## Soliton-self compression in highly nonlinear chalcogenide photonic nanowires with ultralow pulse energy |

Optics Express, Vol. 19, Issue 21, pp. 19955-19966 (2011)

http://dx.doi.org/10.1364/OE.19.019955

Acrobat PDF (1244 KB)

### Abstract

We design As_{2}Se_{3} and As_{2}S_{3} chalcogenide photonic nanowires to optimize the soliton self-compression with short distances and ultralow input pulse energy. We numerically demonstrate the generation of single optical cycle in an As_{2}S_{3} photonic nanowire: a 5.07 fs compressed pulse is obtained starting from 250 fs input pulse with 50 pJ in 0.84 mm-long As_{2}S_{3} nanowire. Taking into account the high two photon absorption (TPA) coefficient in the As_{2}Se_{3} glass, accurate modeling shows the compression of 250 fs down to 25.4 fs in 2.1 mm-long nanowire and with 10 pJ input pulse energy.

© 2011 OSA

## 1. Introduction

1. L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature **426**(6968), 816–819 (2003). [CrossRef] [PubMed]

2. M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express **16**(2), 1300–1320 (2008). [CrossRef] [PubMed]

4. Y. K. Lizé, E. C. Mägi, V. G. Ta’eed, J. A. Bolger, P. Steinvurzel, and B. J. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express **12**(14), 3209–3217 (2004). [CrossRef] [PubMed]

5. R. R. Gattass, G. T. Svacha, L. M. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express **14**(20), 9408–9414 (2006). [CrossRef] [PubMed]

6. S. G. Leon-Saval, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, and M. W. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express **12**(13), 2864–2869 (2004). [CrossRef] [PubMed]

7. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. **45**(13), 1095–1098 (1980). [CrossRef]

8. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, “Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers,” Opt. Lett. **8**(5), 289–291 (1983). [CrossRef] [PubMed]

8. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, “Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers,” Opt. Lett. **8**(5), 289–291 (1983). [CrossRef] [PubMed]

9. C. M. Chen and P. L. Kelley, “Nonlinear pulse compression in optical fibers: scaling laws and numerical analysis,” J. Opt. Soc. Am. B **19**(9), 1961–1967 (2002). [CrossRef]

2. M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express **16**(2), 1300–1320 (2008). [CrossRef] [PubMed]

10. M. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, “Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires,” Opt. Express **13**(18), 6848–6855 (2005). [CrossRef] [PubMed]

*et al.*[10

10. M. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, “Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires,” Opt. Express **13**(18), 6848–6855 (2005). [CrossRef] [PubMed]

_{2}S

_{3}and As

_{2}Se

_{3}have been the subject of intense investigations due to their high nonlinear coefficient

*n*(100-1000 times larger than of silica glass), low linear loss and low to moderate two photon absorption (TPA) coefficient [11

_{2}11. J. M. Harbold, F. O. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As-S-Se glasses for all-optical switching,” Opt. Lett. **27**(2), 119–121 (2002). [CrossRef] [PubMed]

_{2}S

_{3}and As

_{2}Se

_{3}nanowires with ultra low input energy at a pump wavelength of 1550 nm [12

12. D. I. Yeom, E. C. Mägi, M. R. E. Lamont, M. A. F. Roelens, L. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett. **33**(7), 660–662 (2008). [CrossRef] [PubMed]

13. D. D. Hudson, S. A. Dekker, E. C. Mägi, A. C. Judge, S. D. Jackson, E. Li, J. S. Sanghera, L. B. Shaw, I. D. Aggarwal, and B. J. Eggleton, “Octave spanning supercontinuum in an As_{2}S_{3} taper using ultralow pump pulse energy,” Opt. Lett. **36**(7), 1122–1124 (2011). [CrossRef] [PubMed]

_{2}Se

_{3}and As

_{2}S

_{3}chalcogenide photonic nanowires for soliton self-compression. In Section 2, we study the theory and the numerical modeling behind accurate calculation of the optical properties of photonic nanowires including chromatic dispersion, effective mode area and nonlinear coefficient. In addition, the cut-off condition of single mode operation in photonic nanowires is determined. Section 3 shows the results of the optical properties modeling and analyzes the soliton-self compression in chalcogenide photonic nanowire glasses. Aiming to optimize the soliton-effect compression in photonic nanowire, we select the 800 nm core diameter nanowire size for which large region of the anomalous group velocity dispersion and low third-order dispersion are found at pump wavelength of 1550 nm for the air-chalcogenide (As

_{2}Se

_{3}and As

_{2}S

_{3}) photonic nanowires. We show that we can generate less than one optical cycle in 800 nm diameter As

_{2}S

_{3}nanowires at very low pulse energy of pJ levels. In fact, pumping the 800 nm air-As

_{2}S

_{3}nanowire at λ

_{p}= 1550 nm with 50 pJ energy allows the compression of a pre-chirped 250 fs down to 5.07 fs. Therefore, soliton-effect compression in the anomalous dispersion regime in the 800 nm diameter As

_{2}Se

_{3}nanowire has been studied and shows the possibility of generating 25.4 fs starting from 250 fs with 10 pJ energy at λ

_{p}= 1550 nm. The effect of TPA has been also studied since As

_{2}Se

_{3}presents a high TPA coefficient comparing to As

_{2}S

_{3}.

## 2. Theory and numerical analysis

### 2.1 Mode propagation

_{11}) guiding for

*V*< 2.405.

### 2.2 Chromatic dispersion

_{11}. We apply a full vectorial finite element method (FEM) with dense meshes made up of 10

^{4}~10

^{5}elements according to the dimensions of the photonic nanowire. In fact, by dividing the fiber cross-section into curvilinear hybrid edge/nodal elements and applying the finite element procedure, we obtain the following eigenvalue equation [15

15. M. Zghal and R. Cherif, “Impact of small geometrical imperfections on chromatic dispersion and birefringence in photonic crystal fibers,” Opt. Eng. **46**(12), 128002 (2007). [CrossRef]

**K**] and [

**M**] are the finite element matrices, {

**E**} is the discretized electric field vector consisting of the edge and nodal variables. Resolving Eq. (1) in the As-S and As-Se wavelength ranges gives the effective index

*n*of the fundamental mode as a function of the optical wavelength. Thus, the group velocity dispersion (GVD) referred to as chromatic dispersion (

_{eff}*D*) can be determined from the second derivative of the mode effective index as a function of the wavelength. It is given by:where

_{c}*c*is the velocity of light in vacuum.

### 2.3 Evanescent field and effective nonlinearity

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]

*S*is the longitudinal component of the Poynting vector,

_{z}*n*

_{2}is the nonlinear index and

**r**is the cross sectional position vector. Because of a significant fraction of the optical mode propagates in the air outside the core and

*n*of the cladding (air) is negligible compared to that of the core glass, the integrals in the numerator are evaluated only over the glass core region. The integrals in the denominator are evaluated over the total transverse section of the fiber. In addition, to obtain complete information about the power residing in the evanescent field, we evaluate the fractional power

_{2}*η*outside the core. It is given by

_{EF}*η*is the fractional power inside the core and it is expressed by:

### 2.4 Nonlinear propagation

^{13}time and frequency discretization points and a longitudinal step size <1 µm were used in our simulations. To start the resolution, we need to set the input pulse shape and duration. We consider the injection of an input soliton order

*N*having an envelope field expression given by [18]:where

*P*is the peak power and

_{0}*T*is the input soliton duration defined as T

_{0}_{FWHM}/1.763. T

_{FWHM}is the input pulse full width at half maximum (FWHM) duration.

*C*is the chirp parameter controlling the initial chirp. The soliton order

*N*is defined as [18]

## 3. Numerical results

_{2}Se

_{3}and air-As

_{2}S

_{3}nanowires and determine the cut-off condition for single mode operation in these photonic nanowires. Then, we analyze the soliton-self compression in both As

_{2}Se

_{3}and As

_{2}S

_{3}air-chalcogenide photonic nanowires. The study is based on the optimization of initial chirp in order to generate efficient soliton-self compression with the lowest input pulse energy.

### 3.1 Air-As_{2}Se_{3} nanowires

_{2}Se

_{3}photonic nanowires by using the Sellmeier equation of the As

_{2}Se

_{3}glass defined as

*A*= −4.5102,

*B*= 12.0582,

*C*= 0.0018 µm

^{−2}and

*D*= 0.0878 µm

^{2}[20

20. R. Cherif, A. Ben-Salem, M. Zghal, P. Besnard, T. Chartier, L. Brilland, and J. Troles, “Highly nonlinear As_{2}Se_{3}-based chalcogenide photonic crystal fiber for midinfrared supercontinuum generation,” Opt. Eng. **49**(9), 095002 (2010). [CrossRef]

_{2}Se

_{3}nanowires with core diameters ranging from 600 nm to 1000 nm.

_{2}Se

_{3}nanowire diameter shifts the first zero dispersion wavelength of the nanowire toward midinfrared wavelengths which enlarges the region of the anomalous dispersion regime. As the core diameter is reduced to sub-micron dimensions, the waveguide dispersion becomes dominant over the material dispersion (bulk As

_{2}Se

_{3}) allowing the overall-GVD to be highly engineered. We find that the 900 nm air-As

_{2}Se

_{3}has a zero dispersion wavelength around 1550 nm. The 800 nm air-As

_{2}Se

_{3}presents a positive chromatic dispersion value at 1550 nm and low third-order dispersion (

*β*= −0.48 ps

_{2}^{2}.m

^{−1}and

*β*= 7.79 × 10

_{3}^{−3}ps

^{3}.m

^{−1}). Consequently, pumping at this wavelength in the anomalous dispersion regime is attractive to simulate soliton-effect compression. Before investigating the nonlinear propagation in such air-As

_{2}Se

_{3}nanowires, one should characterize the optical properties of the air-As

_{2}Se

_{3}nanowires under investigation.

_{2}Se

_{3}nanowire diameter at 1550 nm. The dominance of the evanescent field begins to appear and exceeds 50% of the total light with nanowire diameters less than 370 nm. The single mode operation is found in nanowires with diameters less than

*d*= 448 nm. At this critical diameter, more than 85% of the light is inside the core. For the 800 nm air-As

_{SM}_{2}Se

_{3}nanowire, 98% of the total light propagates inside the core. Figure 2(b) shows the calculated nonlinear coefficient γ of the different air-As

_{2}Se

_{3}nanowires and their effective mode area

_{p}= 1550 nm. We notice that the mode confinement determined by the effective mode area becomes stronger when reducing the core diameter of the air-As

_{2}Se

_{3}nanowire. This behavior continues linearly to evolve and shows an optimal nanowire size exhibiting the minimum effective mode area / the highest effective nonlinearity with a core diameter of about 450 nm. After this optimum value, the mode confinement diverges rapidly. This is justified by the fact that the air-As

_{2}Se

_{3}nanowire no longer tightly confines the light so that the evanescent field starts to dominate. For the 800 nm air-As

_{2}Se

_{3}nanowire, the effective mode area is evaluated to be

*A*= 0.3 µm

_{eff}^{2}. Thus, a very high nonlinear coefficient is exhibited and found to be around 145.3 W

^{−1}.m

^{−1}by taking

*n*= 1.1 × 10

_{2}^{−17}m

^{2}.W

^{−1}[21

21. 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 As_{2}Se_{3} chalcogenide fibers,” J. Opt. Soc. Am. B **21**(6), 1146–1155 (2004). [CrossRef]

_{2}Se

_{3}photonic nanowires, we introduce them in the GNLSE as inputs to investigate the nonlinear propagation in the 800 nm air-As

_{2}Se

_{3}nanowire. As we found that the 800 nm air-As

_{2}Se

_{3}performs in the anomalous dispersion regime around a pump wavelength of 1550 nm, we select, based on the availability, a femtosecond laser delivering 250 fs FWHM at 1550 nm [10

10. M. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, “Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires,” Opt. Express **13**(18), 6848–6855 (2005). [CrossRef] [PubMed]

_{2}Se

_{3}glass are set to be

*τ*= 23fs,

_{1}*τ*= 164.5fs and

_{2}*f*= 0.148 [22]. The coefficient loss

_{R}*α*= 1 dB.m

^{−1}[23

23. C. Xiong, E. Magi, F. Luan, A. Tuniz, S. Dekker, J. S. Sanghera, L. B. Shaw, I. D. Aggarwal, and B. J. Eggleton, “Characterization of picosecond pulse nonlinear propagation in chalcogenide As_{2}S_{3} fiber,” Appl. Opt. **48**(29), 5467–5474 (2009). [CrossRef] [PubMed]

*α*= 2.5 × 10

_{2}^{−12}m/W [21

21. 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 As_{2}Se_{3} chalcogenide fibers,” J. Opt. Soc. Am. B **21**(6), 1146–1155 (2004). [CrossRef]

_{2}Se

_{3}glass, we select a very low input pulse energy to characterize the soliton-self compression in the 800 nm air-As

_{2}Se

_{3}nanowire. We set the input pulse energy to 10 pJ at a pump wavelength of 1550 nm and inject an input hyperbolic-secant pulse initially chirped with

*C*= −0.3 which is found to optimize the temporal compression. This optimal value of the chirp is determined by carrying out several calculations, at a fixed input pulse energy, in which we vary the initial chirp and register the shortest FWHM duration of the generated compressed pulse

*T*, as seen in Fig. 3 . We find that positive chirp degrades the temporal compression while negative chirp enhances the soliton-effect compression (

_{comp}*C*= −0.3 provides maximum temporal compression).

24. A. Ben Salem, R. Cherif, and M. Zghal, “Generation of few optical cycles in air-silica nanowires,” Proc. SPIE **8001**, 80011J (2011). [CrossRef]

9. C. M. Chen and P. L. Kelley, “Nonlinear pulse compression in optical fibers: scaling laws and numerical analysis,” J. Opt. Soc. Am. B **19**(9), 1961–1967 (2002). [CrossRef]

*N*= 14.5. We characterize the compression efficiency by the evaluation of two parameters namely the compression factor

*F*and the quality factor

_{c}*Q*. The compression factor

_{c}*F*, defined as the ratio of the FWHM pulse duration at the beginning and the end of the nanowire, is found to be 9.84. The correspondent quality factor

_{c}_{Qc=Pcomp/(P0Fc)}[10

**13**(18), 6848–6855 (2005). [CrossRef] [PubMed]

*P*) normalized to the input peak power (

_{comp}*P*) and the compression factor (

_{0}*F*) is evaluated to be 0.21. Spectral evolution of the initial pre-chirped hyperbolic-secant pulse is depicted in Fig. 4(b).

_{c}_{2}Se

_{3}nanowires. We notice the generation of over 700 nm bandwidth of near infrared SC showing a symmetrical broadening which confirms that self phase modulation is the dominant effect giving such broadening and leading to temporal soliton-self compression.

### 3.2 Air-As_{2}S_{3} nanowires

_{2}S

_{3}photonic nanowires, we used the Sellmeier equation of the As

_{2}S

_{3}glass defined as

*A*= 1.898367,

_{1}*A*= 1.922297,

_{2}*A*= 0.87651,

_{3}*A*= 0.11887,

_{4}*A*= 0.95699, λ

_{5}_{1}= 0.15 µm, λ

_{2}= 0.25µm, λ

_{3}= 0.35µm, λ

_{4}= 0.45µm and λ

_{5}= 27.3861µm [25]. The unit of λ is µm.

_{2}S

_{3}nanowires. We notice the similar chromatic dispersion behavior as air-As

_{2}Se

_{3}nanowires: when the diameter increases the region of the anomalous dispersion regime shifts toward infrared wavelengths. Air-As

_{2}S

_{3}nanowires with diameters ranging from 600 nm to 1000 nm exhibit positive chromatic dispersion around 1550 nm. We found very low GVD and third-order dispersion coefficients (

*β*= −1.54 ps

_{2}^{2}.m

^{−1}and

*β*= 5.65 × 10

_{3}^{−3}ps

^{3}.m

^{−1}) for the 800 nm air-As

_{2}S

_{3}nanowire. Pumping at this wavelength will excite soliton-self compression in the anomalous dispersion regime in the 800 nm air-As

_{2}S

_{3}nanowire. A detailed study of the fundamental mode has been achieved for air-As

_{2}S

_{3}nanowires.

_{2}S

_{3}nanowire diameter. The evanescent field starts to dominate and exceeds 50% of the total light with nanowire diameters less than 420 nm. With a critical diameter

*d*= 533 nm, air-As

_{SM}_{2}S

_{3}nanowires experience fundamental mode propagation. At this diameter, more than 82% of the light propagates inside the core. For the 800 nm air-As

_{2}Se

_{3}nanowire, 4% of the light resides in the evanescent field while 96% of the remaining light propagates inside the core. Thus, high nonlinear coefficient is exhibited and evaluated to be around 48.7 W

^{−1}.m

^{−1}by taking

*n*= 4 × 10

_{2}^{−18}m

^{2}.W

^{−1}[26

26. D.-P. Wei, T. Galstian, I. Smolnikov, V. Plotnichenko, and A. Zohrabyan, “Spectral broadening of femtosecond pulses in a single-mode As-S glass fiber,” Opt. Express **13**(7), 2439–2443 (2005). [CrossRef] [PubMed]

_{2}Se

_{3}nanowires and their effective mode area at 1550 nm. Similar behavior of the nonlinear coefficient is depicted for air-As

_{2}S

_{3}nanowires as the air-As

_{2}Se

_{3}nanowires. The highest effective nonlinearity is exhibited for an optimal nanowire size of 540 nm. We find that the highest effective nonlinearity and the mode confinement depend on the contrast of the core-cladding refractive-index difference. In fact, when the refractive index difference

*Δn*between the core and the air-cladding increases for a certain optical wavelength, the optimal photonic nanowire diameter presenting the highest effective nonlinearity shifts and becomes smaller. This is the case at 1550 nm for As

_{2}S

_{3}(

*Δn*= 1.43) and As

_{2}Se

_{3}(

*Δn*= 1.83) glasses showing optimal nanowire diameters of 540 nm and 450 nm, respectively. More light confinement with 2% for the 800 nm air-As

_{2}Se

_{3}nanowire is found compared to that in the 800 nm air-As

_{2}S

_{3}nanowire.

_{2}S

_{3}nanowire. As the 800 nm air-As

_{2}Se

_{3}, we select the femtosecond laser delivering 250 fs FWHM pulse at 1550 nm. We take

*τ*= 15.5fs,

_{1}*τ*= 230.5fs and

_{2}*f*= 0.1 to model the Raman response function of the As

_{R}_{2}S

_{3}glass and set

*α*= 1 dB.m

^{−1}[23

23. C. Xiong, E. Magi, F. Luan, A. Tuniz, S. Dekker, J. S. Sanghera, L. B. Shaw, I. D. Aggarwal, and B. J. Eggleton, “Characterization of picosecond pulse nonlinear propagation in chalcogenide As_{2}S_{3} fiber,” Appl. Opt. **48**(29), 5467–5474 (2009). [CrossRef] [PubMed]

_{2}S

_{3}nanowire, a very low input pulse energy of 50 pJ is taken. This corresponds to the excitation of an input soliton order of

*N*= 10.56. In order to optimize the soliton-self compression, the input hyperbolic-secant pulse is chosen initially chirped with

*C*= −0.2 (Similar approach has been performed to determine the optimal chirp value). Figure 7 shows a maximum compressed pulse with duration of 5.07 fs in 0.84 mm nanowire length. Thus, less than single optical cycle is generated at a pump wavelength of 1550 nm. Good agreement was found with the analytical expression determining the optimal soliton-self compression distance [9

9. C. M. Chen and P. L. Kelley, “Nonlinear pulse compression in optical fibers: scaling laws and numerical analysis,” J. Opt. Soc. Am. B **19**(9), 1961–1967 (2002). [CrossRef]

*F*= 49.3 and a quality factor

_{c}*Q*= 0.28 are achieved.

_{c}_{2}S

_{3}with only 50 pJ input energy. We notice that the impact of the TPA is not discussed here because As

_{2}S

_{3}glass exhibits a very low TPA coefficient comparing to that of the As

_{2}Se

_{3}glass and simulations show no effect on the generated SC. We recall that previous experimental work has been performed at the same pump wavelength of 1550 nm using short segment of 10 cm of a highly nonlinear silica fiber with sub-nJ laser source [27

27. B. Kibler, R. Fischer, P.-A. Lacourt, F. Courvoisier, R. Ferriere, L. Larger, D. N. Neshev, and J. M. Dudley, “Optimised one-step compression of femtosecond fibre laser soliton pulses around 1550 nm to below 30 fs in highly nonlinear fibre,” Electron. Lett. **43**(17), 915–916 (2007). [CrossRef]

_{2}Se

_{3}and air-As

_{2}S

_{3}structures) show shorter compressed pulse in only few millimeter-long fibers at pJ energy levels. Thus, chalcogenide photonic nanowires are very promising for efficient broadband soliton-self compression with short lengths and very low input pulse energy.

## 4. Conclusion

_{2}S

_{3}and As

_{2}Se

_{3}glasses. Most attractive optical properties of photonic nanowire are the existence of the evanescent field surrounding the nanowire and the strong radial confinement of the light which make photonic nanowires well suited for an efficient and controlled interaction of guided light with matter and perfect devices for sensing applications [28

28. G. Brambilla, “Optical fibre nanotaper sensors,” Opt. Fiber Technol. **16**(6), 331–342 (2010). [CrossRef]

_{2}S

_{3}nanowire while 25.4fs compressed pulse is generated in the As

_{2}Se

_{3}with consideration of TPA. Thus, very high compression factors of 49.3 and 9.84 have been achieved starting from 250 fs for chalcogenide (As

_{2}S

_{3}and As

_{2}Se

_{3}) nanowires, respectively. All the compressed pulses are obtained at very low input pulse energy with pJ levels in just few millimeters-long nanowires. The study was based on the adjustment of the initial chirp in order to maximize the compression. In addition, the generation of midinfrared two octaves spanning SC around 1550 nm in only 0.84 mm air-As

_{2}S

_{3}nanowire is shown. Chalcogenide photonic nanowires are very promising devices for designing midinfrared light coherent sources with short lengths and low powers. They are suitable waveguides for high soliton-effect compression which opens new horizon toward extreme nonlinear optics and attosecond physics.

## Acknowledgments

## References and links

1. | L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature |

2. | M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express |

3. | E. C. Mägi, P. Steinvurzel, and B. J. Eggleton, “Tapered photonic crystal fibers,” Opt. Express |

4. | Y. K. Lizé, E. C. Mägi, V. G. Ta’eed, J. A. Bolger, P. Steinvurzel, and B. J. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express |

5. | R. R. Gattass, G. T. Svacha, L. M. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express |

6. | S. G. Leon-Saval, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, and M. W. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express |

7. | L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. |

8. | L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, “Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers,” Opt. Lett. |

9. | C. M. Chen and P. L. Kelley, “Nonlinear pulse compression in optical fibers: scaling laws and numerical analysis,” J. Opt. Soc. Am. B |

10. | M. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, “Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires,” Opt. Express |

11. | J. M. Harbold, F. O. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As-S-Se glasses for all-optical switching,” Opt. Lett. |

12. | D. I. Yeom, E. C. Mägi, M. R. E. Lamont, M. A. F. Roelens, L. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett. |

13. | D. D. Hudson, S. A. Dekker, E. C. Mägi, A. C. Judge, S. D. Jackson, E. Li, J. S. Sanghera, L. B. Shaw, I. D. Aggarwal, and B. J. Eggleton, “Octave spanning supercontinuum in an As |

14. | L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express |

15. | M. Zghal and R. Cherif, “Impact of small geometrical imperfections on chromatic dispersion and birefringence in photonic crystal fibers,” Opt. Eng. |

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

17. | T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. |

18. | G. P. Agrawal, |

19. | K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. |

20. | R. Cherif, A. Ben-Salem, M. Zghal, P. Besnard, T. Chartier, L. Brilland, and J. Troles, “Highly nonlinear As |

21. | 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 As |

22. | A. Ben-Salem, R. Cherif, and M. Zghal, “Raman response of a highly nonlinear As |

23. | C. Xiong, E. Magi, F. Luan, A. Tuniz, S. Dekker, J. S. Sanghera, L. B. Shaw, I. D. Aggarwal, and B. J. Eggleton, “Characterization of picosecond pulse nonlinear propagation in chalcogenide As |

24. | A. Ben Salem, R. Cherif, and M. Zghal, “Generation of few optical cycles in air-silica nanowires,” Proc. SPIE |

25. | M. Bass, |

26. | D.-P. Wei, T. Galstian, I. Smolnikov, V. Plotnichenko, and A. Zohrabyan, “Spectral broadening of femtosecond pulses in a single-mode As-S glass fiber,” Opt. Express |

27. | B. Kibler, R. Fischer, P.-A. Lacourt, F. Courvoisier, R. Ferriere, L. Larger, D. N. Neshev, and J. M. Dudley, “Optimised one-step compression of femtosecond fibre laser soliton pulses around 1550 nm to below 30 fs in highly nonlinear fibre,” Electron. Lett. |

28. | G. Brambilla, “Optical fibre nanotaper sensors,” Opt. Fiber Technol. |

**OCIS Codes**

(160.4330) Materials : Nonlinear optical materials

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

(320.5520) Ultrafast optics : Pulse compression

(320.7140) Ultrafast optics : Ultrafast processes in fibers

(320.6629) Ultrafast optics : Supercontinuum generation

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: August 10, 2011

Revised Manuscript: September 16, 2011

Manuscript Accepted: September 20, 2011

Published: September 27, 2011

**Citation**

Amine Ben Salem, Rim Cherif, and Mourad Zghal, "Soliton-self compression in highly nonlinear chalcogenide photonic nanowires with ultralow pulse energy," Opt. Express **19**, 19955-19966 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-21-19955

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### References

- L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003). [CrossRef] [PubMed]
- M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express16(2), 1300–1320 (2008). [CrossRef] [PubMed]
- E. C. Mägi, P. Steinvurzel, and B. J. Eggleton, “Tapered photonic crystal fibers,” Opt. Express12(5), 776–784 (2004). [CrossRef] [PubMed]
- Y. K. Lizé, E. C. Mägi, V. G. Ta’eed, J. A. Bolger, P. Steinvurzel, and B. J. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express12(14), 3209–3217 (2004). [CrossRef] [PubMed]
- R. R. Gattass, G. T. Svacha, L. M. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express14(20), 9408–9414 (2006). [CrossRef] [PubMed]
- S. G. Leon-Saval, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, and M. W. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express12(13), 2864–2869 (2004). [CrossRef] [PubMed]
- L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett.45(13), 1095–1098 (1980). [CrossRef]
- L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, “Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers,” Opt. Lett.8(5), 289–291 (1983). [CrossRef] [PubMed]
- C. M. Chen and P. L. Kelley, “Nonlinear pulse compression in optical fibers: scaling laws and numerical analysis,” J. Opt. Soc. Am. B19(9), 1961–1967 (2002). [CrossRef]
- M. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, “Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires,” Opt. Express13(18), 6848–6855 (2005). [CrossRef] [PubMed]
- J. M. Harbold, F. O. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As-S-Se glasses for all-optical switching,” Opt. Lett.27(2), 119–121 (2002). [CrossRef] [PubMed]
- D. I. Yeom, E. C. Mägi, M. R. E. Lamont, M. A. F. Roelens, L. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett.33(7), 660–662 (2008). [CrossRef] [PubMed]
- D. D. Hudson, S. A. Dekker, E. C. Mägi, A. C. Judge, S. D. Jackson, E. Li, J. S. Sanghera, L. B. Shaw, I. D. Aggarwal, and B. J. Eggleton, “Octave spanning supercontinuum in an As2S3 taper using ultralow pump pulse energy,” Opt. Lett.36(7), 1122–1124 (2011). [CrossRef] [PubMed]
- L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express12(6), 1025–1035 (2004). [CrossRef] [PubMed]
- M. Zghal and R. Cherif, “Impact of small geometrical imperfections on chromatic dispersion and birefringence in photonic crystal fibers,” Opt. Eng.46(12), 128002 (2007). [CrossRef]
- M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express12(13), 2880–2887 (2004). [CrossRef] [PubMed]
- T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett.78(17), 3282–3285 (1997). [CrossRef]
- G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).
- K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron.25(12), 2665–2673 (1989). [CrossRef]
- R. Cherif, A. Ben-Salem, M. Zghal, P. Besnard, T. Chartier, L. Brilland, and J. Troles, “Highly nonlinear As2Se3-based chalcogenide photonic crystal fiber for midinfrared supercontinuum generation,” Opt. Eng.49(9), 095002 (2010). [CrossRef]
- 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. B21(6), 1146–1155 (2004). [CrossRef]
- A. Ben-Salem, R. Cherif, and M. Zghal, “Raman response of a highly nonlinear As2Se3-based chalcogenide photonic crystal fiber,” Proc. PIERS, 1256–1260, Marrakesh, Morocco (2011).
- C. Xiong, E. Magi, F. Luan, A. Tuniz, S. Dekker, J. S. Sanghera, L. B. Shaw, I. D. Aggarwal, and B. J. Eggleton, “Characterization of picosecond pulse nonlinear propagation in chalcogenide As2S3 fiber,” Appl. Opt.48(29), 5467–5474 (2009). [CrossRef] [PubMed]
- A. Ben Salem, R. Cherif, and M. Zghal, “Generation of few optical cycles in air-silica nanowires,” Proc. SPIE8001, 80011J (2011). [CrossRef]
- M. Bass, Handbook of Optics (McGraw Hill, 1997).
- D.-P. Wei, T. Galstian, I. Smolnikov, V. Plotnichenko, and A. Zohrabyan, “Spectral broadening of femtosecond pulses in a single-mode As-S glass fiber,” Opt. Express13(7), 2439–2443 (2005). [CrossRef] [PubMed]
- B. Kibler, R. Fischer, P.-A. Lacourt, F. Courvoisier, R. Ferriere, L. Larger, D. N. Neshev, and J. M. Dudley, “Optimised one-step compression of femtosecond fibre laser soliton pulses around 1550 nm to below 30 fs in highly nonlinear fibre,” Electron. Lett.43(17), 915–916 (2007). [CrossRef]
- G. Brambilla, “Optical fibre nanotaper sensors,” Opt. Fiber Technol.16(6), 331–342 (2010). [CrossRef]

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