Abstract

Theoretical analysis and experimental demonstration are presented for the generation of cylindrical vector beams (CVBs) via mode conversion in fiber from HE11 mode to TM01 and TE01 modes, which have radial and azimuthal polarizations, respectively. Intermodal coupling is caused by an acoustic flexural wave applied on the fiber, whereas polarization control is necessary for the mode conversion, i.e. HE11xTM01 and HE11yTE01 for acoustic vibration along the x-axis. The frequency of the RF driving signal for actuating the acoustic wave is determined by the phase matching condition that the period of acoustic wave equals the beatlength of two coupled modes. With phase matching condition tunability, this approach can be used to generate different types of CVBs at the same wavelength over a broadband. Experimental demonstration was done in the visible and communication bands.

© 2016 Optical Society of America

1. Introduction

Cylindrical vector beams (CVBs), specifically with radial and azimuthal polarizations, have been drawing considerable research attention. Exploitation of their unique properties, such as tight focusing and special polarization distribution [1,2], have been stimulated in a variety of applications, e.g. second harmonic generation (SHG) [3], optical tweezers [4,5], micro/nanofabrication [6], surface plasmon polariton (SPP) excitation [7,8], etc. Recently, there is a burst of enthusiasm on investigation of the CVBs for mode division multiplexing to achieve high-capacity optical communication [9,10]. A series of previously reported the CVBs generation techniques, including both active (intra-cavity) [11–16] and passive (extra-cavity) [17–22], were implemented in free-space optics. The CVBs generated in free space using these techniques, if used in fiber-based optical communication systems [23], would inevitably meet with problems like insertion loss and assembling issue due to the need of light coupling between free space and optical fiber. Therefore, the generation of CVBs in fiber is greatly desired in such circumstance.

The fiber-based generation of CVBs has been studied using eigenmodes in optical fiber [24]. Excitation of the radially polarized TM01 mode in a two-mode optical fiber was demonstrated by coupling with an offset linearly polarized Gaussian beam output from a single-mode fiber [25]. Different combinations of modes from the LP11 group were selectively excited in a two-mode fiber by coupling with a Laguerre-Gaussian beam generated using a holographic mask, and then converted to an azimuthal or radial CVBs with half-wave plates in free space [26]. The vector modes of a two-mode fiber was selectively excited by a linearly polarized fundamental Gaussian laser beam, depending on the input beam polarization, the fiber length, and the launch condition [27]. These techniques, although are fiber-based, depend on the condition of external coupling and thus are technically challenging in aspect of engineering. An in-fiber technique may adopt intermodal coupling within fiber such that the CVBs are generated inside the fiber circuit without critical manipulation of optical beam alignment. Intermodal coupling may be induced by applying external perturbation, preferably in controllable fashion. Long period ber gratings (LPFGs) could be naturally thought about as candidates. LPFGs could be formed by the mechanical means [28], exposing the ber using a ultra-violet (UV) laser [29], or a CO2 laser [30], and so on, whereas not all types of LPFGs are suitable for generating CVBs unless they have an asymmetric refractive index distribution across the core of fiber [28,30].

The generation of CVBs with high modal purity in fiber was demonstrated using micro-bend LPFG mechanically formed on a so-called vortex fiber which strongly disperses vector modes in the LP11 group [31,32]. Recently, it was successfully demonstrated that an LPFG written by irradiating a two-mode ber from one side with a CO2 laser is capable of generating the CVBs [30].

In some application like wavelength division multiplexing involving several wavelengths and mode division multiplexing involving several modes, the wavelength tunability and mode selectivity for the CVBs generation are appreciated. Thus in this article, we report a technique for in-fiber generation of different CVBs with wavelength tunability and mode selectivity over broadband. The intermodal coupling caused by the asymmetric refractive index distribution, which is induced by the acoustic flexural wave applied on the unjacketed fiber, is theoretically analyzed. Then the coupling coefficients between the fundamental HE11 mode and the LP11-group higher-order modes are summarized. The phase matching condition for mode conversion is discussed subsequently. Experimental results using the few-mode fiber (Corning SMF-28) for the visible band (532 nm, 633 nm) and the two-mode fiber (OFS) for the optical communication band (1540 nm - 1560 nm) are presented. The output beams show annular intensity patterns in absence of polarizer and characteristic intensity patterns under polarizer, which confirm radial and azimuthal polarizations of the generated CVBs. The utilization efficiency of the laser power reached 35% and a modal purity of ~30 dB was measured using the optical heterodyne interference method.

2. Principle and experimental conguration

As illustrated in Fig. 1 for a few-mode fiber with a step-index profile, the modes in scalar approximation solution, designated as LP01, LP11 and LP21, correspond to the groups of vector modes {HE11x,HE11y}, {TE01,HE21even/odd,TM01} and {HE31even/odd, EH11even/odd}, respectively. In the LP01 group, the fundamental HE11x and HE11y modes are degenerate with their transverse electric fields parallel to the x and y directions, respectively [24]. In the LP11 group, the TE01 and TM01 modes are separated from the strictly degenerate HE21evenand HE21odd modes with tiny differences of modal effective refractive index, and have electric fields with azimuthal and radial polarizations, respectively. Mode conversion via the intermodal coupling between the fundamental modes and the LP11-group higher-order modes may thus be adopted for generating the CVBs in a few-mode fiber.

 figure: Fig. 1

Fig. 1 Schematic of the index profile of a few-mode fiber denoted with modal indices and intensity patterns for (a) the scalar modes and (b) corresponding groups of the vector modes. Field directions are denoted on the intensity patterns of vector modes.

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An acoustic flexural wave propagating in the z-direction with vibration along the x-axis in an unjacketed fiber may induce the asymmetric refractive index modulation with respect to the vibration direction and consequently cause the intermodal coupling, i.e. to transfer energy from one mode to another. The induced asymmetric refractive index modulation at the cross section of the fiber can be expressed as [33,34]

Δn(r,ϕ)=N0rcos(ϕ),
where r and ϕ are the radial and azimuthal variables in cylindrical coordinates, respectively, and ϕ = 0 is set for the acoustic flexural wave vibration along the x-axis. N0 = n0(1 + χ)K2u0, where n0 is the refractive index of the core, χ = −0.22 is the elasto-optical coefficient of silica, K and u0 are the wavevector and amplitude of the acoustic flexural wave, respectively. For the acoustically-induced fiber grating, the coupling coefcient κpm between a fundamental p mode and a higher-order m mode can be expressed as [35,36]
κpm=πλε0μ0n0EtpΔn(r,ϕ)Etmrdrdϕ.
In weakly guidance approximation, the transverse components of the electric fields of the fundamental and higher-order vector modes can be expressed as [24]
Etp=upF01(r),
and
Etm=Φm(ϕ)F11(r),
where F1(r),(=0,1)is the radial function of the corresponding scalar mode LP1,(=0,1), up = x^,y^ is the unit vector in x- or y-directions for p =HE11x, HE11y, and Φm(ϕ) is the field direction function given in Table 1. We may rewrite the Eq. (2) as κpm=Cκrκϕpm such that
C=(π/λ)ε0/μ0n0N0,
κr=F01(r)F11(r)r2dr,
and
κϕpm=02πupΦm(ϕ)cosϕdϕ,
where the term cosϕ in Eq. (7) originates from the acoustic flexural wave vibration along the x-axis as expressed in Eq. (1). Thus the azimuthal component κϕpm reveals allowed or forbidden the intermodal coupling between p and m modes, as shown in Table 1, which tells that the mode for an output CVB is selected via polarization control on the input light.

Tables Icon

Table 1. κϕpm for Coupling between Fundamental Modes and LP11-group Higher-order Modes due to the Acoustic Flexural Wave Vibrating along the x-axis

To guarantee the success of the mode conversion, the phase matching condition LB = Λ should be satisfied at the same time. LB = λnpm is the beatlength of the two coupled modes, where λ is the resonance wavelength and Δnpm is the modal refractive index difference. Λ=πRCext/f is the period of the acoustic flexural wave propagating along the unjacketed fiber [33], where R is the ber radius and Cext = 5760 m/s is the phase velocity of the acoustic wave in silica. The plots of the beatlengths for the LP11-group higher-order modes converted from a fundamental mode are shown in Fig. 2(a), and the required frequencies f of the RF driving signal applied on the acoustic transducer are shown in Fig. 2(b) for the SMF-28 fiber based on the phase matching condition of the acoustically-induced ber grating

f=πRCext(Δnpm/λ)2.
As seen in Fig. 2(b), the RF driving frequencies are different for different output modes due to the effective refractive index differences between the higher-order modes. The frequency difference is
Δfmm'=2πRCextλ2ΔnpmΔnmm',
where Δnmm' is the effective refractive index difference between higher-order modes. Therefore, the mode selection at the same wavelength is achievable via tuning the frequency of the RF driving signal. In the example shown in Fig. 2(b), the generation of TE01 and TM01 modes at λ = 633 nm requires a setting of f = 0.8227 MHz and 0.8289 MHz, respectively. The frequency difference Δf = 6.2 kHz can be easily discriminated by an electrical function generator. Compared to the mechanical micro-bend [28,31] and CO2-laser writing technology [30], this approach is highly advantageous with the tunability for phase matching in generating different types of CVBs at the same wavelength or varying wavelengths of CVBs over a broad band.

 figure: Fig. 2

Fig. 2 (a) Beatlength and (b) acoustic wave frequency as functions of the resonance wavelength for the SMF-28 fiber (Corning). Insets show the zoomed-in curves at λ = 532 and 633 nm.

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Figure 3(a) shows the process flow for generating the CVBs. The beam is firstly purified as an HE11 mode by stripping out all higher-order modes after polarization control that defines the mode as either HE11x or HE11y. Mode conversion is then performed to obtain a desired CVB in a segment of unjacketed ber (50 mm long) with one end glued with epoxy to the tip of the horn-like acoustic transducer and the other end xed on a ber clamp. The acoustic wave was generated and then amplied at the tip of the horn-like acoustic transducer by applying an RF driving signal on the piezoelectric transducer. To obtain the desired CVB, the mode conversion is selected via polarization control, i.e. HE11x→TM01 and HE11y→TE01, and the phase matching condition is satisfied via frequency tuning on the RF driver.

 figure: Fig. 3

Fig. 3 (a) The process flow for generating CVBs. (b) Experimental setup for optical communication band based on the Two-Mode Step-Index Fiber (OFS). PC: polarization controller; MO: micro-objective; MS: mode stripper; GT: Glan-Taylor prism polarizer; SMF: single-mode ber; TMF: two-mode fiber; CCD: charge coupled device.

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3. Experimental results and discussions

Two types of optical fibers were adopted in the experiment, the SMF-28 fiber (Corning) and the Two-Mode Step-Index Fiber (OFS). The SMF-28 fiber, with a core radius of ρco = 4.5 µm, a cladding radius of ρcl = 62.5 µm and a step index of ∆ = 0.32%, were used as a few-mode fiber in the visible band. Experiment for the SMF-28 fiber was done with wavelength at 633 nm and 532 nm to acquire the required RF driving frequencies for the desired CVB modes. Beatlength and acoustic frequency as functions of the resonance wavelength as shown in Fig. 2 are deduced from the experimental results. To examine the modal field of the CVBs, the beam was projected on a CCD covered by a linear polarizer through a micro-objective in free space. The intensity patterns at various polarizations are shown in Figs. 4(a)-4(d) for the SMF-28 fiber [31]. The Two-Mode Step-Index Fiber, with a core radius of ρco = 10 µm, a cladding radius of ρcl = 62.5 µm, and a step index of ∆ = 0.32%, is suitable for generating CVBs in the optical communication band. Figure 3(b) shows the experimental setup for generation of CVBs in optical communication band with all-fiber devices. Experiment was done at λ = 1540 nm, 1545 nm, 1550 nm, 1555 nm and 1560 nm to acquire the required RF driving frequencies for desired modes of the CVBs, Theoretic calculation on the beatlength and the acoustic frequency as functions of the resonance wavelength has also been done based on Eq. (8) and the results are shown in Fig. 5 with experimental measurement denoted with solid dots. As the input power to the polarization controller (PC) was set at 6.8 mW, an output power of 2.4 mW was received for the CVBs, so the power utilization efficiency reached 35%. The system lost 1.4 mW from the PC and 3.0 mW from the mode stripper (MS) [37]. The modal intensity patterns at various polarizations at λ = 1550 nm are shown in Figs. 4(e) and 4(f). In experiment, the generated CVBs show annular intensity patterns in absence of polarizer, whereas splits appear in the patterns after adding a polarizer and rotate for rotating polarizer.

 figure: Fig. 4

Fig. 4 Images taken by the CCD in absence of polarizer (a1-f1) and in presence of polarizer at different polarization orientations [(a2 - a5) to (f2 - f5)]. (a, c, e) are for TM01 mode; (b, d, f) are for TE01 mode; (a, b), (c, d), and (e, f) are for λ = 633 nm, 532 nm, and 1550 nm, respectively. The image sizes are 1.8 mm × 1.8 mm (a-d) and 2.25 mm × 2.25 mm (e, f), respectively.

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 figure: Fig. 5

Fig. 5 Beatlengths and RF driving frequencies as functions of the resonance wavelength deduced from experimental data denoted as solid dots.

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Subsequently, the modal purity was measured for the generated CVBs using the optical heterodyne interference method [38]. When the HE11x.(HE11y) mode is converted to the TM01 (TE01) mode in presence of the acoustic vibration, the frequency of the obtained mode after conversion will be downshifted by an amount equal to the acoustic frequency f. Thus the signal waveform for interference of the output waves can be expressed as

s(t)=βI1I2cos(2πft),
where I1 and I2 are the respective powers of the HE11x.(HE11y) and TM01 (TE01) modes, and β is the photo-electric conversion coefcient of the photodetector. Taking the example at λ = 633 nm in Fig. 4(a), the power of HE11x and TM01 modes became equalized so that the visibility of the heterodyne interference signal reached the maximum by tuning RF driving voltage to 5.1 V, as shown the blue curve in Fig. 6. By further increasing the RF driving voltage to 7.4 V, the visibility of heterodyne interference signal reached the minimum, as shown the red curve in Fig. 6, when the power of HE11x was converted to that of TM01 at maximum limit. The time waveforms of the detected heterodyne interference signals in these two extreme cases presented a maximum and a minimum peak-to-peak amplitudes (Vp−p) of 1 V (blue curve) and 0.12 V (red curve), respectively. Assuming a unity total power, i.e. I1 + I2 = 1, the former was for the case I1:I2 = 50%:50% and the later for the case of most complete conversion which derived I1:I2 = 0.1%:99.9% or a modal purity of ~30 dB. The same modal purity was experimentally reached for the converted TE01 mode as well, while similar results were obtained in the optical communication band.

 figure: Fig. 6

Fig. 6 Time waveforms of the interference signal with different power ratios between HE11x and TM01 at 633 nm.

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4. Conclusion

Intermodal coupling due to the asymmetrical refractive index modulation induced by applying acoustic flexural wave on fiber can be utilized to achieve CVBs with TM01 and TE01 modal fields, which have the characteristics of radial and azimuthal polarizations. Mode conversion of eitherHE11x→TM01 or HE11y→TE01 for acoustic vibration along the x-axis is chosen via polarization control at the input. The phase matching condition allowing the mode conversion is satisfied by tuning the acoustic wave frequency. A power utilization efficiency of 35% and a modal purity of ~30 dB were achieved for generated CVBs experimentally. This approach is advantageous with tunability for phase matching in generating different types of CVBs at the same wavelength over a broad wavelength range and implementable in fiber circuit.

Acknowledgments

This work is financially supported by the 973 Programs (2012CB921900, 2013CB328702), the NSFC (11404263, 61377055, 61405161, and 11174153, 11574161), the Fundamental Research Funds for the Central Universities (3102015ZY060).

References and links

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5. E. M. Furst and A. P. Gast, “Micromechanics of dipolar chains using optical tweezers,” Phys. Rev. Lett. 82(20), 4130–4133 (1999). [CrossRef]  

6. M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007). [CrossRef]  

7. C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013). [CrossRef]   [PubMed]  

8. L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013). [CrossRef]   [PubMed]  

9. X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012). [CrossRef]   [PubMed]  

10. B. Ndagano, R. Brüning, M. McLaren, M. Duparré, and A. Forbes, “Fiber propagation of vector modes,” Opt. Express 23(13), 17330–17336 (2015). [CrossRef]   [PubMed]  

11. Y. Kozawa and S. Sato, “Generation of a radially polarized laser beam by use of a conical Brewster prism,” Opt. Lett. 30(22), 3063–3065 (2005). [CrossRef]   [PubMed]  

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14. V. G. Niziev, R. S. Chang, and A. V. Nesterov, “Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer,” Appl. Opt. 45(33), 8393–8399 (2006). [CrossRef]   [PubMed]  

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19. X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32(24), 3549–3551 (2007). [CrossRef]   [PubMed]  

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References

  • View by:

  1. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
    [Crossref] [PubMed]
  2. Q. W. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
    [Crossref]
  3. D. P. Biss and T. G. Brown, “Polarization-vortex-driven second-harmonic generation,” Opt. Lett. 28(11), 923–925 (2003).
    [Crossref] [PubMed]
  4. Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004).
    [Crossref] [PubMed]
  5. E. M. Furst and A. P. Gast, “Micromechanics of dipolar chains using optical tweezers,” Phys. Rev. Lett. 82(20), 4130–4133 (1999).
    [Crossref]
  6. M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007).
    [Crossref]
  7. C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
    [Crossref] [PubMed]
  8. L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).
    [Crossref] [PubMed]
  9. X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
    [Crossref] [PubMed]
  10. B. Ndagano, R. Brüning, M. McLaren, M. Duparré, and A. Forbes, “Fiber propagation of vector modes,” Opt. Express 23(13), 17330–17336 (2015).
    [Crossref] [PubMed]
  11. Y. Kozawa and S. Sato, “Generation of a radially polarized laser beam by use of a conical Brewster prism,” Opt. Lett. 30(22), 3063–3065 (2005).
    [Crossref] [PubMed]
  12. D. Pohl, “Operation of a ruby laser in the purely transverse electric mode TE01,” Appl. Phys. Lett. 20(7), 266–267 (1972).
    [Crossref]
  13. M. A. Ahmed, A. Voss, M. M. Vogel, and T. Graf, “Multilayer polarizing grating mirror used for the generation of radial polarization in Yb:YAG thin-disk lasers,” Opt. Lett. 32(22), 3272–3274 (2007).
    [Crossref] [PubMed]
  14. V. G. Niziev, R. S. Chang, and A. V. Nesterov, “Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer,” Appl. Opt. 45(33), 8393–8399 (2006).
    [Crossref] [PubMed]
  15. J. F. Bisson, J. Li, K. Ueda, and Y. Senatsky, “Radially polarized ring and arc beams of a neodymium laser with an intra-cavity axicon,” Opt. Express 14(8), 3304–3311 (2006).
    [Crossref] [PubMed]
  16. K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett. 31(14), 2151–2153 (2006).
    [Crossref] [PubMed]
  17. K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89(25), 251114 (2006).
    [Crossref]
  18. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27(5), 285–287 (2002).
    [Crossref] [PubMed]
  19. X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32(24), 3549–3551 (2007).
    [Crossref] [PubMed]
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2015 (5)

2013 (4)

S. Ramachandran and P. Kristensen, “Optical vortices in fiber,” Nanophotonics 2(5–6), 455–474 (2013).

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref] [PubMed]

L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).
[Crossref] [PubMed]

2012 (3)

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Y. Kang, J. Ko, S. M. Lee, S. K. Choi, B. Y. Kim, and H. S. Park, “Measurement of the entanglement between photonic spatial modes in optical fibers,” Phys. Rev. Lett. 109(2), 020502 (2012).
[Crossref] [PubMed]

S. Liu, P. Li, T. Peng, and J. Zhao, “Generation of arbitrary spatially variant polarization beams with a trapezoid Sagnac interferometer,” Opt. Express 20(19), 21715–21721 (2012).
[Crossref] [PubMed]

2009 (2)

N. K. Viswanathan and V. V. G. K. Inavalli, “Generation of optical vector beams using a two-mode fiber,” Opt. Lett. 34(8), 1189–1191 (2009).
[Crossref] [PubMed]

Q. W. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

2007 (3)

2006 (6)

2005 (2)

2004 (2)

Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004).
[Crossref] [PubMed]

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre-Gaussian beams,” Opt. Commun. 237(1-3), 89–95 (2004).
[Crossref]

2003 (2)

D. P. Biss and T. G. Brown, “Polarization-vortex-driven second-harmonic generation,” Opt. Lett. 28(11), 923–925 (2003).
[Crossref] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

2002 (3)

1999 (1)

E. M. Furst and A. P. Gast, “Micromechanics of dipolar chains using optical tweezers,” Phys. Rev. Lett. 82(20), 4130–4133 (1999).
[Crossref]

1997 (1)

1996 (2)

T. A. Birks, P. S. J. Russell, and D. O. Culverhouse, “The acousto-optic effect in single–mode fiber tapers and couplers,” J. Lightwave Technol. 14(11), 2519–2529 (1996).
[Crossref]

M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21(23), 1948–1950 (1996).
[Crossref] [PubMed]

1972 (1)

D. Pohl, “Operation of a ruby laser in the purely transverse electric mode TE01,” Appl. Phys. Lett. 20(7), 266–267 (1972).
[Crossref]

Ahmed, M. A.

Aït-Ameur, K.

Alfano, R. R.

Alhassen, F.

P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[Crossref] [PubMed]

Biener, G.

Birks, T. A.

T. A. Birks, P. S. J. Russell, and D. O. Culverhouse, “The acousto-optic effect in single–mode fiber tapers and couplers,” J. Lightwave Technol. 14(11), 2519–2529 (1996).
[Crossref]

Biss, D. P.

Bisson, J. F.

Bomzon, Z.

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Brown, T. G.

Brüning, R.

Bu, J.

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89(25), 251114 (2006).
[Crossref]

Burge, R. E.

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89(25), 251114 (2006).
[Crossref]

Cai, X.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Chang, R. S.

Chiang, K. S.

J. L. Dong and K. S. Chiang, “Temperature-insensitive mode converters with CO2-laser written long-period fiber gratings,” IEEE Photonics Technol. Lett. 27(9), 1006–1009 (2015).
[Crossref]

Choi, S. K.

Y. Kang, J. Ko, S. M. Lee, S. K. Choi, B. Y. Kim, and H. S. Park, “Measurement of the entanglement between photonic spatial modes in optical fibers,” Phys. Rev. Lett. 109(2), 020502 (2012).
[Crossref] [PubMed]

Courjon, D.

T. Grosjean, D. Courjon, and M. Spajer, “An all-fiber device for generating radially and other polarized light beams,” Opt. Commun. 203(1-2), 1–5 (2002).
[Crossref]

Culverhouse, D. O.

T. A. Birks, P. S. J. Russell, and D. O. Culverhouse, “The acousto-optic effect in single–mode fiber tapers and couplers,” J. Lightwave Technol. 14(11), 2519–2529 (1996).
[Crossref]

Dashti, P. Z.

P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[Crossref] [PubMed]

de Saint Denis, R.

Ding, J.

Dong, J. L.

J. L. Dong and K. S. Chiang, “Temperature-insensitive mode converters with CO2-laser written long-period fiber gratings,” IEEE Photonics Technol. Lett. 27(9), 1006–1009 (2015).
[Crossref]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Du, C.

Du, L.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref] [PubMed]

L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).
[Crossref] [PubMed]

Duparré, M.

Erdogan, T.

Fang, H.

L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).
[Crossref] [PubMed]

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref] [PubMed]

Feurer, T.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007).
[Crossref]

Forbes, A.

Furst, E. M.

E. M. Furst and A. P. Gast, “Micromechanics of dipolar chains using optical tweezers,” Phys. Rev. Lett. 82(20), 4130–4133 (1999).
[Crossref]

Gao, F.

Gao, W.

Gast, A. P.

E. M. Furst and A. P. Gast, “Micromechanics of dipolar chains using optical tweezers,” Phys. Rev. Lett. 82(20), 4130–4133 (1999).
[Crossref]

Graf, T.

Grosjean, T.

T. Grosjean, D. Courjon, and M. Spajer, “An all-fiber device for generating radially and other polarized light beams,” Opt. Commun. 203(1-2), 1–5 (2002).
[Crossref]

Guo, C. S.

Hasman, E.

Hierle, R.

Hu, X.

Huang, H.

Huang, L.

Inavalli, V. V. G. K.

Jiang, B.

Johnson-Morris, B.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Kang, Y.

Y. Kang, J. Ko, S. M. Lee, S. K. Choi, B. Y. Kim, and H. S. Park, “Measurement of the entanglement between photonic spatial modes in optical fibers,” Phys. Rev. Lett. 109(2), 020502 (2012).
[Crossref] [PubMed]

Karimi, E.

Kim, B. Y.

Y. Kang, J. Ko, S. M. Lee, S. K. Choi, B. Y. Kim, and H. S. Park, “Measurement of the entanglement between photonic spatial modes in optical fibers,” Phys. Rev. Lett. 109(2), 020502 (2012).
[Crossref] [PubMed]

Kleiner, V.

Ko, J.

Y. Kang, J. Ko, S. M. Lee, S. K. Choi, B. Y. Kim, and H. S. Park, “Measurement of the entanglement between photonic spatial modes in optical fibers,” Phys. Rev. Lett. 109(2), 020502 (2012).
[Crossref] [PubMed]

Kozawa, Y.

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

S. Ramachandran and P. Kristensen, “Optical vortices in fiber,” Nanophotonics 2(5–6), 455–474 (2013).

Lavery, M. P. J.

Lee, H. P.

P. Z. Dashti, F. Alhassen, and H. P. Lee, “Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber,” Phys. Rev. Lett. 96(4), 043604 (2006).
[Crossref] [PubMed]

Lee, S. M.

Y. Kang, J. Ko, S. M. Lee, S. K. Choi, B. Y. Kim, and H. S. Park, “Measurement of the entanglement between photonic spatial modes in optical fibers,” Phys. Rev. Lett. 109(2), 020502 (2012).
[Crossref] [PubMed]

Lei, D. Y.

L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).
[Crossref] [PubMed]

Lei, T.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref] [PubMed]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Li, J.

Li, P.

Li, S.

Liu, S.

Liu, X.

Low, D. K. Y.

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89(25), 251114 (2006).
[Crossref]

Maier, S. A.

L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).
[Crossref] [PubMed]

Mao, D.

Marrucci, L.

McLaren, M.

Meier, M.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007).
[Crossref]

Milione, G.

Min, C.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref] [PubMed]

L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).
[Crossref] [PubMed]

Mo, Q.

Moh, K. J.

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89(25), 251114 (2006).
[Crossref]

Ndagano, B.

Nesterov, A. V.

Nguyen, T. A.

Ni, W. J.

Niziev, V. G.

Nolan, D. A.

O’Brien, J. L.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Park, H. S.

Y. Kang, J. Ko, S. M. Lee, S. K. Choi, B. Y. Kim, and H. S. Park, “Measurement of the entanglement between photonic spatial modes in optical fibers,” Phys. Rev. Lett. 109(2), 020502 (2012).
[Crossref] [PubMed]

Passilly, N.

Peng, T.

Petrov, D.

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre-Gaussian beams,” Opt. Commun. 237(1-3), 89–95 (2004).
[Crossref]

Pohl, D.

D. Pohl, “Operation of a ruby laser in the purely transverse electric mode TE01,” Appl. Phys. Lett. 20(7), 266–267 (1972).
[Crossref]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

S. Ramachandran and P. Kristensen, “Optical vortices in fiber,” Nanophotonics 2(5–6), 455–474 (2013).

S. Ramachandran, Z. Wang, and M. Yan, “Bandwidth control of long-period grating-based mode converters in few-mode fibers,” Opt. Lett. 27(9), 698–700 (2002).
[Crossref] [PubMed]

Ren, Y.

Roch, J. F.

Romano, V.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007).
[Crossref]

Russell, P. S. J.

T. A. Birks, P. S. J. Russell, and D. O. Culverhouse, “The acousto-optic effect in single–mode fiber tapers and couplers,” J. Lightwave Technol. 14(11), 2519–2529 (1996).
[Crossref]

Sato, S.

Schadt, M.

Senatsky, Y.

Shen, J.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref] [PubMed]

Shen, Z.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref] [PubMed]

Sorel, M.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Spajer, M.

T. Grosjean, D. Courjon, and M. Spajer, “An all-fiber device for generating radially and other polarized light beams,” Opt. Commun. 203(1-2), 1–5 (2002).
[Crossref]

Stalder, M.

Strain, M. J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Tang, D.

L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).
[Crossref] [PubMed]

Thompson, M. G.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Treussart, F.

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Ueda, K.

Viswanathan, N. K.

Vogel, M. M.

Volpe, G.

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre-Gaussian beams,” Opt. Commun. 237(1-3), 89–95 (2004).
[Crossref]

Voss, A.

Wang, H. T.

Wang, J.

S. Li, Q. Mo, X. Hu, C. Du, and J. Wang, “Controllable all-fiber orbital angular momentum mode converter,” Opt. Lett. 40(18), 4376–4379 (2015).
[Crossref] [PubMed]

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Wang, Q.

L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).
[Crossref] [PubMed]

Wang, X. L.

Wang, Z.

Willner, A. E.

Xie, G.

Xu, J.

Yan, M.

Yang, D.

Yonezawa, K.

Yu, S.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref] [PubMed]

Yuan, G.

L. Du, D. Y. Lei, G. Yuan, H. Fang, X. Zhang, Q. Wang, D. Tang, C. Min, S. A. Maier, and X. Yuan, “Mapping plasmonic near-field profiles and interferences by surface-enhanced Raman scattering,” Sci. Rep. 3, 3064 (2013).
[Crossref] [PubMed]

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
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Yuan, X.

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Figures (6)

Fig. 1
Fig. 1 Schematic of the index profile of a few-mode fiber denoted with modal indices and intensity patterns for (a) the scalar modes and (b) corresponding groups of the vector modes. Field directions are denoted on the intensity patterns of vector modes.
Fig. 2
Fig. 2 (a) Beatlength and (b) acoustic wave frequency as functions of the resonance wavelength for the SMF-28 fiber (Corning). Insets show the zoomed-in curves at λ = 532 and 633 nm.
Fig. 3
Fig. 3 (a) The process flow for generating CVBs. (b) Experimental setup for optical communication band based on the Two-Mode Step-Index Fiber (OFS). PC: polarization controller; MO: micro-objective; MS: mode stripper; GT: Glan-Taylor prism polarizer; SMF: single-mode ber; TMF: two-mode fiber; CCD: charge coupled device.
Fig. 4
Fig. 4 Images taken by the CCD in absence of polarizer (a1-f1) and in presence of polarizer at different polarization orientations [(a2 - a5) to (f2 - f5)]. (a, c, e) are for TM01 mode; (b, d, f) are for TE01 mode; (a, b), (c, d), and (e, f) are for λ = 633 nm, 532 nm, and 1550 nm, respectively. The image sizes are 1.8 mm × 1.8 mm (a-d) and 2.25 mm × 2.25 mm (e, f), respectively.
Fig. 5
Fig. 5 Beatlengths and RF driving frequencies as functions of the resonance wavelength deduced from experimental data denoted as solid dots.
Fig. 6
Fig. 6 Time waveforms of the interference signal with different power ratios between HE 1 1 x and TM01 at 633 nm.

Tables (1)

Tables Icon

Table 1 κ ϕ p m for Coupling between Fundamental Modes and LP11-group Higher-order Modes due to the Acoustic Flexural Wave Vibrating along the x-axis

Equations (10)

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Δ n ( r , ϕ ) = N 0 r cos ( ϕ ) ,
κ p m = π λ ε 0 μ 0 n 0 E t p Δ n ( r , ϕ ) E t m r d r d ϕ .
E t p = u p F 01 ( r ) ,
E t m = Φ m ( ϕ ) F 11 ( r ) ,
C = ( π / λ ) ε 0 / μ 0 n 0 N 0 ,
κ r = F 01 ( r ) F 11 ( r ) r 2 d r ,
κ ϕ p m = 0 2 π u p Φ m ( ϕ ) cos ϕ d ϕ ,
f = π R C ext ( Δ n p m / λ ) 2 .
Δ f m m ' = 2 π R C e x t λ 2 Δ n p m Δ n m m ' ,
s ( t ) = β I 1 I 2 cos ( 2 π f t ) ,

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