## All-solid highly nonlinear singlemode fibers with a tailored dispersion profile |

Optics Express, Vol. 19, Issue 1, pp. 66-80 (2011)

http://dx.doi.org/10.1364/OE.19.000066

Acrobat PDF (2505 KB)

### 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

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]

_{w}) to counterbalance the intrinsic material dispersion of the optical glass (D

_{m}). 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]

_{co}) and cladding (n

_{cl}) refractive indices achievable through doping is typically low (

*Δn*

_{max}= n

_{co}– n

_{cl}~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

^{−1}km

^{−1}.

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]

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. 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]

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]

*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.

## 2. Dispersion of circularly symmetric, high index contrast SIFs

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]

_{eff}(λ), D

_{w}(λ) and D(λ) on the structural parameters

*d*and

*Δn*. The left column in Fig. 1 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 (n

_{co}= 1.80, n

_{cl}= 1.52 and

*d*= 1.7 μm), the general conclusions drawn from Fig. 1 are valid for any other set of parameters.

_{eff}tends to n

_{co}for vanishingly small wavelengths (λ <<

*d*), and to n

_{cl}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, D

_{w}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*(DS

_{w}) 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 D

_{w}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]

*d*or

*Δn*will have on the

*total*dispersion, it is instructive to overimpose the

*material*dispersion curve, taken with a negative sign (-D

_{m}), to the D

_{w}curves previously calculated. In the example in Figs. 1(c) and 1(d), the material dispersion of the core glass (SF57, a commercially available lead silicate, n = 1.80 at 1.55 μm [20

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

_{w}and –D

_{m}intersect correspond to ZDWs in the total profile; at those wavelengths where D

_{w}> -D

_{m}the total dispersion is anomalous, while elsewhere it is normal, as shown in Figs. 1(e) and 1(f). From the previous empirical observations on the dependence of D

_{w}and DS

_{w}on the structural parameters of a SIF it is now straightforward to derive a simple recipe to design fibers with a desired value of waveguide dispersion

*and*waveguide dispersion slope at a given wavelength: first (i) for a given core glass and an arbitrary initial choice of cladding refractive index the fiber diameter is tuned to generate the desired total dispersion slope; then (ii)

*Δn*is adjusted to match the required absolute dispersion, with little influence on the slope determined in (i).

_{co}of each fiber design, indicating that at wavelengths shorter than the marker the fibers do support multiple modes. Figures 1(a) and 1(b) show that the single mode condition approximately occurs for n

_{eff}~(n

_{co}+ n

_{cl})/2. Most importantly though, Figs. 1(c) and 1(d) show that fibers are always multimoded when their waveguide dispersion contribution is anomalous, which we verified numerically also for a broad range of other SIF designs. This means that whenever a SIF presents a ZDW at wavelengths shorter than the zero

*material*dispersion wavelength (ZMDW), which is only possible through some anomalous waveguide dispersion contribution, the fiber will certainly be multimoded at that wavelength, Figs. 1(e) and 1(f). Therefore, simple SIFs with low absolute value of dispersion at wavelengths shorter than the ZMDW cannot be strictly single moded, which may prevent their use in applications such as all optical signal processing of telecoms data or supercontinuum-generation. As we will show in more detail through the example of a fabricated fiber in Section 5, a simple and effective way to restore effectively single mode guidance without perturbing the dispersive properties of a SIF is to introduce a second outer cladding with a refractive index n

_{ocl}between n

_{co}and n

_{cl}, thereby generating a W-shaped refractive index profile. Since high order modes (HOMs) have a larger fraction of the electromagnetic field in the cladding as compared to the fundamental mode (FM) [18], see also Fig. 6(a) , by carefully optimizing n

_{ocl}and the diameter of the outer cladding region

*d*

_{ocl}, a high leakage loss can be introduced for all HOMs, while leaving the loss and dispersive properties of the FM almost unperturbed.

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]

_{eff}= n

_{eff}(

*d*/λ, n

_{co}, n

_{cl}). Therefore for any real scaling factor M ≠ 0 we can obtain a

*scaling rule*for the waveguide dispersion:

*d*, n

_{co}and n

_{cl}, it is possible to obtain D

_{w}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

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]

- 1. Choose the wavelength of operation λ
_{t}and a high refractive index glass to be used in the core. This will determine a value of core index n_{co}(λ_{t}) which will not change throughout the procedure, making each SIF design dependent only on diameter and index difference, {*d*,*Δn*(λ_{t})}. 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 λ_{t}. - 2. Select a target value of dispersion D
_{t}and dispersion slope DS_{t}at λ_{t}, from which the target*waveguide*dispersion D_{wt}= D_{t}- D_{m}and*waveguide*dispersion slope DS_{wt}= DS_{t}- DS_{m}can be obtained. Choose a desired accuracy on the values of dispersion (ε_{D}) and dispersion slope (ε_{DS}). - 3. Choose initial guess values of fiber diameter and index difference {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.
*d*^{(0)},*Δn*^{(0)}}, which will also obviously determine n_{cl}^{(0)}= n_{co}^{(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 ). Calculate the waveguide dispersion curve of this initial fiber through Eq. (1) and evaluate D_{w}^{(0)}and DS_{w}^{(0)}at λ_{t}. 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 D_{w}over a broad enough wavelength range around λ_{t}is required. - 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 DS_{err}^{(1)}= |DS_{w}^{(1)}– DS_{wt}| < ε_{DS}. The structure {*d*^{(1)},*Δn*^{(0)}} will have a dispersion slope at λ_{t}well matched to the target one, but some residual error in the absolute value of waveguide dispersion, D_{err}^{(1)}= |D_{wt}– D_{w}^{(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, DS_{err}^{(2)}= |DS_{w}^{(2)}– DS_{wt}| < ε_{DS}. Estimate D_{err}^{(2)}= |D_{wt}– D_{w}^{(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, D_{err}^{(n + 1)}< ε_{D}and DS_{err}^{(n + 1)}< ε_{DS}.

_{t}= 0 ps/nm/km and DS

_{t}= 0 ps/nm

^{2}/km at λ

_{t}= 1.55 μm. ε

_{D}and ε

_{DS}are set to 0.01 ps/nm/km and 10

^{−6}ps/nm

^{2}/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.

_{t}= 0 ps/nm/km could be restored, for example, by reducing the core diameter by just ~1%. The blue curve, finally, shows the effect of considering the wavelength dependence of a real cladding. Here we have chosen another lead silicate glass, LLF1 [20

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

*Δn*= 0.273 at 1.55 μm, not too distant from the theoretical design requirement of

*Δn*= 0.255. By slightly reducing the core diameter to 1.68 μm in order to compensate for the higher

*Δn*, a curve close to the design target (but with a small, nonzero dispersion slope at 1.55 μm) is once again achieved, demonstrating that (i) the approximations introduced are sensible, (ii) the design procedure discussed in the previous section provides an excellent first approximate solution for the design of a real fiber and (iii) a final simulation including the material dispersion of all glasses is probably needed in the end to fine tune the target dimensions.

## 4. Choice of core and cladding glasses

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

*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 D

_{w}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.

*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]

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]

*Δn*required may or may not be achievable through glasses of the same family. The fabricated lead silicate fiber presented in the next section is an example of a high

*Δn*fiber (

*Δn*= 0.27) achieved with glasses of the same family, while several reported examples of fibers with a silica clad and a semiconductor core (either amorphous, crystalline or polycrystalline) clearly demonstrate that widely different optical materials with a high

*Δn*can coexist in the same fiber [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]

*d*

_{ocl}can be used as an additional free parameter to tailor the differential mode loss (see Section 5).

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]

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]

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

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]

^{2}/km) with an absolute value of dispersion below 5 ps/nm/km for all-optical wavelength conversion and regeneration in the 1.55 μm wavelength region. The commercially available glass Schott SF57 was chosen as a core material due to its relatively high linear and nonlinear refractive indices and good thermal stability. As shown in Fig. 1, modeling indicated that the dispersion targets would be met by a fiber with approximately

*d*= 1.7 μm and

*Δn*= 0.27. After a search for a compatible and commercially available glass presenting an index contrast close to this target, we decided to employ in the cladding another lead silicate, LLF1, providing

*Δn*= 0.273 at 1.55 μm. Since SF57 has a ZMDW at around 2 μm, such a SIF would be multimoded at telecoms wavelengths (see Section 2). Therefore, we performed finite element method simulations of various W-type fibers to select a glass for the outer cladding and optimize its diameter to generate a significantly high confinement loss for the LP

_{11}mode (e.g. > 50 dB/m) without affecting the loss and dispersion of the LP

_{01}mode. We observed that with a careful choice of the outer cladding diameter several glasses could be used for this task. For fabrication compatibility we finally opted for a third glass of the same lead silicate family, SF6 (n = 1.76 at 1.55 μm). As shown in Fig. 6(b), the choice of a

*d*

_{ocl}/

*d*ratio around 4.5 produces a differential mode loss of more than three orders of magnitude, sufficient to create effectively singlemode guidance without altering the dispersive properties of the fundamental mode of the inner step-index waveguide.

*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]

^{2}, 820 W

^{−1}km

^{−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]

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]

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

*d*= 1.37 μm and

*d*

_{ocl}= 4

*d*, a three times higher nonlinearity of γ = 2600 W

^{−1}km

^{−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

^{−1}km

^{−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

*nonlinearity*of these dispersion controlled fibers. From the scaling rule in Eq. (4) one would expect it also to affect the

*bandwidth*of the dispersion controlled region, with narrower bandwidths achievable at shorter wavelengths. To confirm this prediction, in Fig. 7 we present four different fiber designs obtained with the previously discussed algorithm. In this example the core glass is, once again, SF57. The dispersion targets were set as D

_{t}= 3 ps/nm/km and DS

_{t}= 0 ps/nm

^{2}/km at λ

_{t}= 1.05, 1.55, 2 and 2.5 μm, respectively. The optimum values for

*d*and

*Δn*for all fibers are reported in the figure and confirm the expected trend of larger diameters and smaller index contrasts required as the wavelength of interest λ

_{t}is increased. These simulations show the flexibility of the proposed method in tailoring the overall dispersion. They also illustrate how the spectral width of the flat dispersion region increases with λ

_{t}, as a result of the fact that shorter wavelengths require higher values of D

_{w}, hence a smaller

*d*, resulting in a narrower spectral region of anomalous waveguide dispersion, see Eq. (4). At wavelengths close to or longer than the ZMDW it is possible to engineer D

_{w}to match the absolute value and slope of D

_{m}over very broad bandwidths, in some cases exceeding a full octave, allowing flat and ultrawide bandwidth dispersion designs. Demonstrations of this concept have already been provided, for example, by various silica HFs [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]

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]

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]

_{t}= 1.05 μm would require a cladding with n

_{cl}~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]

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

_{2}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]

_{t}was set to 0 ps/nm/km at λ

_{t}= 2 μm, while DS

_{t}= 0.05 ps/nm

^{2}/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]

_{t}= 0 ps/nm/km at λ

_{t}= 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/nm

^{2}/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

^{−1}km

^{−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]

## 6. Discussion and conclusions

*Δn*multi-glass fibers.

_{co}- n

_{cl})/n

_{co}<< 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. D. Gloge, “Weakly guiding fibers,” Appl. Opt. **10**(10), 2252–2258 (1971). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | G. P. Agrawal, |

2. | J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. |

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 |

4. | F. Poletti, P. Horak, and D. J. Richardson, “Soliton spectral tunneling in dispersion-controlled holey fibers,” IEEE Photon. Technol. Lett. |

5. | J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. |

6. | J. M. Stone and J. C. Knight, “Visibly “white” light generation in uniform photonic crystal fiber using a microchip laser,” Opt. Express |

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. |

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. |

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. |

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. |

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 |

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 |

13. | K. Hansen, “Dispersion flattened hybrid-core nonlinear photonic crystal fiber,” Opt. Express |

14. | K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,” Opt. Express |

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 |

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 |

18. | A. W. Snyder, and J. D. Love, |

19. | A. Ferrando, E. Silvestre, P. Andres, J. Miret, and M. Andres, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express |

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. |

22. | T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Annu. Rev. Mater. Res. |

23. | S. H. Wemple, “Material dispersion in optical fibers,” Appl. Opt. |

24. | F. X. Gan, “Optical-Properties of Fluoride Glasses - a Review,” J. Non-Cryst. Solids |

25. | D. E. Zelmon, S. S. Bayya, J. S. Sanghera, and I. D. Aggarwal, “Dispersion of barium gallogermanate glass,” Appl. Opt. |

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. |

27. | G. Ghosh, “Sellmeier Coefficients and Chromatic Dispersions for Some Tellurite Glasses,” J. Am. Ceram. Soc. |

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 |

29. | W. S. Rodney, I. H. Malitson, and T. A. King, “Refractive index of Arsenic Trisulfide,” J. Opt. Soc. Am. |

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. |

31. | N. Sugimoto, T. Nagashima, T. Hasegawa, S. Ohara, K. Taira, and K. Kikuchi, “Bismuth-based optical fiber with nonlinear coefficient of 1360 W |

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. |

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 |

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 |

35. | A. S. Markus, G. Nicolai, W. Lothar, and R. Philip St, “Optical Properties of Chalcogenide-Filled Silica-Air PCF,” in |

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. |

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 |

38. | X. Feng, T. M. Monro, P. Petropoulos, V. Finazzi, and D. Hewak, “Solid microstructured optical fiber,” Opt. Express |

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 |

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. |

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. |

42. | K. Kikuchi, K. Taira, and N. Sugimoto, “Highly nonlinear bismuth oxide-based glass fibres for all-optical signal processing,” Electron. Lett. |

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. |

44. | D. Gloge, “Dispersion in weakly guiding fibers,” Appl. Opt. |

45. | D. Gloge, “Weakly guiding fibers,” Appl. Opt. |

**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

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- J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11(10), 662–664 (1986). [CrossRef] [PubMed]
- 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]
- 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]
- J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- K. Hansen, “Dispersion flattened hybrid-core nonlinear photonic crystal fiber,” Opt. Express 11(13), 1503–1509 (2003). [CrossRef] [PubMed]
- 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]
- 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]
- 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).
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- T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Annu. Rev. Mater. Res. 36(1), 467–495 (2006). [CrossRef]
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- F. X. Gan, “Optical-Properties of Fluoride Glasses - a Review,” J. Non-Cryst. Solids 184, 9–20 (1995). [CrossRef]
- 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]
- 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]
- G. Ghosh, “Sellmeier Coefficients and Chromatic Dispersions for Some Tellurite Glasses,” J. Am. Ceram. Soc. 78(10), 2828–2830 (1995). [CrossRef]
- 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]
- 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]
- 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]
- 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.
- 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]
- 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]
- 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]
- 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.
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- D. Gloge, “Dispersion in weakly guiding fibers,” Appl. Opt. 10(11), 2442–2445 (1971). [CrossRef] [PubMed]
- D. Gloge, “Weakly guiding fibers,” Appl. Opt. 10(10), 2252–2258 (1971). [CrossRef] [PubMed]

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