soliton-self compression in highly nonlinear chalcogenide photonic nanowires with ultralow pulse...

Soliton-self compression in highly nonlinear

chalcogenide photonic nanowires with ultralow

pulse energy

Amine Ben Salem,* Rim Cherif, and Mourad Zghal

University of Carthage, Engineering School of Communication of Tunis (Sup’Com), Cirta’Com Laboratory, Ghazala

Technopark, 2083, Ariana, Tunisia

*[email protected]

Abstract: We design As2Se3 and As2S3 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 As2S3 photonic nanowire: a 5.07 fs compressed pulse is

obtained starting from 250 fs input pulse with 50 pJ in 0.84 mm-long As2S3

nanowire. Taking into account the high two photon absorption (TPA)

coefficient in the As2Se3 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 Optical Society of America

OCIS codes: (160.4330) Nonlinear optical materials; (190.4370) Nonlinear optics, fibers;

(320.5520) Pulse compression; (190.5530) Pulse propagation and temporal solitons; (320.7140)

Ultrafast processes in fibers; (320.6629) Supercontinuum generation.

References and links

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#152737 - $15.00 USD Received 10 Aug 2011; revised 16 Sep 2011; accepted 20 Sep 2011; published 27 Sep 2011(C) 2011 OSA 10 October 2011 / Vol. 19, No. 21 / OPTICS EXPRESS 19955

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1. Introduction

Highly nonlinear optical waveguides have great interest for compact, low power and all

optical nonlinear applications. In fact, photonic nanowires with diameters smaller than the

wavelength of the guided light attract considerable interest due to their unique optical and

nonlinear properties for wide range of applications [1]. They are obtained by tapering optical

fibers which is the commonly used method for reducing optical fiber dimensions and

engineering the waveguide dispersion [2–4]. These structures are not only suitable for

nanophotonic devices but also enable nonlinear process such as soliton-effect compression

and broadband supercontinuum (SC) generation at low input pulse energies [5,6]. Generation

of few-optical cycles directly from oscillators requires special designed cavities with high

reflectivity dispersion compensating mirrors, and initial energy in the order of hundreds of µJ.

Therefore, the used compression technique consists of using external passive or active

dispersion compensation schemes in order to compress the laser pulse initially broadened by

self-phase modulation (SPM) in a waveguide. In both techniques, the required dispersion

compensation requires complex electronically controlled feedback systems. An impressive

method toward the monocycle regime relying on the soliton-effect compression has been used

to successfully compress low-energy ps-pulses without additional dispersion compensation

schemes [7,8]. This method exploits the property of propagating high-order soliton in the

anomalous dispersion regime in optical fibers where efficient compression results from the

interplay between the dispersion and the self phase modulation effects. Therefore scaling laws

have been developed for the soliton-self compression parameters, for hyperbolic-secant

pulses, with numerical and analytical methods [8,9].

The introduction of highly nonlinear photonic nanowires with anomalous group velocity

dispersion at visible and near-infrared wavelengths has enormously contributed in the study of

soliton-self compression techniques and the generation of few to single optical cycles.

Specifically, the broad region of anomalous dispersion regime can be shifted for photonic

nanowires and extends into the visible for silica nanowires and into the midinfrared for

chalcogenide nanowires. Large anomalous group velocity dispersion region with low third-

order dispersion are required to achieve efficient soliton-self compression [2,10]. In the 800

nm region, Foster et al. [10], experimentally demonstrated soliton-self compression by


performing a cross correlation frequency resolved optical grating (XFROG) measurements.

They showed the generation of 6.8 fs compressed pulse at low input energy from initial 70 fs

in 980 nm core diameter air-silica photonic nanowire. In addition, they theoretically predicted

soliton-self compression of 30 fs input pulse to 1.8 fs in 650 µm-long 800 nm-diameter air-

silica nanowire.

Most achievements in ultrafast nonlinear optics have been made in photonic nanowires

based on silica glass but studies on highly nonlinear glasses have been recently started too.

Chalcogenide glasses based on As2S3 and As2Se3 have been the subject of intense

investigations due to their high nonlinear coefficient n2 (100-1000 times larger than of silica

glass), low linear loss and low to moderate two photon absorption (TPA) coefficient [11].

Recent works have showed the generation of SC in such photonic chalcogenide As2S3 and

As2Se3 nanowires with ultra low input energy at a pump wavelength of 1550 nm [12,13].

However, to our knowledge, soliton self-compression in such highly nonlinear nanowires has

not been studied so far.

In this paper, we investigate the linear and the nonlinear properties of As2Se3 and As2S3

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

(As2Se3 and As2S3) photonic nanowires. We show that we can generate less than one optical

cycle in 800 nm diameter As2S3 nanowires at very low pulse energy of pJ levels. In fact,

pumping the 800 nm air-As2S3 nanowire at λp = 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 As2Se3 nanowire has been studied

and shows the possibility of generating 25.4 fs starting from 250 fs with 10 pJ energy at λp =

1550 nm. The effect of TPA has been also studied since As2Se3 presents a high TPA

coefficient comparing to As2S3.

2. Theory and numerical analysis

2.1 Mode propagation

Since they exhibit large refractive index difference between the core and the air-cladding,

photonic nanowires with core diameters less than one micron are modeled as circular rods in

air [14]. Thus, Maxwell’s equations can be reduced to the following Helmholtz equation

satisfied by the vectorial electric field E; it is given by [14]:

2 2 2 2

0E ( )E 0n k β∇ + − = (1)

where∇ is the Laplacian operator, 0

2 /k π λ= is the free space wavenumber, n = n(r) is the

refractive index profile of the photonic nanowire and β is the propagation constant of the

optical mode. The eigenvalue equations of Eq. (1) for the hybrid modes HEνm and EHνm are

given by [14]:

2 2 4' ' ' '

0

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

cl

c c

J U K W J U n K W V

UJ U WK W UJ U n WK W k n UW

υ υ υ υ

υ υ υ υ

νβ + + =

(2)


where Jv is the Bessel function of the first kind, Kv is the modified Bessel function of the

second kind, 2 2 2

0/ 2

cU d k n β= − , 2/22

0

2

clnkdW −= β , 2/22

0 clc nndkV −= , and d is

the nanowire core diameter. We assume that the index of the air-cladding ncl is 1.0, and use

the Sellmeier-type dispersion formula to obtain the refractive index nc of the chalcogenide

core material. The V-number is the normalized frequency and related to the numerical

aperture2 2

c clNA n n= − . It is expressed by )./( NAdV λπ= .

Like conventional optical fibers, photonic nanowires experience single-mode (HE11)

guiding for V < 2.405.

2.2 Chromatic dispersion

In order to determine the chromatic dispersion of the chalcogenide nanowires, we need to

calculate the effective index / (2 )eff

n βλ π= of the fundamental mode HE11. We apply a full

vectorial finite element method (FEM) with dense meshes made up of 104~10

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]:

[ ] { } [ ] { } { }2 2

0 0effk n− =K E M E (3)

where [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 neff of the fundamental mode as a function of the

optical wavelength. Thus, the group velocity dispersion (GVD) referred to as chromatic

dispersion (Dc) can be determined from the second derivative of the mode effective index as a

function of the wavelength. It is given by:

c

2

eff

2

d nλD

c dλ= − (4)

where c is the velocity of light in vacuum.

2.3 Evanescent field and effective nonlinearity

With their small core dimensions and the large core-cladding refractive-index difference,

chalcogenide nanowires exhibit tighter light confinement and higher nonlinear coefficient than

standard fibers. However, in nanowires, the optical mode can extend evanescently outside the

core boundaries, and then an accurate estimation of the nonlinear coefficient γ is needed. The

nonlinear coefficient γ is then defined as [16]:

( )

2 2

2

22

.2 z

z

n S d

S d

πγ

λ= ∫

∫

r

r

(5)

where Sz is the longitudinal component of the Poynting vector, n2 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 n2 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 ηEF outside the core. It is given by EF

1η η= − where η is the

fractional power inside the core and it is expressed by:


/2 2

0 0

2

0 0

. .

. .

d

z

z

S rdr d

S rdr d

π

π

ϕη

ϕ∞=∫ ∫

∫ ∫ (6)

2.4 Nonlinear propagation

Considering the optical waveguide properties of the chalcogenide photonic nanowire, the

investigation of the nonlinear propagation and the soliton-self compression are based on the

resolution of the generalized nonlinear Schrödinger equation (GNLSE). The authors in ref

[17]. attempt to overcome the limitations of the slowly-varying envelope approximation

(SVEA) and have demonstrated that the concept of envelope and first-order equation can be

used even in the extreme case of single-optical-cycle-regime. The GNLSE is given by [18]:

1

2

0 0

2

0

12 ! 2

( , ) ( ') ( , ') '

m m

m

mm eff

jA A jA j j

z m t A t

A z t R t A z t t dt

β ααγ

ω

+

≥

+∝

∂ ∂ ∂= − + + + + ∂ ∂ ∂

× −

∑

∫ (7)

where A(z,t) is the slowly varying envelope, α is the loss coefficient and βm the mth

-order

dispersion coefficients. α2 is the TPA coefficient of the core glass and ω0 is the pump central

frequency. The nonlinear response function R(t) includes the instantaneous and the delayed

Raman contributions. It is given by [18]:

( ) (1 ) ( ) ( )R R R

R t f t f h tδ= − + (8)

fR is the fractional contribution of the material. The delayed Raman response hR(t) is expressed

through the Green’s function of the damped harmonic oscillator [19]:

1 2

1 2 2 1

² ²( ) exp( )sin( )

²R

t th t

τ ττ τ τ τ+

= − (9)

where the parameters τ1 and τ2 correspond respectively to the inverse of the phonon oscillation

frequency and the bandwidth of the Raman gain spectrum.

The resolution of the GNLSE is performed by the symmetrized split step Fourier method.

The 4th-order Runge-Kutta algorithm was used in our calculations. To have accurate

numerical results, 213

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]:

2

0 2

0 0

(0, ) sec ( )exp( )2

t tA t P h iC

T T= − (10)

where P0 is the peak power and T0 is the input soliton duration defined as TFWHM /1.763.

TFWHM 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] 2 2

0 0 2/ /

D NLN L L T Pγ β= = where

2

2

0 / βTLD = is the dispersion length and 1

0( )

NLL Pγ −=

is the nonlinear length.


3. Numerical results

In this section, we determine the optical properties of air-chalcogenide nanowires which are

produced from tapering conventional single mode fibers. We investigate the optical field

distribution in air-As2Se3 and air-As2S3 nanowires and determine the cut-off condition for

single mode operation in these photonic nanowires. Then, we analyze the soliton-self

compression in both As2Se3 and As2S3 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-As2Se3 nanowires

We have carried out a rigorous calculation of the chromatic dispersion of the different air-

As2Se3 photonic nanowires by using the Sellmeier equation of the As2Se3 glass defined as

222 )/()( λλλλ CDBAn +−+= where A = −4.5102, B = 12.0582, C = 0.0018 µm−2

and D =

0.0878 µm2 [20]. The unit of λ is µm. Figure 1 depicts the chromatic dispersion as a function

of the wavelength of air-As2Se3 nanowires with core diameters ranging from 600 nm to 1000

nm.

1000 1200 1400 1600 1800 2000 2200-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

Ch

rom

atic d

isp

ers

ion

[ps/(

nm

.km

)]

Wavelength [nm]

600 nm

700 nm

800 nm

900 nm

1000 nm

bulk As2Se

3

Fig. 1. Calculated chromatic dispersion of air-As2Se3 nanowires with core diameters ranging

from 600 nm to 1000 nm.

As we can see from Fig. 1, increasing the air-As2Se3 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

As2Se3) allowing the overall-GVD to be highly engineered. We find that the 900 nm air-

As2Se3 has a zero dispersion wavelength around 1550 nm. The 800 nm air-As2Se3 presents a

positive chromatic dispersion value at 1550 nm and low third-order dispersion (β2 = −0.48

ps2.m

−1 and β3 = 7.79 × 10

−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-As2Se3 nanowires, one should characterize

the optical properties of the air-As2Se3 nanowires under investigation.

Figure 2(a) depicts the calculated fractional powers inside and outside the core as a

function of the air-As2Se3 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 dSM = 448

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


As2Se3 nanowire, 98% of the total light propagates inside the core. Figure 2(b) shows the

calculated nonlinear coefficient γ of the different air-As2Se3 nanowires and their effective

mode area 2 2

/eff z z

A S dA S dA= ∫ ∫ at λp = 1550 nm. We notice that the mode confinement

determined by the effective mode area becomes stronger when reducing the core diameter of

the air-As2Se3 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-As2Se3 nanowire no longer tightly

confines the light so that the evanescent field starts to dominate. For the 800 nm air-As2Se3

nanowire, the effective mode area is evaluated to be Aeff = 0.3 µm2. Thus, a very high

nonlinear coefficient is exhibited and found to be around 145.3 W−1

.m−1

by taking n2 = 1.1 ×

10−17

m2.W

−1 [21].

Fig. 2. (a) Fractional powers inside and outside the core and (b) effective mode area (Aeff) and

nonlinear coefficient (γ) of various air-As2Se3 nanowire diameters at λp = 1550 nm.

After determining the optical properties of air-As2Se3 photonic nanowires, we introduce

them in the GNLSE as inputs to investigate the nonlinear propagation in the 800 nm air-

As2Se3 nanowire. As we found that the 800 nm air-As2Se3 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]. The Raman response

parameters of the As2Se3 glass are set to be τ1 = 23fs, τ2 = 164.5fs and fR = 0.148 [22]. The

coefficient loss α = 1 dB.m−1

[23].


-0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0

24

28

32

36

40

44

48

52

Chirp parameter, C

Tco

mp[fs]

4

5

6

7

8

9

10

Fc

Fig. 3. Impact of the initial chirp on the compression efficiency.

Taking into account the high two photon absorption coefficient (α2 = 2.5 × 10−12

m/W

[21]) and the high nonlinearity exhibited in As2Se3 glass, we select a very low input pulse

energy to characterize the soliton-self compression in the 800 nm air-As2Se3 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 Tcomp, as seen in Fig. 3. We find

that positive chirp degrades the temporal compression while negative chirp enhances the

soliton-effect compression (C = −0.3 provides maximum temporal compression).

Figure 4(a) shows a maximum generated compressed pulse with a duration of 25.4 fs in

2.1 mm nanowire length. The optimal soliton-self compression length is numerically

determined from the simulations ensuring that a maximum-compressed and preserved soliton-

shape is reached [24] without the presence of high pulse intensity fluctuations or peak

perturbations. Good agreement is found with the analytical model giving optimal distance

proposed in [9]. This nonlinear interaction corresponds to the injection of a soliton order N =

14.5. We characterize the compression efficiency by the evaluation of two parameters namely

the compression factor Fc and the quality factor Qc. The compression factor Fc, 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 )/( 0 ccompc FPPQ = [10] which is equal to the peak

power of the compressed pulse (Pcomp) normalized to the input peak power (P0) and the

compression factor (Fc) is evaluated to be 0.21. Spectral evolution of the initial pre-chirped

hyperbolic-secant pulse is depicted in Fig. 4(b).

The supercontinuum is generated with taking into account the effect of TPA (for which we

extracted the maximum compressed pulse) and then without TPA and we notice its big effect

on the spectral generated bandwidth. In fact, an extra 500 nm bandwidth is generated when

one neglects the TPA. Thus, a perfect modeling has to consider the effect of TPA in order to

obtain correct results simulating the nonlinear propagation in highly nonlinear air-As2Se3

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.


Fig. 4. (a) Temporal and (b) spectral evolution of 250 fs input pulse with 10 pJ input energy in

the 800 nm air-As2Se3 nanowire at λp = 1550 nm, with and without TPA.

3.2 Air-As2S3 nanowires

To evaluate the chromatic dispersion in air-As2S3 photonic nanowires, we used the Sellmeier

equation of the As2S3 glass defined as ∑ −+=i

iiAn )/(1)(222 λλλλ where A1 = 1.898367,

A2 = 1.922297, A3 = 0.87651, A4 = 0.11887, A5 = 0.95699, λ1 = 0.15 µm, λ2 = 0.25µm, λ3 =

0.35µm, λ4 = 0.45µm and λ5 = 27.3861µm [25]. The unit of λ is µm.

Figure 5 depicts the calculated chromatic dispersion of air-As2S3 nanowires. We notice the

similar chromatic dispersion behavior as air-As2Se3 nanowires: when the diameter increases

the region of the anomalous dispersion regime shifts toward infrared wavelengths. Air-As2S3

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

(β2 = −1.54 ps2.m

−1 and β3 = 5.65 × 10

−3 ps

3.m

−1) for the 800 nm air-As2S3 nanowire. Pumping

at this wavelength will excite soliton-self compression in the anomalous dispersion regime in

the 800 nm air-As2S3 nanowire. A detailed study of the fundamental mode has been achieved

for air-As2S3 nanowires.


1000 1200 1400 1600 1800 2000-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Ch

rom

atic d

isp

ers

ion

[ps/(

nm

.km

)]

Wavelength [nm]

600 nm

700 nm

800 nm

900 nm

1000 nm

bulk As2S

3

Fig. 5. Calculated chromatic dispersion of air-As2S3 nanowires with core diameters ranging

from 600 nm to 1000 nm.

Figure 6(a) shows the calculated fractional powers inside and outside the core at a

wavelength of 1550 nm as a function of the air-As2S3 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 dSM = 533 nm, air-As2S3 nanowires experience fundamental mode

propagation. At this diameter, more than 82% of the light propagates inside the core. For the

800 nm air-As2Se3 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 n2 = 4 × 10−18

m2.W

−1 [26].

Fig. 6. (a) Fractional powers inside and outside the core and (b) effective mode area (Aeff) and

nonlinear coefficient (γ) of different air-As2S3 nanowires at λp = 1550 nm.

In fact, Fig. 6(b) shows the calculated nonlinear coefficient of different air-As2Se3

nanowires and their effective mode area at 1550 nm. Similar behavior of the nonlinear

coefficient is depicted for air-As2S3 nanowires as the air-As2Se3 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 ∆n 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 As2S3 (∆n = 1.43) and As2Se3 (∆n = 1.83) glasses showing

optimal nanowire diameters of 540 nm and 450 nm, respectively. More light confinement with

2% for the 800 nm air-As2Se3 nanowire is found compared to that in the 800 nm air-As2S3

nanowire.

We are now in the process of investigating the nonlinear propagation in the 800 nm air-

As2S3 nanowire. As the 800 nm air-As2Se3, we select the femtosecond laser delivering 250 fs

FWHM pulse at 1550 nm. We take τ1 = 15.5fs, τ2 = 230.5fs and fR = 0.1 to model the Raman

response function of the As2S3 glass and set α = 1 dB.m−1

[23]. Because of the high

nonlinearity exhibited in the 800 nm air-As2S3 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]. A compression factor Fc = 49.3 and a quality factor Qc

= 0.28 are achieved.

-250 -200 -150 -100 -50 0 50 100 150 200 2500,0

0,5

1,0

1,5

2,0

2,5

Pe

ak p

ow

er

[kW

]

Time [fs]

z = 0

z = 0.84 mm

5.07 fs

Fig. 7. Temporal evolution of 250 fs input pulse with 50 pJ input energy in the 800 nm air-

As2S3 nanowire at λp = 1550 nm.

Figure 8 depicts the spectral evolution and approximately two octave spanning

supercontinuum is generated in the 800 nm air-As2S3 with only 50 pJ input energy. We notice

that the impact of the TPA is not discussed here because As2S3 glass exhibits a very low TPA

coefficient comparing to that of the As2Se3 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]. Although 30 fs compressed pulse has been generated, air-

chalcogenide nanowires (as demonstrated in both air-As2Se3 and air-As2S3 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.


750 1000 1250 1500 1750 2000 2250 2500 2750-40

-30

-20

-10

0

z = 0

z = 0.84 mm

No

rma

lize

d in

ten

sity [

dB

]

Wavelength [nm]

Fig. 8. Spectral evolution of 250 fs input pulse with 50 pJ input energy in the 800 nm air-As2S3

nanowire at λp = 1550 nm.

4. Conclusion

We have performed a numerical study of soliton self-compression in photonic nanowires.

Detailed studies of the optical properties have been achieved in chalcogenide photonic

nanowires based on As2S3 and As2Se3 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]. Soliton-effect compression has been investigated in chalcogenide photonic nanowires

and pulses in the monocycle regime have been generated in As2S3 nanowire while 25.4fs

compressed pulse is generated in the As2Se3 with consideration of TPA. Thus, very high

compression factors of 49.3 and 9.84 have been achieved starting from 250 fs for

chalcogenide (As2S3 and As2Se3) 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-As2S3 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

The work is partially supported by the “Institut Télécom” through the “Futur et Ruptures”

PhD thesis of A. Ben-Salem. The authors thank Professor John Dudley from Institut Femto-

ST, Université de Franche-Comté, Besançon, France for helpful discussions and collaboration.


soliton-self compression in highly nonlinear chalcogenide photonic nanowires with ultralow pulse...

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