Host Liquid Effect on Thermo-Optical Pattern of a Self-Phase Modulated Laser Beam Passing Through Au Nanoparticles Colloids
Subject Areas : Journal of Optoelectronical NanostructuresHoda Aleali 1 , Ahmad Mehramiz 2 , Elham Valizadeh Pilehroud 3
1 - Department of metrology, Research Center of Quality Assessment and Management Systems, Standard Research Institute (SRI), Karaj, 3174734563, Iran
2 - Department of Physics, Faculty of Basic Sciences, Imam Khomeini International University, Qazvin, Iran
3 - Department of Physics, Faculty of Basic Sciences, Imam Khomeini International University, Qazvin, Iran
Keywords: Thermo-optical nonlinearity, Host liquid’s properties, Far-field intensity, Colloidal gold nanoparticles, Self-phase modulation, Photonic devices,
Abstract :
In this paper, the influence of host liquid’s properties on far-field intensity distribution of a continuous Gaussian laser beam passing through the synthesized colloidal gold nanoparticles (AuNPs) is experimentally and numerically studied considering the different form of heat transfer modes. Our results reveal that dispersed NPs in liquids with more viscosity or less thermal expansion coefficient, lead to more concentric far-field diffraction patterns. By changing the viscosity and thermal expansion coefficient, the form of diffraction patterns due to the convection effect, can dramatically change compared to the strength of the thermal nonlinear refraction. The effect of the linear absorption coefficient of the medium on diffraction patterns of the colloids is also investigated. It is shown that by increasing the linear absorption coefficient of the medium, the number of the rings and the beam divergence increase under exposure of the 532 nm laser beam. Our observations show the excellent sensitivity of the diffraction ring pattern technique to characterize the different modes of heat transfer and thermo-optical nonlinear properties of the NPs colloids.
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Islamic Azad University
| Journal of
Spring 2024 / Vol. 9, No. 2 |
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1. INTRODUCTION
Linear and nonlinear optical properties of nanomaterials have attracted many attentions resulting in optimal designing of optical devices [1-6]. Among the nanomaterials, gold nanoparticles have been introduced based on their optical properties as a suitable candidate for applications such as optical hyperthermia, new generation of medical devices, the resonance of the surface plasmon (SPR)-based optical biosensor, optical devices, etc. [6-9]. AuNPs colloids are able to absorb laser beam energy due to their excitation of surface plasmon resonance [10-19]. In this case, after absorption of the laser beam, the colloids are locally heated, and the temperature of the heated region increases, causing laser induced thermal lens effect. Great attention has been paid to study the thermal nonlinear properties of the colloidal nanoparticles under exposure to CW laser light at wavelength of 532 nm using the Z-scan method [10-18]. It has been found that thermal third-order nonlinear refractive index induced by linear absorption of laser energy is the main mechanism responsible for observed nonlinearity in the colloids.
Different refractive indexes originated by thermal third-order nonlinear refraction result in a phase shift of light wave that creates an interference pattern at a far-field distance. Recently, the far-field intensity distribution of the Gaussian laser beam passing through the liquids has been presented experimentally and theoretically for optical photonic devices [20-30]. Karimzadeh [26] has shown the temporal evolution of the diffraction patterns formed on a screen because of conduction and convection effects. At first, a bright spot is created. Then, the size of spot quickly increases and interference rings are appeared. For several seconds, a flattening of the top is obtained and considerably transformed into stable rings. The observed time development could be due to the following mechanisms: First, the thermal conduction self-phase modulation occurred in the medium; this creates the interference rings. Second, the top flattening of rings appears due to the thermal convection effects. Shi, et al. have shown that the distorted diffraction ring pattern affects the spatial self-phase modulation applications in nonlinear photonic devices such as the all-optical switch and all-optical information converter that can fairly tune the response time [31]. One can find that changing the surrounding solvent and concentration of colloidal metal NPs can change the properties of colloids such as absorption spectrum, optical limiting and nonlinear optical properties [32-35]. In order to search for nanomaterials that meet the requirement of implementing proper optical devices, it would be necessary to predict their behavior under exposure to laser light.
To this aim, the far-field intensity distribution of the CW laser beam passing through the NPs colloids with different host medium as a thermal nonlinear medium, including thermal conduction and thermal convection in the heat transfer equation, is numerically analyzed. Using the thermal nonlinear coefficient of the colloids extracted by Z-scan method, the influence of the physical properties of the host medium on intensity profile at a far distance is predicted. The obtained numerical far-field intensity distribution of the CW laser beam passing through the AuNP colloids are confirmed by the experimental results using 532 nm laser beam. Finally, the key physical mechanism that contributes to the strongest thermo-optical effect of the colloids with the lowest thermal conductivity is described.
2. Numerical studies of the pattern of self-phase modulated laser
2.1. The laser interaction with the thermal nonlinear medium
In order to analyze the far-field intensity distribution of the laser beam passing through the thermal nonlinear medium, the electric field at any position z of the sample must be calculated. At first, we need to solve the Maxwell equations for the interaction of the laser beam and the nonlinear sample. Then, the propagation of the laser beam in the free space from the exit surface of the sample to the observation plane at a far distance is calculated. The magnitude and phase of the electric field of a Gaussian beam change in the z direction due to passing through the nonlinear thin media. One can calculate the phase shift, ∆φ, and the electric field intensity, I, as follows [36-37]:
(1) |
(2) |
where 
is the propagation length inside the sample, 
is the absorption coefficient, including linear and nonlinear absorption, and 
is the variation of the sample refractive index. It is assumed that the third-order nonlinear refraction is the only mechanism for generating nonlinear effects, and nonlinear absorption phenomena are negligible in the sample. Then, the refractive index and the material absorption coefficient are written as 
and 
, respectively, where 
is the linear refractive index, 
is the third-order nonlinear refractive index, and 
is the linear absorption coefficient.
When the sample is exposed to laser light, it absorbs a portion of light energy. The absorbed energy creates a spatial temperature distribution in the sample, followed by the process of heat diffusion in the medium. The created temperature gradient acts as a lens, and a phase difference in the wave occurs that is called the thermal lens effect [10-11, 30, 38-43]. This effect produces a diffraction pattern on the far-field plane. The intensity of the diffracted laser beam can be obtained at a distant screen perpendicular to the direction of light propagation, using the Fraunhofer approximation in the Fresnel-Kirchhoff diffraction integral as:
(3) |
where 
is the beam radius, 
is the laser beam wavelength in vacuum, 
is the wavenumber, 
is the radius of curvature of the beam wave front, d is the distance between the sample and the screen in the far-field, 
is the effective length of the sample, and 
is the electric field at the focal point. By determining the thermo-optical phase shift of the light electric field due to heat transfer in the sample, the far-field intensity distribution of the Gaussian laser beam on the observation plane (equation 3) can be solved numerically.
2.2. Thermo-optical phase shift
To obtain the thermo-optical phase shift, first, we need to solve the heat transfer equation to obtain the temperature distribution along with the laser beam propagation. Heat transfer is a process whereby thermal energy is transferred in response to a temperature difference by various mechanisms, such as thermal conduction and thermal convection. In the case of convection, when the light radiation absorbs the energy, the temperature of the irradiated region increases, decreasing its density. In this case, the gravitational force applied to the particles causes the higher-density particles in the upper part of the radiation to move downwards and replaces the lower-density particles. Therefore, a convective flow is created in the liquid. Given two modes of heat transfer, including conduction and convection, the heat transfer equation can be formulated as follows:
Where 
is the specific heat capacity, 
is the density, 
is the thermal conductivity coefficient, 
is the convective velocity due to the equilibrium between the fluid viscous forces and the heat buoyancy force and directed [20, 31], 
is the thermal expansion of the coefficient, 
is the maximum temperature, g is the gravitational acceleration, 
is the laser beam waist, and 
is the viscosity of the sample. By applying the proper boundary conditions [38-39] and the Green's function for the convection and conduction heat transfer equation [40], the temperature distribution can be obtained in terms of the absorbed energy of the laser at each point x and y after the time t [25, 30].
where 
is the heat diffusion coefficient. The induced temperature gradient changes the refractive index of the material according to relation 
, where 
is the thermo-optical coefficient of the sample. Created phase difference due to the change in refractive index is obtained by substituting equation 5 in relation
as follows [25]:
(6)
where 
is the on-axis phase shift.
The numerically far-field intensity distribution of the Gaussian laser beam passing through the thermal nonlinear media with different viscosities and thermal expansion coefficients are shown in Fig. 1. In this study, the input parameters were set based on reliable and real amounts [25]. For this simulation, Fig. 1. The simulated far-field diffraction patterns and normalized intensity of the laser beam propagating through the colloidal nanoparticles with host medium viscosities of a, b) As it is clearly shown in Fig. 1, by increasing the viscosity of the host medium, which causes the convection current to decrease, the diffraction rings pattern and normalized intensity profile become more symmetrical. The results suggest that the convection heat flow can explain the observed asymmetric nature of the far-field intensity distribution in the medium with the lower viscosity. The normalized intensity profiles as a function of x are also plotted for the colloids with different viscosity of host medium in Fig. 1(b), 1(d) and 1(f). Compared to the condition of more convective mode, in the less convective mode, the graph is more symmetric with respect to the y-axis (x = 0). Fig. 1 also shows that by decreasing the thermal expansion coefficient of the host medium, the diffraction rings and normalized intensity profile become more symmetrical due to the decrease in the convection current. As it is clear, by decreasing the thermal expansion coefficient, less particles collide with each other, and less convection occurs. According to Fig. 1, one can find that the obtained number of diffraction rings (about 6 interference fringes) and beam divergence (about 15 mm) are the same for all viscosities and thermal expansion coefficients. It is worth noting that compared to the drastic change in the symmetry of the diffraction pattern arising from a change in convection velocity of the colloids (Fig. 1), the amount of phase shift occurred in the medium does not dramatically change. The influence of the linear absorption coefficient of the medium on intensity profile at a far distance is also investigated numerically. Fig. 2 illustrates that by increasing the linear absorption coefficient, the beam divergence and the number of circular rings increase leading to the significant enhancement of thermal nonlinear effect attributed to either higher linear absorption coefficient of the host medium or higher nanoparticle concentration. Fig. 2. The simulated far-field diffraction patterns of the laser beam propagating through the colloidal nanoparticles with linear absorption coefficients of a) α= α1=0.25 cm-1 b) α=2α1 and c) α= 4α1. 3. Experimental results and discussion (a) Fig. 3. Schematic diagram of optical geometry for recording diffraction patterns of the AuNP colloids. The linear absorption coefficient of about 0.56 cm-1 was set for all samples by dilution of the prepared AuNPs colloids [11]. To obtain the third-order thermo-optical coefficient of the AuNPs colloids, the closed Z-scan technique has been used (Experimental Z-scan data and the theoretical fits of the colloids have been presented in supplementary material) [11]. In order to accurately show the effect of host liquid’s properties, experiments were performed under the same experimental conditions such as laboratory temperature, experimental geometry, the beam profile, laser intensity and the linear absorption coefficient of the solutions. The experimental patterns of the far-field intensity distribution of continuous laser beam passing through gold nanoparticles in cyclohexanone [14], castor oil and water with different optical properties (Table I) are shown in Fig. 4. Fig. 4. The experimental far-field diffraction patterns of the laser beam propagating through the dispersed AuNPs in a) water b) castor oil and c) the reported far-field diffraction patterns of the laser beam propagating through the dispersed AuNPs in cyclohexanone [14]. The horizontal axis is y-axis ranging from -35 mm to 35 mm. Table I Physical parameters used for simulation of the far-field intensity distribution of laser beam propagation through gold nanoparticle colloids. Castor oil Water Physical parameters 947 956 997 1926 1800 4186 0.138 0.17 0.6 121 70 30 56 57 56 2.3 1.8 0.5 dn/dt In order to investigate the effect of the linear absorption coefficient that contributes to the thermo-optical properties of the colloids, samples A and B were also synthesized by laser ablation of the pure gold plate in castor oil, with the value of 0.21 and 0.80 cm-1 for α, as described in our previous work [13]. Fig. 5 (a-c) show the diffraction pattern images at applied incident laser power of 40 mW for the colloids at different linear absorption coefficient and pure castor oil. Fig. 5. The experimental patterns of the laser beam propagating through a) castor oil, b) sample A and c) sample B. The horizontal axis is y-axis ranging from -35 mm to 35 mm. We will compare the prediction of the model to the experimental data considering the values of the host medium physical parameters listed in Tables I and II. Fig. 6 depicts the simulated far-field diffraction patterns of 60 mW applied laser beam propagating through the AuNPs dispersed in water, castor oil and cyclohexanone. As it is clearly illustrated in Fig. 4 and 6, the behavior of the experimental results for the diffraction pattern images for the AuNPs colloids are in a good agreement with the prediction of the model. A low divergence of the transmitted laser light is observed without any interference rings in Fig. 4(a) and 6(a) for the AuNPs dispersed in water with the highest thermal conductivity. As shown in both Fig. 4 and 6, it seems that less symmetrical diffraction pattern for the AuNPs in cyclohexanone is obtained from the highest convection current due to the least viscosity and highest thermal expansion coefficient. Moreover, based on the obtained results, it is obvious that compared to the AuNPs in the castor oil and water, AuNPs in cyclohexanone, with the lowest thermal conductivity, present the largest far-field diffraction pattern (beam divergence) with more interference fringes. According to the results of the experimental and theoretical data for the closed Z-scan measurement of the AuNPs colloids shown in the supplementary, one can find that unlike the closed Z-scan method, the modes of heat transfer, including conduction and convection can be analyzed and distinguished by the recorded diffraction pattern images for the AuNPs colloids. Thus, this technique can be used to characterize the modes of heat transfer and the thermo-optical properties of nanoparticle colloids. Table II Physical parameters used for simulation of the far-field intensity distribution of laser beam propagation through the samples A and B. Sample B Sample A Castor oil Physical parameters 78 20 9 1.9 1.6 1.4 dn/dt (a) (b) (c) Fig. 6. The simulated far-field diffraction patterns of the laser beam propagating through the dispersed AuNPs in a) water b) castor oil and c) cyclohexanone. The horizontal axis is y-axis ranging from -30 mm to 30 mm. It is clear that the behavior of experimental far-field diffraction patterns shown in Fig. 5 also confirms the obtained numerical far-field diffraction patterns (Fig. 7) of the laser beam passing through the AuNPs colloids. Our results show that gold NPs dispersed in the castor oil are able to strongly absorb the wavelength of 532 nm light leading to an exhibition of strong thermal nonlinear refractive index of the colloids. It worth mentioning that by increasing the linear absorption coefficient of the colloids, induced nonlinear refractive index enhances which is attributed to the concentration of AuNPs in this work. Fig. 8. The time development of the temperature changes during laser beam propagating through AuNPs in different liquid environments, including water, castor oil, and cyclohexanone. In order to investigate the key physical mechanism that contributes to the strong thermo-optical effect of the AuNP colloids, the amount of temperature difference in the center of the laser beam along with the z-axis is estimated. Fig. 8 shows the time development of the temperature changes during laser beam propagation in AuNPs in different liquid environments, including water, castor oil, and cyclohexanone using equation 5. As it is shown in this figure, at the applied low power laser irradiation, the temperature increases over time development of heat transfer. After the time t, the temperature reaches a maximum then remains clamped at a constant value. Our results in this Fig. show that the maximum temperature difference induced in the center of the laser beam passing through the liquid with the lowest thermal conductivity is the highest and leads to the largest thermal nonlinear refraction. 4. Conclusion The far-field intensity distribution of a continuous Gaussian laser beam passing through the gold nanoparticles suspended in liquids with different physical properties was numerically and experimentally investigated to characterize the heat transfer and thermo-optical properties. We found that by increasing the thermal expansion coefficient, the top of the diffraction ring pattern became more squeezed, indicating the enhancement of the convection effect. The numerical study conducted for more viscose solution showed that the most symmetrical diffraction rings were observed for liquid with the highest viscosity, causing the lowest convection current. The amount of nonlinear refraction induced in the colloids was not affected by the applied ranges of thermal expansion coefficient and viscosity parameters in this study. 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and the on-axis phase shift is taken with an arbitrary magnitude of 
. According to the recently reported values of the linear absorption coefficient of different colloidal nanoparticles with the radius range of 10-70 nm, this parameter is arbitrarily set as 
[10-11, 25, 42-43]. The thermal diffusivity is also fixed at
.
; c, d) 
; e, f)
and with thermal expansion coefficients of a, b) 
; c, d) 
; e, f) 
It is noted the increasing
and decreasing 
show the same results.
The diffraction patterns were recorded by a digital camera on a screen in the far field plane about 4m from the sample using a continuous low power (100mW) diode-pumped Nd:YVO4 laser operating at a wavelength of 532nm. The Schematic diagram of optical geometry used to record the thermo-optical diffraction patterns for the AuNP colloids is shown in Fig. 3. In the experimental setup, a continuous laser beam was focused onto the surface of the colloidal gold nanoparticles placed inside a 5-mm cell by a lens of focal length 500 mm. The cell was placed between the lens and the focus point. The spot size in the focal region is 39 mm (HW1/e2M). 
Fig. 7. The simulated far-field diffraction of the laser beam propagating through a) castor oil, b) sample A and c) sample B, respectively. The horizontal axis is y-axis ranging from -30mm to 30mm.
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