## Chalcogenide microporous fibers for linear and nonlinear applications in the mid-infrared

Optics Express, Vol. 18, Issue 8, pp. 8647-8659 (2010)

http://dx.doi.org/10.1364/OE.18.008647

Acrobat PDF (1141 KB)

### Abstract

A new type of microstructured fiber for mid-infrared light is introduced. The chalcogenide glass-based microporous fiber allows extensive dispersion engineering that enables design of flattened waveguide dispersion windows and multiple zero-dispersion points – either blue-shifted or red-shifted from the bulk material zero-dispersion point – including the spectral region of CO_{2} laser lines ∼10.6 μm. Supercontinuum simulations for a specific chalcogenide microporous fiber are performed that demonstrate the potential of the proposed microstructured fiber design to generate a broad continuum in the middle-infrared region using pulsed CO_{2} laser as a pump. In addition, an analytical description of the Raman response function of chalcogenide As_{2}Se_{3} is provided, and a Raman time constant of 5.4 fs at the 1.54 μm pump is computed. What distinguishes the microporous fiber from the microwire, nanowire and other small solid-core designs is the prospect of extensive chromatic dispersion engineering combined with the low loss guidance created by the porosity, thus offering long interaction lengths in nonlinear media.

© 2010 OSA

## 1. Introduction

1. P. Domachuk, N. A. Wolchover, M. Cronin-Golomb, A. Wang, A. K. George, C. M. B. Cordeiro, J. C. Knight, and F. G. Omenetto, “Over 4000 nm bandwidth of mid-IR supercontinuum generation in sub-centimeter segments of highly nonlinear tellurite PCFs,” Opt. Express **16**(10), 7161–7168 (2008). [CrossRef] [PubMed]

2. 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, X. 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]

_{2}Se

_{3}step-index fiber and photonic crystal fiber (PCF) seeded at 2.5 μm with a 0.1 nJ, 100 fs at 1 kHz pulsed laser have reported a SC output extending from 2.1 to 3.2 μm [3,4]. While small solid core fibers greatly enhance the achievable optical nonlinearities, they generally offer limited freedom for engineering the group velocity’s chromatic dispersion (GVD). Typically in small-core fibers, the strong waveguide dispersion enables one to blue-shift the first zero dispersion point (ZDP) – with respect to the material zero dispersion wavelength (ZDM) of compound glasses – in the near-infrared range (1.0 – 2.5 μm) where several laser sources are conveniently available for pumping. The latter scheme was adopted in [2

2. 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, X. 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]

_{2}lasers (9.3 – 10.6 μm). We then show with numerical simulations the potential of seeding at these large wavelengths for opening a SC window inside the 5-12 μm region that has mostly remained out of reach so far.

## 2. Geometry and linear properties of microporous fibers

5. A. Hassani, A. Dupuis, and M. Skorobogatiy, “Low loss porous terahertz fibers containing multiple subwavelength holes,” Appl. Phys. Lett. **92**(7), 071101 (2008). [CrossRef]

5. A. Hassani, A. Dupuis, and M. Skorobogatiy, “Low loss porous terahertz fibers containing multiple subwavelength holes,” Appl. Phys. Lett. **92**(7), 071101 (2008). [CrossRef]

6. A. Hassani, A. Dupuis, and M. Skorobogatiy, “Porous polymer fibers for low-loss Terahertz guiding,” Opt. Express **16**(9), 6340–6351 (2008). [CrossRef] [PubMed]

8. A. Dupuis, J.-F. Allard, D. Morris, K. Stoeffler, C. Dubois, and M. Skorobogatiy, “Fabrication and THz loss measurements of porous subwavelength fibers using a directional coupler method,” Opt. Express **17**(10), 8012–8028 (2009). [CrossRef] [PubMed]

7. S. Atakaramians, S. Afshar V, B. M. Fischer, D. Abbott, and T. M. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express **16**(12), 8845–8854 (2008). [CrossRef] [PubMed]

9. S. Atakaramians, S. Afshar V, H. Ebendorff-Heidepriem, M. Nagel, B. M. Fischer, D. Abbott, and T. M. Monro, “THz porous fibers: design, fabrication and experimental characterization,” Opt. Express **17**(16), 14053–14063 (2009). [CrossRef] [PubMed]

*A*) compared to an equivalent rod-in-air fiber. This property of porous core fibers warrants an investigation of their nonlinear properties in highly-nonlinear chalcogenide glasses for mid-IR applications such as supercontinuum generation where tight field confinement and low losses are generally desirable for enhancing the nonlinear processes. Moreover, one expects that porosity introduces an additional design parameter that can be used to manipulate the fiber dispersion properties to the benefit of the fiber’s non-linear response.

_{eff}_{2}Se

_{3}) chalcogenide glass is chosen here as the dielectric material because of its wide bulk transparency (2 – 14 μm), high refractive index and large nonlinearity in the mid-IR spectrum. Although As

_{2}Se

_{3}exhibits relative large losses (∼5 dB/m) at 10.6 μm after fiberization [10

10. CorActive High-Tech Infrared Fibers, “Mid-Infrared Transmission Optical Fiber,” (CorActive High-Tech Inc., 2009). http://www.coractive.com/an/pdf/irtgeneral.pdf

_{2}lasers [11

11. B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO_{2} laser transmission,” Nature **420**(6916), 650–653 (2002). [CrossRef] [PubMed]

*N*layers of subwavelength holes of diameter

*d*in a triangular lattice of pitch Λ (also of subwavelength dimension:

*N*= 4 layers of subwavelength holes. Still, the results and discussion presented thereafter provide a key direction for scaling to larger (

*N*>4) microporous fibers. We emphasize that strict periodicity is not required for this waveguide operation since it is the overall average refractive index of the porous core that guides light via total internal reflection; not the photonic bandgap effect.

_{2}Se

_{3}glass is modeled (in Fig. 2 ) via the following Sellmeier equation [12

12. Amorphous Materials, “AMTIR-2: Arsenic Selenide Glass As–Se,” (Amorphous Materials Inc., 2009). http://www.amorphousmaterials.com/amtir2.htm

*A*

_{0}= 2.234921,

*A*

_{1}= 0.24164,

*A*

_{2}= 0.347441,

*A*

_{3}= 1.308575, and

*λ*is expressed in microns. The corresponding material zero-dispersion wavelength (ZDM) of As

_{2}Se

_{3}is 7.225μm. The wavelength-dependant absorption coefficient

*k*(cm

^{−1}) was provided at discrete wavelengths and cubic spline interpolation was used to estimate values at intermediate wavelengths of interest (dotted blue curve in Fig. 2).

*N*= 4, the fundamental mode effective refractive index (

*n*) and field distributions (

_{eff}*E*,

_{x}*E*,

_{y}*E*,

_{z}*S*) were computed through 2nd-order accurate fully-vectorial finite-element calculations with terminating PML layers. Scanning of geometrical parameters (Λ = 0.20, 0.25, 0.30, ..., 1.0μm;

_{z}*d*= 0.12, 0.14, 0.16, ..., 0.90μm) was performed for a broad range of input wavelengths (

*λ*= 3.0, 3.5, 4.0, ..., 16.0 μm) so as to evaluate the GVD in the vicinity of the principal wavelength of interest: 10.5 μm. Post-processing routines include: hundredfold increase in data density for

*n*(

_{eff}*λ*) via cubic spline interpolation, then fitting the interpolated

*n*(

_{eff}*λ*) curve with a polynomial of degree 11, and evaluating the GVD (ps/km∙nm) with the equation

*p*of a given fiber, or in other words the areal density of the cross-section occupied by holes, is:where the full diameter

*N*. It follows that the fraction of cross-sectional area occupied by solid glass material is given by

*N*= 4, of solid material still remains in the core even when

*d*= Λ due to the material-filled interstices between the holes, and the six core-cladding interspaces located at the

*f*) of modal absorption to bulk material absorption loss can be evaluated to first-order approximation via the expression [13]:where

_{α}*z*. The value of

*f*as a function of geometrical parameters (Λ,

_{α}*d*) is shown in a density plot [Fig. 3(b) ] alongside that of

*f*[Fig. 3(a)]. We note that

_{m}*n*

_{mat}= 2.7678 and

*α*

_{mat}= 1.4 m

^{−1}(or 4.81 dB/m) for As

_{2}Se

_{3}at λ = 10.5 μm. Figure 3(b) shows that modal absorption in a porous fiber can be lowered by half the initial bulk absorption value for a diameter-to-pitch ratio

*f*) has a strong correlation with the cross-section areal density of material (

_{α}*f*) in the core. In other words, lower confinement losses are achieved in designs with large porosity.

_{m}*n*is plotted in Fig. 4(a) and again illustrates the close relationship with the fraction

_{eff}*f*of modal field in the solid material pictured in Fig. 3(b). The effective mode area

_{α}*A*defined as [14

_{eff}14. S. Afshar V and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express **17**(4), 2298–2318 (2009). [CrossRef] [PubMed]

*d*parameter space where minimum optimization of

*A*can be achieved. In the present case, minimization of

_{eff}*A*at λ = 10.5 μm is obtained for Λ = 0.40 μm and

_{eff}*d*→0 (i.e. the limit of the air-suspended core).

*D*and dispersion slope

*d*) in Fig. 5(a) and Fig. 5(b) respectively. In these plots we can identify several regions of low and flattened dispersion for λ = 10.5 μm. Two such examples of low dispersion engineering in microporous fibers occur at (Λ = 0.5,

*d*= 0.38)μm and (Λ = 0.7,

*d*= 0.62)μm, for which the detailed dispersion curves are respectively shown on Fig. 6(a) and Fig. 6(b). In both figures the As

_{2}Se

_{3}material dispersion is plotted (blue curve) to appreciate the strong contribution of the waveguide dispersion to the total GVD. The waveguide dispersion grows stronger as the core diameter gets smaller which can result in very steep dispersion slopes as predicted from the inverse relation between

*A*and the absolute GVD value [15

_{eff}15. M. Moenster, G. Steinmeyer, R. Iliew, F. Lederer, and K. Petermann, “Analytical relation between effective mode field area and waveguide dispersion in microstructure fibers,” Opt. Lett. **31**(22), 3249–3251 (2006). [CrossRef] [PubMed]

_{2}Se

_{3}at 7.225μm.

*N*, Λ,

*d*), opens up the possibility of seeding with large wavelengths (5 – 12 μm) in the mid-IR for optimum phase-matching of nonlinear optical processes such as FWM and SC generation, as discussed in more detail in Section 4.

## 3. Nonlinear properties of microporous fibers

### 3.1 Effective nonlinearity in microporous fibers

*γ*defined as [16

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

*γ*was evaluated both in As

_{2}Se

_{3}glass [Fig. 7(a) ] and inside the gas-filled holes [Fig. 7(b)] where Argon serves as exemplar nonlinear gas. The implemented values for the nonlinear index of As

_{2}Se

_{3}[17

17. R. E. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers,” J. Opt. Soc. Am. B **21**(6), 1146–1155 (2004). [CrossRef]

18. Y.-H. Chen, S. Varma, I. Alexeev, and H. M. Milchberg, “Measurement of transient nonlinear refractive index in gases using xenon supercontinuum single-shot spectral interferometry,” Opt. Express **15**(12), 7458–7467 (2007). [CrossRef] [PubMed]

^{2}/W and

^{2}/W respectively.

*γ*= 2π

*n*

_{2}/(

*λA*), one anticipates that for given values of input wavelength (

_{eff}*λ*= 10.5 μm) and nonlinear index (

*n*

_{2}), the nonlinearity

*γ*

_{mat}in the solid material is maximal where

*A*is minimized, as accordingly shown in Fig. 7(a) and Fig. 4(b). While

_{eff}*γ*

_{mat}may be maximized in the suspended rod limit (

*d*→0), the conclusion is different for the nonlinear gas interaction where optimization of

*γ*

_{gas}is obtained for

*d*>0 and within a distinct ellipsoidal region of the Λ-

*d*parameter space [see Fig. 7(b)]. Of greater interest is the recognition that not only one can have relatively high values of the

*γ*

_{mat}and

*γ*

_{gas}parameters, but also one could operate in the region of low and flattened dispersion [see Figs. 5(a), 5(b)] for which phase-matching with a given nonlinear optical process is optimized. Therefore, what distinguishes the microporous fiber from the microwire, nanowire and other small solid-core designs is the prospect of extensive chromatic dispersion engineering. Combined with the low attenuation created by the porosity, one realizes that microporous fibers enable long interaction lengths in nonlinear media.

20. F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science **298**(5592), 399–402 (2002). [CrossRef] [PubMed]

21. P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. **103**(4), 043602 (2009). [CrossRef] [PubMed]

### 3.2 Nonlinear Schrodinger equation and the Raman response of As_{2}Se_{3}

*h*(

_{R}*t*). Assuming a Lorentzian profile for the Raman gain spectrum, the Raman response function may be expressed in a convenient form [19]:where the parameters

*h*(

_{R}*t*), and

*f*is the fractional contribution of the Raman response to the total nonlinear response:

_{R}^{−1}in quantitative accord with experimental measurements [17

17. R. E. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers,” J. Opt. Soc. Am. B **21**(6), 1146–1155 (2004). [CrossRef]

*f*= 0.115 in close agreement with the previously reported value

_{R}*f*= 0.1 in [22].

_{R}*T*in Eq. (6) is defined as the first moment of the nonlinear response function [19]:

_{R}*T*= 5.40 fs, which is to our best knowledge the first time a numerical value of

_{R}*T*for As

_{R}_{2}Se

_{3}has been proposed in the literature.

23. A. K. Atieh, P. Myslinski, J. Chrostowski, and P. Galko, “Measuring the Raman Time Constant (T_{R}) for Soliton Pulses in Standard Single-Mode Fiber,” J. Lightwave Technol. **17**(2), 216–221 (1999). [CrossRef]

*T*can be calculated via linear regressions (shown on Fig. 9 ) depending on the input pulse duration.

_{R}*λ*= 1.54 μm carrier wavelength and duration

*τ*

_{FWHM}≥ 100 fs (i.e. for FWHM pulse spectral bandwidths: Δ

*ν*

_{FWHM}≤ 4.4 THz), the slope value

*T*= 4.25 fs can be adopted; while for

_{R}*τ*

_{FWHM}≈91 fs (Δ

*ν*

_{FWHM}≈4.84 THz) and

*τ*

_{FWHM}≈83 fs (Δ

*ν*

_{FWHM}≈5.3 THz) the corresponding respective values

*T*= 5.36 fs and

_{R}*T*= 7.44 fs may be more appropriate. As evidenced on Fig. 9, the linear approximation of the Raman gain slope is a rough one and becomes questionable for pulses with FWHM spectral bandwidths > 4.4 THz in which the increase in Raman gain significantly deviates from the nearly linear rate in the vicinity of the carrier frequency

_{R}*ν*

_{0}.

*T*= 5.40 fs [derived earlier from Eq. (8)] was implemented for all numerical simulations. To convert the latter value for a different wavelength of interest, we applied the 1/λ scaling rule of the Raman gain coefficient [23

_{R}23. A. K. Atieh, P. Myslinski, J. Chrostowski, and P. Galko, “Measuring the Raman Time Constant (T_{R}) for Soliton Pulses in Standard Single-Mode Fiber,” J. Lightwave Technol. **17**(2), 216–221 (1999). [CrossRef]

24. R. H. Stolen, “Nonlinearity in fiber transmission,” Proc. IEEE **68**(10), 1232–1236 (1980). [CrossRef]

*T*= 0.792 fs for

_{R}*λ*= 10.5 μm.

## 4. Supercontinuum bandwidth simulations

*d*= 0.24) μm as a reference case, SC simulations were performed by solving Eq. (7) via the symmetrized split-step Fourier method with implementation of the Kerr and Raman responses of As

_{2}Se

_{3}and the first

*m*= 10 Taylor series coefficients

*β*of the propagation constant

_{m}*β*(

*ω*). At the

*λ*= 10.5 μm wavelength, the fiber is pumped in the anomalous dispersion regime (

*D*= 5.6 ps/(km∙nm)) with effective mode area

*A*= 11 μm

_{eff}^{2}and nonlinear coefficient

*γ*= 571 W

^{−1}km

^{−1}. We here restrict ourselves to short pulse pumping 100 fs ≤

*τ*

_{FWHM}≤ 10 ps for which we have soliton orders

*N*> 5 (where

_{sol}*L*= 1/(

_{NL}*γP*

_{0})). In this regime, SC generation is mainly driven by an initial nonlinear temporal compression of the pulse with creation of higher-order solitons and their successive fission into

*N*fundamental solitons via intrapulse Raman scattering. The

_{sol}*N*fundamental solitons ejected by the fission process have peak powers

_{sol}*P*

_{0}is the peak input pulse power and

*s*= 1, 2,...,

*N*denotes the order in which they are ejected from the higher-order soliton [25

_{sol}25. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. **78**(4), 1135–1184 (2006). [CrossRef]

*P*

_{1}is of prime importance since it is the most energetic fundamental soliton that mostly produces dispersive waves – also referred as Cherenkov radiation – which generates new wavelengths.

*T*= 1 ps and

_{FWHM}*T*= 0.1 ps correspond to fission lengths

_{FWHM}*L*= 1.57 cm and

_{fiss}*L*= 0.4 mm respectively, thus soliton fission dominates and significant spectral broadening is observed on Fig. 10(a). In the case of the shortest pulse (

_{fiss}*T*= 0.1 ps), we notice the formation of a two-peaked structure which concords with the description of power transfer from the pump to both blue-shifted and red-shifted dispersive waves [26

_{FWHM}26. P. Falk, M. H. Frosz, and O. Bang, “Supercontinuum generation in a photonic crystal fiber with two zero-dispersion wavelengths tapered to normal dispersion at all wavelengths,” Opt. Express **13**(19), 7535–7540 (2005). [CrossRef] [PubMed]

*E*

_{0}= 5 nJ and

*T*= 1 ps pulse with the exception here that modulation instability (MI) plays a prominent role as witnessed by the strong fluctuations in the spectral regions where the GVD is anomalous. The latter MI effect can be expected from the characteristic length of modulation instabilities (

_{FWHM}*L*∼4

_{MI}*L*), which is ten times shorter than the fission length (

_{NL}*L*= 6.7 mm) in this configuration.

_{fiss}*P*

_{0}= 0.846 kW and peak solitonic power

*P*

_{1}= 3.2 kW. Considering the 11 μm

^{2}effective mode area, the latter powers translates to sizable intensity values of 15.4 GW/cm

^{2}and 58 GW/cm

^{2}respectively. Previously, supercontinuum generation in an As

_{2}Se

_{3}glass small-core step-index fiber and a PCF fiber have sustained ∼3.5 GW/cm

^{2}intensities at 1 kHz rate with no material damage reported [4]. Still, it remains unclear whether the proposed As

_{2}Se

_{3}microporous fibers can sustain peak intensities ≥ 10 GW/cm

^{2}due to lack of available data in that regime. Nevertheless, we emphasize that contrary to standard small-core fibers where peak intensity is centered at the solid glass center; the peak power in microporous fibers is mostly concentrated in the air holes [as shown in Fig. 1(b)] thus considerably reducing the risk of permanent damage to the glass structure.

_{2}laser sources in this wavelength range; in contrast to the more expensive and relatively complex OPO technology.

_{2}Se

_{3}(∼11.5 μm) would most likely lead to thermal dissipation issues in a practical implementation. Thus other highly-nonlinear compound glasses with larger long-wavelength transmission edges such as TAS (Te-As-Se glass) may be used alternatively. Moreover, the rapid progress in quantum cascade lasers (QCL) peak powers and beam quality [27

27. M. Pushkarsky, M. Weida, T. Day, D. Arnone, R. Pritchett, D. Caffey, and S. Crivello, “High-power tunable external cavity quantum cascade laser in the 5-11 micron regime,” Proc. SPIE **6871**, 68711X (2008). [CrossRef]

## 5. Conclusion

*N*, Λ and

*d*). While the present study concentrates on small-core fibers with

*N*= 4 layers of holes, we stress that this type of waveguide could also be suited for the design of large mode area fibers (LMA) where typically

*N*>>4. The proposed microporous geometry is a simple design ready to be implemented using current PCF technology with relatively few changes in the fabrication process.

*d*= 0.24 μm, numerical simulations of the nonlinear Schrodinger equation theoretically shows that a broad SC bandwidth of 3100 nm extending from 8.5 μm to 11.6 μm can be generated in a 10 cm long chalcogenide As

_{2}Se

_{3}microporous fiber pumped with a 0.9 nJ picosecond pulse at 10.5 μm wavelength.

## Acknowledgements

## References and links

1. | P. Domachuk, N. A. Wolchover, M. Cronin-Golomb, A. Wang, A. K. George, C. M. B. Cordeiro, J. C. Knight, and F. G. Omenetto, “Over 4000 nm bandwidth of mid-IR supercontinuum generation in sub-centimeter segments of highly nonlinear tellurite PCFs,” Opt. Express |

2. | 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, X. Feng, and D. J. Richardson, “Mid-IR Supercontinuum Generation From Nonsilica Microstructured Optical Fibers,” IEEE J. Sel. Top. Quantum Electron. |

3. | L. B. Shaw, P. A. Thielen, F. H. Kung, V. Q. Nguyen, J. S. Sanghera, and I. D. Aggarwal, “IR supercontinuum generation in As-Se photonic crystal fiber,” presented at the Conf. Adv. Solid State Lasers (ASSL), Seattle, WA, 2005, Paper TuC5. |

4. | J. S. Sanghera, I. D. Aggarwal, L. B. Shaw, C. M. Florea, P. Pureza, V. Q. Nguyen, and F. Kung, “Nonlinear properties of chalcogenide glass fibers,” J. Optoelectron. Adv. Mater. |

5. | A. Hassani, A. Dupuis, and M. Skorobogatiy, “Low loss porous terahertz fibers containing multiple subwavelength holes,” Appl. Phys. Lett. |

6. | A. Hassani, A. Dupuis, and M. Skorobogatiy, “Porous polymer fibers for low-loss Terahertz guiding,” Opt. Express |

7. | S. Atakaramians, S. Afshar V, B. M. Fischer, D. Abbott, and T. M. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express |

8. | A. Dupuis, J.-F. Allard, D. Morris, K. Stoeffler, C. Dubois, and M. Skorobogatiy, “Fabrication and THz loss measurements of porous subwavelength fibers using a directional coupler method,” Opt. Express |

9. | S. Atakaramians, S. Afshar V, H. Ebendorff-Heidepriem, M. Nagel, B. M. Fischer, D. Abbott, and T. M. Monro, “THz porous fibers: design, fabrication and experimental characterization,” Opt. Express |

10. | CorActive High-Tech Infrared Fibers, “Mid-Infrared Transmission Optical Fiber,” (CorActive High-Tech Inc., 2009). http://www.coractive.com/an/pdf/irtgeneral.pdf |

11. | B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO |

12. | Amorphous Materials, “AMTIR-2: Arsenic Selenide Glass As–Se,” (Amorphous Materials Inc., 2009). http://www.amorphousmaterials.com/amtir2.htm |

13. | A. W. Snyder, and J. D. Love, Optical Waveguide Theory,” Chapman Hall, New York, (1983). |

14. | S. Afshar V and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express |

15. | M. Moenster, G. Steinmeyer, R. Iliew, F. Lederer, and K. Petermann, “Analytical relation between effective mode field area and waveguide dispersion in microstructure fibers,” Opt. Lett. |

16. | M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express |

17. | R. E. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers,” J. Opt. Soc. Am. B |

18. | Y.-H. Chen, S. Varma, I. Alexeev, and H. M. Milchberg, “Measurement of transient nonlinear refractive index in gases using xenon supercontinuum single-shot spectral interferometry,” Opt. Express |

19. | G. P. Agrawal, Nonlinear Fiber Optics, 4th Ed.,” Academic Press, New York, (2006). |

20. | F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science |

21. | P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. |

22. | J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Raman response function and supercontinuum generation in chalcogenide fiber,” presented at the Conference on Lasers and Electro-Optics (CLEO), San Jose, CA, 2008, Paper CMDD2. |

23. | A. K. Atieh, P. Myslinski, J. Chrostowski, and P. Galko, “Measuring the Raman Time Constant (T |

24. | R. H. Stolen, “Nonlinearity in fiber transmission,” Proc. IEEE |

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

26. | P. Falk, M. H. Frosz, and O. Bang, “Supercontinuum generation in a photonic crystal fiber with two zero-dispersion wavelengths tapered to normal dispersion at all wavelengths,” Opt. Express |

27. | M. Pushkarsky, M. Weida, T. Day, D. Arnone, R. Pritchett, D. Caffey, and S. Crivello, “High-power tunable external cavity quantum cascade laser in the 5-11 micron regime,” Proc. SPIE |

**OCIS Codes**

(060.2390) Fiber optics and optical communications : Fiber optics, infrared

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(060.4005) Fiber optics and optical communications : Microstructured fibers

(320.6629) Ultrafast optics : Supercontinuum generation

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: February 1, 2010

Manuscript Accepted: March 16, 2010

Published: April 9, 2010

**Citation**

Bora Ung and Maksim Skorobogatiy, "Chalcogenide microporous fibers for linear and nonlinear applications in the mid-infrared," Opt. Express **18**, 8647-8659 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-8-8647

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