H.A. Rose, Phys. Rev. Lett. 92 (25) (2004) 255003. [4] P. Fischer, C.T.A. Brown, J.E. Morris, C. López-Mariscal, E.M. Wright, W. Sibbett, K. Dholakia, Opt. Express 13 (17) (2005) 6657. [5] V. Peet, S. Shchemeljov, Phys. Rev. A 68 (2003) 043411. [6] D.N. Rao, S.V. Rao, F.J. Aranda, D.V.G.L.N. Rao, M. Nakashima, J.A. Akkara, J. Opt. Soc. Am. B 14 (10) (1997) 2710. [7] M. Fujiwara, R. Kuroda, H. Nakatsuka, J. Opt. Soc. Am. B 2 (10) (1985) 1634. [8] M.J. Stimson, D.J. Ulness, A.C. Albrecht, Chem. Phys. Lett. 263 (1996) 185. [9] M. Pfeiffer, A. Lau, J. Chem. Phys. 108 (10) (1998) 4159 (and 4173–4182). [10] A.A. Al-ghamdi, Appl. Opt. 40 (15) (2001) 2485. [11] S.A. Kandjani, R. Barille, S. Dabos-Seignon, J.-M. Nunzi, E. Ortyl, S. Kucharski, Opt. Lett. 30 (23) (2005) 3177. [12] T. Iwai, T. Asakura, Proc. IEEE 84 (5) (2002) 765. [13] L.L. Wang, T. Tschudi, T. Halldo´rsson, P.R. Pe´tursson, Appl. Opt. 37 (10) (1998) 1770. [14] S. Pitois, C. Finot, L. Provost, D.J. Richardson, J. Opt. Soc. Am. B 25 (9) (2008) 1537. [15] T. Baba, Nat. Photon. 2 (2008) 465. [16] Herbert G. Winful, Phys. Rev. Lett. 90 (2003) 023901. [17] M. Soljacic, S.G. Johnson, S.H. Fan, M. Ibanesca, E. Ippen, J.D. Joannopoulos, J. Opt. Soc. Am. B 19 (2002) 2052. [18] X.D. Yang, M.B. Yu, D.L. Kwong, C.W. Wong, Phys. Rev. Lett. 102 (2009) 173902. [19] Emanuel Istrate, Edward H. Sargent, Appl. Phys. Lett. 86 (2005) 151112. [20] Emanuel Istrate, Alexander A. Green, Edward H. Sargent, Phys. Rev. B 71 (2005) 195122. [21] Q.F. Dai, Y.W. Li, H.Z. Wang, Appl. Phys. Lett. 89 (2006) 061121. [22] K.S. Wu, J.W. Dong, H.Z. Wang, Appl. Phys. B 91 (2008) 145. [23] P.M. Bell, J.B. Pendry, L. Martin Moreno, A.J. Ward, Comput. Phys. Commun. 85 (1995) 306.