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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 10, Iss. 22 — Nov. 4, 2002
  • pp: 1285–1290
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Microstructured optical fibers: where’s the edge?

Boris T. Kuhlmey, Ross C. McPhedran, C. Martijn de Sterke, Peter A. Robinson, Gilles Renversez, and Daniel Maystre  »View Author Affiliations


Optics Express, Vol. 10, Issue 22, pp. 1285-1290 (2002)
http://dx.doi.org/10.1364/OE.10.001285


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Abstract

We establish that Microstructured Optical Fibers (MOFs) have a fundamental mode cutoff, marking the transition between modal confinement and non-confinement, and give insight into the nature of this transition through two asymptotic models that provide a mapping to conventional fibers. A small parameter space region where neither of these asymptotic models holds exists for the fundamental mode but not for the second mode; we show that designs exploiting unique MOF characteristics tend to concentrate in this preferred region.

© 2002 Optical Society of America

Microstructured Optical Fibers (MOFs) have received considerable attention since pioneering work demonstrated some of their remarkable properties, such as guidance in hollow cores [1

1. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.S. Russel, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999). [CrossRef] [PubMed]

], unprecedented dispersion characteristics [2–7

2. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: An efficient modal model,” J. Lightwave Technol. 17, 1093–1102 (1999). [CrossRef]

], “endlessly” single-modedness [8

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

], and the support of modes with extremely low or high effective area [2

2. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: An efficient modal model,” J. Lightwave Technol. 17, 1093–1102 (1999). [CrossRef]

,9

9. J. C. Knight, T. A. Birks, R. F. Cregan, P. St. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998). [CrossRef]

]. These unique properties have far-reaching consequences in fundamental and applied areas as diverse as frequency comb generation [10

10. R. Holzwarth, M. Zimmermann, Th. Udem, T. W. Hänsch, P. Russbìldt, K. G¤bel, R. Poprawe, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light frequency comb generation with a diode-pumped Cr:LiSAF laser,” Opt. Lett. 26, 1376–1378 (2001) [CrossRef]

], supercontinuum generation [3

3. 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]

,11

11. A. V. Husakou and J. Herrmann, “Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers,” Phys. Rev. Lett. 87, 203901 (2001). [CrossRef] [PubMed]

,12

12. J. P. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, and S. Coen, “Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping,” J. Opt. Soc. Am. B 19, 765–771 (2002). [CrossRef]

] and dispersion management [5

5. J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. S. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonic Tech. Lett. 12, 807–809 (2000). [CrossRef]

].

In two recent papers [16

16. N. A. Mortensen, “Effective area of photonic crystal fibers,” Opt. Express 10, 341–348 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-7-341. [CrossRef] [PubMed]

,17

17. B. T. Kuhlmey, R. C. McPhedran, and C. M. de Sterke, “Modal ‘cutoff’ in Microstructured Optical Fibers,” Opt. Lett. 27, 1684–1686 (2002). [CrossRef]

] criteria were established for recognizing the transition of the second mode1 from being unconfined to confined, which we identify with cutoff. Mortensen [16

16. N. A. Mortensen, “Effective area of photonic crystal fibers,” Opt. Express 10, 341–348 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-7-341. [CrossRef] [PubMed]

] used the rapid decrease in the mode’s effective area at the transition, whereas Kuhlmey et al. [17

17. B. T. Kuhlmey, R. C. McPhedran, and C. M. de Sterke, “Modal ‘cutoff’ in Microstructured Optical Fibers,” Opt. Lett. 27, 1684–1686 (2002). [CrossRef]

] used effective area and four other criteria to pinpoint the transition. Curve 3 in Fig. 1 shows the locus of the transition of the second mode as a function of wavelength normalized to hole spacing Λ, for MOFs of various hole diameters d in silica. Note that this curve crosses the horizontal axis at d/Λ=0.406. Though the transition is gradual for MOFs with only a few rings of air holes, it becomes sharper when the number of air holes increases [17

17. B. T. Kuhlmey, R. C. McPhedran, and C. M. de Sterke, “Modal ‘cutoff’ in Microstructured Optical Fibers,” Opt. Lett. 27, 1684–1686 (2002). [CrossRef]

].

Fig. 1. Operation regimes of MOFs. Lower right inset: cross section of a MOF with 3 rings of holes. Other insets: asymptotic models for large (CF1) and small (CF2) wavelengths. The shaded transition region represents the parameter subspace where MOFs cannot be described by either asymptotic model and therefore behave most unlike conventional optical fibers. Data sets are described in the text.

Using the same criteria as in [17

17. B. T. Kuhlmey, R. C. McPhedran, and C. M. de Sterke, “Modal ‘cutoff’ in Microstructured Optical Fibers,” Opt. Lett. 27, 1684–1686 (2002). [CrossRef]

], it appears that the fundamental mode2 also undergoes a cutoff transition between confined and non-confined states. For long wavelengths, the fundamental mode fills the entire fiber cross-section, whereas for small wavelength it becomes confined in the core. However, instead of having the sharp transition between those states exhibited by the second mode, the transition is characterized by two loci, with a transition region of finite width in between. This was established for structures of up to N r=10 rings of holes, with conclusions for larger structures following by extrapolation . Above the highest of these loci [curve (1)], in the region denoted by CF1, the fundamental mode fills the entire fiber cross section, and its properties can be accurately predicted on the basis of a conventional fiber model (CF1, using the same symbol for the model and the region of parameter space in which it is valid) that we describe below. Below the second locus [curve (2)], in the region denoted by CF2, the fundamental mode is tightly confined in the core, with its properties given by a second conventional fiber model (CF2). In the transition region between CF1 and CF2, the fundamental mode changes its character and its behavior is thus not only sensitive to the MOF design (i.e., to d/Λ and N r), but is also unlike that of the modes of conventional fibers. We stress that, as we decrease the wavelength from large values, the fiber at first shows no localized modes (region CF1), but that one of its extended modes undergoes a smooth transition to emerge as a localized mode in region CF2.

We established the mode boundaries of Fig. 1 using a multipole method [13

13. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002). [CrossRef]

,14

14. B. T. Kuhlmey, T. P. White, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19, 2331–2340 (2002). [CrossRef]

], which can calculate MOF modes and their losses accurately over a wide parameter range. We studied the comportment of MOFs at the telecommunications wavelength of λ= 1.55 μm, and varied the hole spacing Λ, while keeping the hole diameter to spacing ratio d/Λ constant. The MOFs were taken to consist of air holes (refractive index unity) in a matrix with refractive index n m= 1.44402362. For given d/Λ, we studied the variation of the loss [Im(n eff)] as a function of normalized wavelength λ/Λ. At small λ/Λ, the loss increases gently, before rising very steeply in the transition region, and then increasing slowly once again in the second conventional fiber region (see Fig. 2.A). To locate the boundaries of regions accurately, we used the second derivative of the log-log plot of the losses, a function which peaks at the boundaries between regions [17

17. B. T. Kuhlmey, R. C. McPhedran, and C. M. de Sterke, “Modal ‘cutoff’ in Microstructured Optical Fibers,” Opt. Lett. 27, 1684–1686 (2002). [CrossRef]

]. Carrying out this procedure for various hole diameters, we established the two boundary curves for the fundamental mode, shown for the first time in Fig. 1. These curves tend to approach one another for decreasing hole size, and reach λ=0 for hole sizes d/Λ somewhere between 0 and 0.06 inclusive. Counting only modes confined to the core, MOFs in silica can be said to be “endlessly” single-moded in the region below the CF1 area of Fig. 1, and to the left of d/Λ = 0.406, where the second mode boundary drops to zero [17

17. B. T. Kuhlmey, R. C. McPhedran, and C. M. de Sterke, “Modal ‘cutoff’ in Microstructured Optical Fibers,” Opt. Lett. 27, 1684–1686 (2002). [CrossRef]

]. This observation corroborates and somewhat sharpens the prediction of endless single mode behavior made by Birks et al. [8

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

].

Fig. 2. A: Imaginary part of n eff as a function of wavelength on pitch, rescaled by (λ/Λ)2, for a silica structure with 3 layers of holes, with d/Λ taking the values 0.075 (top curve), 0.15, 0.3, 0.45, 0.6, 0.75, 0.8 and 0.85. B: Imaginary (thin curves) and real (thick curves) part of n eff as a function of fiber radius N r Λ divided by λ for MOFs with d/Λ=0.3, for 4 (red), 6 (blue) and 8 (green) rings of holes, and for the corresponding homogenized fiber (black). All calculations in this report were done for varying pitch at fixed λ=1.55μm, where the losses in dB/m are given by 3.52×107Im(n eff).

In the CF1 region of Fig.1, the fundamental mode fills the entire confining region. Its behavior is modeled accurately by using homogenization arguments [18

18. G. W. Milton, The Theory of Composites (Cambridge University Press, 2002). [CrossRef]

] to establish effective dielectric constants and thereby refractive indices for the cladding region. Homogenization theory predicts an effective dielectric constant given by the mean of the dielectric constants of air and silica for the electric field parallel to the fiber axis. In contrast, for small d/Λ the Maxwell-Garnett formula can be used to derive effective constants for the transverse electric field component [18

18. G. W. Milton, The Theory of Composites (Cambridge University Press, 2002). [CrossRef]

]. With f being the air filling fraction of the fiber we have:

n¯z=[fnair2+(1f)nm2]12,(Extraordinaryindex)
(1)
n¯nm[(Tf)(T+f)]12,(Ordinaryindex)
whereT=(nm2+nair2)(nm2nair2).
(2)

Figure 3: Width of the transition between the large wavelength asymptotic regime (CF1) and the intermediate regime as a function of Nrb, for the fundamental mode (A, b f≈ 2.97) and the second mode (B, b 2≈ 1.55). For the second mode the width of the intermediate regime tends to zero with increasing number of rings, whereas a finite transition region remains for the fundamental mode, even for N r→∞.

For short wavelengths, MOFs have already been successfully modeled by several authors as step index fibers with varying cladding index [5

5. J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. S. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonic Tech. Lett. 12, 807–809 (2000). [CrossRef]

,8

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

,11

11. A. V. Husakou and J. Herrmann, “Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers,” Phys. Rev. Lett. 87, 203901 (2001). [CrossRef] [PubMed]

,12

12. J. P. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, and S. Coen, “Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping,” J. Opt. Soc. Am. B 19, 765–771 (2002). [CrossRef]

,20

20. J. C. Knight, T. A. Birks, P. St. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. B 15, 748–752 (1998). [CrossRef]

,21

21. F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,“ Opt. Fiber Technol. 6, 181–191 (2000). [CrossRef]

]. In the model CF2 shown in Fig. 1 the refractive index of the cladding is given by the effective index of the fundamental space-filling mode (FSM) [8

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

]. Best agreement was found for a core radius of approximately a=0.64Λ [21

21. F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,“ Opt. Fiber Technol. 6, 181–191 (2000). [CrossRef]

]. Based on an asymptotic analysis of this model, it appears that at short wavelengths n FSM can be approximated by

nFSM=nmn2(λΛ)2
(3)

As mentioned earlier, the sharpness of the transition region with increasing N r evolves differently for the fundamental and the second mode. This is illustrated in Fig. 3, where we plot the width of the transition region (more precisely the width of the peak of the second derivatives of the curves in Fig. 1.A) versus 1/Nrb, where b is adjusted to give the best straight-line behavior of all datasets in each frame. As the number of confining rings N r increases, the width of the transition region tends to zero for the second mode (Fig. 3.B), whereas for the fundamental mode this width remains finite (Fig. 3.A). Thus, in an infinite system, the transition region for the second mode disappears, whereas for the fundamental mode there is always a parameter region in which this mode behaves fundamentally differently than the modes of a conventional fiber. Note the linearity of the data for different hole diameters in Fig. 3, showing that the power law exponents for both modes are independent of d/Λ.

The points in Fig. 1 indicate experimental and theoretical data from recent publications of MOF designs with unconventional properties. The first data set concerns MOFs used experimentally for supercontinuum generation, taken from Refs. [3

3. 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]

,11–12

11. A. V. Husakou and J. Herrmann, “Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers,” Phys. Rev. Lett. 87, 203901 (2001). [CrossRef] [PubMed]

]. They all lie in the CF2 regime, and indeed the key property for supercontinuum generation - highly shifted zero dispersion wavelength and small core size - can be delivered by the CF2 model, already known to be successful for such MOFs [11

11. A. V. Husakou and J. Herrmann, “Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers,” Phys. Rev. Lett. 87, 203901 (2001). [CrossRef] [PubMed]

,12

12. J. P. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, and S. Coen, “Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping,” J. Opt. Soc. Am. B 19, 765–771 (2002). [CrossRef]

]. Data set 2 shows the location of experimental zero-dispersion wavelength measures, which were compared to theoretical values from a CF2 model in the original publication [5

5. J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. S. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonic Tech. Lett. 12, 807–809 (2000). [CrossRef]

]. For the two lower points (b and d) which lie in the CF2 region, comparison with the CF2 model gave good agreement, for point c agreement was approximate and for point a, lying in the transition region, the agreement was unsatisfactory.

The third data set consists of regions of observed or predicted flat or oscillating dispersion, taken from Refs. [2

2. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: An efficient modal model,” J. Lightwave Technol. 17, 1093–1102 (1999). [CrossRef]

,4

4. A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25, 790–792 (2000). [CrossRef]

,6

6. W. H. Reeves, J. C. Knight, and P. St. J. Russell,“Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609. [CrossRef] [PubMed]

,7

7. B. Kuhlmey, G. Renversez, and D. Maystre, “Chromatic dispersion and losses of microstructured optical fibers,” Appl. Optics OT, in press.

,21

21. F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,“ Opt. Fiber Technol. 6, 181–191 (2000). [CrossRef]

]. All data points herein are located exactly in the transition region, using the increased and highly configurable wavelength dependence of structural dispersion to compensate material dispersion. The consequences of being in the transition region, and therefore close to cutoff, are that confinement losses are highly wavelength dependent, and that the waveguide dispersion is sensitive to the actual fiber geometry. Such high sensitivity to structural imperfections was observed by Monro et al. [22

22. T. Monro, P. J. Bennett, N. G. Broderick, and D. J. Richardson, “Holey fibers with random cladding distributions,” Opt. Lett. 25, 206–208 (2000). [CrossRef]

], and indeed the fiber parameters used by these authors are in the transition region (data line 4).

In studying the influence of the number of rings on dispersion [7

7. B. Kuhlmey, G. Renversez, and D. Maystre, “Chromatic dispersion and losses of microstructured optical fibers,” Appl. Optics OT, in press.

], we observed that the dispersion does not necessarily converge with the ring number. Data set 5 shows the location of an example where the dispersion converges with N r in a limited wavelength range before diverging with N r. The divergent wavelength range crosses the transition line from the intermediate to the homogenized regime CF1, where we have seen N r dictates mode properties.

Although we tried to map as many published MOF designs as possible onto Fig. 1, a few were omitted: some were overlapping the transition region and the CF2 region and had more conventional dispersion properties, while others were beyond the scope of this study (e.g. grossly non-circular holes). One theoretical study by Monro et al. [2

2. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: An efficient modal model,” J. Lightwave Technol. 17, 1093–1102 (1999). [CrossRef]

] had two examples of MOFs lying in the CF1 region, with both displaying conventional dispersion. It should be emphasized that no experimental MOF has been published with parameters in the CF1 region.

Footnotes

1The second mode is defined as the mode having, for a given fiber geometry, the second largest real part of n eff. It usually has the second lowest loss, and its field distribution is similar to the TE1 mode of conventional fibers.
2The fundamental mode is defined as the mode having, for a given fiber geometry, the largest real part of n eff. It is the mode with the lowest losses and for the fibers studied here is doubly degenerate. It is most similar in terms of field distribution to the HE1,1 mode of conventional fibers.
3Note that n FSM also has importance in relation to the boundary of CF1, which appears to occur when n eff= n FSM.

References and links

1.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.S. Russel, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999). [CrossRef] [PubMed]

2.

T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: An efficient modal model,” J. Lightwave Technol. 17, 1093–1102 (1999). [CrossRef]

3.

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]

4.

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25, 790–792 (2000). [CrossRef]

5.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. S. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photonic Tech. Lett. 12, 807–809 (2000). [CrossRef]

6.

W. H. Reeves, J. C. Knight, and P. St. J. Russell,“Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609. [CrossRef] [PubMed]

7.

B. Kuhlmey, G. Renversez, and D. Maystre, “Chromatic dispersion and losses of microstructured optical fibers,” Appl. Optics OT, in press.

8.

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

9.

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998). [CrossRef]

10.

R. Holzwarth, M. Zimmermann, Th. Udem, T. W. Hänsch, P. Russbìldt, K. G¤bel, R. Poprawe, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light frequency comb generation with a diode-pumped Cr:LiSAF laser,” Opt. Lett. 26, 1376–1378 (2001) [CrossRef]

11.

A. V. Husakou and J. Herrmann, “Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers,” Phys. Rev. Lett. 87, 203901 (2001). [CrossRef] [PubMed]

12.

J. P. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, and S. Coen, “Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping,” J. Opt. Soc. Am. B 19, 765–771 (2002). [CrossRef]

13.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002). [CrossRef]

14.

B. T. Kuhlmey, T. P. White, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19, 2331–2340 (2002). [CrossRef]

15.

T. P. White, R. C. McPhedran, C. M. de Sterke, and M. J. Steel, “Confinement losses in microstructured optical fibers,” Opt. Lett. 26, 1660–1662 (2001). [CrossRef]

16.

N. A. Mortensen, “Effective area of photonic crystal fibers,” Opt. Express 10, 341–348 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-7-341. [CrossRef] [PubMed]

17.

B. T. Kuhlmey, R. C. McPhedran, and C. M. de Sterke, “Modal ‘cutoff’ in Microstructured Optical Fibers,” Opt. Lett. 27, 1684–1686 (2002). [CrossRef]

18.

G. W. Milton, The Theory of Composites (Cambridge University Press, 2002). [CrossRef]

19.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1996).

20.

J. C. Knight, T. A. Birks, P. St. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. B 15, 748–752 (1998). [CrossRef]

21.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,“ Opt. Fiber Technol. 6, 181–191 (2000). [CrossRef]

22.

T. Monro, P. J. Bennett, N. G. Broderick, and D. J. Richardson, “Holey fibers with random cladding distributions,” Opt. Lett. 25, 206–208 (2000). [CrossRef]

OCIS Codes
(060.2270) Fiber optics and optical communications : Fiber characterization
(060.2430) Fiber optics and optical communications : Fibers, single-mode

ToC Category:
Research Papers

History
Original Manuscript: September 23, 2002
Revised Manuscript: October 24, 2002
Published: November 4, 2002

Citation
Boris Kuhlmey, Ross McPhedran, C. de Sterke, Peter Robinson, Gilles Renversez, and Daniel Maystre, "Microstructured optical fibers: where�??s the edge?," Opt. Express 10, 1285-1290 (2002)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-22-1285


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References

  1. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.S. Russel, P. J. Roberts, D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999). [CrossRef] [PubMed]
  2. T. M. Monro, D. J. Richardson, N. G. R. Broderick, P. J. Bennett, "Holey optical fibers: An efficient modal model," J. Lightwave Technol. 17, 1093-1102 (1999). [CrossRef]
  3. J. K. Ranka, R. S. Windeler, 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]
  4. A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, "Nearly zero ultraflattened dispersion in photonic crystal fibers," Opt. Lett. 25, 790-792 (2000). [CrossRef]
  5. J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch,W. J. Wadsworth, P. S. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photonic Tech. Lett. 12, 807-809 (2000). [CrossRef]
  6. W. H. Reeves, J. C. Knight, P. St. J. Russell,"Demonstration of ultra-flattened dispersion in photonic crystal fibers," Opt. Express 10, 609-613 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609</a>. [CrossRef] [PubMed]
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