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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 8 — Apr. 12, 2010
  • pp: 8647–8659
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Chalcogenide microporous fibers for linear and nonlinear applications in the mid-infrared

Bora Ung and Maksim Skorobogatiy  »View Author Affiliations


Optics Express, Vol. 18, Issue 8, pp. 8647-8659 (2010)
http://dx.doi.org/10.1364/OE.18.008647


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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 CO2 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 CO2 laser as a pump. In addition, an analytical description of the Raman response function of chalcogenide As2Se3 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

In this theoretical contribution, we introduce a novel type of MOF for the middle-infrared (mid-IR): the chalcogenide microporous fiber with subwavelength holes which enables superior control of the GVD compared to suspended core fibers of a “wagon wheel” type MOF. We demonstrate that with appropriate engineering of the microporosity, one can create zero-dispersion points in the mid-IR above the ZDM of the chalcogenide glass, and in the wavelength range of CO2 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

The basic geometry of a microporous fiber is schematically depicted in Fig. 1
Fig. 1 (a) Refractive index distribution in 4-layers As2Se3 (Λ = 0.5μm, d = 0.42μm) microporous fiber, and (b) fundamental mode power (a.u.) distribution at the specific wavelength 10.5 μm.
. In this design, the solid core is pierced with N layers of subwavelength holes of diameter d in a triangular lattice of pitch Λ (also of subwavelength dimension: Λλ). The total outer diameter of the fiber core is given by df=(2N+1)Λ, and an infinite air cladding is assumed here for convenience. Due to computational constraints and in order to simplify analysis, the present investigation focuses on the case of 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.

The refractive index’ chromatic dispersion of bulk As2Se3 glass is modeled (in Fig. 2
Fig. 2 Wavelength dependence of bulk As2Se3 refractive index (solid line), and absorption coefficient (dotted line) [12].
) 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

]:
n(λ)=1+λ2(A02λ2A12+A22λ2192+A32λ24A12)
(1)
where 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 As2Se3 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).

Keeping the number of layers fixed to N = 4, the fundamental mode effective refractive index (neff) and field distributions (Ex, Ey, Ez, Sz) 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; 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 neff (λ) via cubic spline interpolation, then fitting the interpolated neff (λ) curve with a polynomial of degree 11, and evaluating the GVD (ps/km∙nm) with the equation D=(λ/c)d2neff/dλ2.

The porosity p of a given fiber, or in other words the areal density of the cross-section occupied by holes, is:
p=NhAhAf=Nhπ(d/2)2π(df/2)2=[3(N2+N)+1][4(N2+N)+1](dΛ)2
(2)
where the full diameter df=(2N+1)Λ and the total number of holes in the fiber Nh=3(N2+N)+1 both depends on the number of layers N. It follows that the fraction of cross-sectional area occupied by solid glass material is given by fm=1p. We note from Eq. (2) that a substantial fraction, exactly 24.7% for 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 ±30°, ±90° and ±150° angles [see Fig. 1(a)].

The value of the chromatic dispersion parameter D and dispersion slope dD/dλ at the specific wavelength λ = 10.5 μm are plotted as a function of (Λ, d) in Fig. 5(a)
Fig. 5 (a) Dispersion parameter (ps/km∙nm) and (b) dispersion slope (ps/km∙nm2) in N = 4 layers As2Se3 microporous fiber at λ = 10.5 μm as a function of geometrical parameters (Λ, d)
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)
Fig. 6 Dispersion curves (ps/km∙nm) showing near-zero and flattened dispersion at λ = 10.5 μm for parameters (a) (Λ = 0.5, d = 0.38)μm, and (b) (Λ = 0.7, d = 0.62)μm. Blue curve is bulk As2Se3.
and Fig. 6(b). In both figures the As2Se3 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 Aeff and the absolute GVD value [15

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]

]. The latter effect help explains the sharp transition in Fig. 5(a) from positive to negative dispersion regime in going from Λ = 0.40 μm to Λ = 0.35 μm. A more significant feature shown on Figs. 6(a), 6(b) is the formation of several zero-dispersion points (ZDP), and most notably the creation of a ZDP at λ = 10.5 μm red-shifted from the ZDM of As2Se3 at 7.225μm.

The ability of microporous fibers to tailor the dispersive properties of the waveguide through several degrees of structural freedom (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

The effective nonlinearity of the waveguides was evaluated via the nonlinear parameter 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]

]:
γi=2πλtotaln2i|Sz|2dA|totalSzdA|2                 , i=(mat,gas)
(5)
where n2i denotes the value of the nonlinear index in the solid material or the gaseous medium. As a matter of fact, the hollow nature of the microporous fiber and its flexible dispersive properties not only make this type of waveguide a viable candidate for performing nonlinear interactions in the glass material; but also within the gas-filled holes. Therefore the value of the nonlinear parameter γ was evaluated both in As2Se3 glass [Fig. 7(a)
Fig. 7 Nonlinear parameter value (W−1m−1) in (a) As2Se3 glass, and in (b) Argon gas-filled holes at λ = 10.5 μm as a function of (Λ, d) for a N = 4 layers microporous fiber.
] and inside the gas-filled holes [Fig. 7(b)] where Argon serves as exemplar nonlinear gas. The implemented values for the nonlinear index of As2Se3 [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]

] and Argon [18

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]

] are n2As-Se=2.4×1017m2/W and n2Argon=9.8×1020m2/W respectively.

From the standard definition of the nonlinear parameter [19

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

], γ = 2πn 2/(λAeff), one anticipates that for given values of input wavelength (λ = 10.5 μm) and nonlinear index (n 2), the nonlinearity γ mat in the solid material is maximal where Aeff is minimized, as accordingly shown in Fig. 7(a) and Fig. 4(b). While 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.

Pertaining to nonlinear optical interactions in gases, wavelength conversion in the visible spectrum through stimulated Raman scattering has been demonstrated in a hollow core PCF filled with hydrogen gas [20

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]

]. The same type of setup, using rubidium vapor instead of hydrogen, showed high-efficiency FWM-frequency conversion at low microwatt pump powers [21

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]

]. An attractive scheme is to use the linear and nonlinear optical interactions in the gas-filled holes of microporous fibers for remote sensing and spectroscopy of gaseous analytes.

3.2 Nonlinear Schrodinger equation and the Raman response of As2Se3

The following numerical simulations of the nonlinear optical interactions in chalcogenide microporous fibers is based on the scalar nonlinear Schrodinger equation (NLSE):
Az+α2Aim2imβmm!mAtm=iγ[|A|2A+iω0t(|A|2A)TRA|A|2t]
(6)
where A=A(z,t) is the slowly-varying pulse envelope, and first-order approximations are used to include self-steepening effects and the delayed ionic Raman response function hR (t). Assuming a Lorentzian profile for the Raman gain spectrum, the Raman response function may be expressed in a convenient form [19

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

]:
hR(t)=τ12+τ22τ1τ22exp(tτ2)sin(tτ1)
(7)
where the parameters τ1=23.1fs and τ2=195fs were here found to yield the best fit [solid line in Fig. 8(a)
Fig. 8 (a) Raman response function h(t) of As2Se3 glass, and (b) corresponding Raman gain gR spectrum for pump wavelength λ = 1.54 μm.
] with recently published results [22

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.

]. The parameter τ1 relates to the phonon oscillation frequency while τ2 defines the characteristic damping time of the network of vibrating atoms.

The Raman gain spectrum gR(Δω) shown on Fig. 8(b) was obtained with a λ = 1.54 μm CW pump and calculated from gR(Δω)=8ω0n2fRIm[h˜R(Δω)]/(3c) where Im[h˜R(Δω)] is the imaginary part of the Fourier transform of hR (t), and fR is the fractional contribution of the Raman response to the total nonlinear response: R(t)=(1fR)δ(t)+fRhR(t), where the first term accounts for the instantaneous electronic response. The 5.1×1011m/W peak gain coefficient is located at the frequency shift of 229.3 cm−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]

]. From the gR(Δω) curve we calculated a fractional contribution fR = 0.115 in close agreement with the previously reported value fR = 0.1 in [22

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.

].

The characteristic Raman time constant TR in Eq. (6) is defined as the first moment of the nonlinear response function [19

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

]:

TR0tR(t)dtfR0thR(t)dt
(8)

On substituting Eq. (7) with the relevant numerical parameters into the last expression, we find TR = 5.40 fs, which is to our best knowledge the first time a numerical value of TR for As2Se3 has been proposed in the literature.

To cross-check the validity of the latter result, the Raman time constant was also estimated from the slope of the Raman gain spectrum gR(Δω) that is assumed to vary linearly in the vicinity of the pump frequency [19

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

]:

TRfRd(Im[h˜R(Δω)])d(Δω)|Δω=0
(9)

Based on the procedure described in [23

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

], several values of TR can be calculated via linear regressions (shown on Fig. 9
Fig. 9 Raman gain gR spectrum of As2Se3 glass at λ = 1.54 μm pump (circles) inside the 0 – 7 THz range, with linear slope approximations shown for calculating TR values.
) depending on the input pulse duration.

Considering Fourier-transform-limited Gaussian pulses of λ = 1.54 μm carrier wavelength and duration τ FWHM ≥ 100 fs (i.e. for FWHM pulse spectral bandwidths: Δν FWHM ≤ 4.4 THz), the slope value TR = 4.25 fs can be adopted; while for τ FWHM ≈91 fs (Δν FWHM ≈4.84 THz) and τ FWHM ≈83 fs (Δν FWHM ≈5.3 THz) the corresponding respective values TR = 5.36 fs and TR = 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 ν 0.

4. Supercontinuum bandwidth simulations

Taking a 10 cm long microporous fiber with (Λ = 0.40, 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 As2Se3 and the first m = 10 Taylor series coefficients βm of the propagation constant 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 Aeff = 11 μm2 and nonlinear coefficient γ = 571 W−1km−1. We here restrict ourselves to short pulse pumping 100 fs ≤ τ FWHM ≤ 10 ps for which we have soliton orders Nsol > 5 (where Nsol2=LD/LNLwith LD=TFWHM2/(ln(16)|β2|) and LNL = 1/(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 Nsol fundamental solitons via intrapulse Raman scattering. The Nsol fundamental solitons ejected by the fission process have peak powers Ps=P0(2Nsol2s+1)2/Nsol2 where P 0 is the peak input pulse power and s = 1, 2,..., Nsol denotes the order in which they are ejected from the higher-order soliton [25

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

]. It follows that the most powerful of these fundamental solitons is the first one with an increased peak power of P1=P0(2Nsol1)2/Nsol2. The parameter 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.

In all simulations, unchirped Gaussian pulses were adopted. Polarization coupling effects, which are assumed to be small here, were not included in the calculation since the purpose of this particular study is the adequate estimation of the output spectral bandwidth; not its exact fine spectral structure.

At the 0.9 nJ seed energy, the shorter pulses TFWHM = 1 ps and TFWHM = 0.1 ps correspond to fission lengths Lfiss = 1.57 cm and Lfiss = 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 (TFWHM = 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

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]

]. The same spectral splitting can be seen on the SC spectrum yielded by the E 0 = 5 nJ and TFWHM = 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 (LMI ∼4LNL), which is ten times shorter than the fission length (Lfiss = 6.7 mm) in this configuration.

The broadest and un-segmented SC calculated from −20 dB below the peak output power, has a bandwidth of 3100 nm (between 8.5 and 11.6 μm) and is obtained with the 0.9 nJ pulse of 1 ps duration. Although a more detailed investigation is needed to accurately optimize the main parameters of the system (seed energy, pulse duration, wavelength, fiber geometry and length) for maximal broadening, the above theoretical study demonstrates the potential of dispersion-tailored microporous fibers for SC generation in the mid-IR.

The pulse with 0.9 nJ energy and 1 ps duration yields the broadest SC with an input peak power of P 0 = 0.846 kW and peak solitonic power P 1 = 3.2 kW. Considering the 11 μm2 effective mode area, the latter powers translates to sizable intensity values of 15.4 GW/cm2 and 58 GW/cm2 respectively. Previously, supercontinuum generation in an As2Se3 glass small-core step-index fiber and a PCF fiber have sustained ∼3.5 GW/cm2 intensities at 1 kHz rate with no material damage reported [4

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. 8, 2148–2155 (2006).

]. Still, it remains unclear whether the proposed As2Se3 microporous fibers can sustain peak intensities ≥ 10 GW/cm2 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.

The motivation for selecting a 10.5 μm seed lies on the current relative accessibility and cost-effectiveness of CO2 laser sources in this wavelength range; in contrast to the more expensive and relatively complex OPO technology.

The location of the seed wavelength (10.5 μm) near the multiphonon absorption edge of As2Se3 (∼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]

] indicate that these cheaper and compact sources could eventually be considered in the near future for seeding a SC with a pump inside the 5-9 μm region.

5. Conclusion

A novel type of microstructured fiber for mid-IR is proposed: the chalcogenide microporous fiber with subwavelength holes provides considerable chromatic dispersion engineering capabilities through proper tuning of its constitutive geometrical parameters (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.

The results presented in this work clearly demonstrate the potential of dispersion-tailored microporous fibers for nonlinear-phase matching applications and for supercontinuum generation. In particular, for geometrical parameters Λ = 0.40 μm and 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 As2Se3 microporous fiber pumped with a 0.9 nJ picosecond pulse at 10.5 μm wavelength.

In summary, the tunable dispersive and attenuating properties of microporous fibers promise to provide significant flexibility for the design of linear and nonlinear middle-infrared applications.

Acknowledgements

This project is supported in part by the Fonds Québecois de la Recherche sur la Nature et les Technologies (FQRNT), and by a Collaborative Research and Development Grant in association with CorActive High-Tech Inc.

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 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]

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. 8, 2148–2155 (2006).

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]

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]

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]

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]

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 CO2 laser transmission,” Nature 420(6916), 650–653 (2002). [CrossRef] [PubMed]

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 17(4), 2298–2318 (2009). [CrossRef] [PubMed]

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]

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]

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]

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 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]

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 (TR) 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]

25.

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

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]

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]

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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References

  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]
  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. 8, 2148–2155 (2006).
  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]
  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]
  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]
  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]
  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 CO2 laser transmission,” Nature 420(6916), 650–653 (2002). [CrossRef] [PubMed]
  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 17(4), 2298–2318 (2009). [CrossRef] [PubMed]
  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]
  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]
  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]
  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 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]
  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 (TR) 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]
  25. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]
  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]
  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]

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