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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 1 — Jan. 3, 2011
  • pp: 66–80
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All-solid highly nonlinear singlemode fibers with a tailored dispersion profile

Francesco Poletti, Xian Feng, Giorgio M. Ponzo, Marco N. Petrovich, Wei H. Loh, and David J. Richardson  »View Author Affiliations


Optics Express, Vol. 19, Issue 1, pp. 66-80 (2011)
http://dx.doi.org/10.1364/OE.19.000066


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Abstract

We investigate a novel approach to obtain highly nonlinear fibers with a tailored group velocity dispersion around a desired wavelength region of interest. Rather than exploiting longitudinal holes to control the average refractive index of the cladding and hence the fiber’s waveguide dispersion, as in holey fibers, we propose using an all-solid cladding with a suitably chosen refractive index difference relative to the core. We demonstrate numerically that this solution allows a large freedom in the manipulation of the overall fiber dispersive properties, while enabling, in practice, a much more accurate control of the fiber’s structural properties during fabrication. Effectively single mode guidance over a broad wavelength range can be achieved through the use of a second outer cladding forming a W-type index profile. We derive simple design rules for dispersion controlled fibers, based on which an algorithm for the automatic dispersion optimization is proposed, implemented and used to design various nonlinear fibers for all-optical processing and supercontinuum generation. Fabrication of a lead silicate fiber with flattened dispersion at telecoms wavelengths confirms the potential of these new fibers.

© 2011 OSA

1. Introduction

The accurate control of the group velocity dispersion (GVD) profile of an optical fiber is paramount to the efficient exploitation of most fiber-based nonlinear optical effects. For example, a tailored dispersion profile is essential for the phase matching of parametric processes [1

1. G. P. Agrawal, Nonlinear fiber optics, 3rd ed. (Academic Press, San Diego, 2001).

] or the control of soliton dynamics such as Raman soliton self frequency shifting [2

2. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11(10), 662–664 (1986). [CrossRef] [PubMed]

], dispersive wave generation and trapping [3

3. A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nat. Photonics 1(11), 653–657 (2007). [CrossRef]

] or soliton spectral tunneling [4

4. F. Poletti, P. Horak, and D. J. Richardson, “Soliton spectral tunneling in dispersion-controlled holey fibers,” IEEE Photon. Technol. Lett. 20(16), 1414–1416 (2008). [CrossRef]

]; a zero dispersion wavelength (ZDW) close to the pump wavelength is also one of the prerequisites for efficient and broadband supercontinuum generation [5

5. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]

], where a good control of the fiber’s GVD is also crucial to enhance the energy transfer to either shorter or longer wavelengths [6

6. J. M. Stone and J. C. Knight, “Visibly “white” light generation in uniform photonic crystal fiber using a microchip laser,” Opt. Express 16(4), 2670–2675 (2008). [CrossRef] [PubMed]

,7

7. J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, M. Feng, and D. J. Richardson, “Mid-IR supercontinuum generation from nonsilica microstructured optical fibers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 738–749 (2007). [CrossRef]

].

Major effort has therefore been devoted over the past several decades to develop technologies allowing fine control of the overall dispersion of optical fibers by modifying the waveguide dispersion (Dw) to counterbalance the intrinsic material dispersion of the optical glass (Dm). Historically, the first dispersion controlled fibers, including dispersion shifted, flattened and compensating fibers, were developed in the context of optical telecommunications to mitigate the adverse temporal pulse spreading induced by GVD in the newly discovered ultra low-loss third telecommunication window. The preform fabrication process, typically based on modified chemical vapor deposition (MCVD), allowed the creation of often complex refractive index profiles from a ultra-high purity silica glass host to create an optical waveguide with a controlled amount of waveguide dispersion. This technology was later on extended to the realization of smaller core fibers with flattened dispersion at telecoms wavelengths for nonlinear applications [8

8. M. Takahashi, R. Sugizaki, J. Hiroishi, M. Tadakuma, Y. Taniguchi, and T. Yagi, “Low-loss and low-dispersion-slope highly nonlinear fibers,” J. Lightwave Technol. 23(11), 3615–3624 (2005). [CrossRef]

]. This well refined fabrication technology produces fiber preforms with a remarkably precise and reproducible radially symmetric refractive index profile, while the all-solid nature of these fibers ensures that such a profile is preserved from preform to fiber with an excellent stability of all structural dimensions along the fiber length. As a result, these fibers typically present well controllable and reproducible dispersion profiles, which also tend to have good stability along the longitudinal direction. The downside of this approach is that the maximum difference between core (nco) and cladding (ncl) refractive indices achievable through doping is typically low (Δn max = nco – ncl ~0.05), which ultimately limits the amount of waveguide dispersion that can be introduced and prevents the overall dispersion of these fibers being radically different from the dispersion of the core glass. The maximum nonlinearity of these fibers is also quite small, typically limited to ~30 W−1km−1.

A second, more recent method to achieve waveguidance and at the same time a broader range of dispersion profiles, requires the incorporation of longitudinal air holes in the cross section of single-glass fibers, known as holey fibers (HFs) or photonic crystal fibers (PCFs) [9

9. J. C. Knight, T. A. Birks, P. S. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996). [CrossRef] [PubMed]

]. The much higher refractive index contrast between glass and air, ranging from the ~0.45 of silica structures to more than 2 for glasses made of heavier constituent atoms, and the vast freedom in the choice of shape, size and topology of the holes, results in much higher values of fiber nonlinearity together with an unprecedented level of control of the dispersive properties. HFs with a ZDW down to the visible region of the spectrum [10

10. 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 Photon. Technol. Lett. 12(7), 807–809 (2000). [CrossRef]

], two or even three ZDWs at tailored spectral positions [4

4. F. Poletti, P. Horak, and D. J. Richardson, “Soliton spectral tunneling in dispersion-controlled holey fibers,” IEEE Photon. Technol. Lett. 20(16), 1414–1416 (2008). [CrossRef]

,11

11. M. L. V. Tse, P. Horak, F. Poletti, N. G. R. Broderick, J. H. V. Price, J. R. Hayes, and D. J. Richardson, “Supercontinuum generation at 1.06 mum in holey fibers with dispersion flattened profiles,” Opt. Express 14(10), 4445–4451 (2006). [CrossRef] [PubMed]

], or a flat dispersion region extending over a bandwidth of several hundred nanometers have all been reported [12

12. W. H. Reeves, J. C. Knight, P. S. J. Russell, and P. J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10(14), 609–613 (2002). [PubMed]

15

15. F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, “Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers,” Opt. Express 13(10), 3728–3736 (2005). [CrossRef] [PubMed]

]. However, producing holey structures with the required structural precision in both transverse and longitudinal directions to reliably and reproducibly achieve a desired dispersion profile has proven much more difficult than for all-solid, low index contrast fibers. Temperature gradients within the fiber furnace, coupled with different surface tensions and gas pressures experienced by holes with dissimilar size, typically tend to create unpredictable structural distortions when drawing a preform down to the size of a cane or a fiber. Such distortions are difficult to control or pre-compensate, and as a result it is extremely challenging to obtain an accurate and reproducible dispersion profile in a highly nonlinear HF [16

16. X. Feng, F. Poletti, A. Camerlingo, F. Parmigiani, P. Petropoulos, P. Horak, G. M. Ponzo, M. N. Petrovich, W. H. Loh, and D. J. Richardson, “Dispersion controlled highly nonlinear fibers for all optical processing at telecoms wavelengths,” Opt Fiber Technol (invited and submitted, 2010).

].

In this work we propose and demonstrate a third alternative method to obtain dispersion controlled fibers with a high value of effective nonlinearity, where two or three high refractive index glasses with large index contrast (Δn ranging from 0.05 to more than 2) are combined in an all-solid, circularly symmetric geometry. Such fibers provide at the same time an excellent fabrication reproducibility and stability, and a highly tailorable dispersion control, thus combining the best qualities of low contrast, all-solid conventional fibers with those of high contrast HFs. Furthermore, through simultaneous use of high Δn and small core sizes, they can typically achieve extremely high values of nonlinearity, as required for nonlinear applications, where simpler pumps at lower peak powers or shorter fiber lengths less prone to longitudinal fluctuations of diameter and hence dispersion can be used.

Here we present general design rules and a simple algorithm to design high index contrast, step-index fibers (SIFs) with an arbitrary value of dispersion (D) and dispersion slope (DS) at a selected wavelength within the transparency window of the core glass. We study the singlemode operation regime of these fibers and propose the introduction of a second outer cladding to strip off the few high order modes present at shorter wavelengths and thus obtain an effectively singlemode operation. We then apply the proposed rules to the design of dispersion flattened fibers (zero D and DS at a given wavelength) and of fibers for supercontinuum generation. Finally, in order to prove the potential of such a novel fiber design concept, we discuss the design and fabrication of a recently reported highly nonlinear dispersion flattened fiber.

2. Dispersion of circularly symmetric, high index contrast SIFs

To understand the proposed fiber design approach, it is instructive to study the waveguide dispersion of a simple step-index fiber when the contrast between core and cladding refractive indices is large. For all fibers in this work we assume a circular radial symmetry, which is useful since it allows the use of semi-analytical calculation methods to simplify the numerical analysis, but not essential. Using an extrusion-based fabrication approach for example, fibers without circular symmetry could be obtained, which may represent a future extension of the method presented here [17

17. A. W. Snyder and X. H. Zheng, “Optical Fibers of Arbitrary Cross-Sections,” J. Opt. Soc. Am. A 3(5), 600–609 (1986). [CrossRef]

].

As an illustrative example, Eq. (1) is solved with this second method for a range of SIFs to show the dependence of neff(λ), Dw(λ) and D(λ) on the structural parameters d and Δn. The left column in Fig. 1
Fig. 1 Wavelength dependence of effective index (neff), waveguide dispersion (Dw) and total dispersion (D) for step index fibers with an SF57 glass in the core and: variable core diameter d with Δn = 0.28 (left column) and variable Δn with d = 1.7 μm (right column).
shows the effect of a diameter change for a fixed Δn, while the right column shows the effect of changing Δn when d is fixed. Note that although for these calculations we have assumed specific structural values, approximately corresponding to those of the fabricated dispersion flattened fiber discussed in Section 5 (nco = 1.80, ncl = 1.52 and d = 1.7 μm), the general conclusions drawn from Fig. 1 are valid for any other set of parameters.

Figures 1(a) and 1(b) show that, as is well known, neff tends to nco for vanishingly small wavelengths (λ << d), and to ncl for λ >> d. As a result, the waveguide dispersion contribution is negligible in both the short and long wavelength limit, Figs. 1(c) and 1(d). For any practical optical wavelength in between, Dw assumes an approximately sinusoidal wavelength dependence, going from a positive (anomalous) contribution at shorter wavelengths to a negative (normal) contribution at longer wavelengths. The key point to observe here is that the waveguide dispersion slope (DSw) is to good approximation only influenced by changes in diameter (where smaller diameters generate larger slopes, as is seen in Fig. 1(c)), while a change in index contrast shifts the Dw curves with respect to wavelength (larger Δn shifts the curves towards longer wavelengths) and compresses/expands them vertically, but leaves their slope nearly unchanged, Fig. 1(d). A similar behavior has been previously observed in HFs, where changing the hole-to-hole spacing is equivalent to scaling d for SIFs, while modifying the air filling fraction acts like a change in Δn [19

19. A. Ferrando, E. Silvestre, P. Andres, J. Miret, and M. Andres, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express 9(13), 687–697 (2001). [CrossRef] [PubMed]

].

It is finally worth stressing that, as already observed by Ferrando et al. [19

19. A. Ferrando, E. Silvestre, P. Andres, J. Miret, and M. Andres, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express 9(13), 687–697 (2001). [CrossRef] [PubMed]

], the dimensionless nature of the effective index implies that its dependence on the structural parameters can only occur through dimensionless ratios, i.e. neff = neff(d/λ, nco, ncl). Therefore for any real scaling factor M ≠ 0 we can obtain a scaling rule for the waveguide dispersion:

Dw(Md, λ,nco,ncl)=1MDw(d, λ/M,nco,ncl).
(4)

As a result, once a waveguide dispersion curve is known for a specific combination of d, nco and ncl, it is possible to obtain Dw for any other particular fiber diameter of interest by appropriately stretching the curve, without the need to recalculate Eq. (1). Note also that the 1/M scaling factor implies that smaller cores generate higher absolute values of waveguide dispersion (shifted to shorter wavelengths), as shown in Fig. 1(c).

3. Automatic dispersion optimization routine

  • 1. Choose the wavelength of operation λt and a high refractive index glass to be used in the core. This will determine a value of core index ncot) which will not change throughout the procedure, making each SIF design dependent only on diameter and index difference, {d, Δnt)}. For simplicity of notation, in the following steps the explicit wavelength dependence of all variables will be dropped and all calculated values will be implicitly referred to the target wavelength λt.
  • 2. Select a target value of dispersion Dt and dispersion slope DSt at λt, from which the target waveguide dispersion Dwt = Dt - Dm and waveguide dispersion slope DSwt = DSt - DSm can be obtained. Choose a desired accuracy on the values of dispersion (εD) and dispersion slope (εDS).
  • 3. Choose initial guess values of fiber diameter and index difference {d (0), Δn (0)}, which will also obviously determine ncl (0) = nco (0) - Δn (0). Here the superscript numbers indicate the progressive step in the algorithm. Note that this initial choice will have an influence on the number of steps required by the algorithm to converge, but will not generally prevent its convergence (see the example in Fig. 2
    Fig. 2 Optimization steps in the automatic design of a dispersion flattened SIF. The material dispersion (-Dm) of the SF57 core is shown by the red dashed line. Optimization targets are Dt = 0 ps/nm/km and DSt = 0 ps/nm2/km at λt = 1.55 μm. Initial {d (0), Δn (0)} conditions are: (a) {4 μm, 0.25}; (b) {1.3 μm, 0.4}. Both optimizations reach the same optimum fiber with d = 1.78 μm and Δn = 0.26, and the optimum total dispersion is shown by the black line.
    ). Calculate the waveguide dispersion curve of this initial fiber through Eq. (1) and evaluate Dw (0) and DSw (0) at λt. Note that although these quantities need to be evaluated at one wavelength, in order to be able to apply the scaling rule in the next step, calculation of Dw over a broad enough wavelength range around λt is required.
    Fig. 2Optimization steps in the automatic design of a dispersion flattened SIF. The material dispersion (-Dm) of the SF57 core is shown by the red dashed line. Optimization targets are Dt = 0 ps/nm/km and DSt = 0 ps/nm2/km at λt = 1.55 μm. Initial {d (0), Δn (0)} conditions are: (a) {4 μm, 0.25}; (b) {1.3 μm, 0.4}. Both optimizations reach the same optimum fiber with d = 1.78 μm and Δn = 0.26, and the optimum total dispersion is shown by the black line.
  • 4. Through a numerical optimization routine and using the scaling rule in Eq. (4), modify d until a new value of diameter d (1) is found such that DSerr (1) = |DSw (1) – DSwt| < εDS. The structure {d (1), Δn (0)} will have a dispersion slope at λt well matched to the target one, but some residual error in the absolute value of waveguide dispersion, Derr (1) = |Dwt – Dw (1)|.
  • 5. Modify the index difference to Δn (1), recalculate the waveguide dispersion through Eq. (1) with {d (1), Δn (1)} and repeat step 4 to obtain a new optimum diameter d (2) such that, again, DSerr (2) = |DSw (2) – DSwt| < εDS. Estimate Derr (2) = |Dwt – Dw (2)|, for {d (2), Δn (1)}.
  • 6. Through a numerical optimization routine applied to step 5, modify Δn until, after n steps, the desired combination of diameter and index contrast {d (n + 1), Δn (n)} is found such that, at the same time, Derr (n + 1) < εD and DSerr (n + 1) < εDS.

Figure 2 shows two examples of dispersion optimization using this algorithm, where the optimization loops have been implemented using the simplex method. In both examples the core glass is SF57 and the targets are Dt = 0 ps/nm/km and DSt = 0 ps/nm2/km at λt = 1.55 μm. εD and εDS are set to 0.01 ps/nm/km and 10−6 ps/nm2/km, respectively. Two rather different initial guesses for {d (0), Δn (0)} have been chosen to demonstrate the convergence of the algorithm and the independence of the results from the initial guess: {4 μm, 0.25} is shown in Fig. 2(a) while {1.3 μm, 0.4} is used in Fig. 2(b). The waveguide dispersion of these starting fibers is shown by the pink dash-dot line. As can be seen, both optimizations converge towards the same optimum result, d = 1.78 μm, Δn = 0.26 (black curves). Less than 20 total optimization steps and a computation time of less than a minute on a standard PC are required.

4. Choice of core and cladding glasses

Having presented and validated a fiber design process to tailor the dispersive properties of all solid SIFs with high index contrast, in this section we add a few comments on the choice of suitable glasses and on possible fabrication approaches to realize such structures. A detailed discussion of the main optical, thermal and mechanical properties of the glasses commonly used in the fabrication of highly nonlinear fibers is outside the scope of this work. And for this the reader is referred to the works in refs [7

7. J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, M. Feng, and D. J. Richardson, “Mid-IR supercontinuum generation from nonsilica microstructured optical fibers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 738–749 (2007). [CrossRef]

,22

22. T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Annu. Rev. Mater. Res. 36(1), 467–495 (2006). [CrossRef]

] and in references therein.

For high contrast SIFs operating at wavelengths close to or shorter than the first high order mode cut-off wavelength (circular markers in Fig. 1) the fraction of power guided in the core is typically larger than 85-90% [18

18. A. W. Snyder, and J. D. Love, Optical waveguide theory (Chapman and Hall, London; New York, 1983).

]. Therefore, the most critical choice in the entire fiber design procedure regards the glass to be employed in the core. Not only will this glass have a direct influence on the transparency range, nonlinearity and ultimate loss of the dispersion controlled fibers, but through its material dispersion it will also indirectly determine the number of guided modes (and thus whether or not a second outer cladding is required), and the bandwidth of the dispersion controlled region.

Despite these large differences in ZMDW, however, the vast majority of optical glasses amenable to fiber fabrication share a qualitatively similar material dispersion wavelength dependence, which is well exemplified by the Dm curve of SF57 shown in Fig. 1(e) and shown for several other glasses in Fig. 5
Fig. 5 Refractive index (left) and material dispersion (right) of some common optical glasses: 1. silica [1]; 2. ZBLAN [24]; 3. and 4. Schott lead silicates [20]; 5. barium gallogermanate [25]; 6. bismuth silicate [26]; 7. zinc tellurite [27]; 8. lead gallate [28]; arsenic trisulfide [29].
. As can be seen, the ZMDW typically separates two qualitatively different regions: at wavelengths much shorter than the ZMDW, Dm(λ) is very steep and normal, while at wavelengths longer than the ZMDW, Dm(λ) is anomalous with a much shallower and in most cases close to linear wavelength dependence.

Generally, from Fig. 5 it is evident that in order to have some sort of dispersion control at wavelengths much shorter than the ZMDW, large values of anomalous dispersion are required. From the behavior highlighted in Fig. 1(c) this can only be obtained with small enough fiber diameters. Small core diameters however also shift the Dw curves to short wavelengths, see the scaling rule in Eq. (4), and this must be compensated by using larger values of Δn, see Fig. 1(d). In contrast, at wavelengths close to or longer than the ZMDW, larger core diameters and hence smaller Δn are sufficient to achieve a waveguide dispersion contribution similar in magnitude and opposite in sign to the material one. Therefore, based on the choice of core glass and on where its ZMDW is positioned with respect to the intended operational range of the fiber, significantly different values of d and Δn can be expected, which ultimately also influence the most suitable fabrication approach to be adopted.

Dispersion controlled fibers operating at wavelengths larger than the ZMDW and requiring smaller index contrasts (e.g. Δn ~0.05-0.2) are most likely to be based on glasses of the same family, with tailored compositional variations. For example, SIFs with core and cladding made of tellurite [30

30. A. Mori, K. Kobayashi, M. Yamada, T. Kanamori, K. Oikawa, Y. Nishida, and Y. Ohishi, “Low noise broadband tellurite-based Er3+-doped fibre amplifiers,” Electron. Lett. 34(9), 887–888 (1998). [CrossRef]

], bismuth [31

31. N. Sugimoto, T. Nagashima, T. Hasegawa, S. Ohara, K. Taira, and K. Kikuchi, “Bismuth-based optical fiber with nonlinear coefficient of 1360 W−1km−1,” Optical Fiber Communications Conference (OFC) 2004, PDP26.

] or chalcogenide [32

32. R. Mossadegh, J. S. Sanghera, D. Schaafsma, B. J. Cole, V. Q. Nguyen, P. E. Miklos, and I. D. Aggarwal, “Fabrication of single-mode chalcogenide optical fiber,” J. Lightwave Technol. 16(2), 214–217 (1998). [CrossRef]

] based glasses of slightly different compositions have been already demonstrated, although in all these cases no attempt was ever made to control the overall fiber dispersion, as we suggest in this work.

In case a third glass is required in the outer cladding to enforce singlemode operation, a much greater freedom exists in the choice of its properties. In this case, thermo-mechanical compatibility with the other two glasses should be the main factor determining the glass choice, and the outer diameter d ocl can be used as an additional free parameter to tailor the differential mode loss (see Section 5).

Different fabrication methods have been reported so far to realize high index contrast step-index fibers, for example the double crucible technique [32

32. R. Mossadegh, J. S. Sanghera, D. Schaafsma, B. J. Cole, V. Q. Nguyen, P. E. Miklos, and I. D. Aggarwal, “Fabrication of single-mode chalcogenide optical fiber,” J. Lightwave Technol. 16(2), 214–217 (1998). [CrossRef]

], the Taylor wire method [33

33. J. Ballato, T. Hawkins, P. Foy, R. Stolen, B. Kokuoz, M. Ellison, C. McMillen, J. Reppert, A. M. Rao, M. Daw, S. R. Sharma, R. Shori, O. Stafsudd, R. R. Rice, and D. R. Powers, “Silicon optical fiber,” Opt. Express 16(23), 18675–18683 (2008). [CrossRef]

], the high pressure chemical vapor deposition technique [34

34. N. Healy, J. R. Sparks, M. N. Petrovich, P. J. A. Sazio, J. V. Badding, and A. C. Peacock, “Large mode area silicon microstructured fiber with robust dual mode guidance,” Opt. Express 17(20), 18076–18082 (2009). [CrossRef] [PubMed]

], the pumping of molten glasses inside silica templates [35

35. A. S. Markus, G. Nicolai, W. Lothar, and R. Philip St, “Optical Properties of Chalcogenide-Filled Silica-Air PCF,” in Advances in Optical Materials, OSA Technical Digest (CD) (Optical Society of America, 2009), AThD3.

,36

36. M. A. Schmidt, N. Granzow, N. Da, M. Peng, L. Wondraczek, and P. S. J. Russell, “All-solid bandgap guiding in tellurite-filled silica photonic crystal fibers,” Opt. Lett. 34(13), 1946–1948 (2009). [CrossRef] [PubMed]

] or the extrusion, drilling and stacking technique [16

16. X. Feng, F. Poletti, A. Camerlingo, F. Parmigiani, P. Petropoulos, P. Horak, G. M. Ponzo, M. N. Petrovich, W. H. Loh, and D. J. Richardson, “Dispersion controlled highly nonlinear fibers for all optical processing at telecoms wavelengths,” Opt Fiber Technol (invited and submitted, 2010).

]. The most suitable method will in general depend on the particular combination of glasses involved and whether or not a second cladding is required. In any case, in order to fabricate robust fibers, particular attention has to be devoted to the thermal, chemical and mechanical compatibility of all the glasses involved, a discussion of which is beyond the scope of this paper.

5. Fabricated dispersion flattened fiber with a W-type refractive index profile

In the past few years we have developed and perfected a fabrication technique for soft glass fibers based on extrusion and stacking, which has been successfully applied to the fabrication of all-solid fibers made of two different glasses [37

37. X. Feng, F. Poletti, A. Camerlingo, F. Parmigiani, P. Horak, P. Petropoulos, W. H. Loh, and D. J. Richardson, “Dispersion-shifted all-solid high index-contrast microstructured optical fiber for nonlinear applications at 1.55 microm,” Opt. Express 17(22), 20249–20255 (2009). [CrossRef] [PubMed]

,38

38. X. Feng, T. M. Monro, P. Petropoulos, V. Finazzi, and D. Hewak, “Solid microstructured optical fiber,” Opt. Express 11(18), 2225–2230 (2003). [CrossRef] [PubMed]

]. Using the same approach, we have also recently fabricated a W-index profiled dispersion flattened fiber for all-optical processing of telecoms data, following the design prescriptions of this work. A detailed discussion of its fabrication and characterization has already been presented [39

39. A. Camerlingo, X. Feng, F. Poletti, G. M. Ponzo, F. Parmigiani, P. Horak, M. N. Petrovich, P. Petropoulos, W. H. Loh, and D. J. Richardson, “Near-zero dispersion, highly nonlinear lead-silicate W-type fiber for applications at 1.55 microm,” Opt. Express 18(15), 15747–15756 (2010). [CrossRef] [PubMed]

]. Here we will expand on its design concept, showing how it straightforwardly follows from the design rules previously discussed, summarize its main properties and present an improved design.

Using a room temperature drill, polish and stacking technique for the two inner cylindrical regions of the fiber, and extrusion for the outer cladding, we obtained a cane with the desired d ocl/d ratio of 4.54. This ratio was exactly maintained when the cane was subsequently drawn down to fiber dimensions, and several bands with excellent longitudinal stability but slightly different outer diameters were obtained. The fiber shown in Fig. 6(c) has d = 1.63 μm and d ocl = 7.4 μm, which generate the flat and slightly normal dispersion profile shown in Fig. 6(d), measured with an interferometer using a supercontinuum source [39

39. A. Camerlingo, X. Feng, F. Poletti, G. M. Ponzo, F. Parmigiani, P. Horak, M. N. Petrovich, P. Petropoulos, W. H. Loh, and D. J. Richardson, “Near-zero dispersion, highly nonlinear lead-silicate W-type fiber for applications at 1.55 microm,” Opt. Express 18(15), 15747–15756 (2010). [CrossRef] [PubMed]

]. The effective area, nonlinear coefficient and propagation loss of the fiber were 1.9 μm2, 820 W−1km−1 and 2.1 dB/m, respectively. Note that this value of loss is close to the bulk loss of the core glass and is mostly due to a relatively high residual level of impurities in the commercial glass. Purer glasses are expected to exhibit 1-2 orders of magnitude lower losses, which would make these fibers even more appealing for nonlinear-based applications. Nonlinear absorption is negligible at telecoms wavelengths for lead silicate glasses. As expected, an effectively single mode behavior was observed even after transmission over just one meter of fiber [39

39. A. Camerlingo, X. Feng, F. Poletti, G. M. Ponzo, F. Parmigiani, P. Horak, M. N. Petrovich, P. Petropoulos, W. H. Loh, and D. J. Richardson, “Near-zero dispersion, highly nonlinear lead-silicate W-type fiber for applications at 1.55 microm,” Opt. Express 18(15), 15747–15756 (2010). [CrossRef] [PubMed]

]. Note that, as shown in Fig. 6(d), by using fiber with a marginally larger core (e.g. + 2%), slightly anomalous and flat dispersions is also achievable.

As already shown by a number of experiments, this fiber has extremely promising properties for all-optical processing applications [40

40. A. Camerlingo, F. Parmigiani, X. Feng, F. Poletti, P. Horak, W. H. Loh, D. J. Richardson, and P. Petropoulos, “Wavelength Conversion in a Short Length of a Solid Lead-Silicate Fiber,” IEEE Photon. Technol. Lett. 22(9), 628–630 (2010). [CrossRef]

,41

41. A. Camerlingo, F. Parmigiani, X. Feng, F. Poletti, P. Horak, W. Loh, D. Richardson, and P. Petropoulos, “Multichannel Wavelength Conversion of 40Gbit/s Non-Return-to-Zero DPSK Signals in a Lead Silicate Fibre,” IEEE Photon. Technol. Lett. 22(15), 1153–1155 (2010). [CrossRef]

]; its simple fabrication process and the accuracy achieved in the control of its structural and dispersive properties fully demonstrate the potential of the novel fiber concept proposed in this work.

Additional simulations indicate that by using glasses with even higher nonlinear refractive indices it should be possible to achieve a significant improvement in the total value of nonlinearity, while maintaining single modality and a similarly flat dispersion profile. For example, by using a bismuth oxide based glass (n = 2.02 at 1.55 μm [42

42. K. Kikuchi, K. Taira, and N. Sugimoto, “Highly nonlinear bismuth oxide-based glass fibres for all-optical signal processing,” Electron. Lett. 38(4), 166–167 (2002). [CrossRef]

]) surrounded by two concentric lead silicate claddings made of SF2 and SF57 (n = 1.62 and 1.80, respectively [20

20. Schott Optical glass catalogue 2009, available from http://www.schott.com.

]) with d = 1.37 μm and d ocl = 4d, a three times higher nonlinearity of γ = 2600 W−1km−1 could be achieved in a singlemode, dispersion flattened fiber. Such a fiber would represent a remarkable improvement over the nonlinear and dispersive properties of state-of-the-art highly nonlinear Bismuth fibers (γ~1200 W−1km−1 and D = −270 ps/nm/km) [26

26. T. Hasegawa, T. Nagashima, and N. Sugimoto, “Determination of nonlinear coefficient and group-velocity-dispersion of bismuth-based high nonlinear optical fiber by four-wave-mixing,” Opt. Commun. 281(4), 782–787 (2008). [CrossRef]

].

6. Further examples of dispersion tailored fiber designs

It is worth stressing that due to the particular choice of core glass not all the 4 designs in this example are of practical significance. The fiber for 2.5 μm operation, for example, would have limited scope due to the poor mid IR transmission of silicate-based glasses. In this case, non-silicate glasses with longer phonon absorption edge should be used, as shown later on. Moreover, the dispersion flattened fiber at λt = 1.05 μm would require a cladding with ncl ~1.32, typical of a liquid rather than a solid medium, suggesting that a SF57 micro-rod immersed in a liquid or, more practically, a liquid filled wagon wheel fiber [43

43. J. Y. Y. Leong, P. Petropoulos, J. H. V. Price, H. Ebendorff-Heidepriem, S. Asimakis, R. C. Moore, K. E. Frampton, V. Finazzi, X. Feng, T. M. Monro, and D. J. Richardson, “High-nonlinearity dispersion-shifted lead-silicate holey fibers for efficient 1μm pumped supercontinuum generation,” J. Lightwave Technol. 24(1), 183–190 (2006). [CrossRef]

], would produce the desired dispersion.

In Fig. 8
Fig. 8 Two examples of dispersion tailored fibers for supercontinuum generation. (a) tellurite fiber, d = 2.82 μm, nco = 1.994, ncl = 1.840 at λt = 2 μm. (b) silica fiber with a GLS core, d = 0.68 μm, nco = 2.395, ncl = 1.450 at λt = 1.05 μm
we provide two additional examples of dispersion controlled fiber designs obtained through the proposed method. Rather than dispersion flattened fibers, here we target fibers with dispersive profiles suitable for efficient and wide-bandwidth supercontinuum generation, where a ZDW must be positioned close to the pump wavelength and an anomalous dispersion region at longer wavelengths is beneficial to exploit soliton dynamics [5

5. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]

]. Figure 8(a) shows the calculated dispersion of a fiber for mid-IR supercontinuum generation from a 2 μm pump. The core material, a tellurite glass (TeO2 based, n = 1.994 at 2 μm [27

27. G. Ghosh, “Sellmeier Coefficients and Chromatic Dispersions for Some Tellurite Glasses,” J. Am. Ceram. Soc. 78(10), 2828–2830 (1995). [CrossRef]

], ), was chosen for its long infrared absorption edge; the target Dt was set to 0 ps/nm/km at λt = 2 μm, while DSt = 0.05 ps/nm2/km was optimized to provide an octave spanning region of flat dispersion. The optimum fiber, with |D| < 10 ps/nm/km between 1.8 and 4.5 μm, has d = 2.82 μm and an index difference Δn ~0.15 at 2 μm, which seems achievable through moderate compositional modifications of the core glass [27

27. G. Ghosh, “Sellmeier Coefficients and Chromatic Dispersions for Some Tellurite Glasses,” J. Am. Ceram. Soc. 78(10), 2828–2830 (1995). [CrossRef]

].

The fiber design in Fig. 8(b) provides an example of a fiber with a much more extreme index contrast. The design target was to position the shortest ZDW at 1.05 μm to favor efficient supercontinuum generation in the near IR from an Yb fiber laser pump. The results in Fig. 7 indicate that a significantly large index contrast would be required for a lead silicate dispersion flattened SIF operating at around 1 μm. Simulations also showed that even for bismuth and tellurite core glasses a cladding with a refractive index typical of a liquid or a highly porous solid would be needed. In order to obtain an all solid fiber design we then explored the use of core glasses with even higher refractive indices. For example, the dispersion profile in Fig. 8(b), was obtained by fixing silica (n = 1.450) as the cladding material and a target dispersion Dt = 0 ps/nm/km at λt = 1.05 μm. It was found that a gallium lanthanum sulphide (GLS) based core glass (n = 2.395 at 1.05 μm) would provide sufficient waveguide dispersion to achieve the target, and that by setting d = 0.68 μm and DS = 1.8 ps/nm2/km the second ZDW could be positioned at sufficiently long wavelengths, around 1.5 μm. Interestingly, the combination of such a high index contrast with a sub-μm core, would produce a calculated effective nonlinearity of 220000 W−1km−1, suggesting that only millimeter to centimeter lengths would be sufficient for its application in nonlinear devices. The resulting nonlinearity and dispersion profile are promising properties for efficient supercontinuum generation from a fs/ps fiber laser pump [5

5. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]

]. We believe that fabrication of such a fiber could be possible either through the direct drawing of a silica capillary filled with a chalcogenide glass core or by high pressure pumping of the molten soft glass inside a silica hollow fiber.

6. Discussion and conclusions

We have investigated a novel approach to modify the waveguide dispersion and hence control the overall dispersive properties of highly nonlinear fibers. Rather than exploiting holes in the cladding, whose size and shape along the transverse and longitudinal direction is difficult to control in practice with the required level of accuracy, we propose using all-solid fibers with a large and suitably selected index difference between core and cladding. This solution results in a much simpler control of the structural properties of the fabricated fiber, which simplifies the practical achievement of any targeted dispersion profile. The obvious drawback of this method, as compared to holey fiber technology, is that for each fiber design a pair of glasses with specific index contrasts and compatible thermo-mechanical properties is required. However, as we have shown through the example of a fabricated fiber and through reference to results in the literature, a number of fabrication techniques are already available and could be further developed to fabricate such high Δn multi-glass fibers.

Through numerical simulations we have studied the dispersive properties of simple step-index fibers and shown how the overall dispersion and dispersion slope can be well controlled by adjusting core diameter and index contrast. Based on a few empirical rules, we have presented a general design method to obtain highly nonlinear fibers with tailored dispersive properties at a specific wavelength of interest, and an algorithm for the automatic design of dispersion controlled fibers. A few examples of realistically achievable fibers for telecoms all-optical processing and for supercontinuum generation have been also presented.

We have shown that the position of the ZMDW with respect to the operational wavelength is key to determining the structural parameters, the nonlinearity and ultimately the fabrication method of these dispersion controlled fibers. For operation at wavelengths much shorter than the ZMDW, high index contrasts and small core diameters are needed, producing extremely high nonlinearities. Operation at wavelengths longer the ZMDW reduces the effective nonlinearity of the fibers, due to larger cores and smaller index contrasts, but offers a wider dispersion controlled bandwidth. It is worth noting that in this latter operational regime fibers tend to satisfy the relation (nco - ncl)/nco << 1 and therefore can be effectively considered as ‘weakly guiding’. As a results, their modes will be essentially linearly polarized (LP) and their properties can be predicted by using well known simplified methods [44

44. D. Gloge, “Dispersion in weakly guiding fibers,” Appl. Opt. 10(11), 2442–2445 (1971). [CrossRef] [PubMed]

,45

45. D. Gloge, “Weakly guiding fibers,” Appl. Opt. 10(10), 2252–2258 (1971). [CrossRef] [PubMed]

].

We have also studied the singlemode condition for simple high contrast step index fibers and shown that single modality cannot be obtained when the waveguide dispersion contribution is anomalous. In this case an additional outer cladding forming a W-shaped profile may introduce a sufficiently large differential mode loss to generate effectively singlemode guidance even at wavelengths where the step-index equivalent fiber would be moderately multimode.

In conclusion, we believe that due to their outstanding nonlinear properties, combined with their highly tailorable and easily achievable dispersive properties, the all-solid, high index contrast fibers proposed in this work may play an important role in many future nonlinear optics based devices, from optical parametric oscillators and amplifiers to supercontinuum sources and all optical processing components.

Acknowledgments

This research has received funding from the Engineering and Physics Science Research Council (UK) and the European Communities Seventh Framework Programme FP/2007-2013 under grant agreement 224547 (PHASORS). Dr Francesco Poletti gratefully acknowledges the support of a Royal Society University Fellowship. The authors would like to thank Angela Camerlingo and Dr. Periklis Petropoulos for measuring the properties of the fabricated lead silicate W-profiled fiber.

References and links

1.

G. P. Agrawal, Nonlinear fiber optics, 3rd ed. (Academic Press, San Diego, 2001).

2.

J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11(10), 662–664 (1986). [CrossRef] [PubMed]

3.

A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nat. Photonics 1(11), 653–657 (2007). [CrossRef]

4.

F. Poletti, P. Horak, and D. J. Richardson, “Soliton spectral tunneling in dispersion-controlled holey fibers,” IEEE Photon. Technol. Lett. 20(16), 1414–1416 (2008). [CrossRef]

5.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]

6.

J. M. Stone and J. C. Knight, “Visibly “white” light generation in uniform photonic crystal fiber using a microchip laser,” Opt. Express 16(4), 2670–2675 (2008). [CrossRef] [PubMed]

7.

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, M. Feng, and D. J. Richardson, “Mid-IR supercontinuum generation from nonsilica microstructured optical fibers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 738–749 (2007). [CrossRef]

8.

M. Takahashi, R. Sugizaki, J. Hiroishi, M. Tadakuma, Y. Taniguchi, and T. Yagi, “Low-loss and low-dispersion-slope highly nonlinear fibers,” J. Lightwave Technol. 23(11), 3615–3624 (2005). [CrossRef]

9.

J. C. Knight, T. A. Birks, P. S. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996). [CrossRef] [PubMed]

10.

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 Photon. Technol. Lett. 12(7), 807–809 (2000). [CrossRef]

11.

M. L. V. Tse, P. Horak, F. Poletti, N. G. R. Broderick, J. H. V. Price, J. R. Hayes, and D. J. Richardson, “Supercontinuum generation at 1.06 mum in holey fibers with dispersion flattened profiles,” Opt. Express 14(10), 4445–4451 (2006). [CrossRef] [PubMed]

12.

W. H. Reeves, J. C. Knight, P. S. J. Russell, and P. J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10(14), 609–613 (2002). [PubMed]

13.

K. Hansen, “Dispersion flattened hybrid-core nonlinear photonic crystal fiber,” Opt. Express 11(13), 1503–1509 (2003). [CrossRef] [PubMed]

14.

K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,” Opt. Express 11(8), 843–852 (2003). [CrossRef] [PubMed]

15.

F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, “Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers,” Opt. Express 13(10), 3728–3736 (2005). [CrossRef] [PubMed]

16.

X. Feng, F. Poletti, A. Camerlingo, F. Parmigiani, P. Petropoulos, P. Horak, G. M. Ponzo, M. N. Petrovich, W. H. Loh, and D. J. Richardson, “Dispersion controlled highly nonlinear fibers for all optical processing at telecoms wavelengths,” Opt Fiber Technol (invited and submitted, 2010).

17.

A. W. Snyder and X. H. Zheng, “Optical Fibers of Arbitrary Cross-Sections,” J. Opt. Soc. Am. A 3(5), 600–609 (1986). [CrossRef]

18.

A. W. Snyder, and J. D. Love, Optical waveguide theory (Chapman and Hall, London; New York, 1983).

19.

A. Ferrando, E. Silvestre, P. Andres, J. Miret, and M. Andres, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express 9(13), 687–697 (2001). [CrossRef] [PubMed]

20.

Schott Optical glass catalogue 2009, available from http://www.schott.com.

21.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

22.

T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Annu. Rev. Mater. Res. 36(1), 467–495 (2006). [CrossRef]

23.

S. H. Wemple, “Material dispersion in optical fibers,” Appl. Opt. 18(1), 31–35 (1979). [CrossRef] [PubMed]

24.

F. X. Gan, “Optical-Properties of Fluoride Glasses - a Review,” J. Non-Cryst. Solids 184, 9–20 (1995). [CrossRef]

25.

D. E. Zelmon, S. S. Bayya, J. S. Sanghera, and I. D. Aggarwal, “Dispersion of barium gallogermanate glass,” Appl. Opt. 41(7), 1366–1367 (2002). [CrossRef] [PubMed]

26.

T. Hasegawa, T. Nagashima, and N. Sugimoto, “Determination of nonlinear coefficient and group-velocity-dispersion of bismuth-based high nonlinear optical fiber by four-wave-mixing,” Opt. Commun. 281(4), 782–787 (2008). [CrossRef]

27.

G. Ghosh, “Sellmeier Coefficients and Chromatic Dispersions for Some Tellurite Glasses,” J. Am. Ceram. Soc. 78(10), 2828–2830 (1995). [CrossRef]

28.

T. Mito, S. Fujino, H. Takebe, K. Morinaga, S. Todoroki, and S. Sakaguchi, “Refractive index and material dispersions of multi-component oxide glasses,” J. Non-Cryst. Solids 210(2-3), 155–162 (1997). [CrossRef]

29.

W. S. Rodney, I. H. Malitson, and T. A. King, “Refractive index of Arsenic Trisulfide,” J. Opt. Soc. Am. 48(9), 633–636 (1958). [CrossRef]

30.

A. Mori, K. Kobayashi, M. Yamada, T. Kanamori, K. Oikawa, Y. Nishida, and Y. Ohishi, “Low noise broadband tellurite-based Er3+-doped fibre amplifiers,” Electron. Lett. 34(9), 887–888 (1998). [CrossRef]

31.

N. Sugimoto, T. Nagashima, T. Hasegawa, S. Ohara, K. Taira, and K. Kikuchi, “Bismuth-based optical fiber with nonlinear coefficient of 1360 W−1km−1,” Optical Fiber Communications Conference (OFC) 2004, PDP26.

32.

R. Mossadegh, J. S. Sanghera, D. Schaafsma, B. J. Cole, V. Q. Nguyen, P. E. Miklos, and I. D. Aggarwal, “Fabrication of single-mode chalcogenide optical fiber,” J. Lightwave Technol. 16(2), 214–217 (1998). [CrossRef]

33.

J. Ballato, T. Hawkins, P. Foy, R. Stolen, B. Kokuoz, M. Ellison, C. McMillen, J. Reppert, A. M. Rao, M. Daw, S. R. Sharma, R. Shori, O. Stafsudd, R. R. Rice, and D. R. Powers, “Silicon optical fiber,” Opt. Express 16(23), 18675–18683 (2008). [CrossRef]

34.

N. Healy, J. R. Sparks, M. N. Petrovich, P. J. A. Sazio, J. V. Badding, and A. C. Peacock, “Large mode area silicon microstructured fiber with robust dual mode guidance,” Opt. Express 17(20), 18076–18082 (2009). [CrossRef] [PubMed]

35.

A. S. Markus, G. Nicolai, W. Lothar, and R. Philip St, “Optical Properties of Chalcogenide-Filled Silica-Air PCF,” in Advances in Optical Materials, OSA Technical Digest (CD) (Optical Society of America, 2009), AThD3.

36.

M. A. Schmidt, N. Granzow, N. Da, M. Peng, L. Wondraczek, and P. S. J. Russell, “All-solid bandgap guiding in tellurite-filled silica photonic crystal fibers,” Opt. Lett. 34(13), 1946–1948 (2009). [CrossRef] [PubMed]

37.

X. Feng, F. Poletti, A. Camerlingo, F. Parmigiani, P. Horak, P. Petropoulos, W. H. Loh, and D. J. Richardson, “Dispersion-shifted all-solid high index-contrast microstructured optical fiber for nonlinear applications at 1.55 microm,” Opt. Express 17(22), 20249–20255 (2009). [CrossRef] [PubMed]

38.

X. Feng, T. M. Monro, P. Petropoulos, V. Finazzi, and D. Hewak, “Solid microstructured optical fiber,” Opt. Express 11(18), 2225–2230 (2003). [CrossRef] [PubMed]

39.

A. Camerlingo, X. Feng, F. Poletti, G. M. Ponzo, F. Parmigiani, P. Horak, M. N. Petrovich, P. Petropoulos, W. H. Loh, and D. J. Richardson, “Near-zero dispersion, highly nonlinear lead-silicate W-type fiber for applications at 1.55 microm,” Opt. Express 18(15), 15747–15756 (2010). [CrossRef] [PubMed]

40.

A. Camerlingo, F. Parmigiani, X. Feng, F. Poletti, P. Horak, W. H. Loh, D. J. Richardson, and P. Petropoulos, “Wavelength Conversion in a Short Length of a Solid Lead-Silicate Fiber,” IEEE Photon. Technol. Lett. 22(9), 628–630 (2010). [CrossRef]

41.

A. Camerlingo, F. Parmigiani, X. Feng, F. Poletti, P. Horak, W. Loh, D. Richardson, and P. Petropoulos, “Multichannel Wavelength Conversion of 40Gbit/s Non-Return-to-Zero DPSK Signals in a Lead Silicate Fibre,” IEEE Photon. Technol. Lett. 22(15), 1153–1155 (2010). [CrossRef]

42.

K. Kikuchi, K. Taira, and N. Sugimoto, “Highly nonlinear bismuth oxide-based glass fibres for all-optical signal processing,” Electron. Lett. 38(4), 166–167 (2002). [CrossRef]

43.

J. Y. Y. Leong, P. Petropoulos, J. H. V. Price, H. Ebendorff-Heidepriem, S. Asimakis, R. C. Moore, K. E. Frampton, V. Finazzi, X. Feng, T. M. Monro, and D. J. Richardson, “High-nonlinearity dispersion-shifted lead-silicate holey fibers for efficient 1μm pumped supercontinuum generation,” J. Lightwave Technol. 24(1), 183–190 (2006). [CrossRef]

44.

D. Gloge, “Dispersion in weakly guiding fibers,” Appl. Opt. 10(11), 2442–2445 (1971). [CrossRef] [PubMed]

45.

D. Gloge, “Weakly guiding fibers,” Appl. Opt. 10(10), 2252–2258 (1971). [CrossRef] [PubMed]

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:
Fiber Optics and Optical Communications

History
Original Manuscript: August 3, 2010
Revised Manuscript: October 25, 2010
Manuscript Accepted: October 27, 2010
Published: December 21, 2010

Citation
Francesco Poletti, Xian Feng, Giorgio M. Ponzo, Marco N. Petrovich, Wei H. Loh, and David J. Richardson, "All-solid highly nonlinear singlemode fibers with a tailored dispersion profile," Opt. Express 19, 66-80 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-1-66


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References

  1. G. P. Agrawal, Nonlinear fiber optics, 3rd ed. (Academic Press, San Diego, 2001).
  2. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11(10), 662–664 (1986). [CrossRef] [PubMed]
  3. A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nat. Photonics 1(11), 653–657 (2007). [CrossRef]
  4. F. Poletti, P. Horak, and D. J. Richardson, “Soliton spectral tunneling in dispersion-controlled holey fibers,” IEEE Photon. Technol. Lett. 20(16), 1414–1416 (2008). [CrossRef]
  5. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]
  6. J. M. Stone and J. C. Knight, “Visibly “white” light generation in uniform photonic crystal fiber using a microchip laser,” Opt. Express 16(4), 2670–2675 (2008). [CrossRef] [PubMed]
  7. J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, M. Feng, and D. J. Richardson, “Mid-IR supercontinuum generation from nonsilica microstructured optical fibers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 738–749 (2007). [CrossRef]
  8. M. Takahashi, R. Sugizaki, J. Hiroishi, M. Tadakuma, Y. Taniguchi, and T. Yagi, “Low-loss and low-dispersion-slope highly nonlinear fibers,” J. Lightwave Technol. 23(11), 3615–3624 (2005). [CrossRef]
  9. J. C. Knight, T. A. Birks, P. S. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996). [CrossRef] [PubMed]
  10. 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 Photon. Technol. Lett. 12(7), 807–809 (2000). [CrossRef]
  11. M. L. V. Tse, P. Horak, F. Poletti, N. G. R. Broderick, J. H. V. Price, J. R. Hayes, and D. J. Richardson, “Supercontinuum generation at 1.06 mum in holey fibers with dispersion flattened profiles,” Opt. Express 14(10), 4445–4451 (2006). [CrossRef] [PubMed]
  12. W. H. Reeves, J. C. Knight, P. S. J. Russell, and P. J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10(14), 609–613 (2002). [PubMed]
  13. K. Hansen, “Dispersion flattened hybrid-core nonlinear photonic crystal fiber,” Opt. Express 11(13), 1503–1509 (2003). [CrossRef] [PubMed]
  14. K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,” Opt. Express 11(8), 843–852 (2003). [CrossRef] [PubMed]
  15. F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, “Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers,” Opt. Express 13(10), 3728–3736 (2005). [CrossRef] [PubMed]
  16. X. Feng, F. Poletti, A. Camerlingo, F. Parmigiani, P. Petropoulos, P. Horak, G. M. Ponzo, M. N. Petrovich, W. H. Loh, and D. J. Richardson, “Dispersion controlled highly nonlinear fibers for all optical processing at telecoms wavelengths,” Opt Fiber Technol (invited and submitted, 2010).
  17. A. W. Snyder and X. H. Zheng, “Optical Fibers of Arbitrary Cross-Sections,” J. Opt. Soc. Am. A 3(5), 600–609 (1986). [CrossRef]
  18. A. W. Snyder, and J. D. Love, Optical waveguide theory (Chapman and Hall, London; New York, 1983).
  19. A. Ferrando, E. Silvestre, P. Andres, J. Miret, and M. Andres, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express 9(13), 687–697 (2001). [CrossRef] [PubMed]
  20. Schott Optical glass catalogue 2009, available from http://www.schott.com .
  21. J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
  22. T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Annu. Rev. Mater. Res. 36(1), 467–495 (2006). [CrossRef]
  23. S. H. Wemple, “Material dispersion in optical fibers,” Appl. Opt. 18(1), 31–35 (1979). [CrossRef] [PubMed]
  24. F. X. Gan, “Optical-Properties of Fluoride Glasses - a Review,” J. Non-Cryst. Solids 184, 9–20 (1995). [CrossRef]
  25. D. E. Zelmon, S. S. Bayya, J. S. Sanghera, and I. D. Aggarwal, “Dispersion of barium gallogermanate glass,” Appl. Opt. 41(7), 1366–1367 (2002). [CrossRef] [PubMed]
  26. T. Hasegawa, T. Nagashima, and N. Sugimoto, “Determination of nonlinear coefficient and group-velocity-dispersion of bismuth-based high nonlinear optical fiber by four-wave-mixing,” Opt. Commun. 281(4), 782–787 (2008). [CrossRef]
  27. G. Ghosh, “Sellmeier Coefficients and Chromatic Dispersions for Some Tellurite Glasses,” J. Am. Ceram. Soc. 78(10), 2828–2830 (1995). [CrossRef]
  28. T. Mito, S. Fujino, H. Takebe, K. Morinaga, S. Todoroki, and S. Sakaguchi, “Refractive index and material dispersions of multi-component oxide glasses,” J. Non-Cryst. Solids 210(2-3), 155–162 (1997). [CrossRef]
  29. W. S. Rodney, I. H. Malitson, and T. A. King, “Refractive index of Arsenic Trisulfide,” J. Opt. Soc. Am. 48(9), 633–636 (1958). [CrossRef]
  30. A. Mori, K. Kobayashi, M. Yamada, T. Kanamori, K. Oikawa, Y. Nishida, and Y. Ohishi, “Low noise broadband tellurite-based Er3+-doped fibre amplifiers,” Electron. Lett. 34(9), 887–888 (1998). [CrossRef]
  31. N. Sugimoto, T. Nagashima, T. Hasegawa, S. Ohara, K. Taira, and K. Kikuchi, “Bismuth-based optical fiber with nonlinear coefficient of 1360 W−1km−1,” Optical Fiber Communications Conference (OFC) 2004, PDP26.
  32. R. Mossadegh, J. S. Sanghera, D. Schaafsma, B. J. Cole, V. Q. Nguyen, P. E. Miklos, and I. D. Aggarwal, “Fabrication of single-mode chalcogenide optical fiber,” J. Lightwave Technol. 16(2), 214–217 (1998). [CrossRef]
  33. J. Ballato, T. Hawkins, P. Foy, R. Stolen, B. Kokuoz, M. Ellison, C. McMillen, J. Reppert, A. M. Rao, M. Daw, S. R. Sharma, R. Shori, O. Stafsudd, R. R. Rice, and D. R. Powers, “Silicon optical fiber,” Opt. Express 16(23), 18675–18683 (2008). [CrossRef]
  34. N. Healy, J. R. Sparks, M. N. Petrovich, P. J. A. Sazio, J. V. Badding, and A. C. Peacock, “Large mode area silicon microstructured fiber with robust dual mode guidance,” Opt. Express 17(20), 18076–18082 (2009). [CrossRef] [PubMed]
  35. A. S. Markus, G. Nicolai, W. Lothar, and R. Philip St, “Optical Properties of Chalcogenide-Filled Silica-Air PCF,” in Advances in Optical Materials, OSA Technical Digest (CD) (Optical Society of America, 2009), AThD3.
  36. M. A. Schmidt, N. Granzow, N. Da, M. Peng, L. Wondraczek, and P. S. J. Russell, “All-solid bandgap guiding in tellurite-filled silica photonic crystal fibers,” Opt. Lett. 34(13), 1946–1948 (2009). [CrossRef] [PubMed]
  37. X. Feng, F. Poletti, A. Camerlingo, F. Parmigiani, P. Horak, P. Petropoulos, W. H. Loh, and D. J. Richardson, “Dispersion-shifted all-solid high index-contrast microstructured optical fiber for nonlinear applications at 1.55 microm,” Opt. Express 17(22), 20249–20255 (2009). [CrossRef] [PubMed]
  38. X. Feng, T. M. Monro, P. Petropoulos, V. Finazzi, and D. Hewak, “Solid microstructured optical fiber,” Opt. Express 11(18), 2225–2230 (2003). [CrossRef] [PubMed]
  39. A. Camerlingo, X. Feng, F. Poletti, G. M. Ponzo, F. Parmigiani, P. Horak, M. N. Petrovich, P. Petropoulos, W. H. Loh, and D. J. Richardson, “Near-zero dispersion, highly nonlinear lead-silicate W-type fiber for applications at 1.55 microm,” Opt. Express 18(15), 15747–15756 (2010). [CrossRef] [PubMed]
  40. A. Camerlingo, F. Parmigiani, X. Feng, F. Poletti, P. Horak, W. H. Loh, D. J. Richardson, and P. Petropoulos, “Wavelength Conversion in a Short Length of a Solid Lead-Silicate Fiber,” IEEE Photon. Technol. Lett. 22(9), 628–630 (2010). [CrossRef]
  41. A. Camerlingo, F. Parmigiani, X. Feng, F. Poletti, P. Horak, W. Loh, D. Richardson, and P. Petropoulos, “Multichannel Wavelength Conversion of 40Gbit/s Non-Return-to-Zero DPSK Signals in a Lead Silicate Fibre,” IEEE Photon. Technol. Lett. 22(15), 1153–1155 (2010). [CrossRef]
  42. K. Kikuchi, K. Taira, and N. Sugimoto, “Highly nonlinear bismuth oxide-based glass fibres for all-optical signal processing,” Electron. Lett. 38(4), 166–167 (2002). [CrossRef]
  43. J. Y. Y. Leong, P. Petropoulos, J. H. V. Price, H. Ebendorff-Heidepriem, S. Asimakis, R. C. Moore, K. E. Frampton, V. Finazzi, X. Feng, T. M. Monro, and D. J. Richardson, “High-nonlinearity dispersion-shifted lead-silicate holey fibers for efficient 1μm pumped supercontinuum generation,” J. Lightwave Technol. 24(1), 183–190 (2006). [CrossRef]
  44. D. Gloge, “Dispersion in weakly guiding fibers,” Appl. Opt. 10(11), 2442–2445 (1971). [CrossRef] [PubMed]
  45. D. Gloge, “Weakly guiding fibers,” Appl. Opt. 10(10), 2252–2258 (1971). [CrossRef] [PubMed]

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