# Development of Dispersion-Optimized Photonic Crystal Fibers Based on Heavy Metal Oxide Glasses for Broadband Infrared Supercontinuum Generation with Fiber Lasers

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}= 2.74 × 10

^{−20}m

^{2}/W at the wavelength of 1053 nm [4] compared to soft glasses [5] or liquids [6], but its transmission band is limited to approx. 2 μm. The decrease of transmission in silica glass for longer wavelengths, caused by multi-photon absorption by Si–O bondings and vibrational resonances on OH–ions motivates the search for other materials for PCF development that would allow for transmission in mid-infrared (mid-IR). Such transmission is a property of glasses containing heavy atoms with lower excitation energy of optical phonons. A number of these glasses also exhibit higher n

_{2}than fused silica. For SG a number of glasses are used, such as fluoride glasses, chalcogenide glasses containing compounds of sulphur, arsenic and selenium [7,8,9], tellurite glasses [10] and lead oxide glasses [11,12].

_{2}. These glasses have similar linear and nonlinear refractive index to fused silica glass, but their development requires high quality materials that comes at a high cost of the technological process, including the necessity of isolation from external environment to prevent chemical reaction of fluorine compounds with other compounds in the air, and to prevent pollution because of high toxicity of these substances.

_{2}≈ 10

^{−18}m

^{2}/W, among glasses typically used for drawing of fibers, and the zero dispersion wavelength (ZDW) is located in mid-IR (λ

_{ZDW}> 4.5 µm), while the transmission wavelength range extends to over a dozen of micrometers, depending on chemical composition. Pumping of fibers made of these glasses in the anomalous dispersion regime (λ

_{p}> λ

_{ZDW}) requires advanced mode-locked lasers tuned in the range of 4–7 μm. In the paper by Petersen et al. [8] SG in the range of 1.4–13.3 µm was demonstrated in step-index chalcogenide fibers, under pumping with 100 fs–long pulses, centered at a wavelength of λ

_{p}= 6.3 µm and with peak power of P

_{0}= 2.3 MW, from a complex optical parametric amplifier system.

_{rep}= 1 kHz.

_{ZDW}= 1.38 µm. The fiber was pumped using an optical parametric oscillator (OPO) emitting 110 fs–long pulses with f

_{rep}= 80 MHz for λ

_{p}= 1.55 µm and the mean power P

_{avg}= 150 mW. Less than 1 cm of fiber was used, which was enough to generate hyperspectral supercontinuum at a standard pump wavelength, due to high nonlinearity of the fiber and ultrashort pump pulse duration. It also allowed to broaden the supercontinuum spectrum over 3 µm despite usually high absorption of multicomponent oxide glasses at this wavelength due to OH impurities. On the other hand, telluride glasses are fragile what makes development in the low-cost stack-and-draw process problematic. The suspended core geometry does allow high nonlinearity due to strong confinement, but at the same time it is also strongly isolated thermally from the cladding that leads to a fiber being more susceptible to laser damage, compared to other types of PCFs with low air-glass filling factor.

_{6}with n

_{2}= 2.2 × 10

^{−19}m

^{2}/W, are an alternative to tellurite glasses. Omenetto et al. [11] demonstrated a fiber with four air-holes surrounding a core of diameter d

_{r}= 2.6 µm, which exhibited λ

_{ZDW}= 1.30 µm. When pumped with an OPO source with λ

_{p}= 1.55 µm SG was achieved in the range of 0.7–3.0 µm with a dynamics of 40 dBs.

_{p}= 1.55 µm, 100 fs–long pulses, and f

_{rep}= 1.0 kHz [19]. Finally, spectral and coherence evolution were experimentally measured for SC generated in PCFs made of SF

_{6}glass [20]. A significant part of our previous work in multi-component oxide soft glass was related to fibers with normal dispersion profiles and a comprehensive review of coherent supercontinuum generation in soft glass photonic crystal fibers can be found in [21]. Table 1 summarizes selected typical properties of glasses used for development of PCFs.

## 2. Numerical Simulations of Linear Properties of the PCF

_{r}denotes the diameter of the core, d

_{1}—the diameter of the holes directly surrounding the core in the first row, d

_{2}—the diameter of the holes in the second row, and d

_{3}—the diameter of the remaining holes. Due to variable diameters of the holes this structure holds effectively three different filling factors d/Λ in the cladding.

_{PBG-08A}is higher than n

_{PBG-08}by approx. 0.005. The measurement was done using a Michelson interferometer with the accuracy of 0.002. The refractive index characteristic of PBG-08A glass is modelled using Sellmeier’s equation below. The Sellmeier’s coefficients calculated on the basis of experimental results are presented in Table 2.

_{1}, d

_{2}, d

_{3}, on linear properties of the PCF in terms of effective refractive index n

_{eff}(λ), attenuation A(λ), and dispersion D(λ) for the wavelength range of 0.8–5 μm. We assumed that the PCF would be coupled to a mode-locked laser emitting at λ

_{p}= 1.56 µm, therefore ZDW should be lower than the pump wavelength. A commercial-grade simulator, eigenmode solver and propagator was used to perform the calculations [29].

_{1}, d

_{2}and d

_{3}. Selected dispersion characteristics are shown in Figure 4. The change of the diameter d

_{1}has the biggest influence on the location of ZDW and the shape of the dispersion characteristic in the range of 1.0–5.0 μm (see Figure 4a) [30]. The change of the diameter d

_{2}has only small effect on ZDW and influences the dispersion characteristic mainly in the range of 2–4.5 μm (see Figure 4b). The change of the diameter d

_{3}has almost no effect on ZDW but influences the dispersion characteristic in the range of 2.5–5 μm (see Figure 4c). Thus, using three different filling factors in the lattice geometry, one has the opportunity to precisely shape the dispersion characteristics, but at the same time even small variations in the diameters of the air-holes during fiber development, on the level of tens of nanometers, can lead to a significant change of the characteristics.

_{eff}are shown in Figure 6. In this fiber ZDW is located at 1.543 µm and the maximum dispersion value D

_{max}= 36 ps/(nm·km) was obtained for the wavelength of 2.106 µm. For λ

_{p}= 1.56 µm the total fiber dispersion equals D = 2.8 ps/(nm·km) while the group dispersion equals β

_{2}= −3.6 ps

^{2}/km and calculated A

_{eff}is 4.13 μm

^{2}.

_{31}is possible, but its attenuation is higher than attenuation of the fundamental mode (FM) by a factor of 10

^{9}. Theoretical cut-off wavelength for the mode LP

_{31}is 2.38 μm and for the FM it is 4.0 μm, which means that the fiber does not guide light in the core for wavelengths longer than 4.0 μm. Although for the pump wavelength Λ

_{p}= 1.56 µm two modes are guided, the effective coupling efficiency is equal 0.3 for FM and close to zero for the mode LP

_{31}, when a Gaussian beam with numerical aperture 0.6 is considered.

## 3. PCF Development

_{out}.

## 4. Characterization of Linear Properties of Developed PCFs

_{p}= 1.56 µm the attenuation reaches 6.3 dB/m and 7.7 dB/m for the fibers #A2 and #A4, respectively. Higher attenuation of the fiber #A4 compared to #A2 results from higher confinement losses and fabrication imperfections. The latter causes an emission of light to the photonic cladding and outer glass layer through micro-ruptures that are common in soft glasses.

_{p}for pumping at λ

_{p}= 1.56 µm are presented in Table 5. The dispersion of the fiber #A2 for λ

_{p}is located in the anomalous regime. In case of the fiber #A4 ZDW is located close to λ

_{p}and actually the fiber can be excited in the normal or anomalous regime.

_{eff}= 3.11 µm

^{2}, while for the fiber #A4 A

_{eff}= 3.70 µm

^{2}.

## 5. Supercontinuum Generation in Developed PCFs

_{k}associated with Taylor series expansion of the propagation constant β(ω) about central frequency ω

_{0}. At the right-hand side, the nonlinear coefficient is given by γ = n

_{2}∙ω

_{0}/(c∙A

_{eff}), where n

_{2}= 2 × 10

^{−19}m

^{2}/W is the nonlinear refractive index of the fiber glass, here measured using z-scan at 1064 nm [5], the Raman response of glass is parametrized analogically to [38,39], and specifically the first order Raman shift frequency for the fiber glass in this work is Ω

_{R}= ±29 THz, and the Lorentzian fit to the first-order Raman scattering term is described by time-frequency of excited optical fonons τ

_{1}= 5.5 fs, and time-width of Lorentz band τ

_{2}= 32 fs. The contribution of delayed Raman scattering response to the Kerr nonlinearity was f

_{R}= 0.05. The simulation time window corresponded in the spectral domain to the wavelength range of 0.8–5.0 μm. The pump pulse duration (auto-correlation width) was t

_{imp}= 400 fs.

_{imp}= 0.8 nJ the broadening dynamics are limited practically to self-phase modulation (SPM) within a wavelength span of approximately 400 nm and within 20 dB dynamic range. Increasing E

_{imp}to more than 1 nJ results in further spectrum broadening, and for E

_{imp}= 2.4 nJ supercontinuum goes up to 3.6 μm in IR within 20 dB dynamics. In Table 6 dispersion lengthscale L

_{D}, nonlinear lengthscale L

_{NL}, and soliton fission lengthscale L

_{sol}for N-order solitons are summarized, for the pulse energy E

_{imp}= 2.4 nJ. The dispersion lengthscale is expressed as L

_{D}= t

_{0}

^{2}/|β

_{2}|, while the other lengthscales are defined as L

_{NL}= 1/γP

_{0}(where P

_{0}is the peak pump power), L

_{sol}= L

_{D}/N, and the soliton order is expressed as N = L

_{D}/L

_{NL}.

_{imp}= 2.4 nJ and L = 5 cm. At the beginning of the fiber, the spectrum of the pulses expands due to SPM. This is expected, because L

_{NL}is larger than L

_{D}, therefore SG occurs with dominance of nonlinear contribution over dispersion. Around 2 cm of propagation, the high order input soliton has already undergone fission into multiple low order solitons, which is in rough agreement with the 1.3 cm value estimated using formula L

_{sol}= L

_{D}/N. Due to high order N = 334 of the soliton introduced by the pump, the supercontinuum is expected to be time-incoherent, despite femtosecond pumping [40]. The modulation instability lengthscale can be estimated as 16∙L

_{NL}, which in this case is just over 6 cm. This result provides rationale for assuming the fiber length of 5 cm, in order to observe supercontinuum generation before amplification of significant noise. Soliton fission and their subsequent Raman redshift is accompanied by a radiation of higher frequencies, the dispersive waves, which is responsible for broadening of the supercontinuum spectrum towards shorter wavelengths. As a result of the decay the lower-order solitons are shifted towards IR due to Raman scattering (SSFS, soliton self-frequency shift). Because of relatively low anomalous chromatic dispersion at wavelengths redshifted from ZDW (0–36 ps/(nm·km)) broad phase matching can be achieved in the range of 1–4 μm for the degenerated four-wave mixing.

_{2}, third-order dispersion β

_{3}, nonlinear coefficient γ, dispersion length L

_{D}, nonlinear length L

_{NL}, soliton decay length L

_{sol}, order of solitons N, for λ

_{p}= 1.56 µm and E

_{imp}= 2.4 nJ.

_{NL}= 0.3 mm, however L

_{D}is also short, one order of magnitude larger than L

_{NL}, as opposed to two orders of magnitude in the ideal fiber. First 1 cm of propagation is dominated by SPM, which is followed by soliton fission and Raman redshift, accompanied by dispersive wave generation. Calculated soliton order is over three times smaller, than in the fiber considered in the design stage, thus the group delay trace shows several discernible soliton features between around 0.5 and 4 ps of delay (Figure 14c). Due to very short nonlinear length scale, the estimated modulation instability lengthscale is just below 5 cm, suggesting onset of noise amplification and decoherence of supercontinuum pulses over the final 2 mm of the fiber. The width of the spectrum is 0.8–3.7 μm within 20 dB dynamics.

_{ZDW}> λ

_{p}and the pump pulse is introduced at wavelengths with normal dispersion regime. The broadening is again initiated by SPM, because L

_{NL}is still roughly 20 times shorter than L

_{D}. When the redshifted part of SPM reaches and crosses ZDW at 1.714 µm, solitons begin to emerge at anomalous dispersion wavelengths. Their redshift is faintly visible in the group delay trace in Figure 14f just before end of 5 cm of propagation. In this scenario, the redshifting solitons also generate dispersive waves across ZDW, which here result in destructive beating with the normal dispersion-broadened spectral components, giving rise to complicated spectral evolution both in the group delay (Figure 14f) and along the fiber length (Figure 14e). The supercontinuum spectrum covers 1.0–2.9 μm.

_{avg}of the laser source is shown in Figure 15.

_{avg}= 100 mW was obtained, which corresponded to peak power of P

_{0}= 2.95 kW and coupled pulse energy of E

_{imp}= 1.18 nJ. In the physical experiments with the fiber #A2, pumping is in the anomalous dispersion wavelengths, and the spectrum is efficiently broadened towards the short-wave range. For P

_{avg}= 60 mW (E

_{imp}= 0.11 nJ) a peak appears for the wavelength of 0.96 μm caused by the dispersive wave caused by the soliton decay in the long-wavelength range. At this pump power the spectrum is still non-uniform and exhibits a decrease of the intensity in the range of 0.96–1.4 μm along with the spectrum limit at 1.80 μm. The increase of the pump power results in the broadening of the spectrum towards IR. For wavelengths shorter than λ

_{p}the spectrum becomes smooth and flat and the short-wavelength limit is shifted towards visible wavelengths but slower than long-wavelength limit. For P

_{avg}= 660 mW (E

_{imp}= 1.18 nJ) the spectrum still shows a clearly pronounced dispersive wave separated by a slightly less intense plateau in the range of 0.84–1.51 μm wavelengths. For the dynamic range of 30 dB the spectral coverage of SG in fiber #A2 is not less than 0.76–2.4 μm wavelengths, since the detection limit of OSA was 2.4 μm.

_{avg}= 60 mW the pulse is broadened only due to SPM and its width is equal to 0.41 μm (1.35–1.76 μm) within 30 dB dynamics. The increase of the power of the laser in the range of 90–510 mW broadens the flat supercontinuum spectrum in the short-wavelength range. For waves longer than 1.56 μm the intensity decreases with the wavelength. Starting from P

_{avg}= 260 mW a blue-shifted peak appears in the spectrum at about 0.9 μm that is assigned to a dispersive wave related to a soliton, which emerges at the anomalous dispersion side of the ZDW, where enough energy is transferred over to the anomalous dispersion wavelength range of fiber. For the maximum available pump power, the supercontinuum covers wavelength range of 0.86–2.4 μm (measurement limited by OSA sensitivity range). This less reach in terms of blue-shifted wavelength than the width for the fiber #A2, but at the same time the spectrum is flatter than in the case of #A2 fiber.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**The schematic of the structure of the analyzed PCF. The numbers from 1 to 8 represent subsequent rows of holes surrounding the core.

**Figure 3.**Dispersion characteristics for different lattice constants Λ and different filling factors for the first row of air-holes d

_{1}/Λ, and for the other rows of air-holes d

_{2}/Λ.

**Figure 4.**Dispersion characteristics for the lattice constant Λ = 1.5 μm and varied diameters of air-holes in (

**a**) the first row d

_{1}, (

**b**) the second row d

_{2}, and (

**c**) the other rows of the photonic cladding d

_{3}.

**Figure 5.**The close-up of the final dispersion-optimized structure. The diameters of the holes are in scale.

**Figure 6.**(

**a**) Optimal dispersion characteristic and (

**b**) effective mode area of the dispersion-optimized PCF.

**Figure 7.**Numerically simulated distributions of intensity of modes for the wavelength of 1.56 µm: (

**a**) fundamental mode LP

_{01}, (

**b**) mode LP

_{31}.

**Figure 11.**Dispersion characteristics of the fibers (

**a**) #A2 and #A4 (simulation) compared to the dispersion characteristic of the ideal dispersion-optimized structure, (

**b**) A2 and #A4 (both simulated and measured).

**Figure 12.**Numerical simulation of SG in the dispersion-optimized PCF, for pulse energy in the range of 0.2–3.6 nJ. For clarity characteristics are separated vertically by 20 dB.

**Figure 14.**Numerically generated (

**a**,

**d**) supercontinuum spectra for in the range of 0.2–2.4 nJ, (

**b**,

**e**) evolution of the spectra as a function of the length of the fiber for E

_{imp}= 2.4 nJ, (

**c**,

**f**) time–delay spectrograms. The upper rower depicts the fiber #A2, while lower—#A4.

**Figure 15.**Measured supercontinuum spectra for the fibers (

**a**) #A2 and (

**b**) #A4 for different average power of the pumping laser. For clarity characteristics are separated vertically by 20 dB.

**Figure 16.**Measured supercontinuum spectra for the fibers #A2 and #A4 and P

_{avg}= 660 mW. For clarity characteristics are separated vertically by 20 dB.

Fused Silica | ZBLAN | Chalcogenide | Tellurite | Lead Silicate | PBG81 | |
---|---|---|---|---|---|---|

Linear refractive index n | 1.44 | 1.51 | 2.45 | 2.08 | 1.80 | 1.89 |

Nonlinear refractive index n_{2} [10^{−20} m^{2} W^{−1}] | 4.3 | 2.1 | 250 | 51.1 | 8.9–22 | 41.3 |

Transmittance range [μm] | 0.2–2.8 | 0.2–8 | 0.9–12 | 0.5–5 | 0.4–4.5 | 0.4–5.5 |

Zero dispersion wavelength [μm] | 1.27 | 1.72 | 4.9 | 2.22 | 1.96 | 2.03 |

B_{1} | B_{2} | B_{3} | C_{1} | C_{2} | C_{3} |
---|---|---|---|---|---|

2.211153 | 0.355174 | 1.16141 | 0.01834 | 0.073012 | 127.3884 |

Parameter | Value |
---|---|

Λ | 1.50 μm |

d_{1} | 0.57 μm |

d_{1}/Λ | 0.38 |

d_{2} | 0.96 μm |

d_{2}/Λ | 0.64 |

d_{3} | 0.84 μm |

d_{3}/Λ | 0.56 |

d_{r} | 2.43 μm |

#A2 | #A4 | |
---|---|---|

Ø_{out} [μm] | 134 | 123 |

Λ [μm] | ~1.8 | ~1.3 |

d_{1} [μm] | 0.73 | 0.38 |

d_{2} [μm] | 2.00 × 1.35 | 1.19 × 1.03 |

d_{3} [μm] | 1.43 | 0.83 |

d_{1}/Λ | 0.52 | 0.32 |

d_{2}/Λ | 0.74 | 0.75 |

d_{3}/Λ | 0.80 | 0.64 |

d_{r} [μm] | 2.13 | 2.06 |

cladding size [μm] | 33.5 × 29.5 | 24.5 × 20.9 |

**Table 5.**Measured ZDWs and dispersion values at intended pump wavelength for the fibers #A2 and #A4.

#A2 | #A4 | |
---|---|---|

λ_{ZDW} [µm] | 1.326 | 1.525 |

D_{p} @1.56 µm [ps/(nm·km)] | 77.6 | 5.4 |

L_{D} [m] | L_{NL} [mm] | L_{sol} [mm] | N |
---|---|---|---|

44.4 | 0.39 | 133 | 334 |

β_{2}[ps ^{2}/km] | β_{3}[ps ^{3}/km] | γ [km ^{−1} W^{−1}] | L_{D}[m] | L_{NL}[mm] | L_{sol}[mm] | N | |
---|---|---|---|---|---|---|---|

#A2 | −61.5 | 0.42 | 557 | 2.6 | 0.30 | 27.9 | 93 |

#A4 | 25.1 | 0.23 | 468 | 6.4 | 0.36 | 47.6 | 134 |

Dynamics 20 dB | Dynamics 30 dB | |||||
---|---|---|---|---|---|---|

λ_{min} [μm] | λ_{max} [μm] | Δλ [μm] | λ_{min} [μm] | λ_{max} [μm] | Δλ [μm] | |

#A2 | 1.45 | 2.40 | 0.95 | 0.76 | 2.40 | 1.64 |

#A4 | 0.90 | 2.40 | 1.50 | 0.86 | 2.40 | 1.54 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Stępniewski, G.; Pniewski, J.; Pysz, D.; Cimek, J.; Stępień, R.; Klimczak, M.; Buczyński, R.
Development of Dispersion-Optimized Photonic Crystal Fibers Based on Heavy Metal Oxide Glasses for Broadband Infrared Supercontinuum Generation with Fiber Lasers. *Sensors* **2018**, *18*, 4127.
https://doi.org/10.3390/s18124127

**AMA Style**

Stępniewski G, Pniewski J, Pysz D, Cimek J, Stępień R, Klimczak M, Buczyński R.
Development of Dispersion-Optimized Photonic Crystal Fibers Based on Heavy Metal Oxide Glasses for Broadband Infrared Supercontinuum Generation with Fiber Lasers. *Sensors*. 2018; 18(12):4127.
https://doi.org/10.3390/s18124127

**Chicago/Turabian Style**

Stępniewski, Grzegorz, Jacek Pniewski, Dariusz Pysz, Jarosław Cimek, Ryszard Stępień, Mariusz Klimczak, and Ryszard Buczyński.
2018. "Development of Dispersion-Optimized Photonic Crystal Fibers Based on Heavy Metal Oxide Glasses for Broadband Infrared Supercontinuum Generation with Fiber Lasers" *Sensors* 18, no. 12: 4127.
https://doi.org/10.3390/s18124127