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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 4 — Feb. 15, 2010
  • pp: 3754–3761
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Limits of light guidance in optical nanofibers

Alexander Hartung, Sven Brueckner, and Hartmut Bartelt  »View Author Affiliations


Optics Express, Vol. 18, Issue 4, pp. 3754-3761 (2010)
http://dx.doi.org/10.1364/OE.18.003754


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Abstract

Reducing the waist of an optical fiber taper to diameters below 1 µm can be interpreted as creating an optical nanofiber with propagation properties different from conventional optical fibers. Although there is theoretically no cutoff of the fundamental mode expected, a steep decline in transmission can be observed when the fiber diameter is reduced below a specific threshold diameter. A simple estimation of this threshold diameter applicable to arbitrary taper profiles and based on the diameter variation allowing adiabatic transmission behavior is introduced and experimentally verified. In addition, this threshold behavior is supported by investigating the variation of the power distribution of the nanofiber fundamental mode as a function of the fiber diameter.

© 2010 OSA

1. Introduction

In recent years, optical nanofibers have attracted much interest due to their remarkable properties and the multitude of their possible applications. Optical couplers [1

1. L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef] [PubMed]

], micro ring resonators [2

2. M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, “Optical microfiber loop resonator,” Appl. Phys. Lett. 86(16), 161108 (2005). [CrossRef]

], optical refractive index sensors [3

3. P. Polynkin, A. Polynkin, N. Peyghambarian, and M. Mansuripur, “Evanescent field-based optical fiber sensing device for measuring the refractive index of liquids in microfluidic channels,” Opt. Lett. 30(11), 1273–1275 (2005). [CrossRef] [PubMed]

], and nonlinear devices for super continuum generation [4

4. S. G. Leon-Saval, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, and M. W. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express 12(13), 2864–2869 (2004). [CrossRef] [PubMed]

] have been fabricated successfully, and efficient atom trapping and guiding schemes have been proposed [5

5. V. I. Balykin, K. Hakuta, F. Le Kien, J. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70(1), 011401 (2004). [CrossRef]

].

Despite many different possibilities for producing freestanding nanofibers, their fabrication is still challenging because of their low mechanical stability and high demands concerning their diameter uniformity. The most common way is the preparation of optical nanofibers by means of tapering existing optical fibers down to diameters in the range of 1 µm and below. In such a taper configuration, the submicron diameter waist is well applicable for the investigation of the optical transmission properties of nanofibers. The transition regions on both sides of the waist can serve for efficient input and output coupling of the light and operate as a mechanical support simplifying the handling of the nanofiber. Various mechanisms as, for instance, a traveling gas flame [1

1. L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef] [PubMed]

,4

4. S. G. Leon-Saval, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, and M. W. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express 12(13), 2864–2869 (2004). [CrossRef] [PubMed]

,6

6. T. A. Birks and Y. W. Li, “The Shape of Fiber Tapers,” J. Lightwave Technol. 10(4), 432–438 (1992). [CrossRef]

8

8. G. Brambilla, V. Finazzi, and D. J. Richardson, “Ultra-low-loss optical fiber nanotapers,” Opt. Express 12(10), 2258–2263 (2004). [CrossRef] [PubMed]

], an electric strip heater [9

9. L. Shi, X. Chen, H. Liu, Y. Chen, Z. Ye, W. Liao, and Y. Xia, “Fabrication of submicron-diameter silica fibers using electric strip heater,” Opt. Express 14(12), 5055–5060 (2006). [CrossRef] [PubMed]

], a fiber coupler production system [10

10. K. P. Nayak, P. N. Melentiev, M. Morinaga, F. L. Kien, V. I. Balykin, and K. Hakuta, “Optical nanofiber as an efficient tool for manipulating and probing atomic Fluorescence,” Opt. Express 15(9), 5431–5438 (2007). [CrossRef] [PubMed]

], and an indirect CO2 laser heating method [11

11. M. Sumetsky, Y. Dulashko, and A. Hale, “Fabrication and study of bent and coiled free silica nanowires: Self-coupling microloop optical interferometer,” Opt. Express 12(15), 3521–3531 (2004). [CrossRef] [PubMed]

] have been employed for fabricating nanofibers. Our experimental setup is based on a CO2 laser heating principle as briefly described in section 2.

High transmission of fiber tapers is important for many possible applications. For this purpose we will discuss in section 3 the transmission phenomena during the tapering process when the fiber diameter is reduced to submicrometer dimensions. A threshold diameter with strong increasing losses can be observed in the submicron diameter range. This threshold diameter of a nanofiber for efficient light guiding is the main topic of the further discussions in section 4 and 5. Experiments have already revealed a distinct increase in losses of the taper when its waist diameter is decreased below the investigation wavelength [1

1. L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef] [PubMed]

,8

8. G. Brambilla, V. Finazzi, and D. J. Richardson, “Ultra-low-loss optical fiber nanotapers,” Opt. Express 12(10), 2258–2263 (2004). [CrossRef] [PubMed]

,12

12. M. Sumetsky, Y. Dulashko, P. Domachuk, and B. J. Eggleton, “Thinnest optical waveguide: experimental test,” Opt. Lett. 32(7), 754–756 (2007). [CrossRef] [PubMed]

]. According to [1

1. L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef] [PubMed]

], these losses are due to the scattering of raising evanescent fields by surface contaminants. Sumetsky traced these losses back to input and output losses, which therefore occur mainly in the transition regions with varying diameter [12

12. M. Sumetsky, Y. Dulashko, P. Domachuk, and B. J. Eggleton, “Thinnest optical waveguide: experimental test,” Opt. Lett. 32(7), 754–756 (2007). [CrossRef] [PubMed]

]. A formula for the transmission power has been deduced depending on the Landau-Dykhne formula obtained in quantum mechanics [13

13. M. Sumetsky, “How thin can a microfiber be and still guide light?” Opt. Lett. 31(7), 870–872 (2006). [CrossRef] [PubMed]

], the characteristic length of diameter variation and an assumptive Lorentzian variation of the transverse propagation constant along the nanofiber [14

14. M. Sumetsky, “Optics of tunneling from adiabatic nanotapers,” Opt. Lett. 31(23), 3420–3422 (2006). [CrossRef] [PubMed]

].

Our estimation for the threshold diameter as introduced in section 4 relies on the main coupling and energy transfer between the fundamental mode HE11 of the nanofiber with its diameter-dependent propagation constant β(d) and the external radiation modes with propagation constant β = 2π/λ. It is based on the local diameter variation along the nanofiber. Discrimination between the constant diameter taper waist and the changing diameter taper transitions becomes redundant from this point of view. Only the local taper length scale, which might be significantly different or comparable at fixed points within the taper waist and the taper transitions, decides between lossy and adiabatic guidance of light along the submicron-diameter fiber taper regions. The threshold diameter obtained is verified by experiments in section 5. In addition, the diameter-dependent distribution of power density of the fundamental mode is numerically investigated in section 6 to achieve further clarification concerning the threshold behavior of nanofibers.

2. Experimental setup

We have used an indirect laser heating principle for taper preparation due to its high flexibility in controlling the heating impact on the fiber (Fig. 1
Fig. 1 Sketch of the nanofiber fabrication setup using a bidirectional indirect laser heating method.
). The beam of a CO2 laser (10.6 µm wavelength) with a maximum optical power output of 30 W is split with a 50/50-beam splitter into two identical beams and subsequently focused on two opposite sides of the micro furnace (corundum - multi crystalline Al2O3, outer diameter 1.7 mm, inner diameter 1.1 mm) with the standard optical fiber to be tapered placed in its center. The two-sided heating setup assures that the initial cylindrical symmetry of the fiber is maintained for all possible taper diameters. This is achieved with a relatively low power of 6 W per beam. During the drawing process, the fiber is pulled by two translation stages moving in opposite direction. In addition to this pulling motion, the translation stages adopt an oscillatory movement to scan the hot zone of the microfurnace along a fixed length w of the fiber and to achieve a waist of constant diameter and of equal length w [6

6. T. A. Birks and Y. W. Li, “The Shape of Fiber Tapers,” J. Lightwave Technol. 10(4), 432–438 (1992). [CrossRef]

]. The setup allows preparation of silica tapers down to diameters of about 500 nm. Examples of tapers made with this setup are shown in Fig. 2
Fig. 2 Examples of submicron tapers.
.

3. Investigation of transmission properties during taper drawing

The variation of the transmission intensity during the tapering process is not only helpful for control purposes of the process but also gives an insight into the mode guiding and coupling properties of fiber tapers. The coupling strengths of modes can be influenced by the slope of the transition regions. The coupling effects are expected to be negligible for slowly varying, adiabatic tapers [15

15. J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices Part 1: Adiabaticity criteria,” IEE Proc. 138, 343–354 (1991). [CrossRef]

]. If the changes in slope of the taper transitions are strong, higher order modes of equal symmetry or even leaky modes are accessible due to mode coupling, and the transmission observed will then be reduced.

In Fig. 3
Fig. 3 Typical variation of transmission during the tapering process of a standard single-mode fiber. The initial fiber diameter of 125 µm is reduced by a factor of 2 nearly every 250 s.
characteristic transmission phenomena of the overall taper geometry during the drawing process are shown. During the tapering process the waist was kept at a fixed length of 4 mm and the taper transmission was modified by a gradually decreasing waist diameter and by changing the length of the transition regions. As a light source, a tunable laser was used at a wavelength of 1550 nm with a coherence length considerably longer than the overall taper length, to assure that interference phenomena between excited modes become visible for the complete process.

At the beginning of the process, only the fundamental mode HE11 of the standard single-mode fiber is exited in the fiber core. A high effective index difference between the HE11 and higher order cladding modes prevents mode coupling, and nearly no change in transmission is observed. While the cross section is reduced, the influence of the core material on the guiding properties of the fundamental mode diminishes, and the fundamental mode then is guided by the silica-air interface as the higher order modes. Therefore the effective indices of the fundamental and higher order modes approach each other. Calculations show that the smallest effective index difference and therefore the highest mode coupling tendency can be found in the diameter region around 60 µm. If the transition slope is too steep, energy is transferred from the HE11 to the HE12, the nearest mode of the same azimuthal symmetry, and decreased transmission is observed. Higher order modes of different azimuthal symmetry are not expected, due to the cylindrical symmetry maintained by the two-sided heating setup.

Continued reduction and elongation leads to a beating phenomenon with constant amplitude and increasing frequency between the two lowest excited modes [16

16. F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, and J. Bures, “Investigation of power oscillations along tapered monomode fibers,” Appl. Opt. 26(3), 444–449 (1987). [CrossRef] [PubMed]

]. The beating is visible down to the cut-off diameter of the HE12 mode occurring at a value of V = 3.832, corresponding to a fiber diameter of 1815 nm. For observing the HE12 cutoff it is important to use a narrow-band light source fulfilling the coherency requirements. Otherwise the oscillation amplitude will decay gradually with elongation of the taper, and reach zero at a specific elongation length.

4. Estimation of the local taper length scale for adiabatic optical nanofibers

The following estimation of the threshold diameter for highly transmitting nanofibers is based on the length scale criterion for adiabatic fiber tapers first introduced by Love et al [15

15. J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices Part 1: Adiabaticity criteria,” IEE Proc. 138, 343–354 (1991). [CrossRef]

]. Jung et al successfully applied this criterion for the explanation of efficient inline fiber mode filters based on taper transitions that are only adiabatic for the fundamental mode and non-adiabatic for higher order modes [17

17. Y. Jung, G. Brambilla, and D. J. Richardson, “Broadband single-mode operation of standard optical fibers by using a sub-wavelength optical wire filter,” Opt. Express 16(19), 14661–14667 (2008). [CrossRef] [PubMed]

]. It is derived from the fact that the local taper length scale has to be much larger than the coupling length between the fundamental mode and the ruling coupling mode for negligible power transfer. The local taper length scale l is defined as the height of a circular cone with the base matching the local fiber cross-section and the apex angle matching the local taper angle (Fig. 4
Fig. 4 Sketch for the definition of the local taper length scale l based on the local taper angle Ω and the local taper radius r.
). This yields a local taper angle of Ω = arctan(dr/dz), resulting in Ω = r/l for small angles Ω << 1. In our case of a single-mode optical nanofiber that only exhibits the fundamental mode with propagation constant β 1(d), the dominating coupling mode is the radiation mode with a propagation constant of β 2 = 2π/λ, assuming the refractive index of air being equal to 1. The beat length b equals 2π/(β 1-β 2). If l >> b everywhere along the taper, coupling and loss are negligible, and the fundamental mode can propagate adiabatically. On the other hand, if b >> l, coupling to radiation modes becomes possible, and significant losses will occur. Therefore l = b offers an approximate delineation between lossy and adiabatic diameter variations. This results in the condition of Ω = r(β 1-β 2)/2π for a delineation concerning the local taper angle or l = 2π/(β 1-β 2) concerning the local taper length scale as shown in Fig. 5
Fig. 5 Delineation curve between lossy and adiabatic local taper length scale l depending on the nanofiber diameter d. The diameter d is normalized to the wavelength.
.

Although the modeling has been done for a refractive index of n = 1.444 and a wavelength of λ = 1550 nm, the obtained delineation curve is valid for different fiber diameter and wavelength combinations as long as the ratio d/λ does not change. This is due to only small changes Δn/n = 0.02 of the refractive index of pure silica in a wide wavelength range between 400 nm and 1700 nm.

Due to the large difference in propagation constants, a relatively small taper length scale down to 10 µm should be sufficient for fiber diameters above 0.6λ to assure approximately adiabatic behavior. The conditions change strongly for smaller diameters. The requirement for adiabatic behavior grows more than exponentially and leads to d = 0.29λ for a local taper length scale of 1mm and only d = 0.16λ for a giant local taper length scale of 1 km. Increasing the local taper length scale over 6 orders of magnitude results in a change of the threshold diameter of only about a factor of 2.

For a typical taper with a monotonic change in diameter and local taper length scale, the smallest diameter will define the necessary demands concerning uniformity and strongest coupling to radiation modes, and therefore also the overall performance of the taper. The actual loss of a specific nanofiber is not given by the model, since such a value would depend on the specific profile of the taper region.

The results found by [13

13. M. Sumetsky, “How thin can a microfiber be and still guide light?” Opt. Lett. 31(7), 870–872 (2006). [CrossRef] [PubMed]

] support this behavior but exact comparisons are difficult due to different intentions. While we estimate the transmission threshold diameter for a wide range of possible local and global diameter variations, reference [13

13. M. Sumetsky, “How thin can a microfiber be and still guide light?” Opt. Lett. 31(7), 870–872 (2006). [CrossRef] [PubMed]

] deduced a formula for the propagation losses caused by a specific variation of the transverse propagation constant. From these results, changing the characteristic length from 10 mm to 10 km leads to a change of the threshold diameter roughly by a factor of 2.

5. Experimental verification

For experimental verification we prepared submicron taper structures and measured their diameter-dependent transmission characteristic in the critical range between adiabatic and non-adiabatic behavior.

Keeping the heated length w fixed in our taper drawing setup during the whole elongation process results in an exponential taper profile of r(z) = r 0 exp(-z/w) along the symmetry axis z of the fiber [6

6. T. A. Birks and Y. W. Li, “The Shape of Fiber Tapers,” J. Lightwave Technol. 10(4), 432–438 (1992). [CrossRef]

]. Based on this known profile, the local taper angle is then tan(Ω) = dr(z)/dz = -r 0/w exp(-z/w) = -r(z)/w.

This equation corresponds to the definition of the local taper length scale l. Drawing the fiber taper at constant waist length w results in a taper profile with constant local taper length scale l = w.

Figure 6
Fig. 6 Variation of transmission for two identical fiber tapers with a waist length of 6 mm.
shows the variation of transmission during tapering for two equivalent tapering processes. The local fiber diameter of the 0.5 transmission level is taken as threshold diameter dt between adiabatic and lossy propagation. For the nanofibers drawn with a waist length of l = 6 mm, the threshold diameter lies at dt = 0.38 µm (dt/λ = 0.25), which agrees well with the diameter predicted by the length scale criterion.

6. Power density distribution of optical nanofibers

Further numerical simulations concerning the shape of the fundamental mode for small fiber diameters have been performed to further understand the obtained threshold behavior of optical nanofibers. All calculations have been done with a full vectorial finite element method at a wavelength of λ = 1.55 µm, a refractive index of n nanofiber = 1.444 and n air = 1. In Fig. 7
Fig. 7 Axial component of the Poynting vector of nanofibers for different fiber diameters of a) 0.75λ, b) 0.3λ, and c) 0.2λ, respectively. The displayed area size is 2λ x 2λ. Only one of two polarization modes is shown. Red signifies high power density and blue low power density.
, the power flow density along the fiber axis is simulated for different nanofiber diameters. For a relatively big nanofiber diameter of d = 0.75λ, the single polarization mode has the expected Gaussian-like shape. However, for fiber diameters near the experimentally observed transmission threshold, the linearly polarized character and the evanescent fields becomes dominant, and the common assumption of a Gaussian-like distribution is no longer valid [18

18. L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12(6), 1025–1035 (2004). [CrossRef] [PubMed]

].

Furthermore, the fraction of power propagating outside the fiber area changes dramatically within a narrow diameter variation from only 0.18 at d = 0.75λ to 0.97 at d = 0.3λ, indicating a threshold behavior [19

19. M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express 12(13), 2880–2887 (2004). [CrossRef] [PubMed]

]. It can be expected that coupling to outside propagating radiation modes will be less critical for mode distributions concentrated within the fiber than for modes mainly concentrated outside the fiber. Therefore, small deviations from the perfect cylindrical symmetry are sufficient for diameter values around d = 0.2λ to couple light out.

In Fig. 8
Fig. 8 Variation of power density as a function of the fiber diameter to wavelength ratio in the center and at the surface of the fiber. Due to an asymmetric power distribution of the polarized fundamental mode, the direction of polarization has to be considered. The overall guided power is normalized to 1 W.
the variation of the power density as a function of the fiber diameter is shown for three selected points of the fiber cross-section. A maximum value for the center of the fiber can be found at a fiber diameter of d = 0.60λ. Down to this diameter an increasing concentration of the guided light within the fiber area is possible. For smaller fiber diameters this center power density declines rapidly over several orders of magnitude, again indicating threshold behavior below this fiber diameter. At the experimentally achievable diameter of d = 0.25λ, the core power density declined over 2 orders of magnitude compared to the maximum value at d = 0.6λ. The highest power density at the fiber-air interface is reached at a diameter of d = 0.44λ [7

7. J. Bures and R. Ghosh, “Power density of the evanescent field in the vicinity of a tapered fiber,” J. Opt. Soc. Am. A 16(8), 1992–1996 (1999). [CrossRef]

].

Both maximum power density values lie at experimentally achievable local taper length scales. Especially the diameter value for the highest power density at the surface could be interesting for sensor applications. At this diameter, already 68 percent of the guided power is propagating outside the fiber, which offers the possibility of high sensitivity in interaction with external analytes. Furthermore, the guided light is still confined to a region close to the fiber. A decline to a value of 1/e takes place within a distance of only 0.14λ apart from the fiber surface as expected for evanescent waves, promising strongly localized sensing effects. The power density increases due to the reduced cross section of the nanofiber in comparison to an untapered fiber by up to a factor of 75 for the center of the fiber core, and in the same order of magnitude for the core-cladding interface.

7. Summary

A length scale criterion for the delineation between adiabatic and lossy optical nanofibers applicable to arbitrary taper profiles has been derived. For experimentally realizable local taper length scales of about 10mm, the smallest adiabatic diameter turns out to be in the range of about d = 0.24λ (d = 370 nm for λ = 1550 nm or d = 96 nm for λ = 400 nm). This threshold value is consistent with a mode distribution where a power fraction of more than 97 percent is propagating outside the solid taper material.

The observed threshold diameter for effective light guidance of nanofibers is caused by geometric variations or nonuniformities. Since the difference in the propagation constant of the fundamental mode and the radiation threshold vanishes for arbitrary small fiber diameters, the demands on the geometric uniformity grow extremely, restricting the experimentally usable diameters.

For fiber sensing applications that require a high power density at the fiber-air interface, the threshold range of the diameter is attractive due to possible strong interaction with outside media.

Acknowledgement

Funding by the Thuringian Ministry of Education, Science and Culture is gratefully acknowledged.

References and Links

1.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef] [PubMed]

2.

M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, “Optical microfiber loop resonator,” Appl. Phys. Lett. 86(16), 161108 (2005). [CrossRef]

3.

P. Polynkin, A. Polynkin, N. Peyghambarian, and M. Mansuripur, “Evanescent field-based optical fiber sensing device for measuring the refractive index of liquids in microfluidic channels,” Opt. Lett. 30(11), 1273–1275 (2005). [CrossRef] [PubMed]

4.

S. G. Leon-Saval, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, and M. W. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express 12(13), 2864–2869 (2004). [CrossRef] [PubMed]

5.

V. I. Balykin, K. Hakuta, F. Le Kien, J. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70(1), 011401 (2004). [CrossRef]

6.

T. A. Birks and Y. W. Li, “The Shape of Fiber Tapers,” J. Lightwave Technol. 10(4), 432–438 (1992). [CrossRef]

7.

J. Bures and R. Ghosh, “Power density of the evanescent field in the vicinity of a tapered fiber,” J. Opt. Soc. Am. A 16(8), 1992–1996 (1999). [CrossRef]

8.

G. Brambilla, V. Finazzi, and D. J. Richardson, “Ultra-low-loss optical fiber nanotapers,” Opt. Express 12(10), 2258–2263 (2004). [CrossRef] [PubMed]

9.

L. Shi, X. Chen, H. Liu, Y. Chen, Z. Ye, W. Liao, and Y. Xia, “Fabrication of submicron-diameter silica fibers using electric strip heater,” Opt. Express 14(12), 5055–5060 (2006). [CrossRef] [PubMed]

10.

K. P. Nayak, P. N. Melentiev, M. Morinaga, F. L. Kien, V. I. Balykin, and K. Hakuta, “Optical nanofiber as an efficient tool for manipulating and probing atomic Fluorescence,” Opt. Express 15(9), 5431–5438 (2007). [CrossRef] [PubMed]

11.

M. Sumetsky, Y. Dulashko, and A. Hale, “Fabrication and study of bent and coiled free silica nanowires: Self-coupling microloop optical interferometer,” Opt. Express 12(15), 3521–3531 (2004). [CrossRef] [PubMed]

12.

M. Sumetsky, Y. Dulashko, P. Domachuk, and B. J. Eggleton, “Thinnest optical waveguide: experimental test,” Opt. Lett. 32(7), 754–756 (2007). [CrossRef] [PubMed]

13.

M. Sumetsky, “How thin can a microfiber be and still guide light?” Opt. Lett. 31(7), 870–872 (2006). [CrossRef] [PubMed]

14.

M. Sumetsky, “Optics of tunneling from adiabatic nanotapers,” Opt. Lett. 31(23), 3420–3422 (2006). [CrossRef] [PubMed]

15.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices Part 1: Adiabaticity criteria,” IEE Proc. 138, 343–354 (1991). [CrossRef]

16.

F. Gonthier, J. Lapierre, C. Veilleux, S. Lacroix, and J. Bures, “Investigation of power oscillations along tapered monomode fibers,” Appl. Opt. 26(3), 444–449 (1987). [CrossRef] [PubMed]

17.

Y. Jung, G. Brambilla, and D. J. Richardson, “Broadband single-mode operation of standard optical fibers by using a sub-wavelength optical wire filter,” Opt. Express 16(19), 14661–14667 (2008). [CrossRef] [PubMed]

18.

L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12(6), 1025–1035 (2004). [CrossRef] [PubMed]

19.

M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express 12(13), 2880–2887 (2004). [CrossRef] [PubMed]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(060.2400) Fiber optics and optical communications : Fiber properties
(230.7370) Optical devices : Waveguides
(220.4241) Optical design and fabrication : Nanostructure fabrication

ToC Category:
Photonic Crystals

History
Original Manuscript: January 6, 2010
Revised Manuscript: January 26, 2010
Manuscript Accepted: January 29, 2010
Published: February 9, 2010

Citation
Alexander Hartung, Sven Brueckner, and Hartmut Bartelt, "Limits of light guidance in optical nanofibers," Opt. Express 18, 3754-3761 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-4-3754


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References

  1. L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef] [PubMed]
  2. M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, “Optical microfiber loop resonator,” Appl. Phys. Lett. 86(16), 161108 (2005). [CrossRef]
  3. P. Polynkin, A. Polynkin, N. Peyghambarian, and M. Mansuripur, “Evanescent field-based optical fiber sensing device for measuring the refractive index of liquids in microfluidic channels,” Opt. Lett. 30(11), 1273–1275 (2005). [CrossRef] [PubMed]
  4. S. G. Leon-Saval, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, and M. W. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express 12(13), 2864–2869 (2004). [CrossRef] [PubMed]
  5. V. I. Balykin, K. Hakuta, F. Le Kien, J. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70(1), 011401 (2004). [CrossRef]
  6. T. A. Birks and Y. W. Li, “The Shape of Fiber Tapers,” J. Lightwave Technol. 10(4), 432–438 (1992). [CrossRef]
  7. J. Bures and R. Ghosh, “Power density of the evanescent field in the vicinity of a tapered fiber,” J. Opt. Soc. Am. A 16(8), 1992–1996 (1999). [CrossRef]
  8. G. Brambilla, V. Finazzi, and D. J. Richardson, “Ultra-low-loss optical fiber nanotapers,” Opt. Express 12(10), 2258–2263 (2004). [CrossRef] [PubMed]
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