CHAPTER – VI

LINEAR AND NONLINEAR OPTICAL PROPERTIES

6.1 Introduction

6.2 UV-vis-NIR Spectroscopy

6.3 Instrumentation

6.4 Transmittance, Absorbance and Reflectance spectral analysis

6.5 Band gap estimation - Absorption spectra

6.6 Calculation of optical constants

6.7 Nonlinear optical characterization

6.8 Powder SHG measurement - Experimental procedure

6.8.1 SHG efficiency of the grown crystals

6.9 Z-Scan measurement

6.9.1 Experimental procedure

6.10 Conclusion

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CHAPTER - VI

LINEAR AND NONLINEAR OPTICAL PROPERTIES

6.1. Introduction

Nonlinear optics plays a vital role in information technology and

industrial applications. There has been a growing interest in crystal growth

process, particularly, in view of the increasing demand for NLO materials for

device applications. Considerable theoretical and experimental investigations

have been done in order to understand the microscopic origin of nonlinear

behaviour of NLO materials. Knowledge of the optical properties such as

transmittance, absorbance, refractive index, absorption coefficient, extinction

coefficient, optical conductivity, electrical conductivity and band gap is crucial

for the device fabrication in optoelectronic applications [221,222]. The

electrical properties of materials are also dependent upon the band gap which is

closely related to the electronic band structure. Hence the measurement of the

optical constant is necessary to understand the optical properties of the

materials.

To understand the linear optical properties of the grown crystals, the

UV-vis-NIR spectral study was employed. The optical parameters such as band

gap, refractive index, extinction coefficient, optical absorption coefficient,

optical conductivity and electrical conductivity of the samples were evaluated

using theoretical formulae. For nonlinear optical characterization of the

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samples, modified Kurtz and Perry powder technique was adopted. The second

harmonic generation (SHG) efficiency of the materials were found and

compared with the standard KDP. Third order nonlinear optical parameters

were estimated on the basis of thermal origin by employing Z-scan technique

using a low power Nd:YAG laser. This chapter clearly illustrates the linear and

nonlinear optical characterizations of the grown crystals in detail.

6.2. UV-vis-NIR spectroscopy

The word ‘spectroscopy’ is used as a collective term for all the

analytical techniques based on the interaction of light and matter. Absorption

spectroscopy in the different regions of electromagnetic spectrum has been an

important tool to the analyst since a long time [223]. Ultraviolet and visible

absorption spectroscopy is the measurement of light absorption by a sample.

This absorption or attenuation can occur when light passes through a

translucent liquid sample, or when light is reflected from a sample surface. The

difference in the incident light and the transmitted light is used to determine the

actual absorbance.

Any molecular system possesses three types of energy namely electronic

(Eele), vibrational (Evib) and rotational (Erot) with decreasing magnitude in same

order for a system. When an atom or molecule absorbs energy, electrons are

promoted from their ground state to an excited state. The absorption peaks thus

obtained is broad, smooth and never very sharp due to the fact that the

electronic absorption is accompanied with a corresponding change in the

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vibrational and rotational energies as well. Molecules can only absorb radiant

energy in definite units, or quanta, which corresponds to the energy difference

between the ground and excited states. The energy absorbed ∆E in an

electronic transition, which is carried by any one quantum is proportional to its

frequency of oscillation, i.e.,

hC∆E = hυ =

λ ... (6.1)

where h is Planck’s constant (6.626 × 10-34 JS), υ is the frequency, λ is the

related wavelength and C is the velocity of light. The position of absorption

maxima for a molecule depends on the difference in the energy of the ground

state level to that of excited states; larger the difference between the energies,

higher is the frequency of absorption and thus smaller will be the wavelength.

Absorption band shows two important characteristics; position of the band

which depends on the energy difference between electronic level and intensity

which depends on the interaction between the radiation and electronic system

as well as on the energy difference between the ground and excited state.

Absorption of ultraviolet and visible radiation in organic molecule is

restricted to certain functional groups (Chromophores) that contain valence

electrons of low excitation energy. The spectrum of a molecule appears as a

continuous absorption band. The visible region of the spectrum (330 - 780 nm)

comprises photon energies of 36 to 72 kcal/mol, and the near ultraviolet region

extends this energy range to 143 kcal/mol. The accessible part of the UV-vis

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region (wave length of 200 to 800 nm) shows absorption only if conjugated

π-electron systems are present. The possible electronic transitions are σ to σ*

transitions, n to σ* transitions, n to π* and π to π* transitions. Most absorption

spectroscopy of organic compound is based on transitions of n or π electrons to

the π* excited state. This is because the absorption peaks for these transitions

fall in an experimentally convenient region of the spectrum to provide the

π electrons. In inorganic compounds, UV-vis spectra of transitions metal

complex originate from electronic d-d transitions.

6.3. Instrumentation

A spectrophotometer is a device which detects the percentage

transmittance of light of certain intensity and frequency range is passed through

the sample. Thus the instrument compares the intensity of the transmitted light

(I t) with that of incident light.

Transmittance t

0

I(T) =

I ... (6.2)

Absorbance %T

(A) = -log( )100%

... (6.3)

Usually transmittance values are expressed as a percentage (%T). An

optical spectrometer records the wavelength at which the absorption occurs and

it gives spectrum of absorbance (A) versus wavelength. The maximum

absorbance wavelength is called absorption maxima (λmax).

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In the present studies, UV-vis spectroscopy is used for transmittance and

absorption observations. Mainly UV-vis study is under taken to find whether

the grown crystals are transparent in the UV-vis region. Also NLO crystals

must have maximum transmittance in this region and absence of absorptions in

the UV-vis region, enables the suitability of the materials for efficient

frequency conversion for second harmonic generation. If the materials have

lower cut off wavelength (200-400 nm) then the materials can produce higher

harmonic generation.

Optical transmittance and absorbance spectrum of the grown crystals

were recorded using a Perkin Elmer - Lambda 35 UV-vis-NIR spectrophotometer

in the range of 190 - 1100 nm. The study of optical transmittance and

particularly the absorption edge is very useful to find the optical constants of

these crystals and for the investigation of optical properties.

6.4. Transmittance, Absorbance and Reflectance spectral analysis

Optical transmittance spectrum conveys the transparency window of the

optical materials. If the materials have wide transparency window without

absorption at the fundamental wavelengths which shows its potential for

second harmonic generation. Also the desired lower cut off wavelength for

SHG in the transmittance spectrum should lie between 200 nm and 400 nm.

The recorded UV-vis-NIR transmittance spectra of the grown crystal samples

are found to be transparent in the whole visible region as shown in Fig. 6.1.

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Fig. 6.1: Transmittance pattern of the grown crystals

Identification of absorption edge in the absorbance spectrum is very

useful for the elucidation of the optical properties of the grown crystals.

Usually the absorption occurs by excitation of electrons from the filled states to

empty ones. The recorded absorbance spectra of all the grown crystals are

shown in Fig. 6.2. Among the grown crystals, GT and GM are organic

compounds. The absorption spectrum of these GT and GM complex may be

based on transitions of n or π electrons to the π* excited state. Semi organic

complexes such as LVZA, TGBDD and TuTGZC show their wide

transparency in the visible region due to amino acid combination with

inorganic metal salts. Thiourea based crystal complexes such as BTSN and

TPMS have extended transparency window and lower absorption edge in the

UV region which enables them for the production of higher harmonics

generation. The thiourea molecular structure is nearly coplanar and it is a

resonance hybrid of three resonance structures with each contributing roughly

an equal amount. The π-electron delocalization in thiourea molecules in the

semi organic complexes is responsible for their nonlinear optical property and

the absorption in the UV region.

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Fig. 6.2: Absorbance pattern of the grown crystals

The material which has higher transparency and lower reflectance are

suitable for antireflection coatings. The reflectance gives the ratio of the energy

reflected to incident light from a crystal. The reflectance spectra of all the

samples are shown in Fig. 6.3. The reflectacnce of all the samples is minimum

in the visible region.

Fig. 6.3: Reflectance pattern of the grown crystals

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6.5. Band gap estimation - Absorption Spectra

Estimation of band gap plays an important role in Materials Science.

Larger the gap, more tightly the valence electrons are bound to the nucleus.

The dependence of optical absorption coefficient with the photon energy is

useful to study the band structure and the type of the transition of electrons

[224]. The optical absorption coefficient (α) is calculated from the absorbance

(A) using the formula,

2.303log(A)α =

d ... (6.4)

where d is the thickness of the crystal. The optical band gap is calculated by

applying the Tauc model and the Davis and Mott model in the high absorbance

region [225],

mgαhυ = c(hυ - E ) ... (6.5)

where hυ is the photon energy, Eg is the optical band gap and c is a constant.

For direct transition, m = 1/2 or 3/2 depending upon whether the transition is

allowed or forbidden in the quantum mechanical sense. Similarly m= 2 or 3 for

indirect allowed and forbidden transition respectively. The general method of

determining the band gap is to draw a graph between (αhυ)1/m and hυ which

gives best linear type in the band gap edge region. Hence with m = 1/2, a graph

is plotted between (αhυ)2 vs hυ for the grown crystals and are shown in

Fig. 6.4. The band gap (Eg) value is estimated by extrapolating the linear portion

of the photon energy axis [226] and the Eg values are given in Table 6.1.

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Optical band gap is a bond sensitive property, an increase in the average bond

energy results in an increase in optical band gap [227]. In thiourea complexes,

metal- sulphur coordination increases the polar nature of thiourea molecule

resulting in predominant double bond of C=N and a single bond C-S. The

variation in average bond energy of a system is reflected in the reduction of the

optical band gap.

Fig. 6.4: Energy diagram of all the crystals

6.6. Calculation of optical constants

Knowledge of optical constants of a material is essential to assess the

materials for potential optoelectronic applications [225]. The optical properties

of crystals are varied due to the interaction between the crystal and the electric

and magnetic fields of the electromagnetic wave. Using the theoretical

formulae, the optical constants of the materials were calculated from the

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recorded absorption spectra [228]. The extinction coefficient (K) is found in

terms of the absorption coefficient (α),

λαK =

4π ... (6.6)

And the linear refractive index (n) is given by,

2-(R +1) ± (3R -10R -3)n = [ ]

2(R -1) ... (6.7)

The optical conductivity is a measure of the frequency response of the

material when irradiated with light,

opαnC

σ =4π

... (6.8)

where C is the velocity of light. The electrical conductivity is estimated by the

optical method using the relation,

opel

2λσσ =

α ... (6.9)

The internal optical efficiency of the materials depends on the incident

photon energy. Hence the variation of optical constants as function of photon

energy is found in the present work.

Extinction coefficient is the amount of incident light lost due to

scattering and absorption per unit distance in a testing material medium. In

electromagnetic theory, the extinction coefficient is defined as the decay or

damping of the amplitude of the incident electric and magnetic fields. Fig. 6.5

shows the variation of extinction coefficient with the photon energy for all the

grown crystals. For all the crystals, the extinction coefficient decreases with

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increasing photon energy. The low value of extinction coefficient indicates a

less absorption of the medium. Correspondingly the refractive index of the

medium is also changed with the incident photon energy. This changing nature

of the refractive index of the crystals with the photon energy is shown in Figure 6.6.

Fig. 6.5: Extinction Coefficient as a function of Photon energy of all the crystals

Fig. 6.6: Refractive Index as a function of Photon energy of all the crystals

The variation of optical conductivity with photon energy is shown in

Fig. 6.7. The optical conductivity increases with increasing of photon energy

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which may be due to the excitation of electrons by photon energy. The

averaged electrical conductivity based on optical method as a function of

photon energy is shown in Fig. 6.8. It is found from the graph that the electrical

conductivity decreased with the increase in photon energy. The electrical

conductivity values are in the range 101 - 102 (ohm-cm)-1 which indicates the

semiconducting nature of the materials.

Fig. 6.7: Optical Conductivity as a function of Photon energy of all the crystals

Fig. 6.8: Electrical Conductivity as a function of Photon energy of all the crystals

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Table 6.1: Optical parameters of the grown crystals

Sample Absorption

Edge (nm)

Optical Window

(nm)

Optical band gap Absorption

spectra (eV)

Refractive index (Reflectance

Method)

LVZA 232 232-1100 5.41 1.660

GM 337 337-1100 3.38 1.348

TGBDD 303 303-1100 4.88 1.236

GT 263 263-1100 4.57 1.274

TuTGZC 248 248-1100 4.83 1.191

BTSN 297 297-1100 4.01 1.537

TPMS 292 292-1100 4.13 1.582

The optical transmittance window of the crystal samples is given in

Table 6.1. The region of transparency shows the intrinsic property of the

crystals. The higher percentage of transmission in the visible region shows that

the crystals are free from major defects. Also good transmission nature of the

crystals which makes them suitable for photonic applications. As the optical

absorption edge lies in the UV region, the grown crystals can be a better

candidate for the production of higher harmonics.

6.7. Nonlinear optical characterization

Generally three techniques are used for the measurement of second

harmonic generation (SHG) of the materials. They are modified Kurtz and

Perry powder technique, Electric field induced second harmonic generation

(EFISH) experiment and Hyper- Rayleigh Scattering (HRS) technique. The

modified Kurtz and Perry powder technique [229] is a convenient method for

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screening large number of powdered materials for the second order NLO

activity. The third order nonlinear optical parameters such as nonlinear

refractive index, nonlinear absorption coefficient and third- order nonlinear

optical susceptibility are estimated on the basis of thermal origin by Z- scan

technique using a low power He:Ne laser.

6.8. Powder SHG measurement- Experimental procrdure

The experimental arrangement for Kurtz and Perry powder technique for

SHG measurement is shown in Fig. 6.9. Powdered crystal sample is densely

packed in a capillary tube. A fundamental laser beam of 1064 nm wavelength

from an Nd:YAG laser (8 ns, 10 Hz) is made to fall normally on the sample

cell. The transmitted fundamental wave is passed over a monochromator which

separates 532 nm (second harmonic signal) from 1064 nm and is passed

through successive IR filters which remove the residual 1064 nm fundamental

beam and is focussed on to a photomultiplier tube which gives the second

harmonic wave generated by the powder crystal sample. Powdered KDP crystal

is used as reference material.

Fig. 6.9: Experimental arrangement of Powder SHG measurement

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6.8.1. SHG efficiency of the grown crystals

In the present work, the SHG efficiency of the powdered samples

LVZA, GM, TGBDD, GT, TuTGZC, BTSN and TPMS were found relatively

with KDP. The measured values are presented in Table 6.2. In semi organic

crystals, delocalization of electrons are promoted due to metal ions. Hence

LVZA, TuTGZC, BTSN and TPMS have better relative SHG efficiencies than

the organic crystals GM and GT.

Table 6.2: Relative SHG efficiency of the grown crystals

Sample Laser power

(mJ/p) SHG efficiency of sample (mV)

SHG efficiency of KDP (mV)

Relative SHG efficiency

LVZA 2.4 48 35 1.37

GM 2.4 28 38 0.73

TGBDD 2.4 22 35 0.63

GT 5.7 8 15 0.53

TuTGZC 5.7 65 60 1.08

BTSN 9.6 30 32 0.94

TPMS 3.5 59 65 0.91 6.9. Z-scan measurement

The Z-scan is a simple and popular experimental technique to measure

the intensity dependent third order nonlinear susceptibility of the materials.

Z-scan method has gained rapid acceptance by the nonlinear optics community

as a standard technique for the simultaneous measurement of both the nonlinear

refractive index and the nonlinear absorption coefficient. Various Z-scan

methods are used for data analysis such as single beam Z-scan, eclipsing

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Z-scan, two colour Z-scan, time resolved excite probe Z-scan and top hat beam

Z-scan. A single beam method is used for measuring the sign and magnitude of

nonlinear refractive index that has the sensitivity compared to interferometric

methods.

The single beam Z-scan method is based on the intensity dependence of

the thin sample alone a focused Gaussian laser beam. The sample may give

focusing due to a positive nonlinear refraction or defocusing due to a negative

refraction. A Gaussian beam is focussed by a spherical lens onto the sample

and the variation in the beam profile is observed at the far field as the sample is

taken through the focus of the lens. The beam propagation direction is

considered as the Z direction and the sample is moved along that direction, and

hence this technique is known as the Z-scan technique. By properly monitoring

the transmittance change through a small aperture placed at the far field

position (closed aperture), one can determine the amplitude of the phase shift.

By moving the sample through the focus and without placing an aperture at the

detector (open aperture), one can measure the intensity- dependent absorption

as the change of the transmittance through the sample. When both methods

(closed and open) are used for the measurements, the ratio of the signals

determines the nonlinear refraction in the sample.

6.9.1. Experimental procedure

The schematic diagram of Z-scan technique is shown in Fig. 6.10. In

this method, the sample is translated in the Z-direction along the axis of a

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focused Gaussian beam from the He-Ne laser at 632.8 nm and the far field

intensity is measured as a function of the sample position. The transmission of

the beam through an aperture placed in the far field is measured using a photo

detector fed to the digital power meter. By properly monitoring the

transmittance change through a small aperture at the far field position (closed

aperture). One is able to determine the amplitude of the phase shift. By moving

the sample through the focus and without placing an aperture at the detector

(open aperture), one can measure the intensity dependent absorption of the

sample.

Fig. 6.10: Experimental set up for Z- Scan Measurements

The nonlinear parameters were calculated for the closed Z- scan set up

formulated by Sheik - Bahae and David J. Hagan [230]. The difference

between the normalized peak and valley transmission (∆TP- V) is given in terms

of the on axis phase shift ∆ϕ at the focus as,

0.25P-V∆T = 0.406(1-S) ∆φ ... (6.10)

where S is the aperture linear transmittance and is expressed by the relation,

2 2

a a(-2r -w )S = 1- e ... (6.11)

where ra is the aperture radius and wa is the beam radius at the aperture. The

nonlinear refractive index is given by,

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20 eff

∆φn =

kI L ... (6.12)

where 2π

k =λ

(λ is the wavelength of laser), I0 is the intensity of the laser beam

at the focus (Z = 0), Leff is the effective thickness of the sample (-αL

eff1- e

L =α

, α

is the linear absorption coefficient and L is the thickness of the sample).

From the open aperture Z-scan data, the nonlinear absorption coefficient

β is calculated by

0 eff

2 2∆Tβ =

I L ... (6. 13)

where ∆T is the one valley value at the open aperture Z- scan curve. The value

of β will be negative for saturable absorption and positive for two photon

absorption. The real and imaginary parts of the third order nonlinear optical

susceptibility χ(3) are given as,

-4 2 2(3) 0 0 210 (ε C n n )

Reχ =π

(cm2/W) ... (6.14)

-2 2 2(3) 0 0

2

10 (ε C n λβ)Imχ =

4π (cm/W) ... (6.15)

where ε0 is the permittivity of vacuum, n0 is the linear refractive index of the

sample and C is the velocity of light in vacuum. Thus the third order nonlinear

optical susceptibility is expressed as,

(3) (3) 2 (3) 2χ = Re(χ ) + Im(χ ) (esu) ... (6.16)

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In the closed aperture pattern, the medium acts like an intensity

dependent lens. As the sample is scanned along the beam path, its effective

focal length will vary. This change is reflected in the intensity distribution at

the aperture in the far field. The amount of energy transmitted by the aperture

depends on the sign of n2. For a material with positive n2, when the sample is

far from the focus, the intensity is low and hence the energy transmitted

through the aperture remains approximately constant. As the sample gets nearer

to the focus, the intensity is high enough to produce a positive lensing effect.

For Z < 0, this lensing causes the beam to come to focus earlier so that it

diverges more rapidly and hence the aperture transmittance decreases. On the

other hand, when Z > 0, the positive lensing causes the beam divergence to

decrease, resulting an increase in the aperture transmittance. Near Z = 0, a thin

lens has a very little effect on a focussed beam and hence the transmittance

gives low intensity value. The net Z-scan data produces a dispersion shaped

valley-peak pattern for a positive n2 material. Obviously, a negative n2 material

will produce a similar curve, but with the peak and valley reversed about Z = 0.

Figs. 6.11 and 6.12 show the closed and open aperture patterns of all the grown

crystals. In all the samples, a pre-focal peak followed by a post focal valley

which indicates the asymmetric nature of the trace. This result conveys that the

origin of the nonlinear refractive index is thermo-optic. The open aperture

pattern of the samples shows that the saturable absorption is due to the self

focusing nature. In order to get pure effective n2, it is necessary to get a ratio of

the open aperture transmittance to the corresponding closed-aperture scans.

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Fig. 6.11(a): Z-Scan Pattern of LVZA, GM, TGBDD, GT-Closed Aperture (CA)

Fig. 6.11(b): Z-Scan Pattern of LVZA, GM, TGBDD, GT-Open Aperture (OA)

Fig. 6.11(c): Z-Scan Pattern of LVZA, GM, TGBDD, GT-Ratio of OA and CA

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Fig. 6.12(a): Z-Scan Pattern of TuTGZC, BTSN, TPMS - Closed Aperture (CA)

Fig. 6.12(b): Z-Scan Pattern of TuTGZC, BTSN, TPMS - Open Aperture (OA)

Fig. 6.12(c): Z-Scan Pattern of TuTGZC, BTSN, TPMS - Ratio of OA and CA

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The nonlinear parameters such as nonlinear refractive index, nonlinear

absorption coefficient and the third order susceptibilities are calculated and the

results are summarized in Table 6.3. The nonlinear refractive indices of all the

crystal samples are positive and this result indicate the lensing effect is

focusing nature.

Table 6.3: Nonlinear optical parameters of the grown crystals

Parameters LVZA GM TGBDD GT TuTGZC BTSN TPMS

Nonlinear Refractive

Index (n2) × 10-7 (cm2/W)

6.39 7.80 11.8 11.6 11.3 6.29 10.8

Nonlinear Absorption

Coefficient (β) × 10-3 (cm/W)

-8.15 8.21 -24.0 4.91 -5.21 -3.20 -9.43

Real part of the Third order Susceptibility

[Re (χ3)] × 10-5 esu 4.47 3.60 4.56 4.77 4.07 3.77 6.84

Imaginary part of the Third order Susceptibility

[Im(χ3) × 10-4 esu

2.87 1.91 4.68 1.02 0.947 0.968 3.02

Third order Nonlinear optical Susceptibility

(χ3) × 10-4 esu 2.9 1.94 4.71 1.13 1.03 1.04 3.1

6.10. Conclusion

The optical properties such as transmittance, absorbance and reflectance

of all the grown crystals are studied with UV-vis-NIR spectrum. All the

materials have low absorbance, high transmittance and low reflectance in the

UV and visible region. The optical parameters such as extinction coefficient,

refractive index, absorption coefficient, optical conductivity, electrical conductivity

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and band gap are found and their variation with photon energy analysed. The

relative SHG efficiency of all the compounds is investigated. The nonlinear

parameters of all the samples such as nonlinear refractive index, nonlinear

absorption coefficient and third order nonlinear susceptibility are found using

Z-Scan technique. Thus the linear and the nonlinear optical parameters show

the optical efficiency (linear and nonlinear) of the grown crystals.