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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 20 — Sep. 27, 2010
  • pp: 20918–20925
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A micro-structured aperture made of a hollow triangular-core fiber for novel beam shaping

Woosung Ha, Sejin Lee, Jongki Kim, Yoonseob Jeong, Kyunghwan Oh, Jens Kobelke, Kay Schuster, Sonja Unger, Anka Schwuchow, and Jun Ki Kim  »View Author Affiliations


Optics Express, Vol. 18, Issue 20, pp. 20918-20925 (2010)
http://dx.doi.org/10.1364/OE.18.020918


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Abstract

We demonstrate a micro-structured aperture made of a unique hollow triangular-core fiber (HTCF) that consists of a central air hole, a high-index hollow triangular core, and silica cladding for all-fiber novel beam shaping. Detailed fabrication processes to embed a hollow triangular structure into a cylindrical optical fiber are described and unique diffraction patterns out of the HTCF for monochromatic light are analyzed both experimentally and theoretically. Fourier-optic analysis combined with guided mode calculation was pursued to interpret experimental patterns in terms of the beam propagation distance.

© 2010 OSA

1. Introduction

Since the advent of a laser, laser beam shaping has been at the center of interests to both industry and academia, which requires delicate control of intensities and phase profiles of optical fields. One of the well established areas in beam shaping is homogenizing a Gaussian-like beam into a flat-top distribution for applications in lithography, material processing, and display [1

1. F. M. Dickey, “Laser beam shaping,” Opt. Photon. News 14(4), 30–35 (2003). [CrossRef]

]. Generating furthermore complex patterns has been a continuous issue for applications in more fundamental sciences to study light-matter interactions, and has been mainly developed by means of Fourier optics [2

2. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, Greenwood Village, CO, 2005).

] such as diffraction by exotic apertures [3

3. M. Gu and X. S. Gan, “Fresnel diffraction by circular and serrated apertures illuminated with an ultrashort pulsed-laser beam,” J. Opt. Soc. Am. A 13(4), 771–778 (1996). [CrossRef]

], deflection by MEMS mirror devices [4

4. L. J. Hornbeck, “Digital Light Processing for high-brightness, high-resolution applications,” Proc. SPIE 3013, 27–40 (1997). [CrossRef]

,5

5. H. Schenk, P. Dürr, T. Haase, D. Kunze, U. Sobe, H. Lakner, and H. Kück, “Large deflection micromechanical scanning mirrors for linear scans and pattern generation,” IEEE J. Sel. Top. Quantum Electron. 6(5), 715–722 (2000). [CrossRef]

], and holography [6

6. M. L. Huebschman, B. Munjuluri, and H. R. Garner, “Dynamic holographic 3-D image projection,” Opt. Express 11(5), 437–445 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-11-5-437. [CrossRef] [PubMed]

] to name a few.

Prior beam shaping arts have been traditionally based on bulk-optic systems, which restrict their potential applications in emerging research areas of nano- and micro-scale imaging and sensing. Fiber optics could be a strong candidate to miniaturize the beam shaping systems into the micro and sub-micro scale taking full advantage of its flexible guidance with built-in alignment. However, conventional circular-core fibers have provided only the Gaussian-like beam for both near and far fields leaving almost no room to further modify the beam characteristics. Since the late 1990s, there have been alternative optical waveguides based on micro air-silica structures [7

7. P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006). [CrossRef]

], and the authors have also proposed a hollow optical fiber (HOF) that is composed of a central air hole, a high-index ring core, and silica cladding for applications in various photonic devices [8

8. K. Oh, S. Choi, Y. Jung, and J. W. Lee, “Novel hollow optical fibers and their applications in photonic devices for optical communications,” J. Lightwave Technol. 23(2), 524–532 (2005). [CrossRef]

]. The central air hole in the HOF was found to have a significant effect on free-space light propagation, and the authors recently demonstrated an all-fiber hybrid structure to generate a rarely diffracting Bessel-like beam [9

9. J. K. Kim, J. Kim, Y. Jung, W. Ha, Y. S. Jeong, S. Lee, A. Tünnermann, and K. Oh, “Compact all-fiber Bessel beam generator based on hollow optical fiber combined with a hybrid polymer fiber lens,” Opt. Lett. 34(19), 2973–2975 (2009). [CrossRef] [PubMed]

]. Despite successful adoption of the HOF in beam shaping, the beams were cylindrically symmetric about the propagation axis, and beam patterns with low-fold symmetry have not been realized in optical fibers.

There have been researches on polygonal-core fibers [10

10. A. R. Tynes, A. D. Pearson, and D. L. Bisbee, “Loss mechanisms and measurements in clad glass fibers and bulk glass,” J. Opt. Soc. Am. 61(2), 143–153 (1971). [CrossRef]

,11

11. R. B. Dyott, C. R. Day, and M. C. Brain, “Glass-fibre waveguide with a triangular core,” Electron. Lett. 9(13), 288–290 (1973). [CrossRef]

] that are in fact very similar to the stack-and-draw method used in micro air-silica structured fibers, but their primary aims were to simplify the preform fabrication in the early stage of fiber optics without further investigation on near- and far-field patterns. A preliminary study for unique beam shaping with an optical fiber was initiated by Tynes [12

12. A. R. Tynes, “Partially cladded triangular-cored glass optical fibers and lasers,” J. Opt. Soc. Am. 64(11), 1415–1423 (1974). [CrossRef]

]; a triangular core suspended by a glass tube showed unique far-field patterns, which could be understood by his own quasi-ray-optic cavity-like model. Despite such unique beam shaping capabilities, the structure still suffered from interfacial defects and impurities, and further investigation has not been continued due to rapid growth of chemical vapor deposition in preform fabrication. Until nowadays, embedding polygonal-core structures along with micro holes into an optical fiber is still challenging.

Recently, the authors successfully developed a technique to embed a polygonal core into a cylindrical optical fiber with and without a central air hole [13

13. K. Oh, W. Ha, S. Lee, J. Kim, Y. Jeong, and M. Park, “Preforms for preparing polygonal-core optical fiber and preparation method thereof,” Korean patent application 10–2010–0066761 (12 July 2010).

]. Combining with the polygonal core, the central air hole generates various far-field patterns out of the fiber, which can be directly applied to all-fiber beam shaping. In this paper, we introduce a hollow triangular-core fiber (HTCF) as the simplest case to combine a triangular core with a central air hole, for the first time. Detailed fabrication processes and unique diffraction patterns are explained, which could not be achieved by conventional fibers. To understand the origin of unique evolution of the patterns, we also theoretically simulated propagation of the eigenmodes of the HTCF using Fourier optics to have a good agreement with experimental observations.

2. Embedding a hollow triangular core into a cylindrical optical fiber

The whole processes to fabricate a preform for the HTCF are schematically illustrated in Fig. 1(a)
Fig. 1 (a) Schematic fabrication processes to make a preform for the HTCF: the MCVD, side-cutting and polishing, and collapsing. (b) A triangular tube after side polishing. (c) A cross section of the drawn HTCF.
and more details on the fabrication can be found in [13

13. K. Oh, W. Ha, S. Lee, J. Kim, Y. Jeong, and M. Park, “Preforms for preparing polygonal-core optical fiber and preparation method thereof,” Korean patent application 10–2010–0066761 (12 July 2010).

]. Firstly, core layers composed of GeO2-SiO2 glass were deposited inside a silica substrate tube, Heraeus F300 [14] whose outer diameter (OD) and inner diameter (ID) are 25 and 19 mm, respectively, using modified chemical vapor deposition (MCVD). The tube was then partly collapsed to an OD of 19.8 mm and an ID of 11.4 mm for a central air hole. The cylindrical tube was polished to make a triangular cross section, which is also shown in Fig. 1(b); the maximum polishing depth was 1.7 mm. This triangular tube was then further collapsed in the MCVD lathe to a nearly circular shape with an OD of 14.6 mm and an ID of about 1 mm at a high temperature above the melting point of silica. During this high-temperature collapsing process, the middle of each side is pulled outward by the surface tension leaving the vertices of the tube intact. The GeO2 doped ring also follows similar transformation to result in a triangular core with circular air hole in the center. The preform was then drawn to a fiber in optimized conditions to maintain the central hole in the fiber with proper He-gas pressure control. A cross section of the drawn HTCF is shown in Fig. 1(c) with an air-hole diameter of 18 μm, an equilateral-side length of 36 μm, and a cladding diameter of 200 μm. The ratio of the triangular core’s side length to the air-hole diameter is about the square root of three. Attenuation of the drawn HTCF was measured as 14.2 and 65.2 dB/km at the wavelengths of 635 and 1550 nm, respectively. Relatively high loss was attributed to OH overtones. However, the fiber length used in the experiments was only a few centimeters, and the effect of fiber loss was negligible. Note that the time to fabricate the HTCF is comparable to that of the conventional optical fibers because the only additional process was shaping a triangular cross section using a conventional diamond saw.

3. Diffraction analysis and beam shaping by the HTCF

The near-field patterns of the HTCF are shown as a function of the incident-light wavelength λ in Fig. 2
Fig. 2 Near-field patterns of the HTCF for various λ of (a) 500 nm, (b) 600 nm, (c) 700 nm, and (d) 800 nm.
. The HTCF was cleaved at the right angle and various wavelengths were selected by using narrow band-pass interference filters and a tungsten-halogen lamp. For a shorter λ, many modes were overlapped over the whole cross section of the hollow triangular core. As λ increased, fewer modes are guided and the light intensity gradually spread toward the corners and expanded into the cladding.

At the near field, the intensity of the HTCF showed six extrema around the sides of the hollow triangular core as schematically shown in Fig. 4(a) and in its photograph in Fig. 5(a). The six extrema in the near-field pattern are denoted as P 1, P 1`, P 2, P 2`, P 3, and P 3` in Fig. 4(a). As soon as the beam propagates along the axial direction, these initial extrema points were dragged into the center to form three lines P 1P 1`, P 2P 2`, and P 3P 3`, and each line was gradually driven outward from the center along its vertical blue y axis as in Fig. 4(a). As the axial distance increases, these lines merged together to form a shape of scissors at the middles of the triangle’s sides as in Fig. 4(b). The corresponding measurement is shown in Fig. 5(b). As the beam further propagates, the continuously driven lines resulted in the Star of David as in Fig. 4(c) and the corresponding measurement is shown in Fig. 5(c). Until the axial distance reaches the Fraunhofer distance of ~660 μm, the corners and the center of the star indicated by the dashed blue circles in Fig. 4(c) packed together to form a hexagonal distribution as in Fig. 4(d). Corresponding measurement is shown in Fig. 5(d). Beyond this axial position, the beam showed Fraunhofer diffraction such that the shape did not change any longer. Note that this type of diffraction patterns with low-fold symmetry have not been realized in fiber optics even with multicore optical fibers [17

17. L. Yuan, J. Yang, C. Guan, Q. Dai, and F. Tian, “Three-core fiber-based shape-sensing application,” Opt. Lett. 33(6), 578–580 (2008). [CrossRef] [PubMed]

], and the authors believe that this technique based on the central hole can open a new avenue of fiber-optic application for novel beam shaping.

4. Fourier-optic analysis for the guided modes in the HTCF

Drastic evolution of the diffraction patterns out of the HTCF in micro scale has never been reported, and it is very worthwhile to analyze its characteristics based on the intensity distribution of guided modes and their collective propagation in free space. To systematically analyze such unique diffraction evolution, we employed two theoretical electromagnetic wave analyses: 1) full vectorial finite difference frequency domain (FDFD) method with perfectly matched layer (PML) boundary conditions [18

18. Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express 10(17), 853–864 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-10-17-853. [PubMed]

] to obtain guided modes in the HTCF for λ = 635 nm and 2) angular spectrum of plane waves (ASPW) for fast calculation of optical diffraction [2

2. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, Greenwood Village, CO, 2005).

].

In this simulation, we could confirm that the polygonal core embedded in a cylindrical optical fiber can provide very rich diversity of diffraction patterns, which can be controlled by the geometry of the core and the central air hole. This technique can provide a new degree of freedom in fiber-optic design for laser beam shaping applications. Despite good agreement between simulations and measurements, the authors do find that the assumption behind the simulations, decoupled modes during propagation, should be further investigated in detail. Rigorous theoretical analyses for the complex multimode propagation are beyond the scope of this paper, and remains as a future work being pursued by the authors.

5. Conclusion

In conclusion, we successfully developed the novel fabrication processes to embed a hollow triangular core in cylindrical optical fibers by inverting the symmetry of the triangular preform inside out in the optical fiber during high-temperature collapsing, and the HTCF was successfully fabricated. Unique diffraction pattern evolution out of the cleaved HTCF were observed using an LD of λ = 635 nm and a CCD camera, where the intensity extrema showed a systematic change from the near-field pattern to Fraunhofer diffraction. For systematic analyses, forty-six guided modes were found by the FDFD method with PML boundary condition. It was found that the scalar summation of the ten higher-order modes’ intensities by propagation of the ASPW resulted in evolution of the diffraction patterns with a good agreement with experimental measurements. The triangular core with the central hole in an optical fiber was found to give high potential in all-fiber beam shaping, which can be readily applied in novel nano- and micro-pattern generation.

Acknowledgments

This work was supported in part by the Brain Korea 21 Project and in part by the NRF grant funded by the MEST (Nos. 2010-0018442, 2009-00479 EC-FP7/2007-2013 219299 GOSPEL, R15-2004-024-00000-0, and 2009-352-C00042).

References and links

1.

F. M. Dickey, “Laser beam shaping,” Opt. Photon. News 14(4), 30–35 (2003). [CrossRef]

2.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, Greenwood Village, CO, 2005).

3.

M. Gu and X. S. Gan, “Fresnel diffraction by circular and serrated apertures illuminated with an ultrashort pulsed-laser beam,” J. Opt. Soc. Am. A 13(4), 771–778 (1996). [CrossRef]

4.

L. J. Hornbeck, “Digital Light Processing for high-brightness, high-resolution applications,” Proc. SPIE 3013, 27–40 (1997). [CrossRef]

5.

H. Schenk, P. Dürr, T. Haase, D. Kunze, U. Sobe, H. Lakner, and H. Kück, “Large deflection micromechanical scanning mirrors for linear scans and pattern generation,” IEEE J. Sel. Top. Quantum Electron. 6(5), 715–722 (2000). [CrossRef]

6.

M. L. Huebschman, B. Munjuluri, and H. R. Garner, “Dynamic holographic 3-D image projection,” Opt. Express 11(5), 437–445 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-11-5-437. [CrossRef] [PubMed]

7.

P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006). [CrossRef]

8.

K. Oh, S. Choi, Y. Jung, and J. W. Lee, “Novel hollow optical fibers and their applications in photonic devices for optical communications,” J. Lightwave Technol. 23(2), 524–532 (2005). [CrossRef]

9.

J. K. Kim, J. Kim, Y. Jung, W. Ha, Y. S. Jeong, S. Lee, A. Tünnermann, and K. Oh, “Compact all-fiber Bessel beam generator based on hollow optical fiber combined with a hybrid polymer fiber lens,” Opt. Lett. 34(19), 2973–2975 (2009). [CrossRef] [PubMed]

10.

A. R. Tynes, A. D. Pearson, and D. L. Bisbee, “Loss mechanisms and measurements in clad glass fibers and bulk glass,” J. Opt. Soc. Am. 61(2), 143–153 (1971). [CrossRef]

11.

R. B. Dyott, C. R. Day, and M. C. Brain, “Glass-fibre waveguide with a triangular core,” Electron. Lett. 9(13), 288–290 (1973). [CrossRef]

12.

A. R. Tynes, “Partially cladded triangular-cored glass optical fibers and lasers,” J. Opt. Soc. Am. 64(11), 1415–1423 (1974). [CrossRef]

13.

K. Oh, W. Ha, S. Lee, J. Kim, Y. Jeong, and M. Park, “Preforms for preparing polygonal-core optical fiber and preparation method thereof,” Korean patent application 10–2010–0066761 (12 July 2010).

14.

Heraeus website, http://optics.heraeus-quarzglas.com.

15.

S. Choi, K. Oh, W. Shin, and U. C. Ryu, “Low loss mode converter based on adiabatically tapered hollow optical fibre,” Electron. Lett. 37(13), 823–825 (2001). [CrossRef]

16.

W. Ha, S. Lee, Y. Jung, J. K. Kim, and K. Oh, “Acousto-optic control of speckle contrast in multimode fibers with a cylindrical piezoelectric transducer oscillating in the radial direction,” Opt. Express 17(20), 17536–17546 (2009), http://www.opticsinfobase.org/abstract.cfm?uri=oe-17-20-17536. [CrossRef] [PubMed]

17.

L. Yuan, J. Yang, C. Guan, Q. Dai, and F. Tian, “Three-core fiber-based shape-sensing application,” Opt. Lett. 33(6), 578–580 (2008). [CrossRef] [PubMed]

18.

Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express 10(17), 853–864 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-10-17-853. [PubMed]

OCIS Codes
(060.2270) Fiber optics and optical communications : Fiber characterization
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2300) Fiber optics and optical communications : Fiber measurements
(060.2310) Fiber optics and optical communications : Fiber optics
(060.2400) Fiber optics and optical communications : Fiber properties

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: July 9, 2010
Revised Manuscript: September 4, 2010
Manuscript Accepted: September 7, 2010
Published: September 17, 2010

Citation
Woosung Ha, Sejin Lee, Jongki Kim, Yoonseob Jeong, Kyunghwan Oh, Jens Kobelke, Kay Schuster, Sonja Unger, Anka Schwuchow, and Jun Ki Kim, "A micro-structured aperture made of a hollow triangular-core fiber for novel beam shaping," Opt. Express 18, 20918-20925 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-20-20918


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References

  1. F. M. Dickey, “Laser beam shaping,” Opt. Photon. News 14(4), 30–35 (2003). [CrossRef]
  2. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, Greenwood Village, CO, 2005).
  3. M. Gu and X. S. Gan, “Fresnel diffraction by circular and serrated apertures illuminated with an ultrashort pulsed-laser beam,” J. Opt. Soc. Am. A 13(4), 771–778 (1996). [CrossRef]
  4. L. J. Hornbeck, “Digital Light Processing for high-brightness, high-resolution applications,” Proc. SPIE 3013, 27–40 (1997). [CrossRef]
  5. H. Schenk, P. Dürr, T. Haase, D. Kunze, U. Sobe, H. Lakner, and H. Kück, “Large deflection micromechanical scanning mirrors for linear scans and pattern generation,” IEEE J. Sel. Top. Quantum Electron. 6(5), 715–722 (2000). [CrossRef]
  6. M. L. Huebschman, B. Munjuluri, and H. R. Garner, “Dynamic holographic 3-D image projection,” Opt. Express 11(5), 437–445 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-11-5-437 . [CrossRef] [PubMed]
  7. P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006). [CrossRef]
  8. K. Oh, S. Choi, Y. Jung, and J. W. Lee, “Novel hollow optical fibers and their applications in photonic devices for optical communications,” J. Lightwave Technol. 23(2), 524–532 (2005). [CrossRef]
  9. J. K. Kim, J. Kim, Y. Jung, W. Ha, Y. S. Jeong, S. Lee, A. Tünnermann, and K. Oh, “Compact all-fiber Bessel beam generator based on hollow optical fiber combined with a hybrid polymer fiber lens,” Opt. Lett. 34(19), 2973–2975 (2009). [CrossRef] [PubMed]
  10. A. R. Tynes, A. D. Pearson, and D. L. Bisbee, “Loss mechanisms and measurements in clad glass fibers and bulk glass,” J. Opt. Soc. Am. 61(2), 143–153 (1971). [CrossRef]
  11. R. B. Dyott, C. R. Day, and M. C. Brain, “Glass-fibre waveguide with a triangular core,” Electron. Lett. 9(13), 288–290 (1973). [CrossRef]
  12. A. R. Tynes, “Partially cladded triangular-cored glass optical fibers and lasers,” J. Opt. Soc. Am. 64(11), 1415–1423 (1974). [CrossRef]
  13. K. Oh, W. Ha, S. Lee, J. Kim, Y. Jeong, and M. Park, “Preforms for preparing polygonal-core optical fiber and preparation method thereof,” Korean patent application 10–2010–0066761 (12 July 2010).
  14. Heraeus website, http://optics.heraeus-quarzglas.com .
  15. S. Choi, K. Oh, W. Shin, and U. C. Ryu, “Low loss mode converter based on adiabatically tapered hollow optical fibre,” Electron. Lett. 37(13), 823–825 (2001). [CrossRef]
  16. W. Ha, S. Lee, Y. Jung, J. K. Kim, and K. Oh, “Acousto-optic control of speckle contrast in multimode fibers with a cylindrical piezoelectric transducer oscillating in the radial direction,” Opt. Express 17(20), 17536–17546 (2009), http://www.opticsinfobase.org/abstract.cfm?uri=oe-17-20-17536 . [CrossRef] [PubMed]
  17. L. Yuan, J. Yang, C. Guan, Q. Dai, and F. Tian, “Three-core fiber-based shape-sensing application,” Opt. Lett. 33(6), 578–580 (2008). [CrossRef] [PubMed]
  18. Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express 10(17), 853–864 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-10-17-853 . [PubMed]

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