CHAPTER INTRODUCTION

Transcription

1 CHAPTER-4 Z-SCAN CONSTRUCTION AND STUDIES ON NONLINEAR ABSORPTION AND NONLINEAR REFRACTIVE INDEX OF MALONONITRILE DERIVATIVE CRYSTALS FOR OPTICAL SWITCHING 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. 97 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-toluenesulfonate] 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

2 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=n 2 I/ (αλ) and T=βλ/n 2, where n 2 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 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. 98

3 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 nonilluminated parts 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 TEM 00 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; 99

4 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 wo 2 /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 d 1 >>Zo is satisfied. (d 1 is the distance between focal length and the aperture). 100

5 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 decid e 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 101

6 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 TEM 00 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 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 TEM 00 mode. The mathematical solution of the Gaussian beam is in the paraxial form of Helmholtz equation. 102

7 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

8 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 w() z 1 Z w0 Z R Rayleigh range is given by Z R 2 w0 4.2 The calculation of spot diameter at focal length(wo) 1.27 FL M Diameter d 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 Wo W W W m 104

9 W0 12 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 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 eval uated 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 105

10 Figure 4.7: Open aperture method of Z-scan technique 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 (n 2 ). The nonlinear refraction separate from nonlinear 106

11 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 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= n o +n 2 I, 4.4 where n o is the linear index, n 2 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 (χ 3 ) is considered as complex quantity. The magnitude of third order NLO susceptibility can be calculated using the formula [Santhakumari,R.et al;2010]. χ 3 = [Re (χ 3 ) +Im (χ 3 )]. 4.6 The real and imaginary part of third order susceptibility can be defined as ε C n n o o 2 2 Re(χ)(esu)=(cm /W) π ε C n λβn o o 2 2 Im(χ)(esu)=(cm /W) 4π 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. 107

12 ΔT =0.406(1-S) p-v 0.25 ΔΦ 4.9 Where S is the aperture linear transmittance and is calculated using the relation S=1-exp [-2r a 2 /w a 2 ]. The third order nonlinear refractive index of crystal can be defined in terms of on-axis phase shift ΔΦ n 2= K I o L eff w 4.10 Where K w is the wave number is equal to 2 /λ (K=9.923X10 9 ), L eff = [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 ΔT 2 β= I o L eff 4.11 To neglect the nonlinear absorption of closed aperture normalized transmittance (ΔT CA ) can be defined by 4x ΔT CA =1- ΔΦ 2 2 (x +9)(x -1) 4.12 Where x=z/z o, z o is Rayleigh length. The condition for normalized transmittance for open aperture method is given by [For q o (0)<1, where q o (0)=β Io L eff / (1+(z 2 /z o 2 )] (Van Stryland et.al;1998). qo ΔT OA = 3/ 2 m+1 z m 4.13 Second order hyperpolarizability( γ h ) of crystal is related to third order susceptibility. The nonlinear induced polarization per molecule is described by second order hyperpolarizability. γhis calculated from the given relation ( Zhao,M.T et al; 1998). 108

13 χ (3) γ h = L 4 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= (n o 2 +2)/3, n o 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. () r 0c Where, (ρ 0 C) 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 ) NONLINEAR ABSORPTION AND REFRACTIVE INDEX OF OH1 CRYSTAL Figure 4.9: a. Self-focusing effect of the OH1 crystal 109

14 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 x10-5 m/w. The calculated value of nonlinear refractive index of material is 7.490X10-12 m 2 /W. The third order nonlinear susceptibility (χ 3 ) of OH1 crystal is x10-6 esu. 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) 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 n 2 (10-11 m 2 /W) or χ 3 (m 2 /v 2 ) is developed by Boyd; 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 85cm Beam radius of the aperture(w a ) 3.5mm Aperture radius(r a ) 2mm Sample thickness(l) 0.65mm Effective thickness(l eff ) mm Linear absorption coefficient(α) Linear transmittance(s) 0.48 Nonlinear refractive index (n 2 ) 7.490X10-12 m 2 /W Nonlinear absorption coefficient(β) 8.220x10-5 m/w Real part of third order susceptibility[re(χ 3 )] 5.006x10-6 esu Imaginary part of third order susceptibility [Im(χ 3 )] 2.769x10-6 esu Third order nonlinear susceptibility (χ 3 ) 5.721x10-6 esu Second order hyper polarizability(γ h ) x10-6 esu The response time (τ) of OH1 crystal is associated with the change in temperature and calculated using the following relation τ ~ (ρ 0 C) r 2 /κ. Where (ρ 0 C) is heat 110

15 capacity per unit volume (1.187 x10 6 J/m 3 K), κ is thermal conductivity ( W/m K), r is radius of laser beam (12 μm). The response time (τ) of OH1 crystal is 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= πr 2 I 0 and τ is the response time. The calculated pulse energy of OH1 crystal is x10-5 J NONLINEAR ABSORPTION AND REFRACTIVE INDEX OF MOT2 CRYSTAL Fig.4.10 a. Self-defocusing effect of the MOT2 crystal b. 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 (n 2 ) is 1.680X10-14 m 2 /W. The nonlinear absorption (β) of MOT2 is found to be 2.497X10-7 m/w. The third order nonlinear susceptibility (χ 3 ) of MOT2 crystal is X10-8 esu. The measurement details of Z-scan technique is shown in Table.4.2. (Bharath et al;2014) 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 111

16 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 n 2 (10-14 m 2 /w) or χ 3 (m 2 /v 2 ) is developed by Boyd. If the optical nonlinearities of material are relatively large nonlinear susceptibility 10-8 esu 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 crystal Beam radius of the aperture(w a ) 3.5mm Aperture radius(r a ) 1mm Sample thickness(l) 0.51mm Beam radius(wo) 12.22μm Effective thickness(l eff ) mm Linear absorption coefficient(α) Linear transmittance(s) Rayleigh length (Zo) 1.14mm Nonlinear refractive index (n 2 ) 1.680X10-14 m 2 /W Nonlinear absorption coefficient(β) 2.497X10-7 cm/w Real part of third order susceptibility[re(χ 3 )] 1.762X10-8 esu Imaginary part of third order susceptibility [Im(χ 3 )] X10-8 esu Third order nonlinear susceptibility (χ 3 ) X10-8 esu Second order hyper polarizability(γ h ) x10-8 esu 4.7. NONLINEAR ABSORPTION AND REFRACTIVE INDEX OF OE1 CRYSTAL 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 OE 1 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 x10-5 m/w. The change of refractive index affects the transmittance of the sample. The nonlinear refractive index or self-defocusing effect of OE 1 crystal is shown in Fig [4.11b]. The calculated value of nonlinear refractive index of material is 112

17 3.176x10-11 m 2 /W. The third order nonlinear susceptibility (χ 3 ) of OE1 crystal is x10-6 esu. Fig.4.11 a. Self-defocusing effect of the OE1 crystal b. Saturation absorption of the OE1 crystal 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 crystal Beam radius of the aperture(w a ) 3.5mm Aperture radius(r a ) 1mm Sample thickness(l) 0.51mm Beam radius(wo) 12μm Effective thickness(l eff ) mm Linear absorption coefficient(α) Linear transmittance(s) 0.15 Intensity at focus (Io) 26.53MW/m 2 Nonlinear refractive index (n 2 ) 3.176x10-11 m 2 /W Nonlinear absorption coefficient(β) 6.079x10-5 m/w Real part of third order susceptibility[re(χ 3 )] x10-6 esu Imaginary part of third order susceptibility [Im(χ 3 )] x10-6 esu Third order nonlinear susceptibility (χ 3 ) x10-6 esu Second order hyper polarizability(γ h ) x10-6 esu The response time (τ) of OE1 crystal is associated with the change in temperature and calculated using the following relation τ ~ (ρ 0 C) r 2 /κ. Where (ρ 0 C) is heat capacity per unit volume (1.164 x10 6 J/m 3 K), κ is thermal conductivity (0.085 W/m 113

18 K), r is radius of laser beam (12 μm). The response time (τ) of OE1 crystal is 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= πr 2 I 0 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 NONLINEAR ABSORPTION AND REFRACTIVE INDEX OF 3E4HM CRYSTAL Figure 4.12: a. Self-defocusing effect of the 3E4HM crystal b. 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 selfdefocusing 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 (n 2 ) is 1.86X10-11 m 2 /W. The third order nonlinear susceptibility (χ 3 ) of 3E4HM crystal is X10-5 esu. The measurement details of Z-scan technique is shown in Table 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 114

19 for condensed matter has calculated using the relation τ ~ (ρ 0 C) r 2 /κ, where (ρ 0 C) is heat capacity per unit volume (1.189 x10 6 J/m 3 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 crystal Beam radius of the aperture(w a ) 3.5mm Aperture radius(r a ) 3mm Sample thickness(l) 0.48mm Beam diameter 12.22μm Effective thickness(l eff ) 0.40mm Linear absorption coefficient(α) Linear transmittance(s) 0.30 Intensity at focus (Io) 26 MW/m 2 Nonlinear refractive index (n 2 ) 1.86x10-11 m 2 /W Nonlinear absorption coefficient(β) 1.42x10-4 m/w Real part of third order susceptibility[re(χ 3 )] 1.17x10-5 esu Imaginary part of third order susceptibility [Im(χ 3 )] 4.52x10-6 esu Third order nonlinear susceptibility (χ 3 ) 1.262x10-5 esu Second order hyper polarizability(γ h ) x10-6 esu 4.9. NONLINEAR ABSORPTION AND REFRACTIVE INDEX OF Cl1 CRYSTAL Figure 4.13: a. Self-focusing effect of the Cl1 crystal b. Saturation absorption of the Cl1 crystal 115

20 The negative nonlinear absorption has been observed in Cl 1, due to the saturation absorption of material. The calculated value of nonlinear absorption (β) is x10-6 m/w. The change in transmittance (valley -peak) of Cl 1 materials shows selffocusing effect in closed aperture method. The calculated value of nonlinear refractive index of material is 5.476x10-11 m 2 /W. The third order nonlinear susceptibility (χ 3 ) of Cl 1 crystal is X10-6 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 Crystal Beam radius of the aperture(w a ) 3.5mm Aperture radius(r a ) 1mm Sample thickness(l) 0.582mm Beam radius(wo) 12.22μm Effective thickness(l eff ) mm Linear absorption coefficient(α) Linear transmittance(s) 0.15 Intensity at focus (Io) 26.47Mw/m 2 Nonlinear refractive index (n 2 ) 5.476X10-11 m 2 /W Nonlinear absorption coefficient(β) X10-6 m/w Real part of third order susceptibility[re(χ 3 )] X10-6 esu Imaginary part of third order susceptibility [Im(χ 3 )] X10-6 esu Third order nonlinear susceptibility (χ 3 ) X10-6 esu Second order hyper polarizability(γ h ) x10-6 esu 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 ~ (ρ 0 C) r 2 /κ. Where (ρ 0 C) is heat capacity per unit volume (1.229 x10 6 J/m 3 K), κ is thermal conductivity (0.05W/m K), r is radius of laser beam (12.22μm). The response time of Cl1 crystal is x10-4 s. 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= πr 2 I 0 and τ is the response time. The calculated pulse energy of Cl1 crystal is x10-6 J NONLINEAR ABSORPTION AND REFRACTIVE INDEX OF Br1 CRYSTAL The saturation absorption has been observed in Br 1 crystal as shown in Fig.4.14a. The calculated value of nonlinear absorption (β) is 1.795x10-4 m/w. The 116

21 change in transmittance (peak-valley) of Br 1 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 m 2 /W. The third order nonlinear susceptibility (χ 3 ) of Br1 crystal is x10-6 esu. The measurement details of Z- scan technique is shown in Table.4.6. Figure 4.14: a. Self-defocusing effect of the Br1 crystal b. Saturation absorption of the Br1 crystal MECHANISM AND OPTICAL SWITCH CALCULATION The characteristic time scale for nonlinear response of material from the typical value based on n 2 (10-11 m 2 /W) or χ 3 (m 2 /v) is developed by Robert Boyd. As per the characteristic time scale, Br 1 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 ~ (ρ 0 C) r 2 /κ Where (ρ 0 C) is heat capacity per unit volume (1.407 x10 6 J/m 3 K), κ is thermal conductivity (0.0413W/m K), r is radius of laser beam (12.22μm) τ ~ 1.407x10 6 J/m 3 K x (12.22x10-6 ) 2 m 2 / W/m K τ ~5.087x10-3 s 117

22 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= πr 2 I 0 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 Br 1 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 crystal Beam radius of the aperture(w a ) 3.5mm Aperture radius(r a ) 2mm Sample thickness(l) 0.30mm Beam radius(wo) 12.22μm Effective thickness(l eff ) 0.27mm Linear absorption coefficient(α) Linear transmittance(s) 0.48 Intensity at focus (Io) 26.47MW/m 2 Nonlinear refractive index (n 2 ) 8.920x10-11 m 2 /W Nonlinear absorption coefficient(β) 1.795x10-4 m/w Real part of third order susceptibility[re(χ 3 )] 10-6 esu Imaginary part of third order susceptibility [Im(χ 3 )] 10-6 esu Third order nonlinear susceptibility (χ 3 ) 8.836x10-6 esu Second order hyper polarizability(γ h ) x10-6 esu THERMO-OPTIC COEFFICIENT (TOC) Thermal nonlinearity of the continuous laser beam, the effective nonlinear refractive index is given as Chapter.1 n 2 2 dn R dt 4.16 dn n2 2 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 118

23 the range ± K -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 SECOND HARMONIC GENERATION STUDIES (KURTZ-PERRY METHOD) Second harmonic generation of OH1 compound, it is reported by Hunziker et al. MOT2, Cl 1, Br 1, 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 ha ve 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. OE 1 crystal is powdered and filled in microcapillary tube (diameter - 1.5mm). The size of the OE 1 particle is measured through powder XRD experiment. The crystalline size of OE 1 particle is 9.014μm and it is measured using the Scherer equation (Cullity, B.D;1977) Particle Size= FWHM Cosθ 4.18 Where, full width half maximum (FWHM) is and 2θ is The size of the powder KDP particle is μm. The input incident laser energy for OE 1 and KDP powdered sample is 1.8mJ. The sample OE 1 produces 2.3mV while KDP exibit 8.8mV. Eventhough OE 1 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). 119

24 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 10-5 K. 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 120

25 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 n 2 m 2 /W 7.490X X x x X x10-11 β m/w 8.220x X x x x10-4 χ 3 esu 5.722x X x x X x10-6 W(>1) T(<1) Re(χ 3 )/ Im(χ 3 ) TOC K x x x x x x10-5 γ h (esu) 0.847x x x x x x10-6 Response x x x x x10-3 time s SHG SHG Nil SHG Nil Nil Nil 121