Experimental evidence of two-photon absorptionand its saturation in malachite green oxalate:a femtosecond Z-scan studyANSHU GAUR, HAMAD SYED, BALAJI YENDETI, AND VENUGOPAL RAO SOMA*Advanced Centre of Research in High Energy Materials (ACRHEM), University of Hyderabad, Prof. C. R. Rao Road, Gachibowli, Hyderabad,500046 Telangana, India*Corresponding author: soma_venu@uohyd.ac.in

Received 20 June 2018; revised 27 August 2018; accepted 5 October 2018; posted 9 October 2018 (Doc. ID 335566); published 25 October 2018

Third-order nonlinear optical (NLO) properties of malachite green oxalate (MGO) dye were systematically stud-ied at different input intensities and in a wide range of wavelengths by the Z -scan method using ∼150 fs, MHzfemtosecond pulses. The sample transmittance results are explained by fitting the data with phenomenologicalmodels of linear and multi-photon absorption and their saturations. Intensity-dependent measurements demon-strated the influence of saturation on the absorption process. The data obtained suggests that by tuning the inputintensity single or combination of nonlinear phenomena can be achieved in MGO. Wavelength-based measure-ments reveal a strong correlation between linear and NLO responses. The combinations of two- and three-photonabsorption and saturation of two-photon absorption occur simultaneously in a wide wavelength range(750–900 nm). Multi-photon absorption cross sections have been calculated using the NLO coefficients andthe concentration data. Two- and three-photon absorptions (including an excited state) are determined asthe excitation mechanisms of nonlinear absorption in MGO. © 2018 Optical Society of America

https://doi.org/10.1364/JOSAB.35.002906

1. INTRODUCTION

Modern optical technologies and lasers have made tremendousadvances in manipulating the light intensity, wavelength, andtime response of the pulses because of the revelation of non-linear optical (NLO) properties of versatile materials. NLOmaterials are capable of (i) producing light of varying frequen-cies by the phenomena of harmonic and sum/differencefrequency generation [1], (ii) generating ultrashort [femtosec-ond (fs), picosecond (ps), etc.] pulses by suppressing signal oflow intensities, and (iii) protecting sensors and other sensitivecomponents from intense light through nonlinear absorption(NLA). These have become possible broadly with two kindsof NLO materials, namely, saturable absorber (SA), whichabsorbs less fraction of light at higher intensities (applicationsinclude pulse compression, Q-switching, and mode locking),and optical limiter [2] or reverse saturable absorber (RSA),which absorbs more fraction of light at higher intensities(applications such as signal stabilizer [3], pulse shaping, andmode locking [4,5]). Modulation in laser technology usingNLO materials is a young research area and materials havinghigh nonlinear coefficients in a broad wavelength range anddifferent functionality in nonlinear properties are often desir-able. The strongest, second-order, nonlinearity where polariza-tion of charged species is proportional to the square of the

electric field is possible in materials/crystals with noncentro-symmetric structures. On the other hand, almost all materials,including metals, composites, polymers, and ceramics, possessthird-order NLO properties (polarization dependence on thirdpower of the electric field), though in varying degrees. Organicmaterials are expected to have relatively strong NLO propertiesdue to delocalized electrons at π-π� orbitals, which forms a di-pole upon application of an electric field. A series of organicdyes, including Rhodamine [6], brilliant green [7,8], crystalviolet [8,9], methylene blue [10], etc., are shown to exhibitstrong NLO response in pure and composite forms [11–13]and are able to tune the NLO properties of many other classesof materials [14,15]. Other attractive features of organic dyesare easy modification in the functional group attached to it thatresults in different properties, ease of synthesizing, and trans-forming according to device needs. In the present work non-linear properties of malachite green oxalate (MGO) dye isstudied by the simple Z -scan method using fs laser pulses ina broad range of wavelengths. Like crystal violet and brilliantgreen, malachite green (a chloride salt) and malachite green ox-alates (an oxalate salt), belong to a group of triarylmethane dyeswhich contains triphenylmethane structure as its backbone.Malachite green dyes (chloride and oxalates) find applicationsin different areas, e.g., as parasiticides in pharmaceutical, dyematerials in industry, and redox mediators, pH indicators in

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0740-3224/18/112906-09 Journal © 2018 Optical Society of America

biosensors [16,17]. Though these dyes are commonly knownmaterials, to the best of our knowledge, their nonlinear proper-ties as a function of wavelength have not been reported earlier.We present here a systematic investigation of third-order NLOproperties of MGO by the standard Z -scan technique with fslaser excitation in a broad range of wavelengths. The opticallimiting properties of MGO are studied at a wavelength of680 nm at different input powers. Z -scan is a simple techniquedeveloped by Sheik-Bahae [18] for studying odd-order (third,fifth, etc.) nonlinear absorption and refraction of materials. Theuse of fs laser pulses avoids (which is manifested in the presentstudy also) the interference and ambiguity from the long livedphenomena, such as free carrier effect and excited-state absorp-tion, that have higher probabilities from longer nanosecondand picosecond laser pulses [19–21]. The NLO propertiesare discussed by fitting the obtained experimental data withphenomenological models of one- and multi-photon absorp-tions [22,23] and their saturation. Nonlinear absorption mate-rials with different nonlinear absorption processes (such assaturable absorption, two- and multi-photon absorption) arepromising in different applications of nonlinear optics and pho-tonics [24–28]. Therefore, it is imperative to identify their non-linear absorption process mechanism, and to determine therelated parameters to fully exploit the NLO properties.Experimental results show that MGO exhibits more thanone NL absorption process under the excitation of intense laserpulses. The NLO characteristics of MGO can be switched sim-ply by tuning the peak intensity and the excitation wavelength.

2. MATERIALS AND METHODS

The NLO properties of 0.5 mM aqueous solution of MGOdye were measured in the standard Z -scan experimental setupusing a tunable Ti:sapphire laser (make: Coherent, model:Chameleon). This laser delivered light pulses of 150 fs widthand at a repetition rate of 80 MHz. In typical Z -scan experi-ments, the laser beam with an initial beam diameter of 2 mmwas focused into the aqueous MGO sample [in a cuvette of1 mm thickness] using a lens of 10 cm focal length. The cuvettewas placed in a holder attached with a stage that was translatedalong the beam (Z ) direction. The schematic of experimentalarrangement and related parameters [e.g., Rayleigh range (ZR),on-axis intensity (I 00) profile across the focus (I�Z �), etc.] isshown in Fig. 1. The light transmitted from the sample wasconverged using a convex lens of 7.5 cm focal length andcollected by a thermal detector (make: Coherent, model:OP-2 VIS) connected with a power meter (make: Coherent,model: FieldMaxII Laser Power/Energy Meter). The Z -scanmeasurements were performed at (i) 680 nm with five differentinput powers (peak intensities), which generated different in-tensity profiles as a function of Z , and (ii) different wavelengths(700–1000 nm) with similar input peak intensities.

Along with NLO, linear optical properties of the dilutedsolution of MGO were recorded using a UV-visible-NIRspectrophotometer (Perkin Elmer, Lambda 750) and photolu-minescence spectrum. The absorption spectrum of MGO wasrecorded in the 190–1020 nm wavelength range by excitingwith a mercury/halogen lamp and photoluminescence spectrawith a 532 nm green laser (power < 4 mW).

3. RESULTS AND DISCUSSION

A. Linear Optical Study

Linear optical (absorption and emission) properties of MGO(chemical formula: C52H54N4O12, molecular weight:972.02 g/mol, and IUPAC name: [4-[[4-(dimethylamino)phenyl]-phenylmethylidene]cyclohexa-2,5-dien-1-ylidene]-dimethylazanium;2-hydroxy-2-oxoacetate) identified from theUV-visible-NIR absorption and photoluminescence spectra re-corded in low power mode are shown in Figs. 2(a) and 2(b),respectively. The MGO molecule in the UV to visible spectralrange is characterized with broad energy bands centered at618 nm, 425 nm, 317 nm, and 249 nm, with the peak at249 nm being in the form of a small hump. A part of one

Fig. 1. Pictorial representation of different parts and parameters ofthe Z -scan experiment.

Fig. 2. Linear optical characteristics of MGO: (a) UV-visible-NIRoptical absorption and (b) photoluminescence spectra. Molecularstructure of MGO is shown in the inset of (a).

Research Article Vol. 35, No. 11 / November 2018 / Journal of the Optical Society of America B 2907

more UV absorption band appears with lower wavelength sideedge at 225 nm. MGO is devoid of any absorption in the IRrange (700–1050 nm). In Fig. 2(b), the luminescence spec-trum of MGO shows a broad emission peak at 707 nm withexcitation at 532 nm.

The emission peak ranged from 600 nm to 790 nm is as-sociated with the electronic energy band centered at 618 nmand spanning 500–700 nm. Small and narrow peaks in the535–585 nm wavelength range (corresponding to shifts of105–1702 cm−1 from excitation wavenumber) are associatedwith the Raman stokes lines of MGO [29,30]. The absorptionand emission peaks observed in this work are in goodagreement with the previous reports [9,16].

B. Nonlinear Optical Study

To investigate the nonlinear absorption properties of MGO,Z -scan experiments were performed in an open aperture(OA) experimental configuration. The data are recorded interms of transmitted power as a function of sample position(Z -coordinate) with respect to the focal point of the converginglens kept before the sample. This lens creates a continuouslyincreasing intensity profile (Fig. 1) from its position to the fo-cus and symmetrically decreases after the focus. The Z -scandata, therefore, represents the transmitted power as a functionof light intensity. The intensity variation given by I�z� �I 00∕�1� z2∕z2R� is most significant within the few Rayleighlengths (−zR , zR). The Rayleigh length of such a focusingarrangement at 680 nm is 2.17 mm and is in the range of2.23–3.19 mm for wavelengths of 700–1000 nm. A constant0.5 mM concentration solution was used for all the Z -scanstudies.

1. Intensity-Dependent NLO Study at 680 nm

The OA Z -scan spectra of MGO observed with a 680 nmexcitation wavelength and at different input intensities ofI 01 � 40MW∕cm2, I 02�65MW∕cm2, I 03 � 99 MW∕cm2,I 04 � 122 MW∕cm2, and I05 � 153 MW∕cm2 are depictedin Figs. 3(a)–3(c). The normalized transmittance presented inthe diagram is the ratio of Z -dependent transmitted power tothe constant linear transmitted power, measured keeping thesample far away from the focus. The fractional transmittance(ratio of transmitted output power to the incident input power)in the far-field region (z ≫ zR � 2.17 mm) is a constant for allthe input powers suggesting that input intensity is “optimally”high so that in the far field only linear absorption is possible. Ina region close to the focus, the Z -dependent flux is very highleading to the nonlinear characteristics. At the lowest inputpeak intensity (I 01), transmittance (absorption) increases(decreases) slowly, with the laser intensity, as the sample movestoward the focus [Fig. 3(a)]. This transmittance elevation isassociated with the saturation of the linear, one-photon absorp-tion (1PA) resulting from the depletion of the ground state(GS) at reasonably high intensity. 1PA is a naturally occurringlow-intensity phenomenon at 680 nm for MGO [Fig. 2(a)].Short time and high intensity laser pulses raise the GS popu-lation to the first excited state (FES) at a faster rate than the rateby which molecules come down by their own in a spontaneousrelaxation process, leading to depletion of GS (meticulouslycalled bleaching of GS). When the molecules experience higher

peak intensities nearer to the focus, the transmittance startsdecreasing that continues up to the focal point intensity.The behavior where the sample material absorbs photons morethan usual (that at the linear response) and response becomesthe reverse of the above-mentioned absorption saturation iscalled reverse saturable absorption. RSA behavior results frommulti-photon absorption. This process causes molecule excita-tion to higher electronic energy levels in a nonlinear absorptionor intensity-dependent absorption event (by absorbing onephoton in the excited state) or in multi-photon absorption(by absorbing two or more photons in an instantaneous man-ner). In the present fs study, the pulse width and the stopovertime in the ES being very short, the RSA behavior is associated

Fig. 3. OA Z -scan response of MGO at input peak intensities of(a) I01 � 40 MW∕cm2 (squares), I 02 � 65 MW∕cm2 (circles),I 03 � 99 MW∕cm2 (triangles); (b) I04 � 122 MW∕cm2; and(c) I 05 � 153 MW∕cm2. Open symbols (squares, circles, triangles,stars) correspond to the experimental data, while solid lines representthe theoretically fitted data. The graph of ln�1 − T � as a function ofln I 0 is shown in the inset of (a).

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with instantaneously occurring multi-photon absorption.Collectively, the transmittance spectrum of MGO at the lowestpeak intensity, I 01, comprises contributions of two differentphenomena i.e., SA at lower intensities followed by RSA athigher intensities (i.e., RSA-in-SA behavior).

At higher peak intensities of I02 and I 03, the absorptionresponse remains of the same mixed type, i.e., RSA-in-SA.However, the degree of transmission during the RSA valley sys-tematically decreases with the peak intensities associated withthe increase in multi-photon absorption. A crossover during theSA behavior is recorded where the transmittance (saturation) atthe lower intensity I 01 is observed to be higher than that at I 02.At the highest intensity of I04 [Fig. 3(b)], the RSA-in-SAresponse confines to far-focus intensities. Further, the transmis-sion close to the focus region turns to SA again up to the focalpoint intensity for decrease in the absorption. This second SApeak at the higher intensities, which is observed at I 05 also, isassociated with the saturation of the multi-photon absorption.This behavior may occur in a manner similar to the saturationof linear absorption by the bleaching of the lower energy states[31]. The near-focus saturation peak at I 05 is spread over a largeZ -values compared to the I 04 case associated with the strongnonlinear absorption. In addition, the far-focus RSA-in-SAbehavior in the I 05 case turns to only RSA for the disappearanceof saturation of linear absorption. Overall the Z -scan transmit-tance of MGO changes from RSA-in-SA to “SA in RSA-in-SA”type on an increase of peak intensity from 99 MW∕cm2

to 122 MW∕cm2.To interpret the obtained peak intensity-dependent OA

Z -scan data (and also the wavelength-dependent data, whichis discussed in detail in the next section) and determine theNLA parameters, the transmitted data was fitted by solvingthe following differential equation:

dI�z 0�dz 0

� −α�I�I�z 0�, (1)

where I�z 0� is the light intensity within the sample at a thick-ness of z 0, called the penetration depth, and α�I� is the totalabsorption coefficient, which governs the linear and nonlinearabsorption characteristics [32]. In the present study, α isassumed to include the terms so as to cover the flips of SAto RSA and then to SA [Figs. 3(a)–3(c)/peak intensity-dependent study] and RSA to SA to RSA behavior (wave-length-dependent study presented in the next section). Thefar-focus SA behavior at 680 nm [Fig. 3(a)] is fitted by includ-ing the saturation of linear absorption. The RSA valley of thetwo cases (680 and 700–1000 nm) is fitted by instantaneoustwo-photon absorption (2PA). Though MGO has a real state(linear absorption at 680 nm) at the excitation wavelength of680 nm, for the fs pulse study undertaken here the lifetime ofthe molecule in the excited state will be less than the pulse du-ration (i.e., <150 fs), which permitted us to consider it as in-stantaneous. Out of different number-possibility of multi-photon absorption, a decrease in the sample transmission is as-sociated with 2PA since the absorption cross section of highernumber photon absorption generally becomes significant atvery high peak intensities and occurs in a relatively sharp man-ner close to the focus [33]. The near-focus flip of SA from RSA(i.e., RSA-in-SA) behavior [Figs. 3(b)–3(c)] was fitted by

considering the saturation of 2PA. To fit the 680 nm data,the considered transitions in the three-level model are depictedin Fig. 4. In order to fit the wavelength-dependent data[presented in Figs. 5(a)–5(g)], an extended model with afourth energy level is presented in Fig. 5(h). To include a secondRSA valley around the focus region for 750–900 nm cases[Figs. 5(b)–5(e)], the higher numbered multi-photon absorp-tion, i.e., three-photon absorption (3PA), is considered. Thetotal absorption coefficient of MGO (including the 3PA forcovering the wavelength-dependent data), therefore, is given as

α�I� � α1 � β1I � γ0I 2, (2)

where α1, β1, and γ0 are the linear absorption, 2PA, and 3PA co-efficients. The intensity-dependent forms ofα1 and β1 containingthe information of saturation of 1PA and 2PA processes are for-mulated by considering the contributions of de-excitations fromtheFESandsecondexcitedstate (SES), respectively(Fig.4).Outofthe two possible downward transitions from S2, namely, S2 to S1and S2 to S0, only one is considered (S2 to S1) for simplifying thecalculation. S2 to S0 transitions, though not forbidden, are veryrare in suchmolecules. The populations involved in the two proc-esses, 1PA and 2PA, are assumed to be independent of each othersuch that intensity-independent forms of the two absorptioncoefficients are defined as α0 � σ1PA�N − N 2� and β0 �σ2PA�N − N 1�, respectively, where N 1 and N 2 are the instanta-neous populations of the first and second excited states, respec-tively, N is the undepleted population of the GS, andσ1PA and σ2PA are the one-photon/linear and two-photon absorp-tion cross sections. The independent forms of absorption coeffi-cients of these two processes are commonly used by differentgroups [34,35] and implicitly correspond to independency ofthe two processes/populations involved. In such a scenario, rateequations governing the population of excited states are givenas [31,36,37]

dN 2

dt� β1I 2

2hν−N 2

τ2, (3)

dN 1

d t� σ1PA�N − N 1 − N 2�I

hν−N 1

τ1� N 2

τ2: (4)

Fig. 4. Schematic of the electronic energy level model and variouspossible transitions of MGO. 1PA and 2PA stand for one-photon andtwo-photon absorptions, respectively. Vertical wriggly lines (NR1,NR2, NR3) represent nonradiative transition. Solid lines (R1, R2)represent radiative transitions.

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In the above equations, (N − N 1 − N 2) is the instantaneouspopulation of GS after N 1 and N 2 molecules are excited toFES and SES, respectively. The first term in Eq. (4), which isproportional to the instantaneous GS population and photonflux, is the rate of absorption. The τ1 (typically fs) and τ2(typically ps) in the second terms (rate of de-excitation) of theseequations are the relaxation times of the first and second excitedstates, respectively. β1 is the 2PA coefficient with saturationeffect, I and ω are the intensity and angular frequency of theincident light, and h is the Planck’s constant. The rate equationcorresponding to the population at S3 state is not consideredsince the near-focus saturation behavior is associated with the2PA process and not with the 3PA. Considering the steady-statecondition (dN i∕d t � 0), independently for the population atfirst and second excited states, rearrangement of terms inEqs. (3) and (4) leads to

N 1 �N − N 2

�1� hν∕σ1PAIτ1�and N 2 �

β1τ2I 2

2hν: (5)

The term for the rate of de-excitation from S2 to S1 (i.e.,N 2∕τ2)is not considered while formulating theN 1 using the steady-statecondition to maintain the independency of the populations. Theoverall 1PA and 2PA coefficients are given as [38,39]

α1 � σ1PA�N − N 1 − N 2�, (6)

β1 � σ2PA�N − N 1 − N 2�∕hν: (7)

Substitution of N 1 and N 2 into Eqs. (7) and (8) at respectiveplaces leads to the linear and two-photon absorption coefficients,given as

α1 �σ1PA�N − N 2�1� τ1σ1PAI

hν

� α01� I

ISA

, (8)

β1 ��N − N 1�σ2PA1� τ2σ2PA

2�hν�2 I2 � β0

1� I 2I 2SRSA

, (9)

where I SA � hν∕σ1PA × τ1 is the 1PA saturation intensity, andI SRSA � hν

p�2∕σ2PA × τ2) is the 2PA saturation intensity.Substitution of Eqs. (8) and (9) into Eqs. (3) and (2) givesthe overall absorption coefficient valid for both, peak intensityand wavelength-dependent study, and the final differentialequation for the transmitted intensity as [36,40]

α�I� � α01� I

ISA

� β0I

1� I2I2SRSA

� γ0I 2, (10)

dIdz 0

� α0I1� I

I SA

−β0I 2

1� I 2I 2SRSA

− γ0I 3: (11)

A similar set of equations governing the saturation of linear andtwo-photon absorption was considered recently by Reyna et al.[35]. The only difference between the two is the power in thedenominator term, which is due to the difference of the broad-ening assumed (exponent of 1 for the homogeneous case [whichis also the present case since there is no doping involved] or ½ inthe case of inhomogeneous broadening [40]). On the otherhand, there are recent reports on Z -scan studies of materialswhich are based on different fitting models. Sànchez-Esquivelet al. have fitted the W-shape Z -scan response (performed withpicosecond laser source) with a model that considered the linearand excited-state absorptions ignoring 2PA in the rate equationsand developed under steady-state conditions, similar to thepresent study [41,42]. Cesca et al. [43] assumed (followed byTorres et al. [44]) far-focus RSA and near-focus SA behaviorsof transmitted intensity to be due to different phenomena havingdifferent intensity dependences. In their form, the β parameter issplit into two parts describing (i) RSA and (ii) SA contents sep-arately, each part having a hyperbolic form and its own saturation

Fig. 5. OA Z -scan response of MGO at the excitation wavelengths of (a) 700 nm, (b) 750 nm, (c) 800 nm, (d) 850 nm, (e) 900 nm, (f ) 950 nm,and (g) 1000 nm. Open circles correspond to the experimental data and solid lines to the theoretically fitted data. The energy level model for 2PAand 3PA applicable to 750–1000 nm is shown in (h); vertical wriggly lines in S2 and S1 states represent nonradiative transitions. We have assumed aneffective transition from S2 to S0 instead of the complicated S2 to S1 to S0 transitions shown in the dotted region. In 700 nm case only 2PA relatedtransitions are applicable.

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intensity term in the denominator. However, we assumed thehigh-intensity SA peak is the outcome of saturation of 2PA,which occurs more or less in a way similar to the saturationof 1PA, as suggested by Kirkpatrick and others [36,37,40].

Equation (11) is solved for the transmitted intensity, I ,through the sample of thickness L (Fig. 2) considering I�z� �I 00∕�1� �z∕zR�2� as the initial value of the intensity for eachvalue of z, sample position with respect to focus, and treatingβ0, ISA, and ISRSA as fit parameters for peak intensity-depen-dent study at 680 nm (3PA being insignificant, γ-value was setto be zero). The first term on the right-hand side of the aboveequations governs the saturation of the 1PA process. The sat-uration intensity I SA is the one at which the nonlinear 1PAcoefficient becomes half of the linear absorption coefficient(i.e., α0∕2). The α1 will approach α0 for I ≪ ISA; at this limit-ing condition the 1PA will not saturate or it will be indepen-dent of intensity for incident intensity being significantly lower.The α1 approaches zero for I ≫ I SA, suggesting that there canbe total transmission (termination of 1PA) if the incident in-tensity is very high. A careful look at such extreme cases andI�z� values helps setting the close guess for I SA during fitting.Likewise, the numerator of the second term that increases withthe intensity governs 2PA and becomes significant and domi-nates the 1PA at higher intensities (as in I 01–I 04 cases). Thedenominator defines the saturation of the 2PA process and be-comes significant for intensities comparable to I SRSA. Similar toα1, β1 approaches β0 (i.e., 2PA without saturation) for I ≪I SRSA is applicable to the first three input peak intensities wherewe did not observe the saturation of 2PA. The theoreticalZ -scan data for peak intensities of I 01, I 02, and I03 is generatedconsidering β0 and I SA as fit parameters and setting I SRSA highsuch that their effect on the overall absorption coefficient isnegligible. For I 04 and I05 cases, the simultaneous effect ofI SRSA is considered. The fitted values of β0, I SA, and I SRSAfor five input peak intensities are summarized in Table 1.

A close match of the generated transmittance curve, shownby solid lines in Figs. 3(a)–3(c), with experimental Z -scan datasupports (i) the simultaneous presence of 1PA (as saturatedone) and 2PA at I 01–I 04 input peak intensities and saturationof 2PA at I 04–I 05; (ii) the good acceptability of the considered2PA model (i.e., with independent 1PA and 2PA processes at680 nm); and (iii) excludes the possibility of higher numberedmulti-photon absorption for the observed RSA behavior. Theabsence of 3PA is confirmed in the inset of Fig. 3(a), whichdepicts the graph of ln�1 − T � with ln I0 with T as thenormalized/fractional transmitted intensity at the focus. The

line has a slope close to 1 (∼1.11) and clearly suggests the pres-ence of a 2PA process [45]. Therefore, the physical process as-sociated with the observed RSA behavior at 680 nm with fspulse width laser is instantaneous or pure 2PA, though the pho-ton absorption occurs via a real state. The nonlinear absorption(2PA) coefficient of MGO, β0, at all input peak intensities isestimated to be ∼10−8–10−9 cm∕W (except ∼10−7 cm∕W forthe highest peak intensity of I05 ) and systematically increaseswith the input intensity. The increase of the 2PA coefficient ispossibly due to the participation of a greater number ofmolecules in the excitation. However, further detailed studiesare essential to confirm this. At higher peak intensities, morephotons interact with the molecules and involve them into theabsorption process. The nonlinear 1PA saturation intensity,I SA, for the considered peak intensities lies in the10.0–40.5 kW∕cm2 range and similar to β0, continuously in-creases with the input peak intensity. The estimated NLO co-efficients obtained at 680 nm are summarized in Table 1. Thesystematic increase (decrease) in the 1PA saturation intensity(cross section) with the input peak intensities (I 01–I 04) corre-sponds to the stronger bleaching of the GS. At high peak in-tensity, MGO molecules are excited to the FES with a higherrate than they are coming down to the GS in a spontaneousde-excitation process. This leads to the rare availability of mol-ecules at the GS for the further excitation. As a result, the ab-sorption cross section decreases. In Fig. 3(a), the transmittancecrossover at the SA regime for I01 and I02 is accounted for theinterplay between 1PA saturation and 2PA; significantlystronger 2PA at I02 dominates the saturation behavior andfor this reason the SA peak observes to be suppressed.Further, at these peak intensities, though the 2PA coefficientand 1PA saturation intensity systemically increase with the in-put intensity, their physical process does not seem to bestrongly coupled or dependent on each other. Following thevariations for I 01–I04 cases, especially the change in the satu-ration intensity for I 04 from I03 is relatively insignificant com-pared to the changes in the β0 values. Such observationstrengthens the validity of the considered independency of1PA and 2PA processes. Further, the narrow and relativelybroader (second) SA peaks of the I 04 and I 05 cases, respectively[Figs. 3(b)–3(c)], also fit well with the considered 2PA satura-tion model confirming that similar to the saturation of 1PA,two-photon absorption saturates at higher intensities and re-sults in an increase in the transmittance. Being a high intensityphenomenon, the 2PA saturation is governed by higher satu-ration intensities (∼MW∕cm2, compared to ∼kW∕cm2 of 1PAsaturation). Following the instantaneous 2PA mechanismmentioned above, the near-focus saturation will be governedby the bleaching of the GS. With the increase of the laser in-tensity and subsequent 2PA, large population resides at the sec-ond excited state and this may lead to the bleaching of the GS.The saturation (and absorption) behavior of I 04 is governed bystrong saturation intensity, whereas that of I 05 is dominated bystrong 2PA absorption coefficient (compared to previous casesof I01–I 03 also). Strong NLA at I 05 is probably due to theinvolvement of the large number of molecules associated withthe high intensity. The participation is so high that the

Table 1. NLO Parameters of MGO at 680 nm Obtainedwith fs Pulsesa

α0 cm−1I 0

MW∕cm2I SA

kW∕cm2 β0 × 10−8 cm∕WI SRSA

MW∕cm2

5.62 40 10.0 0.61 –5.62 65 13.0 0.66 –5.62 99 40.0 0.69 –5.62 122 40.5 5.92 19.55.62 153 – 27.0 3.30

a1 GM � 10−58 m4 s. GM stands for Goeppert–Mayer.

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influence of 1PA and its saturation on the observed transmit-tance has disappeared.

2. Wavelength-Dependent NLO Study

Broadband NLO absorption properties of MGO are investi-gated by the OA Z -scan technique in the 700–1000 nmwavelength range (in the steps of 50 nm) at an input intensitysimilar to I 03 of the 680 nm study; the observed response isshown in Fig. 5. In the considered spectral range, MGO exhib-ited different nonlinear behaviors from “pure RSA type” at 700and 1000 nm to “RSA followed by SA” at 750–950 nm.Compared to the 680 nm results discussed earlier (Fig. 3),no SA response in the far-field region for 750–1000 nm casesis the result of no or insignificant 1PA at these wavelengths[Fig. 2(a)]. Particularly, pure RSA type NLA was observed at700 nm with relatively stronger decrease in the transmittance.This result is associated with a stronger 2PA absorption derivedfrom insignificant linear absorption [Fig. 2(a)]. It is similar tothe I 05 case of 680 nm when MGO shows strong nonlinearabsorption with higher 2PA coefficient when the linear absorp-tion became inappreciable. This observation also points towardthe fact that linear absorption has some influence on two- ormulti-photon absorption processes. The transmittance re-sponse at 750–900 nm resembles the one at 680 nm withthe highest input peak intensity. The curves include similarwide saturation peak after the RSA valley, confined to thefar-focus region, for 2PA (SA-in-RSA). Since there is no linearabsorption at these excitation wavelengths, the only possiblemechanism for 2PA is through a virtual state, as shown inFig. 5(h). The 2PA saturation thereby is due to the bleachingof the GS similar to the saturation of 1PA (mentioned previ-ously for 680 nm case) that results in an increase in the trans-mittance at higher intensities. However, an additional decreasein the transmittance is also observed around the focus region,which may be associated with the excited state absorption(ESA) from S2 [Fig. 5(h)] or with the instantaneous 3PA wheremolecules of the GS or S2 level absorb photons without delayand go to the S3 level. For the similar reason of short period forwhich pulse is available to molecules (second pulse arrives onlyafter a long gap of the order of nanoseconds) and they stay atthe excited state, we have ignored the negligible contribution ofESA to the overall transmittance response. Further, at 1000 nmthe Z -scan transmittance response again turned to single RSAtype of behavior. However, the valley is relatively wider com-pared to the data obtained at 680 or 700 nm. The wideness ofthe RSA peak is associated with the involvement of one more

(higher intensity) process, such as 2PA saturation or 3PA thatmay change the shape of the pure RSA curve [46,47].Collectively, the transmittance response of MGO with wave-length [with respect to Fig. 3] is an outcome of a variety ofNLA phenomena, including more than one multi-photon ab-sorption and the absorption saturation. For the quantificationof these nonlinear processes, the data is fitted in a way similar tothat reported above using Eq. (11). To fit the experimental datafor 750–950 nm, 2PA (for the RSA valley) and its saturation(for the SA peak) is considered, whereas γ0 was set to zero. Thenear-focus RSA small valley is fitted by incorporating the 3PAcoefficient term (γ0I 2) [37] in the absorption coefficient givenby Eq. (10). The fitted data is shown in the same Fig. 5 withsolid lines. The NLA parameters acquired from data fitting arelisted in Table 2. A close match of the fitted data presented inFig. 5 with the experimental data confirmed that the transmit-tance curves are a main (750–900 nm) consequence of thesimultaneous presence of more than one multi-photon absorp-tion, 2PA and 3PA, including 2PA saturation. Compared to thepure RSA response at 700 nm [Fig. 5(a)], the relatively widerRSA valley at 1000 nm, shown in Fig. 5(g), was supported (bet-ter fits) more by the presence of 2PA saturation and less by3PA. The 2PA saturation smoothened the sharpness of theRSA valley in such a way that the fitted curve matched wellwith the experimental transmittance data of MGO. The fitteddata for the 3PA model has relatively significant deviation. Therelatively simple Z -scan graph (with RSA valley) at 700 and1000 nm is due to smaller linear absorption coefficients at halfof these wavelengths. The emergence of different transmittancecharacteristics suggests that the nonlinearity is strongly depen-dent on the wavelength. Our future endeavor is to incorporateall the possible transitions (ESA, 2PA, 3PA, and lifetimes ofvarious excited states) in the rate equations and obtain theNLO coefficients without any simplifications in the model.To better interpret the Z -scan data, the fitted nonlinear param-eters, β0 and γ0, are plotted as a function of wavelengths and areillustrated in Figs. 6(a) and 6(b).

To compare with linear absorption properties, absorptioncoefficients, α0, at half and one third of the excitation wave-lengths are calculated from the absorbance data presented inFig. 2(a) and are shown in Figs. 6(c) and 6(d), respectively.The data presented in Fig. 6(c) clearly conveys that the2PA coefficients, β0, are in strong resonance with linearabsorption behavior. The 2PA coefficient is maximum attwice the wavelength for which α0 has a local peak. β0 forexcitation wavelengths of 680–1000 nm changes in an

Table 2. Summary of the NLO Coefficients of MGO Obtained from fs Z -Scan Studies

λ (nm) β0 (10−8 cm∕W) I SRSA (MW∕cm2) σ2PA � β0hν∕N 0 106 GM γ0 × 10−18 cm3∕W2 σ3PA � γ0�hν�2∕N 0 10−79 cm6 s2

680 0.69 (at I03) – 0.67 – –700 1.62 – 1.53 – –750 6.48 5.69 5.71 3.25 7.59800 9.90 3.00 8.18 4.01 8.23850 19.0 2.75 14.77 11.0 20.0900 13.2 3.91 9.69 13.1 21.3950 7.06 7.97 4.91 – –1000 3.40 77.7 2.24 – –

2912 Vol. 35, No. 11 / November 2018 / Journal of the Optical Society of America B Research Article

increasing–decreasing manner with a maximum at λ �850 nm having close correspondence with linear absorptionsat half of these wavelengths (340–500 nm) with a maximumat λ∕2 � 425 nm. Almost a similar trend is seen for thecoefficient, γ0, for the 3PA observed at wavelengths of750–900 nm.

3. 2PA Cross Section

Similar to the linear absorption coefficient, the nonlinear ab-sorption coefficient (cross section) is an important parameterwhich signifies the probability of the absorption process.Generally, absorption cross sections of organic materials areevaluated from the concentration data and compared fromthe values reported for other similar kinds of materials forthe correctness/validity of the calculation [38]. In the presentwork, the 2PA cross section of MGO has been calculated usingthe relation σ2PA � β0hν∕N 0 and using the concentrationdata. N 0, which is the instantaneous population of the GS,is substituted by N, the undepleted population of the GS,i.e., 3.01 × 1017 molecules∕cm3 the concentration of MGOmolecules. It is seen that spectral dependence of β0 [Fig. 6(a)]is reflected in the σ2PA calculated from molecular concentra-tion, signifying that the higher (lower) the absorption coeffi-cient is, the stronger (weaker) the absorption and the crosssection will be. Higher-order cross sections are calculated usingthe relation σn � �ℏω�n−1

N αn. In the present study α2 is β0 and α3is γ0. Similarly, for the 3PA cross section as a function of wave-length we see a peak similar to the linear absorption at λ∕3.

4. CONCLUSIONS

In summary, NLO and linear absorption properties of(0.5 mM) MGO dye have been investigated in detail. TheNLO properties were studied using the OA Z -scan at differentwavelengths and varying peak intensities, whereas linear optical

data were collected from the absorption spectra. The nonlinearprocesses and parameters were estimated by fitting the Z -scandata using phenomenological models of linear and multi-photon absorption and their saturation. The peak intensitydependence study suggested that nonlinear 2PA can saturate ina similar fashion as the linear 1PA does. From the wavelength-dependent measurements, the OA Z -scan response of MGO isestablished to be a complex process comprising SA-in-RSA fol-lowed by another RSA, which occurs due to simultaneous two-and/or three-photon absorption and saturation of two-photonabsorption. The nonlinear absorption coefficients (β0 and γ0)calculated from fitting the data are shown to be in resonancewith the linear absorption properties confirming that the non-linearities have occurred through the multi-photon absorptionmechanism. By using moderately low peak intensities and ex-citation wavelengths in resonance with a high linear absorptioncoefficient at half the wavelength, strong 2PA cross sectionswere obtained for the MGO. The results confirm the suitabilityof RSA equipped MGO dye for applications that make useof a wide spectral range, such as optical limiting or ultrashortpulse generation.

Funding. Defence Research and Development Organisation(DRDO) (ERIP/ER/1501138/M/01/319/D(RD)).

Acknowledgment. Dr. Anshu Gaur would like toacknowledge ACRHEM, University of Hyderabad, forpermission to carry out the presented research work. Prof. S.Venugopal Rao acknowledges DRDO, India, for continuedfinancial support.

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