Hole inflation and tapering of stock photonic crystal fibres

doi:10.1364/OPEX.13.006541

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Hole inflation and tapering of stock photonic crystal fibres

W. Wadsworth, A. Witkowska, S. Leon-Saval, and T. Birks »View Author Affiliations

Optics Express, Vol. 13, Issue 17, pp. 6541-6549 (2005)
http://dx.doi.org/10.1364/OPEX.13.006541

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Abstract

We report controlled hole expansion in photonic crystal fibres (PCFs) by heating the fibre while the holes were pressurised. This was done by post-processing an existing fibre, not during fibre fabrication. Small holes in an endlessly single-mode (ESM) PCF were inflated to become large holes. The large-hole PCF was then tapered to produce a “cobweb” PCF with a small highly-nonlinear core, interfaced to the ESM PCF at both ends by gradual transitions. The loss was less than 0.4 dB in the complete structure, which was used to demonstrate supercontinuum generation when pumped with a fs Ti:sapphire laser.

1. Introduction

Optical fibre tapering is a powerful post-processing technique [1

T. A. Birks and Y. W. Li, “The shape of fiber tapers,” IEEE J. Lightwave Technol. 10, 432–438 (1992). [CrossRef]

T. A. Birks, G. Kakarantzas, and P. St.J. Russell, “All-fibre devices based on tapered fibres,” presented at Opt. Fiber Commun. Conf. paper ThK2 (2004).

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). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-13-2864. [CrossRef] [PubMed]

C. M. B. Cordeiro, W. J. Wadsworth, T. A. Birks, and P. St.J. Russell, “Octave supercontinuum generated in tapered conventional fibres by a nanosecond 1064 nm laser,” presented at Conf. Lasers Electro-Opt. (2004), paper CThC2.

] which allows stock optical fibre to be transformed into devices such as couplers, spectral filters and nonlinear optical elements. In tapered conventional fibres there is one design parameter – the overall final diameter profile of the fibre along its length – since the structure within the fibre simply scales with the outer diameter. In contrast, photonic crystal fibres (PCFs)[5

J.C. Knight, T.A. Birks, P.St.J. Russell, and D.M. Atkin, “All-silica single-mode fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996); Errata, Opt. Lett. 22, 484–485 (1997). [CrossRef] [PubMed]

] have small air holes running along the length of the fibre. These can deform when the fibre is heated, giving an extra degree of freedom to the tapering process: the air filling fraction can change as well as the fibre’s outer diameter. We have previously used localised and controlled partial collapse of air holes in PCF to produce devices such as structural long-period gratings[6

G. Kakarantzas, T.A. Birks, and P.St.J. Russell, “Structural long-period gratings in photonic crystal fibers,” Opt. Lett. 27 (12), 1013–1015 (2002). [CrossRef]

]. In these experiments we simply allowed the holes to shrink under surface tension. We have also minimised hole shrinkage to preserve the hole structure, even in very small-pitch PCFs[2

] by reducing the heating time and temperature (‘fast and cold’ tapering). However, in these and other reports of PCF tapering [6

G. Kakarantzas, T.A. Birks, and P.St.J. Russell, “Structural long-period gratings in photonic crystal fibers,” Opt. Lett. 27 (12), 1013–1015 (2002). [CrossRef]

H.C. Nguyen, B.T. Kuhlmey, M.J. Steel, C.L. Smith, E.C. Magi, R.C. McPhedran, and B.J. Eggleton, “Leakage of the fundamental mode in photonic crystal fiber tapers,” Opt. Lett. 30 (10), 1123–1125 (2005). [CrossRef] [PubMed]

] both the core size and the air filling fraction were reduced from their initial values (or kept fixed) by the tapering process.

A much greater range of devices would be possible if the air filling fraction of a PCF (or indeed the absolute hole size) could be increased during tapering, but little attempt has been made to do this. By pressurising the holes during tapering, a modest expansion was achieved to form a mode converter [8

T.A. Birks, G. Kakarantzas, P.St.J. Russell, and D.F. Murphy, “Photonic crystal fibre devices,” Proc SPIE , 4943, 142–151 (2002). [CrossRef]

], in which the ratio d/Λ of hole diameter to pitch increased from 0.45 to 0.66 while the pitch was reduced from 8 to 1.7 μm. Reference has also been made to the blocking off of holes to maintain sufficient pressure and so resist hole collapse under surface tension [9

E. C. Magi, P. Steinvurzel, and B. J. Eggleton “Tapered photonic crystal fibers” Opt. Express 12, 776–784 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-776. [CrossRef] [PubMed]

]. However, in both cases the character of the holey structure was unchanged, with near-circular holes and a relatively low air filling fraction.

In this paper we describe controlled and essentially unlimited hole inflation in PCF from d/Λ =0.4 to very large holes with air filling fraction > 90 %. The inflated fibres were then tapered fast and cold to preserve the new structure whilst reducing the core diameter to 1-2 μm. This allowed us to interface widely different types of PCF. Supercontinuum generation in a “cobweb” PCF with a small core and a very high air filling fraction, interfaced to an endlessly single-mode (ESM) PCF with a large core and a relatively low air filling fraction, was demonstrated as an example application of this type of device.

2. Surface tension and hole collapse/expansion

For a cylindrical hole in a liquid the excess hydrostatic pressure P _st required to resist collapse is related to the surface tension γ of the liquid by[10

D. Tabor “Gases, Liquids and Solids,” Penguin Books, Harmondsworth UK, (1969).

]

P_{st} = 2 \frac{γ}{d},

(1)

where d is the hole diameter. For a given d and internal gas pressure P, the hole will either expand or shrink depending on whether P is greater or less than P _st. Although the viscosity of silica glass does change rapidly with temperature close to the softening point of 1700 °C, the surface tension varies little with temperature[11

W.D. Kingery “Surface tension of some liquid oxides and their temperature coefficients,” J. Am. Ceramic Soc. 42 (1), 6–10 (1959). [CrossRef]

]. Whether a hole in fused silica shrinks or expands therefore depends only on the diameter and the internal pressure: the temperature of the glass and the magnitude of the pressure difference P - P _st only determine the rate of hole expansion or collapse.

Given the commonly-quoted value of γ= 0.3 J/m² for silica[11

W.D. Kingery “Surface tension of some liquid oxides and their temperature coefficients,” J. Am. Ceramic Soc. 42 (1), 6–10 (1959). [CrossRef]

], eq. (1) is conveniently expressed in terms of pressure in bar and hole diameter in μm:

P_{st} (bar) = \frac{6}{d} (μm),

(2)

so an excess pressure of 6 bar is needed to keep a 1-μm hole in (unstable) equilibrium.

3. Loss and Adiabaticity in transitions

For the structural transitions to have low optical loss, the guided mode must transform adiabatically through the transition. In practice this means that any changes in mode size or shape in the structural transition must be over a length scale long compared to the diffraction of the guided mode [12

J.D. Love, “Spot size, adiabaticity and diffraction in tapered fibres,” Electron. Lett. 23, 993–994 (1987). [CrossRef]

]. In this paper we consider both transitions in hole size and in core diameter, starting with ESM PCFs (d/Λ≤0.4[13

T.A. Birks, J.C. Knight, and P.St.J. Russell, “Endlessly single-mode photonic crystal fibre,” Opt. Lett. 22, 961–963 (1997). [CrossRef] [PubMed]

,14

T. A. Birks, D. Mogilevtsev, J. C. Knight, P. St.J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allen, and J. C. Fajardo “The analogy between photonic crystal fibres and step index fibres” Proc. Opt. Fiber Commun. Conf. (OFC ´99, San Diego, California) paper FG4 (1999).

]) with core diameters of 5 or 12 μm, i.e. large compared to the wavelength. For such fibres the mode is well confined to the core at visible and near-infrared wavelengths.

If the hole diameter is increased by inflating the fibre without stretching it, the fundamental mode will still fill the core so the mode field diameter (MFD) will not change much. For example the MFD is plotted against d/Λ for a PCF with a fixed solid core diameter of 5 μm in Fig. 1. We define the core diameter as the distance between the inner edges of the inner ring of air holes

d_{core} = 2 Λ - d = Λ (2 - \frac{d}{Λ}) .

(3)

Field profiles are calculated using a full-vector plane-wave model for round holes and the MFD is calculated under the approximation that the mode field is scalar using

{MFD}^{2} = 4 \times \frac{\int_{0}^{\infty} r^{2} I d A}{\int_{0}^{\infty} I d A},

(4)

where I(r,θ) is the mode intensity[15

W. A. Gambling and H. Matsumura “Simple characterisation factor for practical single-mode fibres” Electron. Lett. 13, 691–693 (1977). [CrossRef]

]. The small change in MFD shown in Fig. 1 with hole diameter suggests that adiabaticity will be easy to fulfil for this type of hole expansion.

Fig. 1. Calculated MFD at a wavelength of 1 μm for PCFs with a 5 μm diameter solid core and varying d/Λ.

Once the holes were inflated we then tapered the fibre by stretching it in a second process to form an interfaced highly-nonlinear PCF. This reduces the core diameter to 1-2 μm. Since this is just the standard tapering process that we have previously applied to PCF[2

], we already know it should be adiabatic.

4. Experimental technique

As outlined in section 2, two conditions must be met for hole expansion in PCF. Firstly the internal pressure must exceed that set by eq. (2), and secondly the fibre must be heated long enough and hot enough to allow the expansion to take place.

We used a gas cell with a fibre chuck and optical window to pressurise the fibre with dry nitrogen at up to 10 bar pressure whilst still allowing optical access for monitoring of the fibre transmission during processing. To process a length of fibre in a controlled manner our standard flame-brush tapering rig was used[1

T. A. Birks and Y. W. Li, “The shape of fiber tapers,” IEEE J. Lightwave Technol. 10, 432–438 (1992). [CrossRef]

]. The fibre was stretched slightly to keep it taut while heated, to an extent that would reduce the transverse scale of the fibre by 8% if d/Λ was unchanged. Transitions from unprocessed fibre to inflated fibre were made by heating a shorter length of fibre with each successive sweep of the burner.

The tapering parameters required for hole inflation are actually the opposite of those needed to taper with little hole collapse. To prevent hole collapse under surface tension without pressure we taper ‘fast and cold’, with a cold flame to minimise the rate of hole collapse, and stretching as quickly as possible to minimise the processing time. In contrast, for hole inflation we must process ‘slow and hot’, using a hot flame for rapid hole inflation and stretching slowly to increase the processing time. We formed a 70 mm inflated section with 30 mm transitions with a 2.8 mm flame and a processing time of ~280 s. The flame made 13 sweeps so one transition had 6 steps, the other 7 steps. The total effective heating time for each portion of fibre was estimated to be 9 sec. With constant flame conditions and tapering and burner speeds, we controlled the inflation of the holes by using different nitrogen pressures.

Fig. 2. Fibre inflation and tapering process to produce a 2-μm-core PCF with large air holes, connected at both ends to 5-μm-core PCF pigtails with small air holes. The example SEMs on the right are to the same scale.

After making sections of fibre with inflated air holes, the fibres could be placed back in the tapering rig and tapered in a conventional ‘fast and cold’ process to reduce the fibre core diameter as required. The entire process is shown schematically in Fig. 2.

5. Fabrication and analysis

Figure 3 shows scanning electron micrographs (SEMs) of a 5-μm-core ESM PCF inflated at pressures from 6 to 10 bar under otherwise identical conditions. The initial fibre had Λ= 3.2 μm, d/Λ = 0.43 and outer diameter OD = 125 μm, making it splice-compatible to conventional step-index fibre designed for 1060 nm light (e.g. Corning 1060). The hole diameter was 3.2 × 0.43= 1.4 μm, so from eq. (2) a pressure of 4.3 bar was required to counter surface tension. The more highly-inflated fibres have the “cobweb” structures of some highly-nonlinear PCFs [16

W.J. Wadsworth, A. Ortigosa-Blanch, J.C. Knight, T.A. Birks, T-P.M. Man, and P.St.J. Russell, “Supercontinuum generation in photonic crystal fibres and optical fibre tapers: A novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002). [CrossRef]

], with a core suspended from thin webs and almost entirely surrounded by air, although the core diameter was of course much greater at this stage.

Parameters measured from the SEMs are given in table 1. For highly inflated fibres (8 and 10 bar) the hole size d in d/Λ is the distance across the flats of the rounded hexagonal holes. The initial core diameter (the solid region between the inside edges of the central ring of holes) was 5.0 μm. During the processing the fibre was stretched slightly (as mentioned above), which in the absence of hole collapse or expansion would have proportionately changed the fibre’s dimensions to those given under the heading “scaled fibre”, the final core diameter being reduced by 8 % to 4.6 μm. The core diameters for all three inflated fibres were slightly smaller than this, indicating that there was some flow of glass from the core into the webs holding the core.

Fig. 3. SEMs of (a) the original 5-μ m-core ESM PCF and (b)-(d) the same PCF inflated at pressures of 6, 8 and 10 bar respectively. All images in each row are at the same scale.

The increased air filling fraction in the inflated-hole fibres also increased their outside diameter. The scaled fibre should have an OD of 115 μm and contain 120 holes of 1.4 × 0.92= 1.29 μm diameter. The total area of glass in the fibre cross-section can thus be calculated, and this will be the same for all the inflated fibres. A greater proportion of air in an inflated fibre will then necessarily increase the fibre OD in a predictable way. Monitoring fibre OD is standard in fibre drawing towers, and if implemented on an inflation rig would give a clear online indication of the hole size attained.

Table 1. Dimensions of the inflated PCFs shown in Fig. 3. The scaled fibre values are obtained by multiplying the initial fibre values by the same factor of 0.92, to represent the effect of the slight tapering if the holes did not deform.

	Initial Fibre	Scaled Fibre	6 bar	8 bar	10 bar
OD	125	115	121	144	163
d _core	5.0	4.6	4.0	4.0	3.7
d	1.4	1.29	2.9	8.0	10.5
Λ	3.2	2.9	3.8	8.3	10.8
d/Λ	0.43	0.43	0.74	0.96	0.98
Air filling fraction	0.16	0.16	0.50	0.91	0.95
Loss (dB)	--	--	0.08	0.10	0.05

Optical losses from 0.05 to 0.3 dB for 1550 nm light were measured during the inflation process. Losses at shorter wavelengths are expected to be even lower as the guided mode will be more strongly confined to the core and will therefore be less effected by changes in hole size.

Fig. 4. SEMs of the 12-μm-core PCF. The inflated fibre has 210 μm OD.

A 12-μm-core ESM PCF was also processed in the same way. This fibre had Λ = 8 μm, d/Λ =0.46 and OD= 125 μm. The mode field diameter matches standard SMF-28 at 1550 nm, allowing low-loss splices to conventional fibre systems. SEMs of this fibre before and after inflation are shown in Fig. 4. The maximum OD obtained in our experiments exceeded 400 μm, more than 3 times that of the un-inflated fibre.

Once a large-hole PCF has been made in this way, we then conventionally tapered the inflated section in a standard ‘fast and cold’ process to yield 100 mm long waists with core diameters of 1.1, 1.6 and 1.9 μm. The fibres were pressurised at 10 bar during this process so there is some further hole inflation, although the fibre is not processed hot enough or slowly enough to allow the holes to deform greatly. SEMs of these fibres are shown in Fig. 5 and 2. Images of the initial and inflated fibres are essentially the same as Fig. 3(a) and (d). The scale reduction during tapering is shown by the bottom row of Fig. 5 which shows the tapered fibre at the same scale as the initial and inflated fibres Fig. 5. Parameters of the inflated and tapered fibres are given in table 2. Note that for tapered fibre (c) the fibre has been elongated by a factor of 3.7, so the area of glass in the fibre cross-section is also reduced by a factor of 3.7. However the final fibre diameter is almost the same as the initial diameter. The absolute hole diameters d in the tapered sections are all larger than in the initial fibre (holes in tapered fibre (a) would be as small as 0.37 μm without inflation or collapse).

Fig. 5. SEM images of the inflated and tapered fibres. Top: initial PCF; Middle: inflated PCF; Bottom: tapered inflated PCF. All pictures to the same scale. Left to right; Final taper core diameters 1.1, 1.6 and 1.9 μm respectively.

Table 2. Parameters for the inflated and tapered fibres shown in Fig. 5

Fig. 5		Total Elongation	OD (μm)	d _core	d (μm)	Λ (μm)	d/Λ (μm)	Loss (dB)
	Initial fibre	--	125	5.0	1.4	3.2	0.43
	Inflated fiber	1.18 (125-115 μm)	165	3.5	10.4	10.8	>0.95	0.27
(a)									--
	taper	14.3 (125-33 μm)	65	1.1	4.9	5.1	>0.95	--
	Inflated fiber	1.18 (125-115 μm)	132	3.6	6.3	6.6	>0.92	0.075
(b)									0.38
	taper	5.2 (125-55 μm)	69	1.6	3.7	3.9	>0.92	0.30
	Inflated fiber	1.18 (125-115 μm)	192	3.2	12.6	12.7	>0.95	0.28
(c)									0.34
	taper	3.7 (125-65 μm)	119	1.9	8.5	8.6	>0.95	0.06

The measured optical losses at 1550 nm for this second tapering stage ranged from 0.05 to 0.3 dB. The insertion loss of the entire structure (from initial ESM PCF to inflated PCF to small-core PCF, and back) was less than 0.4 dB for the 1.9 and 1.6 μm core samples, but was high for 1.1 μm core samples. For a 1.1 μm core diameter, the core is smaller than the measurement wavelength, so guidance may be expected to be weak. We note that the loss from mode mismatch if the untreated fibre was simply butted or spliced to 2 μm core high air filling fraction PCF would be at least 5 dB per junction.

6. Nonlinear application

The structures described in section 5 have final waist sections similar to PCFs and fibre tapers used for supercontinuum generation[17

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000). [CrossRef]

,18

T. A. Birks, W. J. Wadsworth, and P. St.J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 1415–1417 (2000). [CrossRef]

,19

S. Coen, A. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St.J. Russell, “White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber,” Opt. Lett. 26, 1356–1358 (2001). [CrossRef]

,20

J.K. Chandalia, B.J. Eggleton, R.S. Windeler, S.G. Kosinski, X. Liu, and C. Xu “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photonics Technol. Lett. 13 (1), 52–54, (2001) [CrossRef]

,16

], but with some advantages over both. The waist is a PCF (as in [17

,19

,20

,16

]), so the dispersion can be tuned by using different air hole sizes as well as by altering the core diameter. However, uniform PCFs [17

,19

,16

] require that the input light is coupled into a very small core. This is alleviated in conventional fibre tapers [18

T. A. Birks, W. J. Wadsworth, and P. St.J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 1415–1417 (2000). [CrossRef]

] because the input and output are conventional single-mode fibre pigtails. However, in conventional fibre tapers the guided mode is exposed on the outer surface and so is sensitive to environmental contamination, eg by dust.

In contrast, in our device the input and output pigtails are single-mode fibres with a relatively large core diameter, but the waist is a PCF so the guided mode is enclosed and protected. A similar effect was achieved in a pioneering experiment by Chandalia et al. [20

] where an otherwise conventional step-index fibre had large holes in the cladding, which were used to confine the light when the fibre was tapered. Our device has the additional advantage that the PCF pigtails are close to being endlessly single mode, so they guide the whole continuum output in a robust single mode, whereas a conventional step-index core is unlikely to be single-mode and low loss over an octave or more in frequency. Our device is also fabricated from stock ESM PCF and does not require any special preform or fibre.

Fig. 6. Supercontinuum spectra for inflated fibres. Orange and red curves, tapered core diameter of 1.6 μm and coupled power of 123 and 92 mW respectively; blue and green curves, tapered core diameter of 1.9 μm and coupled power of 130 and 103 mW respectively

Figure 6 shows the continuum spectra produced by devices with a 1.6 and 1.9 μm core diameters in the waist when pumped with a fs Ti:sapphire laser (790 nm, pulse duration ~200 fs, repetition rate 75 MHz) with ~100 mW average power coupled into the fibre. The input pigtail was cut to 6 cm length to avoid pulse broadening by the chromatic dispersion of the fibre before the tapered section. The output supercontinuum is naturally in the fundamental fibre mode, as the second mode (if excited) is only weakly guided and is easily stripped with a small bend. Although the inflated and tapered sections are strictly multimoded, we do not expect to excite any high-order modes as the nonlinear process occur in the fundamental mode of the multimode waist. The output continuum is then expected to reach the single mode output pigtail in the fundamental mode and therefore will be output without loss. This is borne out in our nonlinear experiments, where the output power achieved is consistent with the small measured linear propagation loss in the structures, given in Table 2. The spectral extent of the continuum is as expected from previous experiments with similar active structures[17

,18

T. A. Birks, W. J. Wadsworth, and P. St.J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 1415–1417 (2000). [CrossRef]

,16

7. Conclusion

For the first time, we have demonstrated the thermal post-processing of a stock single-mode PCF to form a transition to a cobweb-type PCF structure with a smaller core but larger air filling fraction. In the first stage of the process, the fibre is processed ‘slow and hot’ while the holes are pressurised at several bar to inflate the holes without reducing the cross-sectional area of glass by much. In the second stage, the inflated section is tapered conventionally ‘fast and cold’ to reduce the core size without significantly changing the structure, The insertion loss of complete structures is less than 0.4 dB, and we have demonstrated how they simplify input and output coupling in a supercontinuum generation experiment.

Acknowledgments

WJW is a Royal Society University Research Fellow. AW is on leave from National Institute of Telecommunications, Warsaw, Poland. The authors would like to thank Alan George and Fetah Benabid for providing gas cells.

References and links

1.	T. A. Birks and Y. W. Li, “The shape of fiber tapers,” IEEE J. Lightwave Technol. 10, 432–438 (1992). [CrossRef]
2.	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). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-13-2864. [CrossRef] [PubMed]
3.	T. A. Birks, G. Kakarantzas, and P. St.J. Russell, “All-fibre devices based on tapered fibres,” presented at Opt. Fiber Commun. Conf. paper ThK2 (2004).
4.	C. M. B. Cordeiro, W. J. Wadsworth, T. A. Birks, and P. St.J. Russell, “Octave supercontinuum generated in tapered conventional fibres by a nanosecond 1064 nm laser,” presented at Conf. Lasers Electro-Opt. (2004), paper CThC2.
5.	J.C. Knight, T.A. Birks, P.St.J. Russell, and D.M. Atkin, “All-silica single-mode fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996); Errata, Opt. Lett. 22, 484–485 (1997). [CrossRef] [PubMed]
6.	G. Kakarantzas, T.A. Birks, and P.St.J. Russell, “Structural long-period gratings in photonic crystal fibers,” Opt. Lett. 27 (12), 1013–1015 (2002). [CrossRef]
7.	H.C. Nguyen, B.T. Kuhlmey, M.J. Steel, C.L. Smith, E.C. Magi, R.C. McPhedran, and B.J. Eggleton, “Leakage of the fundamental mode in photonic crystal fiber tapers,” Opt. Lett. 30 (10), 1123–1125 (2005). [CrossRef] [PubMed]
8.	T.A. Birks, G. Kakarantzas, P.St.J. Russell, and D.F. Murphy, “Photonic crystal fibre devices,” Proc SPIE , 4943, 142–151 (2002). [CrossRef]
9.	E. C. Magi, P. Steinvurzel, and B. J. Eggleton “Tapered photonic crystal fibers” Opt. Express 12, 776–784 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-776. [CrossRef] [PubMed]
10.	D. Tabor “Gases, Liquids and Solids,” Penguin Books, Harmondsworth UK, (1969).
11.	W.D. Kingery “Surface tension of some liquid oxides and their temperature coefficients,” J. Am. Ceramic Soc. 42 (1), 6–10 (1959). [CrossRef]
12.	J.D. Love, “Spot size, adiabaticity and diffraction in tapered fibres,” Electron. Lett. 23, 993–994 (1987). [CrossRef]
13.	T.A. Birks, J.C. Knight, and P.St.J. Russell, “Endlessly single-mode photonic crystal fibre,” Opt. Lett. 22, 961–963 (1997). [CrossRef] [PubMed]
14.	T. A. Birks, D. Mogilevtsev, J. C. Knight, P. St.J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allen, and J. C. Fajardo “The analogy between photonic crystal fibres and step index fibres” Proc. Opt. Fiber Commun. Conf. (OFC ´99, San Diego, California) paper FG4 (1999).
15.	W. A. Gambling and H. Matsumura “Simple characterisation factor for practical single-mode fibres” Electron. Lett. 13, 691–693 (1977). [CrossRef]
16.	W.J. Wadsworth, A. Ortigosa-Blanch, J.C. Knight, T.A. Birks, T-P.M. Man, and P.St.J. Russell, “Supercontinuum generation in photonic crystal fibres and optical fibre tapers: A novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002). [CrossRef]
17.	J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000). [CrossRef]
18.	T. A. Birks, W. J. Wadsworth, and P. St.J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 1415–1417 (2000). [CrossRef]
19.	S. Coen, A. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St.J. Russell, “White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber,” Opt. Lett. 26, 1356–1358 (2001). [CrossRef]
20.	J.K. Chandalia, B.J. Eggleton, R.S. Windeler, S.G. Kosinski, X. Liu, and C. Xu “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photonics Technol. Lett. 13 (1), 52–54, (2001) [CrossRef]

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

ToC Category:
Research Papers

History
Original Manuscript: July 18, 2005
Revised Manuscript: August 11, 2005
Published: August 22, 2005

Citation
W. Wadsworth, A. Witkowska, S. Leon-Saval, and T. Birks, "Hole inflation and tapering of stock photonic crystal fibres," Opt. Express 13, 6541-6549 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-17-6541

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References

T. A. Birks and Y. W. Li, "The shape of fiber tapers," IEEE J. Lightwave Technol. 10, 432-438 (1992). [CrossRef]
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