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Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Editor: Alan E. Willner
  • Vol. 34, Iss. 16 — Aug. 15, 2009
  • pp: 2525–2527
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Generation and propagation of radially polarized beams in optical fibers

Siddharth Ramachandran, Poul Kristensen, and Man F. Yan  »View Author Affiliations


Optics Letters, Vol. 34, Issue 16, pp. 2525-2527 (2009)
http://dx.doi.org/10.1364/OL.34.002525


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Abstract

Beams with polarization singularities have attracted immense recent attention in a wide array of scientific and technological disciplines. We demonstrate a class of optical fibers in which these beams can be generated and propagated over long lengths with unprecedented stability, even in the presence of strong bend perturbations. This opens the door to exploiting nonlinear fiber optics to manipulate such beams. This fiber also possesses the intriguingly counterintuitive property of being polarization maintaining despite being strictly cylindrically symmetric, a prospect hitherto considered infeasible with optical fibers.

© 2009 Optical Society of America

Cylindrical vector beams (CVBs), of which radially polarized beams are a subclass, are characterized by a nonuniform spatial distribution of their polarization vector (see top row of Fig. 1 ). This property results in several interesting ramifications, such as (a) focal spot sizes smaller than the diffraction limit [1

1. R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003). [CrossRef] [PubMed]

], (b) the feasibility of electron acceleration [2

2. Y. I. Salamin, Phys. Rev. A 73, 043402 (2006). [CrossRef]

], (c) optical tweezers with minimal scattering forces [3

3. Q. Zhan, Opt. Express 12, 3377 (2004). [CrossRef] [PubMed]

], (d) a focused pattern resembling emissions from an atomic dipole [4

4. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001). [CrossRef] [PubMed]

], and (e) higher efficiency for laser-machining of metals [5

5. A. V. Nesterov and V. G. Niziev, J. Phys. D 33, 1817 (2000). [CrossRef]

].

All these intra- and extra-cavity CVB generation techniques face a debilitating mode-instability problem. The first higher-order mode group in a cylindrically symmetric resonator comprises the almost-degenerate azimuthally [Fig. 1a, TE01 in guided waves] and radially [Fig. 1d, TM01 in guided waves] polarized beams. In a fiber, this mode group additionally comprises two strictly degenerate mixed states [Figs. 1b, 1c, HE21]. Thus, even the slightest perturbations to the cylindrical symmetry of a resonator (free-space or fiber) induces coupling between them, resulting in the formation of the more familiar (undesired) Hermite–Gaussian-like beam—the so-called LP11 mode in a fiber [see colored-line pairs in Figs. 1e, 1f, 1g, 1h illustrating different orientations of the LP11 mode generated by different linear combinations of the CVBs of the top row in Fig. 1]. This means that while previously demonstrated CVB generation techniques in fibers may produce such a mode immediately after the mode converters, to our knowledge a fiber-optic means of delivering them has been infeasible.

Here we describe a class of fibers that addresses this fundamental instability problem by lifting the near-degeneracy of the TM01 (radially polarized), TE01 (azimuthally polarized), and HE21 modes. Our experiments reveal that this fiber maintains either the azimuthally or radially polarized mode with exceptional purity (>99.8%), after propagation over fiber lengths greater than 20m, even in the presence of extreme bends and twists (of radii of curvature as small as 5mm). Our demonstration also points to another intriguing phenomenon previously not observed in fibers—the ability to maintain the polarization state of a signal even though the fiber is strictly cylindrically symmetric. This is because CVBs, in contrast to Gaussian beams, naturally maintain their polarization state during propagation.

Figure 2a shows the measured refractive index profile of the fiber we fabricated to test this concept. Also shown in this plot is the simulated mode profile for the LP11 mode guided by this fiber. Note that this fiber possesses the annular high-index rings that we expect to help with mode stability. However, it also has a step-index central core, as do conventional fibers. This core does not detract from the design philosophy discussed above, but instead it allows for the fundamental mode to be Gaussian shaped, enabling low-loss coupling, either from free-space lasers or conventional single-mode fibers (SMFs). Figure 2b shows the neff for the TM01, HE21, and TE01 modes in this fiber, measured by recording grating resonance wavelengths for a variety of grating periods (the grating coupling schematic and measurement technique are described in the following paragraph). The neff for the desired TM01 mode (radially polarized mode) is separated by at least 1.8×104 from any other guided mode of this fiber. For conventional fibers, the three curves would be indistinguishable in the scale of this plot, with neff differences of the order of 105.

Figure 3a shows the experimental setup used to generate CVBs in this fiber. The fiber input is spliced to the SMF, so that the light entering our fiber is in the conventional fundamental mode. Thereafter, a fiber grating, comprising periodic microbends, couples the fundamental mode to the desired vector mode. Figure 3b shows the mode conversion spectra when the grating period Λ, is 800μm—the measured conversion efficiency exceeds 99.8% at the respective resonance wavelengths λres, for each vector mode. Repeating this measurement for different grating periods yields the neff of the three vector modes as a function of wavelength, as plotted in Fig. 2b. The HE21 resonance can be excited with any state of polarization (SOP) of light entering the microbend grating, but the TE01 or TM01 modes are excited only when the input SOP is parallel or perpendicular, respectively, to the plane of microbend perturbation. Thus we can use the input SOP as well as the grating period to choose the mode we excite, as well as the wavelength at which we do so.

Figure 3c shows experimentally recorded near-field images of the fiber output when the grating is tuned either to the radially polarized (TM01), or the azimuthally polarized (TE01) resonance. All images were obtained after mode propagation over fiber lengths exceeding 20  m. Both beams have annular shapes and appear to be remarkably pure and stable—a condition that is maintained as we perturb the fiber (with bends and twists of radii as small as 5mm). With the polarizer in the beam path, only the projections of the mode that are aligned with polarizer are transmitted, leading to the double-humped intensity profile that rotates in opposite directions as the polarizer is rotated. The insertion loss, measured with a power meter, is less than 5% (0.2dB), and intensity measurements along the azimuth of the annular intensity profiles revealed variations of less than 1% (0.05dB).

Fig. 1 Intensity patterns (white is maximum intensity) of the first higher-order mode group in a fiber. Arrows show the orientation of the electric field in each beam. The top row shows cylindrical vector modes that are the exact vector solutions in a fiber, while the bottom row shows the resultant, unstable LP11 modes commonly obtained at a fiber output. Specific linear combinations of pairs of top row of modes, resulting in the variety of LP11 modes obtained at a fiber output, are shown by colored lines.
Fig. 2 (a) Measured refractive index profile (relative to silica index) for fabricated fiber, and corresponding LP11 mode intensity profile. (b) Effective index for the three vector components of the scalar LP11 mode for fiber shown in (a). neff of radially polarized (TM01) mode separated by 1.8×104 from other modes.
Fig. 3 (a) Experimental setup: the ring-design fiber is spliced to the SMF (bottom branch) for spectral measurements shown in (b), or cleaved and imaged on camera (top branch) for measurements shown in (c). (b) Measured grating resonance spectra for coupling from fundamental LP01 mode to desired antisymmetric mode—efficiency >99.8%. (c) Experimentally recorded near-field images for the radially polarized (TM01) mode (top) and azimuthally polarized (TE01) mode (bottom). Clean annular intensity profile for both. Image rotation with polarizer in beam path consistent with expected polarization orientation for the two modes, confirming the polarization state of the two beams.
Fig. 4 (a) Setup to compare polarization-maintaining characteristics of the CVB fiber and conventional SMF. Input and output gratings on the CVB fiber ensure that light entering or exiting the setup is conventionally polarized (i.e., spatially uniform, as in Gaussian beams), thus facilitating measurements with conventional fiber-optic test sets (such as polarization analyzers). (b) Poincare sphere representation of output SOP, to measure polarization-state variations as both fibers are perturbed. Red traces represent evolution of SOP on the front surface of the sphere (as viewed in the figure), while blue traces show SOP states on back surface of the sphere.
1.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003). [CrossRef] [PubMed]

2.

Y. I. Salamin, Phys. Rev. A 73, 043402 (2006). [CrossRef]

3.

Q. Zhan, Opt. Express 12, 3377 (2004). [CrossRef] [PubMed]

4.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001). [CrossRef] [PubMed]

5.

A. V. Nesterov and V. G. Niziev, J. Phys. D 33, 1817 (2000). [CrossRef]

6.

M. A. Ahmed, J. Schulz, A. Voss, O. Parriaux, J.-C. Pommier, and T. Graf, Opt. Lett. 32, 1824 (2007). [CrossRef] [PubMed]

7.

Y. Kozawa and S. Sato, Opt. Lett. 30, 3063 (2005). [CrossRef] [PubMed]

8.

J.-L. Li, K.-I. Ueda, M. Musha, A. Shirakawa, and L.-X. Zhong, Opt. Lett. 31, 2969 (2006). [CrossRef] [PubMed]

9.

G. Volpe and D. Petrov, Opt. Commun. 237, 89 (2004). [CrossRef]

10.

P. Z. Dashti, F. Alhassen, and H. P. Lee, Phys. Rev. Lett. 96, 043064 (2006). [CrossRef]

11.

A. Witkowska, S. G. L-Saval, A. Pham, and T. A. Birks, Opt. Lett. 33, 306 (2008). [CrossRef] [PubMed]

12.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

OCIS Codes
(140.3300) Lasers and laser optics : Laser beam shaping
(230.5440) Optical devices : Polarization-selective devices
(230.2285) Optical devices : Fiber devices and optical amplifiers

ToC Category:
Optical Devices

History
Original Manuscript: May 5, 2009
Revised Manuscript: June 9, 2009
Manuscript Accepted: July 6, 2009
Published: August 14, 2009

Citation
Siddharth Ramachandran, Poul Kristensen, and Man F. Yan, "Generation and propagation of radially polarized beams in optical fibers," Opt. Lett. 34, 2525-2527 (2009)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-16-2525


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References

  1. R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003). [CrossRef] [PubMed]
  2. Y. I. Salamin, Phys. Rev. A 73, 043402 (2006). [CrossRef]
  3. Q. Zhan, Opt. Express 12, 3377 (2004). [CrossRef] [PubMed]
  4. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001). [CrossRef] [PubMed]
  5. A. V. Nesterov and V. G. Niziev, J. Phys. D 33, 1817 (2000). [CrossRef]
  6. M. A. Ahmed, J. Schulz, A. Voss, O. Parriaux, J.-C. Pommier, and T. Graf, Opt. Lett. 32, 1824 (2007). [CrossRef] [PubMed]
  7. Y. Kozawa and S. Sato, Opt. Lett. 30, 3063 (2005). [CrossRef] [PubMed]
  8. J.-L. Li, K.-I. Ueda, M. Musha, and A. Shirakawa, and L.-X. Zhong, Opt. Lett. 31, 2969 (2006). [CrossRef] [PubMed]
  9. G. Volpe and D. Petrov, Opt. Commun. 237, 89 (2004). [CrossRef]
  10. P. Z. Dashti, F. Alhassen, and H. P. Lee, Phys. Rev. Lett. 96, 043064 (2006). [CrossRef]
  11. A. Witkowska, S. G. L-Saval, A. Pham, and T. A. Birks, Opt. Lett. 33, 306 (2008). [CrossRef] [PubMed]
  12. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

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