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CHAPTER-4

Z-SCAN CONSTRUCTION AND STUDIES ON NONLINEARABSORPTION AND NONLINEAR REFRACTIVE INDEX OF

MALONONITRILE DERIVATIVE CRYSTALS FOR OPTICALSWITCHING APPLICATION

4.1. INTRODUCTION

The demand of internet services is driving the growth of data traffic worldwide.

In every 6 to 12 months, doubling the usage of bandwidth in the internet due to the

data based networks. The development of science and technology in various

disciplines search of new materials are highly relevant area in research. Recently

much attention has paid to control the laser through changing the material structural

properties. In the recent years, third harmonic generation crystals are of interest due to

their attractive properties in the field of optoelectronics.

A promising mechanism of all-optical switching is the Mach Zehnder

interferometer type which required new materials based on low nonlinear absorption

(NLA) and strong nonlinear refractive index (NLRI) (Boudebs et al; 2001).

Nowadays, the fast growth of wavelength- division multiplexing (WDM) interconnect

networks has attracted increasing interest in optical switches and optical amplifiers

(Ben Yoo et al; 2006). The optical switches support new light paths in optical cross

connections (OXCs) (Papadimitriou et al; 2003). There are large third-order nonlinear

response pi-electron conjugated organic materials, such as cyanine dyes, carotenoids,

porphyrins and polymers.

The significant role of optical switches in network nodes is to provide the

fastest response in optical circuits. The response times in optical switches in circuits

are comfortable in few milliseconds. However, optical packet switching requires

response time of nanoseconds and picoseconds. The use of third order optical

nonlinearity for all optical signal processing has been a goal for many years. Many

research articles have reported about third order nonlinear susceptibility of organic

material followed by the report on poly [2,4-hexadiyne-1,6-diol-bis-p-toluene-

sulfonate] in 1976 (Sauteret;1976).The organic materials like phthalocyanines and its

derivatives in 1989 (Mathews;2007), organic metallic compounds (Sun;1970), large

nonlinear refractive index change in 4- N,N-dimethylamino-3-acetamidonitrobenzene

(DAN) (Kim;1993), fullerencies (Venugopal Rao;1998) has undergone wide

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investigation with respect to spectroscopic and structural properties. Similarly,

malononitrile crystals are showing the superior properties for third harmonic

application.

There are two types of optical switches the opto-electro-opto (OEO) and all

optical switches. The material requirements for all optical switches, which have to be

met are W>1 and T<1. These two figures of merit are defined as W=n2I/ (αλ) and

T=βλ/n2, where n2 is the NLRI, α is the linear absorption coefficient, β is the NLA

coefficient, λ is the wavelength, and I is the light irradiance (Wang; 2011). The high

ratio of real and imaginary part of nonlinear susceptibility Re (χ(3))/Im(χ(3)) is

necessary for efficient optical switching (Kuzyk; 1998). The key components of next

generation broadband devices are ultrafast optical switching devices. The materials

with low linear and nonlinear losses are required to implement the optical switching

devices. During the past few years, there have been big improvements in photonic

crystal technology. Eventhough further work is required to satisfy the one of the most

demanding of modern industries. In this chapter, the third-order optical nonlinearity is

described by the nonlinear refractive index, n2 (related to the third-order nonlinear

optical susceptibility (χ(3)) and nonlinear absorption(β) for all-optical switching has

been a considerable interest in condensed matter and the responsible mechanism.

4.2. THEORY OF Z-SCAN

Z-scan technique is a simple technique compared to the previous

measurements of nonlinear refraction interferometer, ellipse rotation, beam distortion

measurements, degenerate four waves mixing and three wave mixing. It is an accurate

method to determine both nonlinear absorption (NLA) and nonlinear refractive index

(NLRI) of crystals, thin films and liquid solutions developed by Shakebahae

et.al;1990. This standard method has widely accepted by nonlinear optics community

due to the simplicity of interpretation. There are two different methods to find the

nonlinear absorption and nonlinear refractive index of the materials, open aperture

and closed aperture methods respectively. Z-scan is a single beam technique for

measuring the sign and magnitude of NLRI and NLA coefficients. Nonlinear

Refractive index directly affects the phase of the propagating electric field while NLA

directly affects the amplitude. The phase and the amplitude of the applied electric

field are separated by thin sample approximation.

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In case of linear optics, Kramers-Kronig relations relate the real and imaginary

parts of frequency dependent quantities (linear susceptibility). It is easier to measure

an absorption spectrum than the frequency dependence of the refractive index. But in

case of nonlinear optics, these relations are useful for some nonlinear optical

interactions (Boyd; 2011).

The physical process of the nonlinear absorption and nonlinear refractive index are

due to the ultrafast bound electronic and excited state processes. The optically

induced excited states provide the response time of the material, it is given by the

characteristic peak and decay times. There are different types ultrafast processes,

namely stimulated Raman scattering, stark effect, and multiphoton absorption, (Sheik

bahae et al; 1991 and Shen et al; 1984). In case of excited state nonlinearity, the

variety of physical processes namely photochemical changes, free carrier absorption

in solids, excited state absorption in molecules and atoms, defect and colour centre

absorption and saturation of absorption (Wei et.al; 1992, Mansour et al;1998, Said et

al; 1992 and Boggess et.al; 1994). The above processes are lead to increased or

decreased transmittance based on multi-photon or saturation absorption.

Nonlinear refractive index of the material depends upon the applied electric field

intensity. The change of refractive index associated with different mechanism based

on polarisation, thermal and electronic origin, as explained in Chapter-1. The change

of refractive index of the material at the applied electric field, it may increases or

decreases compared to the periphery of the materials. The positive refractive index

refers increases of refractive index at illuminated portion and negative refractive

index refers decreases of refractive index at illuminated portion compared to the non-

illuminated parts.

4.3. Z-SCAN CONSTRUCTION

In this experiment, He-Ne laser of wavelength 632.8nm with beam diameter 0.5mm

is used to scan the sample. The Gaussian filter is used to modify the input laser beam

into Gaussian form. The single Gaussian beam TEM00 mode is allowed to pass

through the sample along Z-axis. The focal length of the convex lens is depending on

diameter of incident Gaussian beam. The convex lens of focal length 30 cm has

separated the path length into positive Z-axis and negative Z-axis. The experimental

arrangement is shown in Fig.4.1. The Gaussian beam was focused by a convex lens;

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to produce the beam waist of 12.26μm. The sample holder is attached with a motor

and controlled by software. The strict focusing geometry of this method is allowed to

measure the nonlinear absorption and nonlinear refraction quantity individually by

simple open and close aperture method respectively. In an open aperture method, the

refracted laser beam was collected completely in the detector (field mate coherent). In

closed aperture method, size of the aperture is reduced with respect to the diameter of

the laser beam at the aperture.

Figure 4.1: Z-scan instrument arrangement

The Rayleigh diffraction length (Zo=1.14mm) should satisfy the condition

wo2/λ > L, where L is the thickness of the sample and wo is the radius of the laser

beam at focal length. The length of sample (L) should be less than that of Rayleigh

diffraction length (Zo) (L<<Zo/ΔΦ), where ΔΦ is axis phase shift. To minimize the

phase change in Z-scan experiment, it is sufficient to change the thickness of sample

(L) L<Zo. The aperture size is an important parameter since large aperture reduces the

variations in transmittance. The magnitude and shape of transmittance depends on the

far field condition for the aperture plane d1>>Zo is satisfied. (d1 is the distance

between focal length and the aperture).

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Figure.4.2. Z-scan technique in our laboratory

The aperture size of 2mm was placed between Gaussian filter and convex lens (L1).

The single Gaussian beam of diameter 2mm has been used for z-scan experiment. The

beam diameter at aperture is 7mm. As per the Rayleigh diffraction length condition,

sample should be less than 1mm. There are two different methods are approached for

extract NLRI and NLA data. The convex lens (L2) of diameter 5cm and focal length

of 50mm has been used for open aperture method to converge all the diffracted rays to

sensor. In closed aperture method, replacement of variable aperture in the place of

convex lens (L2). The variable aperture helps to decide the linear transmittance(S)

calculation; variable aperture size of maximum 1mm to 4mm. It is advisable to carry

out the open aperture method for the sample, before precede the closed aperture

method. The sensor has been connected to the digital and analogue output of the

power meter (Field mate-coherent), to characterize the nonlinear observation. Z-scan

translation stage has capable to move 70000microns, the focal length of the lens and

midpoint of the translation stage (35000micron) were placed at the same point on z-

axis. The translation stage was controlled by the z-scan software by making a simple

102

program and simultaneously characterization readings were noted in power meter. Z-

scan experiment is shown in Fig.4.2.

CONSTRUCTION

1. Fix the He-Ne laser on the table and mark the laser point on the wall. It helps

to construct the experiment on perfect linearity.(should not disturb the laser)

2. Gaussian filter is used to produce Gaussian beam and TEM00 mode.(In

Gaussian filter contains two adjustment screws vertical and horizontal

adjustment screws, the center of the output Gaussian beam should fall on the

marked point of wall )

3. The black paper aperture of size 2mm is placed after the Gaussian filter, to

avoid concentric circles of Gaussian. Z-scan experiment of single Gaussian

beam gives good result. Single Gaussian beam means allows the central

maximum of Gaussian beam.

4. Next to the black paper aperture, convex lens is placed (convex lens of focal

length is 30mm)

5. The Sample holder with computerized control moves along the z-axis of

70000micron. It is controlled by the z-scan software.(programmable)

6. The sample should be less than 1mm of thickness.

7. The sensor is placed exactly where the diameter of laser beam is 7mm.

8. Convex lens of 50mm is used only for open aperture to collect the refracted

He-Ne laser beams.

9. The variable aperture is used only for closed aperture method; the refracted

rays should allow the limited aperture sizes (1-to-4mm).

10. In future, it is advisable to use 15mW laser for Z-scan experiment.

4.3.1. GAUSSIAN BEAM

In conventional optics, the electromagnetic radiation is in the form of Gaussian beam

which means transverse electric field and intensity distributions are well

approximated by Gaussian function. If the laser is said to be Gaussian beam,

fundamental transverse of laser is TEM00 mode. The mathematical solution of the

Gaussian beam is in the paraxial form of Helmholtz equation.

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Figure 4.3: Gaussian beam used in the z-scan experiment

The solution of Gaussian function is in the form of complex amplitude. The

electromagnetic waves are combination of electric and magnetic waves and it is

perpendicular to each other. To analyse the properties of the beam, any one of the two

fields is sufficient. The fixed solution of the spot size and the radius of the curvature

have been calculated easily in case of Gaussian beam.

Figure 4.4. Working of Gaussian filter in Z-scan experiment

In role of Gaussian filter in Z-scan technique is to convert the applied electric field

and intensity were distributed uniformly. The accuracy of the solution has been

achieved by Gaussian filter. Fig. 4.4, represents the working of the Gaussian filter.

The Fourier transform of input noise beam has high spatial frequencies, it reduced by

the pinhole for filtering frequencies. The output of the Gaussian filter is shown in

Fig.4.3.

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Figure 4.5: Gaussian beam at focal length of convex lens

The Gaussian beam at focal length is shown in Fig.4.5. Beam width or spot size of

the Gaussian beam, the variation of spot size is given by

2

0( ) 1R

Zw z w

Z

4.1

Rayleigh range is given by20

R

wZ

4.2

The calculation of spot diameter at focal length(Wo)

21.27 FL MDiameter

d

4.3

Where, FL is focal length of the convex lens(L1), λ is wavelength of laser and d is

diameter of input laser, Full width half maximum of Gaussian beam M=1

3 9

3

1.27 30 10 632.8 10 1

2 10Wo

9

0

24109.68 10

2W

90 12054.84 10W

60 12.054 10W m

105

0 12W m

Figure 4.6 a,b: Saturation absorption with Gaussian and without Gaussian filter

In z-scan experiment, it is observed that the open aperture characteristic peak with

Gaussian filter and without Gaussian filter as shown in Fig.4.6 a,b.

4.3.2. OPEN APERTURE METHOD

The interaction of light with matter is changing the properties of the material

and due to the heat transfer to the irradiated material induces the optical absorption.

The nonlinear absorption coefficient (β) was evaluated directly by the Z-scan open

aperture method. The open aperture method is relatively straightforward method of

measuring the change in transmittance with respect to irradiance (I). The nonlinear

absorption of materials is arising due to multiphoton absorption or single photon

absorption. The normalized transmittance(S=1) of the open aperture shows enhanced

transmission at the focus, which means saturation of absorption at high intensity. The

closed aperture is shown in Fig.4.7. The photoinduced changes in the crystal are

caused by the formation of polarized electron-phonon states, which are responsible for

the optical absorption of the organic crystals (Wojciechowski.A et al; 2010). The

value of β is negative for saturation absorption and positive for multi photon

absorption. The imaginary part of third order susceptibility is directly proportional to

nonlinear absorption

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Figure 4.7: Open aperture method of Z-scan technique

4.3.3. CLOSED APERTURE METHOD

Figure 4.8: Closed aperture method of Z-scan technique

The nonlinear refractive index of material was evaluated by the Z-scan closed

aperture method. The sensitivity to nonlinear refraction is entirely due to the aperture.

As the sample is brought closer to focus (at focal length), the irradiance of beam

increases or decreases, depends on the material absorption and refractive index. The

optical absorption of sample at focal length changes the refractive index of the

material. The change of refractive index affects the transmittance of the sample. The

nonlinear refractive index effects are shown in Fig.4.8.The negative nonlinear

refractive index of the sample shows transmittance peak followed by transmittance

valley, similarly the positive nonlinear refractive index shows the transmittance valley

followed by transmittance peak. This technique is useful to find the sign of nonlinear

refractive index. The closed aperture method is affected by both nonlinear absorption

(β) and refractive index (n2). The nonlinear refraction separate from nonlinear

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absorption is simply dividing the transmittance of closed aperture by the open

aperture. The real part of susceptibility is directly proportional to the nonlinear

refractive index.

4.4. THIRD ORDER NONLINEAR SUSCEPTIBILITY

The intensity dependent refractive index of material and the variation of the

refractive index as a function of the incident beam irradiance are given by

n= no+n2I, 4.4

where no is the linear index, n2 is nonlinear index of refraction, I- intensity of

irradiance laser beam within the sample. The absorption coefficient α is no longer

constant; instead it becomes a function of the extinction intensity as in the relation

α=αo+βI. 4.5

The third order susceptibility (χ3) is considered as complex quantity. The magnitude

of third order NLO susceptibility can be calculated using the formula

[Santhakumari,R.et al;2010].

χ3 = [Re (χ3) +Im (χ3)]. 4.6

The real and imaginary part of third order susceptibility can be defined as

-4 23 2o o 210 ε C n n

Re(χ )(esu)= (cm /W)π 4.7

-2 2 23 2o o 2

2

10 ε C n λβnIm(χ )(esu)= (cm /W)

4π 4.8

The real part of susceptibility is directly proportional to the nonlinear refractive

index, and imaginary part of susceptibility is directly proportional to nonlinear

absorption. The nonlinear absorption and nonlinear refractive index of crystal has

measured in open and closed aperture method respectively. In closed aperture method,

on-axis phase shift is calculated from valley-peak or peak valley transmittance. The

equation of on-axis phase shift (ΔΦ) is in terms of normalized transmittance can be

defined as Sheik-bahae.et al.

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0.25p-vΔT =0.406(1-S) ΔΦ

4.9

Where S is the aperture linear transmittance and is calculated using the relation

S=1-exp [-2ra2/wa

2]. The third order nonlinear refractive index of crystal can be

defined in terms of on-axis phase shift

2o eff

ΔΦn =

K I Lw 4.10

Where Kw is the wave number is equal to 2 /λ (K=9.923X109), Leff= [1-exp (-αL)]/α

is an effective thickness, Io is the peak intensity within the sample, L is the thickness

of the sample. From the open aperture Z-scan data, the nonlinear absorption

coefficient is estimated as (Gayathri et al; 2007)

2

o eff

2 ΔTβ=

I L 4.11

To neglect the nonlinear absorption of closed aperture normalized transmittance

(ΔTCA) can be defined by

CA 2 2

4xΔT =1- ΔΦ(x +9)(x -1)

4.12

Where x=z/zo, zo is Rayleigh length. The condition for normalized transmittance for

open aperture method is given by [For qo(0)<1, where qo(0)=β Io Leff / (1+(z2/zo2)]

(Van Stryland et.al;1998).

m

oOA 3/ 2

qΔT =

m+1

z 4.13

Second order hyperpolarizability( hγ ) of crystal is related to third order

susceptibility. The nonlinear induced polarization per molecule is described by second

order hyperpolarizability. hγ is calculated from the given relation (Zhao,M.T et al;

1998).

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(3)

h 4

χγ =L N 4.14

Where N is the density of molecules, L is the local field factor which in the Lorentz

approximation is given by L= (no2+2)/3, no is linear refractive index of the medium.

The calculation of response time of material, associated with thermal

nonlinearity. For condensed matter, the refractive index can either increase or

decrease with change in temperature, depending on the internal structure of the

material. Thermal processes can lead to large and unwanted nonlinear optical effects.

The origin of thermal nonlinearity optical effect is that some fraction of the incident

laser power is absorbed while passing through an optical material. The response time

τ of crystal is associated with the change in temperature.

20( ) rc

4.15

Where, (ρ0C) is heat capacity per unit volume, κ is thermal conductivity; r is

radius of laser beam. This response time is much larger than the pulse duration

produced by most pulsed laser. It leads to the conclusion that the consideration of

thermal nonlinear effects. Thermal effects are usually the dominant nonlinear optical

mechanism for continuous wave laser beams. (Robert Boyd, Nonlinear optics,

Elsevier publication, 2008, page 235-240).

4.5. NONLINEAR ABSORPTION AND REFRACTIVE INDEX OF OH1CRYSTAL

Figure 4.9: a. Self-focusing effect of the OH1 crystal

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b. Multiphoton absorption of the OH1 crystal

Nonlinear absorption and refractive index of OH1 crystal is shown in

Fig.4.9.a,b. The positive multiphoton absorption has been observed in OH1crystal.

The calculated value of nonlinear absorption (β) is 8.2203x10-5m/W. The calculated

value of nonlinear refractive index of material is 7.490X10-12 m2/W. The third order

nonlinear susceptibility (χ3) of OH1 crystal is 5.7217x10-6esu. The measurement

details of Z-scan technique is shown in Table.4.1. The ratio of real and imaginary

susceptibility of OH1 crystal is 1.8. (Bharath et al;2014).

4.5.1. MECHANISM AND OPTICAL SWITCH CALCULATION

The mechanism of nonlinear response of crystal is due to the thermal nonlinear

optical effects. The nonlinear polarization is depending on the applied field strength.

In the same manner mechanism can be explained in terms of nonlinear susceptibility

or nonlinear refractive index. The characteristic time scale for nonlinear response of

material from the typical value based on n2 (10-11m2/W) or χ3 (m2/v2) is developed by

Boyd; 2011. As per the characteristic time scale, OH1 crystal is possibly response in

10-3 seconds for optical switching devices. Third order susceptibility of materials is

depending upon the applied intensity, if increase the intensity of laser OH1 crystal is

possible to response in nanoseconds.

Table.4.1.Z-Scan measurement data of OH1 crystal

Measurement data of OH1 crystal

Optical path length 85cmBeam radius of the aperture(wa) 3.5mmAperture radius(ra) 2mmSample thickness(L) 0.65mmEffective thickness(Leff) 0.6811mmLinear absorption coefficient(α) -0.1425Linear transmittance(S) 0.48Nonlinear refractive index (n2) 7.490X10-12 m2/WNonlinear absorption coefficient(β) 8.220x10-5m/WReal part of third order susceptibility[Re(χ3)] 5.006x10-6esuImaginary part of third order susceptibility [Im(χ3)] 2.769x10-6esuThird order nonlinear susceptibility (χ3) 5.721x10-6esuSecond order hyper polarizability(γh) 0.8465x10-6esu

The response time (τ) of OH1 crystal is associated with the change in temperature

and calculated using the following relation τ ~ (ρ0C) r2 /κ. Where (ρ0C) is heat

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capacity per unit volume (1.187 x106 J/m3 K), κ is thermal conductivity (0.0194 W/m

K), r is radius of laser beam (12 μm). The response time (τ) of OH1 crystal is 9.136

x10-3 s. This response time is much larger than the pulse duration produced by most

pulsed laser. It leads to the conclusion that the consideration of thermal nonlinear

effects. Thermal effects are usually the dominant nonlinear optical mechanism for

continuous wave laser beams. The power or intensity is relevant quantity for

continuous laser beams, but the pulse energy Q=Pτ, where P is consequently power

P= πr2I0 and τ is the response time. The calculated pulse energy of OH1 crystal is

2.6644x10-5 J.

4.6. NONLINEAR ABSORPTION AND REFRACTIVE INDEX OF MOT2CRYSTAL

Fig.4.10 a. Self-defocusing effect of the MOT2 crystalb. Multiphoton absorption of the MOT2 crystal

In open aperture method, MOT2 crystal shows a strong multiphoton absorption

peak at the focal point of a convex lens as shown in Fig [4.10a]. In closed aperture

method, the self-defocusing effect of sample shows the transmittance peak is followed

by valley and it is shown in Fig [4.10b] .The calculated value of the nonlinear

refractive index (n2) is 1.680X10 -14 m2/W. The nonlinear absorption (β) of MOT2 is

found to be 2.497X10-7 m/W. The third order nonlinear susceptibility (χ3) of MOT2

crystal is 2.7409X10-8 esu. The measurement details of Z-scan technique is shown in

Table.4.2. (Bharath et al;2014).

4.6.1. MECHANISM AND OPTICAL SWITCH CALCULATION

The mechanism of nonlinear response of crystal is due to the molecular orientation

polarization. The origin of nonlinearity is the tendency of molecules to become

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aligned in the electric field of an applied optical wave. The optical wave then

experiences a modified value of the refractive index because the average

polarizability per molecule has been changed by the molecular alignment. The

characteristic time scale for nonlinear response of material from the typical value

based on n2 (10-14m2/w) or χ3 (m2/v2) is developed by Boyd. If the optical

nonlinearities of material are relatively large nonlinear susceptibility 10-8esu and they

response in picoseconds time, reported by David F.Eaton. As per the characteristic

time scale MOT2 crystal is possibly response in picoseconds (10-12) time for optical

switching devices. The approximate response time of MOT2 crystal is 10-8 to10-12 s.

Two figures of merit, W and T, have been calculated to be W=0.926>1andT=9.40<1,

respectively.

Table.4.2. Z-Scan measurement data of MOT2 crystal

Measurement data of MOT2 crystalBeam radius of the aperture(wa) 3.5mmAperture radius(ra) 1mmSample thickness(L) 0.51mmBeam radius(Wo) 12.22μmEffective thickness(Leff) 0.4161mmLinear absorption coefficient(α) 0.758Linear transmittance(S) 0.4795Rayleigh length (Zo) 1.14mmNonlinear refractive index (n2) 1.680X10-14 m2/WNonlinear absorption coefficient(β) 2.497X10-7cm/WReal part of third order susceptibility[Re(χ3)] 1.762X10-8esuImaginary part of third order susceptibility [Im(χ3)] 0.9788X10-8esuThird order nonlinear susceptibility (χ3) 2.7409X10-8esuSecond order hyper polarizability(γh) 0.4081x10-8esu

4.7. NONLINEAR ABSORPTION AND REFRACTIVE INDEX OF OE1CRYSTAL

The normalized transmittance(S=1) of the open aperture shows enhanced

transmission at the focus, which means saturation of absorption at high intensity.

Absorption saturation enhances the peak and decreases the valley at focal length as

shown in Fig [4.11a]. The photoinduced changes in the OE1 crystal are caused by the

formation of polarized electron-phonon states, which are responsible for the optical

absorption of the organic crystals. The calculated value of nonlinear absorption (β) is

6.079 x10-5 m/W. The change of refractive index affects the transmittance of the

sample. The nonlinear refractive index or self-defocusing effect of OE1 crystal is

shown in Fig [4.11b]. The calculated value of nonlinear refractive index of material is

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3.176x10-11 m2/W. The third order nonlinear susceptibility (χ3) of OE1 crystal is

3.3396x10-6esu.

Fig.4.11 a. Self-defocusing effect of the OE1 crystalb. Saturation absorption of the OE1 crystal

4.7.1. MECHANISM AND OPTICAL SWITCH CALCULATION

The mechanism of nonlinear response of OE1 crystal is due to the thermal

nonlinear optical effects. In the same manner mechanism can be explained in terms of

nonlinear susceptibility or nonlinear refractive index. OE1 crystal is possibly response

in 10-3 seconds for optical switching devices. Third order susceptibility of materials is

depending upon the applied intensity, if increase the intensity of laser OE1 crystal is

possible to response in nanoseconds.

Table.4.3. Z-Scan measurement data of OE1 crystal

Measurement data of OE1 crystalBeam radius of the aperture(wa) 3.5mmAperture radius(ra) 1mmSample thickness(L) 0.51mmBeam radius(Wo) 12μmEffective thickness(Leff) 0.4384mmLinear absorption coefficient(α) 0.609Linear transmittance(S) 0.15Intensity at focus (Io) 26.53MW/m2

Nonlinear refractive index (n2) 3.176x10-11 m2/WNonlinear absorption coefficient(β) 6.079x10-5m/WReal part of third order susceptibility[Re(χ3)] 2.2505x10-6esuImaginary part of third order susceptibility [Im(χ3)] 2.1709x10-6esuThird order nonlinear susceptibility (χ3) 3.3396x10-6esuSecond order hyper polarizability(γh) 0.4406x10-6esu

The response time (τ) of OE1 crystal is associated with the change in temperature

and calculated using the following relation τ ~ (ρ0C) r2 /κ. Where (ρ0C) is heat

capacity per unit volume (1.164 x106 J/m3 K), κ is thermal conductivity (0.085 W/m

114

K), r is radius of laser beam (12 μm). The response time (τ) of OE1 crystal is 2.044

x10-3 s. Two figures of merit, W and T, have been calculated to be

W=21>1andT=1.2<1, respectively. All the results show that OE1 crystal has potential

application for all-optical switching. The power or intensity is relevant quantity for

continuous laser beams, but the pulse energy Q=Pτ, where P is consequently power

P= πr2I0 and τ is the response time. The calculated pulse energy of Cl1 crystal is

2.491x10-5 J. The measurement details of Z-scan technique is shown in Table.4.3.

4.8. NONLINEAR ABSORPTION AND REFRACTIVE INDEX OF 3E4HMCRYSTAL

Figure 4.12: a. Self-defocusing effect of the 3E4HM crystalb. Multiphoton absorption of the 3E4HM crystal

In open aperture method, 3E4HM crystal shows a strong multiphoton absorption

peak at the focal point of a convex lens as shown in Fig [4.12a].The calculated value

of nonlinear absorption (β) is 1.42x10-4 m/w. In closed aperture method, the self-

defocusing effect of sample shows the transmittance peak is followed by valley and it

is shown in Fig [4.12b]. The calculated value of the nonlinear refractive index (n2) is

1.86X10-11m2/W. The third order nonlinear susceptibility (χ3) of 3E4HM crystal is

1.2628X10-5esu. The measurement details of Z-scan technique is shown in Table.4.4.

4.8.1. MECHANISM AND OPTICAL SWITCH CALCULATION

The thermal nonlinear optical effects were due to the processes of the incident

continuous laser power passing through an optical material. The response time (τ) is

associated with the change in temperature for thermal nonlinearity. The response time

115

for condensed matter has calculated using the relation τ ~ (ρ0C) r2 /κ, where (ρ0C) is

heat capacity per unit volume (1.189 x106 J/m3 K), κ is thermal conductivity

(0.0513W/m K) and r is radius of laser beam (6μm). The numerical value of response

time of 3E4HM crystal is 8.35x10-4 s. This response time is much larger than the pulse

duration produced by most pulsed laser. It leads to the conclusion that the

consideration of thermal nonlinear effects. Thermal effects are usually the dominant

nonlinear optical mechanism for continuous wave laser beams. Two figures of merit,

W and T, have been calculated to be W=18>1andT=4.8<1, respectively. All the

results show that 3E4HM crystal has potential application for all-optical switching.

Table.4.4. Z-Scan measurement data of 3E4HM crystal

Measurement data of 3E4HM crystalBeam radius of the aperture(wa) 3.5mmAperture radius(ra) 3mmSample thickness(L) 0.48mmBeam diameter 12.22μmEffective thickness(Leff) 0.40mmLinear absorption coefficient(α) 0.893Linear transmittance(S) 0.30Intensity at focus (Io) 26 MW/m2

Nonlinear refractive index (n2) 1.86x10-11 m2/WNonlinear absorption coefficient(β) 1.42x10-4m/WReal part of third order susceptibility[Re(χ3)] 1.17x10-5esuImaginary part of third order susceptibility [Im(χ3)] 4.52x10-6esuThird order nonlinear susceptibility (χ3) 1.262x10-5esuSecond order hyper polarizability(γh) 0.2097x10-6esu

4.9. NONLINEAR ABSORPTION AND REFRACTIVE INDEX OF Cl1CRYSTAL

Figure 4.13: a. Self-focusing effect of the Cl1 crystalb. Saturation absorption of the Cl1 crystal

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The negative nonlinear absorption has been observed in Cl1, due to the saturation

absorption of material. The calculated value of nonlinear absorption (β) is 2.3539 x10-

6 m/W. The change in transmittance (valley-peak) of Cl1 materials shows self-

focusing effect in closed aperture method. The calculated value of nonlinear refractive

index of material is 5.476x10-11 m2/W. The third order nonlinear susceptibility (χ3) of

Cl1 crystal is 2.7949X10-6 esu. The measurement details of Z-scan technique is shown

in Table.4.5. (Bharath et al;2014). The nonlinear absorption and refractive index of

Cl1 crystal is shown in Fig.13.a,b.

Table.4.5. Z-Scan measurement data of Cl1 crystal

Measurement data of Cl1 CrystalBeam radius of the aperture(wa) 3.5mmAperture radius(ra) 1mmSample thickness(L) 0.582mmBeam radius(Wo) 12.22μmEffective thickness(Leff) 0.6535mmLinear absorption coefficient(α) 0.9212Linear transmittance(S) 0.15Intensity at focus (Io) 26.47Mw/m2

Nonlinear refractive index (n2) 5.476X10-11 m2/WNonlinear absorption coefficient(β) -2.3539X10-6m/WReal part of third order susceptibility[Re(χ3)] 1.1851X10-6esuImaginary part of third order susceptibility [Im(χ3)] 2.5313X10-6esuThird order nonlinear susceptibility (χ3) 2.7949X10-6esuSecond order hyper polarizability(γh) 0.3591x10-6esu

4.9.1. MECHANISM AND OPTICAL SWITCH CALCULATION

The mechanism of nonlinear response of Cl1 crystal is due to the thermal

nonlinear optical effects. The response time τ of crystal is associated with the change

in temperature. τ ~ (ρ0C) r2 /κ. Where (ρ0C) is heat capacity per unit volume (1.229

x106 J/m3 K), κ is thermal conductivity (0.05W/m K), r is radius of laser beam

(12.22μm). The response time of Cl1 crystal is 3.0036x10-4s. Two figures of merit, W

and T, have been calculated to be W=24>1andT=2.7<1, respectively. All the results

show that Cl1 crystal has potential application for all-optical switching. The power or

intensity is relevant quantity for continuous laser beams, but the pulse energy Q=Pτ,

where P is consequently power P= πr2I0 and τ is the response time. The calculated

pulse energy of Cl1 crystal is 3.7279x10-6 J.

4.10. NONLINEAR ABSORPTION AND REFRACTIVE INDEX OF Br1CRYSTAL

The saturation absorption has been observed in Br1 crystal as shown in Fig

.4.14a. The calculated value of nonlinear absorption (β) is 1.795x10-4 m/W. The

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change in transmittance (peak-valley) of Br1 materials shows self-defocusing effect in

closed aperture method as shown in Fig.4.14b. The calculated value of nonlinear

refractive index of material is 8.920x10-11 m2/W. The third order nonlinear

susceptibility (χ3) of Br1 crystal is 8.8364x10-6esu. The measurement details of Z-

scan technique is shown in Table.4.6.

Figure 4.14: a. Self-defocusing effect of the Br1 crystalb. Saturation absorption of the Br1 crystal

4.10.1. MECHANISM AND OPTICAL SWITCH CALCULATION

The characteristic time scale for nonlinear response of material from the typical

value based on n2 (10-11m2/W) or χ3 (m2/v) is developed by Robert Boyd. As per the

characteristic time scale, Br1 crystal is possibly response in 10-3 seconds for optical

switching devices. For condensed matter, the refractive index can either increase or

decrease with change in temperature, depending on the internal structure of the

material. Thermal processes can lead to large and unwanted nonlinear optical effects.

The origin of thermal nonlinearity optical effect is that some fraction of the incident

laser power is absorbed while passing through an optical material. The response time

τ of crystal is associated with the change in temperature.

τ ~ (ρ0C) r2 /κ

Where (ρ0C) is heat capacity per unit volume (1.407 x106 J/m3 K), κ is thermal

conductivity (0.0413W/m K), r is radius of laser beam (12.22μm)

τ ~ 1.407x106 J/m3 K x (12.22x10-6)2 m2 / 0.0413W/m K

τ ~5.087x10-3 s

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This response time is much larger than the pulse duration produced by most

pulsed laser. It leads to the conclusion that the consideration of thermal nonlinear

effects. Thermal effects are usually the dominant nonlinear optical mechanism for

continuous wave laser beams. The power or intensity is relevant quantity for

continuous laser beams, but the pulse energy Q=Pτ, where P is consequently power

P= πr2I0 and τ is the response time. The calculated pulse energy of Br1 crystal is

6.328x10-8 J. Two figures of merit, W and T, have been calculated to be

W=47>1andT=0.12<1, respectively. All the results show that Br1 crystal has potential

material for all-optical switching. (Bharath et al;2014)

Table.4.6. Z-Scan measurement data of Br1 crystal

Measurement data of Br1 crystalBeam radius of the aperture(wa) 3.5mmAperture radius(ra) 2mmSample thickness(L) 0.30mmBeam radius(Wo) 12.22μmEffective thickness(Leff) 0.27mmLinear absorption coefficient(α) 0.792Linear transmittance(S) 0.48Intensity at focus (Io) 26.47MW/m2

Nonlinear refractive index (n2) 8.920x10-11 m2/WNonlinear absorption coefficient(β) 1.795x10-4m/WReal part of third order susceptibility[Re(χ3)] 10-6esuImaginary part of third order susceptibility [Im(χ3)] 10-6esuThird order nonlinear susceptibility (χ3) 8.836x10-6esuSecond order hyper polarizability(γh) 1.0085x10-6esu

4.11. THERMO-OPTIC COEFFICIENT (TOC)

Thermal nonlinearity of the continuous laser beam, the effective nonlinear

refractive index is given as Chapter.1

2

2

dn Rn

dt

4.16

22

ndn

dt R

4.17

Where, dn/dT is the temperature coefficient of the refractive index, α is linear

absorption coefficient, r is the radius of laser at focal length and k is thermal

conductivity. There is an attempt to calculate the approximate value of thermo-optic

coefficient through Z-scan of malononitrile derivative crystals. Thermo-optic

coefficient can be either positive or negative and for condensed matter typically lies in

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the range ±3 ×10-5K-1. [The American Institute of Physics Handbook, Section 6b]. The

sign of the magnitude is decided through the self-focusing or self-defocusing effect.

The negative sign is consider for self-focusing and positive for self-defocussing. The

approximate thermo-optic constant values are given in Table.4.7.

4.12. SECOND HARMONIC GENERATION STUDIES(KURTZ-PERRY METHOD)

Second harmonic generation of OH1 compound, it is reported by Hunziker et

al. MOT2, Cl1, Br1, 3E4HM crystals are Centro symmetry in nature, polarisation

effects cancel each other as explained in Chapter.1 (1.6). In special cases, some of the

crystal will exhibit both the second and third harmonic generation, like OE1. Second

harmonic generation (SHG) measurements have been carried out as per the Kurtz

Perry powder technique with Q-switched Nd-YAG laser at a wavelength 1064nm

(8ns, 10Hz). Powdered KDP crystal was used as reference material in the SHG

measurement. OE1 crystal is powdered and filled in microcapillary tube (diameter-

1.5mm). The size of the OE1 particle is measured through powder XRD experiment.

The crystalline size of OE1 particle is 9.014μm and it is measured using the Scherer

equation (Cullity, B.D;1977).

-100.9×1.54×10Particle Size=

FWHM×Cosθ 4.18

Where, full width half maximum (FWHM) is 0.1579 and 2θ is 25.946.The

size of the powder KDP particle is 1.025 μm. The input incident laser energy for OE1

and KDP powdered sample is 1.8mJ. The sample OE1 produces 2.3mV while KDP

exibit 8.8mV. Eventhough OE1 is centrosymmetry, it exhibits SHG signal 26% of that

of KDP. Powder XRD is shown in Chapter.2 (2.33b). The transparency of crystal is

starts only at 525nm onwards; due to the absoprtion green efficiency is lesser than

KDP. Due to local molecular disordering and the excitation of anharmonic phonons

described by third rank polar tensors there occurs a possibility to observe the SHG.

SHG effect may possibly higher at optical communication region (IR).

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4.13. CONCLUSION

Figure 4.15: Nonlinear characteristic of malononitrile derivative crystal

In Fig.4.15.shows the OH1 and Cl1 are showing the self-focussing effect and

MOT2, Br1, OE1, 3E4HM crystals were showing self-defocusing effects. In open

aperture method, OH1 and MOT2 crystals are showing minimum transmittance due to

multiphoton absorption. Cl1, Br1, OE1 and 3E4HM were showing maximum

transmittance due to saturation of absorption. The variation of transmittance is

depends on internal structure of materials. The change of nonlinear refractive index

and absorption were due to thermal nonlinear optical effects in organic crystals. The

optical illumination on crystals leads to increase in temperature than its periphery.

The temperature change has been calculated approximately, represented as thermo

optic coefficient. Thermo-optic coefficient of the crystals is coming around 10-5K.

The mechanism of the nonlinear optical effects is depends on the intensity of laser.

There are many mechanisms in nonlinear optical change but the limitation of laser

energy allows the thermal nonlinear effects in crystal.

Z-scan experiment has been constructed and nonlinear refractive index;

nonlinear absorption and third order nonlinear susceptibility have been calculated for

malononitrile derivative crystal. One photon and two photon figure of merit have been

studied for optical switch application. The optical response time of the crystals were

calculated. The limitation of laser energy allows calculating the thermal nonlinearity

of these materials. Malononitrile derivative materials are response in milliseconds at

lower intensity. There is a possibility of response of all the malononitrile derivative

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crystals in nanoseconds to picosecond, if the intensity of laser increases. The

calculated nonlinear optical values are given in Table.4.7. These data are calculated

from the Z-scan experiment of He-Ne laser energy 5mW.

Table.4.7. Z-scan data for malononitrile derivative crystals

OH1 MOT2 OE1 3E4HM Cl1 Br1

n2 m2/W 7.490X10-12 1.680X10-14 3.176x10-11 1.860x10-11 5.476X10-11 8.920x10-11

β m/W 8.220x10-5 2.497X10-7 6.079x10-5 1.420x10-4 2.35410-6 1.795x10-4

χ3 esu 5.722x10-6 2.741X10-8 3.339x10-6 1.262x10-5 2.795X10-6 8.836x10-6

W(>1) 21 0.946 21 18 24 47

T(<1) 6 9 1.2 4.8 2.7 0.12

Re(χ3)/

Im(χ3)

1.8 1.8 1.03 2.60 0.469 2.0

TOC K-1 -0.685x10-5 0.476x10-5 2.969x10-5 0.715x10-5 -1.991x10-5 3.115x10-5

γh (esu) 0.847x10-6 0.409x10-8 0.441x10-6 0.209x10-6 0.359x10-6 1.009x10-6

Response

time s

9.136 x10-3 10-8-10-12 2.044 x10-3 8.35x10-4 3.0036x10-4 5.087x10-3

SHG SHG Nil SHG Nil Nil Nil