Optics Communications 310 (2014) 100–103

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Optics Communications

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n CorrE-m

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Nonlinear and saturable absorption characteristicsof Ho doped InSe crystals

Mustafa Yüksek a,n, H. Gul Yaglioglu b, Ayhan Elmali b, E. Murat Aydın b,Ulaş Kürümb, Aytunç Ateş c

a Department of Electrical–Electronics Engineering, Engineering and Architecture Faculty, Kafkas University, 36100 Kars, Turkeyb Department of Engineering Physics, Faculty of Engineering, Ankara University, 06100 Ankara, Turkeyc Department of Material Engineering, Faculty of Engineering and Natural Sciences, Yıldırım Beyazıt University, 06030 Ankara, Turkey

a r t i c l e i n f o

Article history:Received 11 March 2013Received in revised form28 June 2013Accepted 28 July 2013Available online 6 August 2013

Keywords:SemiconductorNonlinear absorptionSaturable absorberTwo photon absorptionZ-scan

18/$ - see front matter & 2013 Elsevier B.V. Ax.doi.org/10.1016/j.optcom.2013.07.078

esponding author. Fax: +90 474 225 1279.ail address: mustafa_yuksek2001@yahoo.com

a b s t r a c t

InSe:Ho (%0.005) and InSe:Ho (%0.05) single crystals were grown using the Bridgman–Stocbargermethod. The nonlinear and saturable absorption characteristics of InSe:Ho (%0.005) and InSe:Ho(%0.05) single crystals were investigated by open aperture Z-scan technique with 4 ns and 65 ps pulsedurations at 1064 nm. Both crystals show nonlinear absorption for 4 ns pulse duration at low and highinput intensities. However, picosecond measurements show saturable absorption behavior at low inputintensities while nonlinear absorption becomes dominant at high input intensities. This indicates thatthe life time of the doping states is shorter than 4 ns pulse duration. Saturable absorption behavior canbe attributed to filling of the doping states. Our results show that nonlinear absorption coefficientincreases with increasing Ho concentration due to increasing of free carrier concentration.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

The group III–VI materials (III—Ga, In; VI—S, Se, Te) arecommonly referred to as layered (GaSe-type) chalcogenides. GaSe[1–4] and InSe [1,5,6] have been widely investigated during thelast few years due to their outstanding nonlinear optical propertiesand promising materials for photoelectronic applications [7–11].Although nonlinear absorption characteristics of pure and dopedGaSe single crystals have been widely investigated [8,12–18], thestudies about the nonlinear absorption of InSe single crystal islimited [1]. However, nonlinear absorption properties of Ho dopedInSe single crystal has not been studied previously. The structureof InSe single crystal consists of multiple layers of ions eachcontaining four covalently bounded sheets in the sequenceSe–In–In–Se. The layers are bound together by weak van derWaals forces, while the intralayer atoms are bound by strongcovalent forces. Because of this, cleaving is easily possible parallelto layers. When InSe single crystal is doped by Ho molecules, someof the In molecules displace with Ho molecules. Because of theexcess electrons, pure InSe semiconductor crystallizes as n-type.Gürbulak et al. were studied the temperature dependence of Halleffects of Ho doped n-type InSe crystals and they had shown that

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(M. Yüksek).

p-type level occurred at 0.568 eV around the room temperature[19]. The influence of various chemical dopant atoms in GaSecrystals, such as Cl [20], Sn [21,22], Cu [23] was previously studied.The doping of GaSe crystal seems to be the optimal method ofimproving its optical and other physical properties. It is wellknown that dopant atoms induces optical bandgap shift insemiconductors. Therefore, semiconductors are used in variousoptical applications. In our previous study, we investigated thenonlinear optical absorption properties of pure, Ge and Sn dopedGaSe crystals [17,18]. It was found that Ge and Sn doped GaSecrystals showed nonlinear absorption at high input intensitieswhile Ge and Sn doped GaSe crystals showed saturable absorptionat low input intensities for both nanosecond and picosecond pulsedurations. In this study, we studied the influence of Ho doping anddoping concentration on the nonlinear optical absorption of InSesingle crystal by using open aperture Z-scan technique withnanosecond and picosecond laser sources.

2. Experimental

InSe:Ho single crystals were grown using the Bridgman–Stoc-barger method. The melting point of the InSe compound,66075 1C [1] was determined from the phase diagram. 0.0025 gand 0.025 g Ho were added to the starting melts in crystal growthprocedure to produce InSe:Ho (0.005%)–InSe:Ho (0.05%) crystals,

M. Yüksek et al. / Optics Communications 310 (2014) 100–103 101

respectively. The two crystals were grown at the same time. Thegrown InSe:Ho (0.005%)–InSe:Ho (0.05%) ingots had no cracks orfissures on the surface. No polishing or cleaning treatments werecarried out on the cleaved faces of these samples because of thenatural mirror-like cleavage faces [24–26]. The thicknesses of theinvestigated samples were measured using a camera connectedoptic microscope (Nikon-OPTIPHOT-100). The UV–vis absorptionspectra of the samples were recorded using a scanning spectro-photometer (Shimadzu UV-1800) at room temperature (300 K).

Nonlinear optical absorption was examined by the open-aperture (OA) Z-scan method with nanosecond and picosecondlaser sources [27]. The light sources were Q-switched Nd:YAGlasers operating at 1064 nm wavelength and 10 Hz repetition ratewith pulse duration of 4 ns (Quantel Brillant) and 65 ps (Con-tinuum Leopard SV). All OA Z-scan measurements were carried outat room temperature. 200 mm focal length lens was used to focusthe beam for OA Z-Scan experiments.

3. Results and discussions

Linear absorption spectra of the InSe:Ho (%0.005) and InSe:Ho(%0.05) crystals with 150 and 70 mm thicknesses are given in Fig. 1(a) and (b), respectively. The theory of interband absorption showsthat at the edge of optical absorption, the absorption coefficientα varies with the photon energy hν according to the followingformula [28].

α¼ Ahν

ðhν�EgÞn ð1Þ

In above expression A is a constant, Eg is the optical band gap and nassumes values of 1/2, 2, 3/2 and 3 for allowed direct, allowedindirect, forbidden direct and forbidden indirect transitions,respectively. The energy band gap values of the InSe:Ho (%0.005)and InSe:Ho (%0.05) crystals were determined by extrapolation ofthe linear regions on the energy axis (hν) given in Fig. 1(a) and (b).The band gap values of InSe:Ho (%0.005) and InSe:Ho (%0.05)crystals were found as 1.228 eV and 1.235 eV, respectively andthese values agree with the literature [26,29].

Open aperture Z-scan experiments show two distinct nonlinearbehaviors: (i) transmittance reduces with increasing optical inten-sity which is called nonlinear absorption (NA). Two-photonabsorption (TPA), multiphoton absorption (MPA), and free carrierabsorption (FCA) can contribute to NA signal. (ii) Transmittanceincreases with increasing optical intensity which corresponds tosaturable absorption (SA). SA includes one and/or two photonabsorption saturation. The two-photon and multiphoton absorp-tion occur in case hνZ ðEg=2Þ and hνZðEg=nÞ, respectively (nZ3).The TPA is known as the third order nonlinearity, on the otherhand the FCA is known as the fifth nonlinearity [30–32].

Fig. 1. Linear absorption spectrum for (a) InSe:Ho (0.005%) crystal and (b) InSe:Ho (%

Results of OA Z-scan measurements for 1064 nm wavelengthwith 4 ns or 65 ps pulse durations are shown in Figs. 2 and 3,respectively. In our previous study, the Sn and Ge doped GaSecrystals showed SA behavior at high input intensities for both 4 nsand 65 ps pulse durations [17,18]. Interestingly, OA Z-scan mea-surements in this study exhibited different characteristics depend-ing on the pulse duration. InSe:Ho (%0.005) and InSe:Ho (%0.05)crystals show NA behavior at low and high input intensities for4 ns pulse duration as seen from Fig. 2(a) and (b). However, bothcrystals show SA behavior at low input intensities and NA behaviorat high input intensities for 65 ps pulse duration (Fig. 3(a) and (b)).The difference can be explained by considering lifetime of thedoping states. If pulse duration is longer than lifetime of the defectstates, SA behavior; otherwise, NA behavior can be observed.Therefore, we considered different mechanism contributingto the observed signals for ps and ns pulse durations to be ableto fit OA Z-scan data.

NA behavior at low and high input intensities for 4 ns pulseduration (Fig. 2(a) and (b)) indicates that life time of the dopingstates is shorter than 4 ns pulse duration. Therefore, TPA and FCAcontribute to the observed NA signal for 4 ns pulse duration. In thepresence of TPA, the intensity dependent absorption is described by

αðIÞ ¼ α0 þ βI ð2Þwhere α0 is the linear absorption coefficient and β is the nonlinearabsorption coefficient. Experimental normalized transmittance dataexhibiting only TPA were fitted to Eq. (3) [27]

Tðz; S¼ 1Þ ¼ 1ffiffiffiπ

pq0ðz;0Þ

Z 1

�1ln½1þ q0ðz;0Þe�τ2 �dτ ð3Þ

where q0ðz;0Þ ¼ βI0Lef f =ð1þ z2=z20Þ, z is the position of the samplewith respect to the focal position, z0 ¼ kω2

0=2 is the Rayleigh range,ω0 is the beam radius at focus, I0 is the intensity of the incident laserbeam at the focus (z¼ 0), Lef f ¼ ½1�expð�α0LÞ�=α0 is the effectivethickness of the material, and L is the sample length.

Saturable absorption behavior of investigated crystals at lowinput intensities for 65 ps pulse duration (Fig. 3(a) and (b))indicates that lifetime of the doping states is longer than 65 pspulse duration. Filling effect of the doping states at low inputintensity leads to SA behavior. Besides, switching SA behavior toNA behavior at higher intensities indicates that OPA, TPA and FCAcontribute to observed SA signal. Nonlinear absorption effectscontributing to the SA and NA behaviors observed from the openaperture Z-scan experiments can be explained with the followingequation:

dIdz

¼� α0I1þ I=Isat

� β0I2

1þ I2=I2sat� sNðIÞI1þ I2=I2sat

¼�f ðIÞ ð4Þ

where, α0 is the linear absorption coefficient, β0 is the two photonabsorption coefficient, s is the free carrier absorption cross section,

0.05) crystal. The inset shows the graphs of absorbance vs. photon energy.

Fig. 2. Relative transmission at 1064 nm and 4 ns pulse duration for (a) InSe:Ho (0.005%) and (b) InSe:Ho (0.05%) crystals.

Fig. 3. Relative transmission at 1064 nm and 65 ps pulse duration for (a) InSe:Ho (0.005%) and (b) InSe:Ho (0.05%) crystals.

M. Yüksek et al. / Optics Communications 310 (2014) 100–103102

NðIÞ is the intensity dependent free carrier density, I is theintensity of the incident laser beam at the focus and Isat is thesaturation intensity of the material. Free carriers can be generatedby single photon or two photon absorption. Therefore, generatedfree carrier density varies with time as [32]

dNdt

¼ α0Iℏω

þ β0I2

2ℏωð5Þ

Integrating Eq. (5) gives the number of generated free carriers;

N� α0Iℏω

τa þβ0I

2

2ℏωτa ð6Þ

where, τa is the life time of free carriers. When the pulse durationof laser τp is shorter than τa, τa is replaced by τp [32]. By substitutionEq. (6) into Eq. (4) the following equation is obtained.

dIdz

¼� α0I1þ I=Isat

� 1

1þ I2=I2satβ0I

2 þ sα0τpℏω

I2 þ sβ0τp2ℏω

I3� �

ð7Þ

Eq. (7) is rearranged to obtain the following form.

dIdz

¼� α0I1þ I=Isat

� βef f I2

1þ I2=I2sat� DI3

1þ I2=I2satð8Þ

The effective third and fifth order nonlinearities can be expressed as:βef f ¼ β0 þ ðsατp=2ℏωÞ and D¼ ðsβ0τp=2ℏωÞ, respectively. SinceDffi0 for low intensities, βef f and Isat values can be obtained fromcurve fitting. On the other hand since Da0 for higher intensities,one needs to use the value of βef f in Eq. (8) in order to determine Dand Isat from curve fitting.

It is very difficult to find the exact analytical solution of Eq. (8).The Adomian decomposition method [33] provides an approachto solve such SA problems for the OA Z-scan theory [34,35].

According to this model Eq. (8) can be integrated formally

Iout ¼ Iin�Z L

0f ðIÞdz; ð9Þ

Where, Iout is optical intensity transmitted through the sample atthe exit face of the sample, Iin is the optical intensity of theGaussian beam at the input of the sample, and L is the samplethickness. Using the fifth order Adomian decomposition method[34,35], Iout can be expressed in terms of the polynomials. Thenormalized transmittance as a function of the sample relativeposition x is given by

Tðx; LÞ ¼R10 Ioutðx; tÞr dre�α0L

R10 Iinr dr

; ð10Þ

where x¼z/z0 is the sample relative position, z is the sampleposition, z0¼π ω0

2/λ is the Rayleigh length, ω0 is the beam waistof Gaussian spatial profiles at the focus, and λ is the wave length ofthe laser used.

NA coefficients βeff and D which were obtained from OA Z-scanmeasurements for ns and ps pulse durations at several intensitiesare given in Tables 1 and 2, respectively. Chan et. al. were studiedthe βeff and D coefficients of ZnO thin film under femtosecondexcitations [32]. Our D values which are measured by ns excita-tions are two orders of magnitude larger than the D values of ZnOthin film for fs excitations. [32]. The FCA cross section increaseswith increasing intensity. The density of the doping states can alsobe altered by changing the concentration of contributed elementin the semiconductor structures. As seen from Tables 1 and 2, theβeff and D increase with increasing Ho concentration due toincreasing doping states. According to the best of our knowledge,there are no relevant results regarding to nonlinear absorption

Table 1Nonlinear absorption coefficients of the InSe:Ho (%0.005) and InSe:Ho (%0.05)crystals for 4 ns pulse duration at various intensities.

Material Thickness(mm)

Intensity(W/cm2)

β (cm/W) ISAT(W/cm2)

D (cm3/W2)

InSe:Ho(0.005%)

�150 4.6�106 4.53�10�7 5.42�108 3.41�10�22

11�106 4.47�10�7 5.04�10�22

15�106 4.59�10�7 6.85�10�22

23�106 4.64�10�7 8.27�10�22

InSe:Ho(0.05%)

�70 4.6�106 5.91�10�7 5.85�108 3.92�10�22

11�106 5.78�10�7 5.98�10�22

154�106 5.84�10�7 7.14�10�22

23�106 5.69�10�7 9.26�10�22

Table 2Nonlinear absorption coefficients of InSe:Ho (%0.005) and InSe:Ho (%0.05) crystalsfor 65 ps pulse duration at various intensities.

Material Thickness(mm)

Intensity(W/cm2)

Βeff (cm/W) ISAT(W/cm2)

D (cm3/W2)

InSe:Ho(0.005%)

�150 2.8�108 3.56�10�8 2.41�108 –

6.3�108 3.63�10�8 –

9�108 3.68�10�8 8.34�10�24

11�108 3.55�10�8 1.37�10�23

14�108 3.76�10�8 4.74�10�23

InSe:Ho(0.05%)

�70 2.8�108 4.87�10�8 2.63�108 –

6.3�108 5.01�10�8 –

9�108 4.93�10�8 1.04�10�23

11�108 5.04�10�8 5.62�10�23

14�108 4.98�10�8 8.79�10�23

M. Yüksek et al. / Optics Communications 310 (2014) 100–103 103

studies of InSe crystal in the literature to compare with results ofthis study. On the other hand, the nonlinear absorption character-istics of GaSe crystal which is taken place at same family crystalswith InSe crystal has been widely studied. Therefore, we cancompare our NA results with NA results of GaSe crystal. Ourresults showed that NA coefficients of both InSe:Ho (%0.005) andInSe:Ho (%0.05) crystals are greater than that of undoped anddoped GaSe crystals [17,18]. F. Adduci et. al. have reported that thetwo photon absorption coefficient of GaSe crystal is 1.1�10�7

cm/W [16]. From the study of Van Stryland et. al. [12], it can beclearly seen that smaller energy band gap crystals show largernonlinear absorption coefficients under same excitations. For thisreason, it can be said that our results are reasonable. Results inTables 1 and 2 for both InSe:Ho (%0.005) and InSe:Ho (%0.05)crystals show that βeff and D values for 4 ns pulse duration at thesame input intensities are about one order of magnitude largerthan βeff and D values for 65 ps pulse duration. It is known that thethird-order nonlinearities arising from bound-electronic effectsare important in the femtosecond time domain while the free-carrier nonlinearities become significant for laser pulses of nano-second durations and longer. In semiconductors, this increase canbe attributed to behavior of carrier dynamics related with pulseduration [36]. Longer pulses can make competing nonlinearabsorption processes such as two-photon induced free carrierabsorption dominant.

4. Conclusion

The nonlinear optical absorption and saturation behaviors wereinvestigated by open- aperture Z-scan experiment for nanosecondand picosecond pulse durations. Both InSe:Ho (%0.005) and InSe:

Ho (%0.05) crystals show saturable absorption at low inputintensities and nonlinear absorption at high intensities for 65 pspulse duration while they show nonlinear absorption at low andhigh input intensities for 4 ns pulse duration. This observationindicates that the life time of the doping states is between 65 psand 4 ns. Filling the doping states causes saturable absorption for65 ps pulse duration. The nonlinear absorption coefficientincreases with the Ho doping. Our results showed that the non-linear absorption coefficient can be changed by doping in semi-conductor crystals. The nonlinear absorption coefficients innanosecond regime are about one order of magnitude larger thanthat of in picosecond regime.

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