Observation of vector solitons with hidden vorticity - OSA Publishing
March 1, 2012 / Vol. 37, No. 5 / OPTICS LETTERS
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Observation of vector solitons with hidden vorticity Yana V. Izdebskaya,1,* Johannes Rebling,1,2 Anton S. Desyatnikov,1 and Yuri S. Kivshar1 1
Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia 2 University of Applied Sciences, Zwickau 08056, Germany *Corresponding author: [email protected]
Received November 10, 2011; revised December 20, 2011; accepted January 7, 2012; posted January 12, 2012 (Doc. ID 158037); published February 17, 2012
This letter reports the first experimental observation, to our knowledge, of optical vector solitons composed of two incoherently coupled vortex components. We employ nematic liquid crystal to generate stable vector solitons with counterrotating vortices and hidden vorticity. In contrast, the solitons with explicit vorticity and corotating vortex components show azimuthal splitting. © 2012 Optical Society of America OCIS codes: 190.6135, 050.4865, 160.3710.
A light beam that carries phase singularity [1] is called an optical vortex [2,3]. Such singular optical beams can be generated experimentally in different types of linear [2,3] and nonlinear [4] media. Unique features of the vortex beams can be explored in many applications, including optical data transfer and optical tweezers. However, in self-focusing nonlinear optical media, vortices typically become unstable because of the symmetry-breaking azimuthal instabilities [5], and they split into several fundamental optical solitons [6]. When two or more distinct components of an optical beam propagate together and interact, they can form the so-called vector soliton [5]. Multicomponent spatial vortex solitons can also experience strong instabilities. However, as was shown in several theoretical studies [7,8], the stability of the vector vortex solitons depends on their total orbital angular momentum (OAM), or vorticity [9,10]: when the components have equal topological charges, m1;2 1 [as shown in Fig. 1(a)], the composite vortex soliton remains unstable, similar to its scalar counterpart. However, if the vortices counterrotate, m1;2 1 [Fig. 1(b)], and the total OAM vanishes, the theoretical studies suggest that such vector soliton with hidden vorticity may become stable in self-focusing media [10,11], similar to the case of zero charge in both components [12]. However, in spite of many theoretical studies of these types of vector solitons, such composite optical beams have not been observed in experiment. In this letter, for the first time to our knowledge, we study experimentally in nematic liquid crystals (NLCs) the two-component vortex solitons carrying equal or opposite topological charges 1; 1 in their mutually incoherent components. We demonstrate that the incoherently coupled beams carrying explicit vorticity undergo astigmatic transformations and split into two filaments, creating a dipole vector soliton at higher powers. In contrast, a vector soliton formed by two counterrotating optical vortex beams (with hidden vorticity and zero OAM) remains remarkably stable. The experiments are conducted with 6CHBT nematic liquid crystal (the birefringence is Δϵ ≈ 0.16 at the wavelength λ 671 nm). The NLC is sandwiched between two parallel polycarbonate plates separated by 110 μm. 0146-9592/12/050767-03$15.00/0
The NLC molecules orientation, at the angle 45° with respect to z, is determined by surface anchoring. The cell is sealed at the input and output by extra glass interfaces with rubbing in the x-horizontal direction in order to prevent beam depolarization. The experimental setup is shown in Fig. 1, with a single-charged optical vortex generated by the computergenerated hologram DH from the cw laser beam at λ 671 nm. The input beam is split into two beams with equal power P by the beam splitter BS1, and in one arm we use mirror M1 mounted on a piezoelectric transducer, vibrating with the frequency of ≈1 kHz. Driving this transducer imposes a frequency shift onto one beam and makes the superposition of two beams effectively incoherent, as the fast oscillations of the interference pattern
Fig. 1. (Color online) Schematic phase-front view of two components with (a) corotating and (b) counterrotating vortices. Bottom, experimental setup: DH—diffraction hologram, λ∕2— half-wavelength plate, M1—mirror mounted on a piezoelectric transducer, MO—microscope objectives, NLC—nematic liquid crystal cell, F—ND filter, CCD—camera. The dashed squares show two elements for generating composite beams with (c) explicit m1;2 1 and (d) hidden m1;2 1 vorticity. © 2012 Optical Society of America
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average out in the refractive index induced in NLC with slow reorientational nonlinearity. Simple modification of our setup allows us to switch between configurations of two copropagating vortex beams with explicit and hidden vorticities. First, a pair of identical vortex beams with the same topological charges m1;2 1 can be generated with the standard Mach-Zehnder arrangement, as shown in Fig. 1(c). Second, by introducing an additional mirror in one interferometer arm, as shown in Fig. 1(d), we allow different numbers of beam reflections in two arms, thus generating two vortex beams with opposite charges m1;2 1. The input linear extraordinary polarization of both beams is set by the half-wavelength plate. The output light intensity after propagation in the NLC cell is recorded with a CCD camera. First, we investigate the dynamics of two incoherently interacting corotating optical vortices, i.e., a composite (+1,+1)
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Fig. 2. (Color online) Experimental results for the vortex beams of two types: (a)–(d) m1;2 1, and (e)–(h) m1;2 1. (a), (e) input images; (b)–(d) and (f)–(h) output images for various input powers P in each component.
Fig. 3. (Color online) Structure of the components: total (a), (d) and partial (b), (c), (e), (f) intensity patterns of the composite vortex solitons with (a)–(c) m1;2 1 and (d)–(f) m1;2 1 at P 2.9 mW. The dashed arrows show the orientation of each component.
beam with explicit vorticity; see the input image in Fig. 2(a). For low input power P < 0.5 mW, the selffocusing is too weak to overcome diffraction [Fig. 2(b)]. By increasing the power of each component to P > 1.2 mW, the two-component vortex beam undergoes self-focusing, and its radial symmetric intensity distribution breaks up into a pair of filaments [Fig. 2(c)] owing to the anisotropic structure of the planar cell and anisotropy in the induced refractive index profile. For higher powers P > 2.5 mW, the beam transforms into a more stable object, a dipole-mode vector soliton [see Fig. 2(d)]. This dynamics is consistent with recently reported results for the generation of scalar (one-component) vortex beams in NLC [13], where we observed experimentally the astigmatic transformations of vortex beams into spiraling dipole azimuthons [14]. We conclude that the stability properties of the vector optical vortex with explicit vorticity are similar to those of its scalar counterparts. Next, we carry out a similar series of experiments for two incoherently interacting beams carrying opposite topological charges m1;2 1. Because of their mutually incoherent interaction, the input intensity distribution of such a composite beam preserves an annular shape with a dark core [see Fig. 2(e)], while the total OAM of this composite beam vanishes; i.e., the vorticity is hidden. As above, we observe diffraction at low power P < 0.5 mW [Fig. 2(f)], while with a further increase of the power P > 1.2 mW we observe a clear reshaping of intensity in Fig. 2(g), as compared to the case with explicit vorticity in Fig. 2(c). Namely, despite strong self-action
March 1, 2012 / Vol. 37, No. 5 / OPTICS LETTERS
Fig. 4. (Color online) Numerical results. Output intensity distributions for the vortex vector solitons with the topological charges (a) 1; 1 and (b) 1; −1.
experienced by the two-component beam, its intensity distribution preserves the annular shape and hollow core practically without distortions. A further increase of the power leads to the narrowing of the output beam and the formation of a stable vector vortex soliton with hidden vorticity [Fig. 2(h)]. To understand the origin of the different dynamics of the co- and counterrotating vector vortex solitons, we show each component independently for both cases at P 2.9 mW. We use a fast CCD camera with the image frequency 52 fps for recording each component separately by blocking one of the output beams. In Fig. 3 we observe that each component of both composite beams splits into a rotating dipole beam [13]. In the case of explicit vorticity with m1;2 1, the orientation of both components is the same [cf. Figs. 3(b) and 3(c)], reinforcing the dipole profile of total intensity in Fig. 3(a). However, by inverting the topological charge of one of the vortices to m2 −1, we change the orientation of its screwlike transverse phase distribution and corresponding OAM so that the total OAM vanishes. As a result, in the case of two opposite vortices 1; −1 we observe a pattern similar to crossed dipoles [cf. Figs. 3(e) and 3(f)], complementing each other to create annular shape in total intensity in Fig. 3(d). Remarkably, it remains almost unperturbed with respect to the input beam profile in Fig. 2(e), which clearly proves its stability. Finally, to confirm the conclusions of our experiments, we study numerically the propagation of two-component optical beams in isotropic nonlinear media with a Gaussian nonlocal response. In contrast to the previous results obtained for local media [7,9–11], here we find that when the total power of a vector vortex soliton corresponds to a stable scalar vortex beam [15], both configurations (with explicit and hidden vorticities) become stabilized by strong nonlocal response of the medium, although we notice that the dominating long-lived internal modes are drastically different in those two cases. Here we try to match our experimental conditions better
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by applying the same initial elliptic deformation to both input vortex components [13]. In a good agreement with our experimental results of Fig. 3, during the propagation in nonlocal media the total intensity in Fig. 4 shows the formation of two distinctly different structures. First is a dipolelike intensity in Fig. 4(a) for a vortex-vortex coupling, and the second is a doughnutlike ring in Fig. 4(b) for the vortex-antivortex incoherent coupling. While in the former case both components have the same profiles (not shown), in the latter case we observe the structure of two crossed dipoles as in Figs. 3(f) and 3(f). In conclusion, we have shown that the incoherent interaction of two vortex beams in nematic liquid crystals strongly depends on their vorticity. A stable propagation preserving ring-shaped total intensity pattern is observed for vector solitons with counterrotating vortices in two components and hidden vorticity. In contrast, solitons with explicit vorticity and corotating vortex components always transform into the vector dipole solitons, similar to the scalar dipole azimuthons [13]. The authors acknowledge the Australian Research Council for financial support. References 1. J. F. Nye and M. V. Berry, Proc. R. Soc. London A 336, 165 (1974). 2. M. S. Soskin and M. V. Vasnetsov, Progress in Optics, E. Wolf, ed. (Elsevier, 2001), Vol. 42, p. 219. 3. M. R. Dennis, K. O’Holleran, and M. J. Padgett, Progress in Optics, E. Wolf, ed. (Elsevier, 2009), Vol. 52, p. 293. 4. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, Progress in Optics, E. Wolf, ed. (Elsevier, 2005), Vol. 47, p. 291. 5. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003). 6. W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997). 7. A. S. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 87, 033901 (2001). 8. M. S. Bigelow, Q-Han Park, and R. W. Boyd, Phys. Rev. E 66, 046631 (2002). 9. A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, C. Denz, and F. Lederer, Phys. Rev. E 71, 026615 (2005). 10. A. S. Desyatnikov, D. E. Pelinovsky, and J. Yang, J. Math. Sci. 151, 3091 (2008) [Fund. Appl. Math. 12(7), 35 (2006) (in Russian)]. 11. A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, Phys. Lett. A 364, 231 (2007). 12. C. Huang, Opt. Commun. 284, 5786 (2011). 13. Ya. Izdebskaya, A. S. Desytanikov, G. Assanto, and Yu. S. Kivshar, Opt. Express 19, 21457 (2011). 14. S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, Opt. Lett. 31, 1100 (2006). 15. A. I. Yakimenko, Y. A. Zaliznyak, and Yu. Kivshar, Phys. Rev. E 71, 065603 (2005).
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Observation of vector solitons with hidden vorticity Yana V. Izdebskaya,1,* Johannes Rebling,1,2 Anton S. Desyatnikov,1 and Yuri S. Kivshar1 1
Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia 2 University of Applied Sciences, Zwickau 08056, Germany *Corresponding author: [email protected]
Received November 10, 2011; revised December 20, 2011; accepted January 7, 2012; posted January 12, 2012 (Doc. ID 158037); published February 17, 2012
This letter reports the first experimental observation, to our knowledge, of optical vector solitons composed of two incoherently coupled vortex components. We employ nematic liquid crystal to generate stable vector solitons with counterrotating vortices and hidden vorticity. In contrast, the solitons with explicit vorticity and corotating vortex components show azimuthal splitting. © 2012 Optical Society of America OCIS codes: 190.6135, 050.4865, 160.3710.
A light beam that carries phase singularity [1] is called an optical vortex [2,3]. Such singular optical beams can be generated experimentally in different types of linear [2,3] and nonlinear [4] media. Unique features of the vortex beams can be explored in many applications, including optical data transfer and optical tweezers. However, in self-focusing nonlinear optical media, vortices typically become unstable because of the symmetry-breaking azimuthal instabilities [5], and they split into several fundamental optical solitons [6]. When two or more distinct components of an optical beam propagate together and interact, they can form the so-called vector soliton [5]. Multicomponent spatial vortex solitons can also experience strong instabilities. However, as was shown in several theoretical studies [7,8], the stability of the vector vortex solitons depends on their total orbital angular momentum (OAM), or vorticity [9,10]: when the components have equal topological charges, m1;2 1 [as shown in Fig. 1(a)], the composite vortex soliton remains unstable, similar to its scalar counterpart. However, if the vortices counterrotate, m1;2 1 [Fig. 1(b)], and the total OAM vanishes, the theoretical studies suggest that such vector soliton with hidden vorticity may become stable in self-focusing media [10,11], similar to the case of zero charge in both components [12]. However, in spite of many theoretical studies of these types of vector solitons, such composite optical beams have not been observed in experiment. In this letter, for the first time to our knowledge, we study experimentally in nematic liquid crystals (NLCs) the two-component vortex solitons carrying equal or opposite topological charges 1; 1 in their mutually incoherent components. We demonstrate that the incoherently coupled beams carrying explicit vorticity undergo astigmatic transformations and split into two filaments, creating a dipole vector soliton at higher powers. In contrast, a vector soliton formed by two counterrotating optical vortex beams (with hidden vorticity and zero OAM) remains remarkably stable. The experiments are conducted with 6CHBT nematic liquid crystal (the birefringence is Δϵ ≈ 0.16 at the wavelength λ 671 nm). The NLC is sandwiched between two parallel polycarbonate plates separated by 110 μm. 0146-9592/12/050767-03$15.00/0
The NLC molecules orientation, at the angle 45° with respect to z, is determined by surface anchoring. The cell is sealed at the input and output by extra glass interfaces with rubbing in the x-horizontal direction in order to prevent beam depolarization. The experimental setup is shown in Fig. 1, with a single-charged optical vortex generated by the computergenerated hologram DH from the cw laser beam at λ 671 nm. The input beam is split into two beams with equal power P by the beam splitter BS1, and in one arm we use mirror M1 mounted on a piezoelectric transducer, vibrating with the frequency of ≈1 kHz. Driving this transducer imposes a frequency shift onto one beam and makes the superposition of two beams effectively incoherent, as the fast oscillations of the interference pattern
Fig. 1. (Color online) Schematic phase-front view of two components with (a) corotating and (b) counterrotating vortices. Bottom, experimental setup: DH—diffraction hologram, λ∕2— half-wavelength plate, M1—mirror mounted on a piezoelectric transducer, MO—microscope objectives, NLC—nematic liquid crystal cell, F—ND filter, CCD—camera. The dashed squares show two elements for generating composite beams with (c) explicit m1;2 1 and (d) hidden m1;2 1 vorticity. © 2012 Optical Society of America
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average out in the refractive index induced in NLC with slow reorientational nonlinearity. Simple modification of our setup allows us to switch between configurations of two copropagating vortex beams with explicit and hidden vorticities. First, a pair of identical vortex beams with the same topological charges m1;2 1 can be generated with the standard Mach-Zehnder arrangement, as shown in Fig. 1(c). Second, by introducing an additional mirror in one interferometer arm, as shown in Fig. 1(d), we allow different numbers of beam reflections in two arms, thus generating two vortex beams with opposite charges m1;2 1. The input linear extraordinary polarization of both beams is set by the half-wavelength plate. The output light intensity after propagation in the NLC cell is recorded with a CCD camera. First, we investigate the dynamics of two incoherently interacting corotating optical vortices, i.e., a composite (+1,+1)
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Fig. 2. (Color online) Experimental results for the vortex beams of two types: (a)–(d) m1;2 1, and (e)–(h) m1;2 1. (a), (e) input images; (b)–(d) and (f)–(h) output images for various input powers P in each component.
Fig. 3. (Color online) Structure of the components: total (a), (d) and partial (b), (c), (e), (f) intensity patterns of the composite vortex solitons with (a)–(c) m1;2 1 and (d)–(f) m1;2 1 at P 2.9 mW. The dashed arrows show the orientation of each component.
beam with explicit vorticity; see the input image in Fig. 2(a). For low input power P < 0.5 mW, the selffocusing is too weak to overcome diffraction [Fig. 2(b)]. By increasing the power of each component to P > 1.2 mW, the two-component vortex beam undergoes self-focusing, and its radial symmetric intensity distribution breaks up into a pair of filaments [Fig. 2(c)] owing to the anisotropic structure of the planar cell and anisotropy in the induced refractive index profile. For higher powers P > 2.5 mW, the beam transforms into a more stable object, a dipole-mode vector soliton [see Fig. 2(d)]. This dynamics is consistent with recently reported results for the generation of scalar (one-component) vortex beams in NLC [13], where we observed experimentally the astigmatic transformations of vortex beams into spiraling dipole azimuthons [14]. We conclude that the stability properties of the vector optical vortex with explicit vorticity are similar to those of its scalar counterparts. Next, we carry out a similar series of experiments for two incoherently interacting beams carrying opposite topological charges m1;2 1. Because of their mutually incoherent interaction, the input intensity distribution of such a composite beam preserves an annular shape with a dark core [see Fig. 2(e)], while the total OAM of this composite beam vanishes; i.e., the vorticity is hidden. As above, we observe diffraction at low power P < 0.5 mW [Fig. 2(f)], while with a further increase of the power P > 1.2 mW we observe a clear reshaping of intensity in Fig. 2(g), as compared to the case with explicit vorticity in Fig. 2(c). Namely, despite strong self-action
March 1, 2012 / Vol. 37, No. 5 / OPTICS LETTERS
Fig. 4. (Color online) Numerical results. Output intensity distributions for the vortex vector solitons with the topological charges (a) 1; 1 and (b) 1; −1.
experienced by the two-component beam, its intensity distribution preserves the annular shape and hollow core practically without distortions. A further increase of the power leads to the narrowing of the output beam and the formation of a stable vector vortex soliton with hidden vorticity [Fig. 2(h)]. To understand the origin of the different dynamics of the co- and counterrotating vector vortex solitons, we show each component independently for both cases at P 2.9 mW. We use a fast CCD camera with the image frequency 52 fps for recording each component separately by blocking one of the output beams. In Fig. 3 we observe that each component of both composite beams splits into a rotating dipole beam [13]. In the case of explicit vorticity with m1;2 1, the orientation of both components is the same [cf. Figs. 3(b) and 3(c)], reinforcing the dipole profile of total intensity in Fig. 3(a). However, by inverting the topological charge of one of the vortices to m2 −1, we change the orientation of its screwlike transverse phase distribution and corresponding OAM so that the total OAM vanishes. As a result, in the case of two opposite vortices 1; −1 we observe a pattern similar to crossed dipoles [cf. Figs. 3(e) and 3(f)], complementing each other to create annular shape in total intensity in Fig. 3(d). Remarkably, it remains almost unperturbed with respect to the input beam profile in Fig. 2(e), which clearly proves its stability. Finally, to confirm the conclusions of our experiments, we study numerically the propagation of two-component optical beams in isotropic nonlinear media with a Gaussian nonlocal response. In contrast to the previous results obtained for local media [7,9–11], here we find that when the total power of a vector vortex soliton corresponds to a stable scalar vortex beam [15], both configurations (with explicit and hidden vorticities) become stabilized by strong nonlocal response of the medium, although we notice that the dominating long-lived internal modes are drastically different in those two cases. Here we try to match our experimental conditions better
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by applying the same initial elliptic deformation to both input vortex components [13]. In a good agreement with our experimental results of Fig. 3, during the propagation in nonlocal media the total intensity in Fig. 4 shows the formation of two distinctly different structures. First is a dipolelike intensity in Fig. 4(a) for a vortex-vortex coupling, and the second is a doughnutlike ring in Fig. 4(b) for the vortex-antivortex incoherent coupling. While in the former case both components have the same profiles (not shown), in the latter case we observe the structure of two crossed dipoles as in Figs. 3(f) and 3(f). In conclusion, we have shown that the incoherent interaction of two vortex beams in nematic liquid crystals strongly depends on their vorticity. A stable propagation preserving ring-shaped total intensity pattern is observed for vector solitons with counterrotating vortices in two components and hidden vorticity. In contrast, solitons with explicit vorticity and corotating vortex components always transform into the vector dipole solitons, similar to the scalar dipole azimuthons [13]. The authors acknowledge the Australian Research Council for financial support. References 1. J. F. Nye and M. V. Berry, Proc. R. Soc. London A 336, 165 (1974). 2. M. S. Soskin and M. V. Vasnetsov, Progress in Optics, E. Wolf, ed. (Elsevier, 2001), Vol. 42, p. 219. 3. M. R. Dennis, K. O’Holleran, and M. J. Padgett, Progress in Optics, E. Wolf, ed. (Elsevier, 2009), Vol. 52, p. 293. 4. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, Progress in Optics, E. Wolf, ed. (Elsevier, 2005), Vol. 47, p. 291. 5. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003). 6. W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997). 7. A. S. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 87, 033901 (2001). 8. M. S. Bigelow, Q-Han Park, and R. W. Boyd, Phys. Rev. E 66, 046631 (2002). 9. A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, C. Denz, and F. Lederer, Phys. Rev. E 71, 026615 (2005). 10. A. S. Desyatnikov, D. E. Pelinovsky, and J. Yang, J. Math. Sci. 151, 3091 (2008) [Fund. Appl. Math. 12(7), 35 (2006) (in Russian)]. 11. A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, Phys. Lett. A 364, 231 (2007). 12. C. Huang, Opt. Commun. 284, 5786 (2011). 13. Ya. Izdebskaya, A. S. Desytanikov, G. Assanto, and Yu. S. Kivshar, Opt. Express 19, 21457 (2011). 14. S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, Opt. Lett. 31, 1100 (2006). 15. A. I. Yakimenko, Y. A. Zaliznyak, and Yu. Kivshar, Phys. Rev. E 71, 065603 (2005).
