Gordon et al.  reported that the beam shape of incident laser light expands after passing through a liquid medium. This phenomenon was termed “the thermal lens effect,” and it has become a well-known photo-thermal phenomenon. Phenomenological, optical, and spectroscopic studies of the thermal lens effect have been carried out to describe nonlinear defocusing effect [2-8]. Recent progress in laser technology has revealed the various aspects of the thermal lens effect. Based on these efforts, other mechanisms, such as liquid density, electronic population, and molecular orientation, have been found to play important role as well as thermal lens effect. Recent studies term these effects as “the transient lens effect” [9,10]. The main advantage of using the transient lens effect in Photo-Thermal-Spectroscopy is that the sensitivity is 100 to 1000 greater than a traditional absorptiometry .
In this research, a new idea of applying the thermal lens effect in order to develop fluidic optical device is proposed. A schematic of the concept is shown in Fig. 1. A rectangular solid region shown in Fig. 1a represents the liquid medium, which has a temperature field generated by a heater-heat sink system or laser-induced absorption. By controlling the temperature field as well as the refractive index distribution of the liquid medium, the refractive angle of each light ray passing through the liquid medium can be controlled in order to develop fluidic optical devices such as: an optical switching in Fig. 1a to change the direction of the input laser beam, a laser beam shaper in Fig. 1b to transform a Gaussian beam to a flat-top beam and a fluidic divergent lens in Fig. 1c. Merits of these devices include flexibility of optical parameters, versatility and low cost.
2. Fundamental light ray transmitted in one-dimensional refractive index medium
In this section, as a first step to develop fluidic optical device, the refractive characteristics of a probe beam, which is transmitted in one-dimensional temperature distribution in a liquid medium is presented.
2.1. Theoretical background
The light ray is modeled in the domain shown in Fig. 2 in order to calculate the refractive angle of the probe beam, which is transmitted in a one-dimensional temperature distribution in the liquid medium. The light ray direction transmitted in a medium having a refractive index dependent only on the
In which, the light ray passes through the medium at coordinate center,
Figure 2 shows a schematic diagram of the model set up. The rectangular solid medium in the figure represents the domain considered in the calculation which consists of ethylene glycol. In the medium, ethylene glycol has linear temperature distribution in only
The temperature distribution of the liquid medium is modeled with a linear function of the variable
Furthermore, between 0°C and 100°C refractive index of ethylene glycol is a linear function of temperature with refractive index change d
By substituting Eq. (7) into Eq. (4) and solving the differential equation, we can obtain the relationship between
And refractive angle (RA) can be obtained as:
Equation (10) shows the expression of the refractive angle as a function of the temperature gradient and the thickness of the liquid medium (optical path length). Figure 3 shows the relationship between refractive angle and temperature gradient at points where the thickness of sample,
2.2. Experimental set-up
Figure 4 shows the experimental set-up to measure the refractive angle. Fluidic optical device in Fig. 4 is a pyrex vessel (internal size: 21×10×
The temperature distribution in the liquid medium is confirmed by measuring the temperatures at 5 points with 2 mm pitch in the vessel using 5 thermocouples as shown in Fig. 6. The temperature gradient in the experiment is given as:
In which, Δ
A CW laser (
2.3. Results and discussions
Figure 7(a) and (b) show the comparison of theoretical and experimental results at points where the thickness of sample,
3. Fluidic laser beam shaper
Flat-top laser are well known to present significant advantages for laser technology, such as holographic recording system, Z-scan measurement, laser heat treatment and surface annealing in microelectronics and various nonlinear optical processes [15-19]. For CW beams, several approaches to spatially shape Gaussian beams have been developed, such as the use of aspheric lenses, implement beam shaping or the use of diffractive optical devices . However, these methods have some disadvantages: a refractive beam shaping system lead to large aberration  and implemental beam shaping has low energy efficiency and lacks of flexibility ; and the use of refractive optical devices requires complex configuration design and high cost . In practice, a low-cost and flexible method to convert a Gaussian beam into a flat-top beam is required. In this section, a novel method to convert a Gaussian beam into a flat-top beam is discussed. The concept is based on the control of the pump power and propagation distance of the probe beam in the thermal lens system.
3.1. Principle of thermal lens effect
The principle of the transient lens effect is schematically illustrated in Fig.8. A CW diode pumped blue laser is used as pump-beam (BCL-473-030,
In this experiment, the absorbance of the pump-beam is 2.776 and that of the probe-beam is negligible small. Figure 9 shows the laser beam profile of the probe beam after propagating through a divergent lens and a thermal lens. It is clear that, the probe beam change its profile from Gaussian to doughnut beam with a hollow center is created.
Theoretical analysis of laser beam profile change in thermal lens effect is done with a model that includes continuity equation, Navier-Stokes equation, energy conservation equation and Helmholtz equation in 2D cylindrical symmetry coordinate. It is assumed that the change of refractive index is caused only by the temperature change of the liquid medium and the thermal coefficient of the refractive index, d
The temperature distribution is calculated numerically based on the finite difference method. The 1st order upwind scheme and a 2nd order center differencing are applied to discretize the advection term and the diffusion term respectively. The thermal properties of liquid medium can be found in Ref. 24.
To model the propagation of laser through an inhomogeneous medium, the wave equation which includes an absorption term and an inhomogeneous refractive index term is applied :
3.2. Influences of the pump power and the propagation distance on the change of probe beam profile
Influences of the pump power and the propagation distance to the probe beam profile were investigated numerically using the calculation parameters in Table. 1. In this calculation, both of the pump beam and the probe beam are written as follows.
|Pump power, mW||3||0 ~ 7|
|Pump beam diameter, mm||0.8||0.8|
|Probe power, mW||10||10|
|Probe beam diameter, mm||0.8||0.8|
|Absorption coefficient, cm-1||2.0||2.0|
|Distance from experimental section to CCD camera, mm||0 ~ 500||200|
|Phase front curvature radius, ||∞||∞|
Effects of the pump power and the propagation distance to the probe beam profile are shown in Fig. 10(a) and (b) respectively. The vertical axis and horizontal axis show intensity and distance from laser axis respectively. Plots of ‘
3.3. Experimental set-up to shape spatial profile
In order to confirm the role of the fluidic laser beam shaper, a single-beam experiment is set up as shown in Fig. 11. A CW diode blue laser is used as pump and probe-beam (
Figure 12(b) shows the beam profile change from the Gaussian to the flat-top beam. The vertical and horizontal axes show the intensity and distance from the laser axis respectively. The o-line shows the profile of the Gaussian input beam by fitting the laser beam profile measured at the surface of the cuvette. The strange-line shows the profile of the flat-top beam calculated by beam propagation method. The solid-line shows the profile of the flat-top beam measured by CCD camera at propagation distance of 150 mm from the cuvette. Both experimental and calculated results agree well with each other.
In order to explain in more detail about the mechanism of this fluidic beam shaper, the temperature distribution of liquid medium is calculated. As shown in Fig. 13, local heating near the beam axis produces a radially dependent temperature variation, which changes the liquid refractive index in which the lower refractive index is in the region near to the beam center. As a consequence, the radius of curvature of the wave front at the region near the beam center is shorter than one at the beam wing. Therefore the sample liquid locally acts as a micro divergent lens with shorter focal length at beam center. As shown in Fig. 1b, the beam center that passes through shorter focal length is spread out more rapidly than the beam wing. As the probe beam propagates to increasing distance, the intensity in the center region drops rapidly than one in the wing region. At a certain value of propagation distance, the Gaussian beam can be converted into the flat-top beam.
It is noted that, in the case of single-beam shaper, one part of laser beam energy (about 15% in this experiment) is converted into thermal energy in order to change temperature distribution or in other words to change refractive index distribution in the liquid medium. Therefore, in the case of single-beam shaper, the beam shaper has another role, which is as an attenuator. This laser beam shaper/attenuator can be applied in practical laser drilling technology. In the case of applying on only laser beam shaper, the double-beam system is recommended. In this case, it is needed to select dye whose absorbance of the probe-beam is negligible small.
3.4. Relationship between pump power and distance to shape spatial profile
As shown in previous section, the flat-top beam can be obtained only at a fixed distance. In order to control this distance, the influence of pump power is investigated theoretically and experimentally. The calculation parameters are shown in Table. 2. The pump power is changed from 1 to 8 mW. The distance to obtain the flat-top beam is obtained numerically. The relationship between the pump power and the distance to shape spatial profile is shown in Fig. 14(a). The horizontal and vertical axes show pump power and distance to obtain the flat-top beam respectively. As shown in Fig. 14(a), the distance to obtain a flat-top beam is in inverse proportion to the pump power.
In order to validate the numerical prediction, a single beam experiment was carried out. The pump power is changed from 1 to 6 mW and the distance to obtain the flat-top beam was measured. The experimental result shown in Fig. 14(b), shows excellent agreement with calculation prediction. The relationship between pump power and distance to obtain the flat-top beam can be explained by the interaction between energy absorption of liquid medium with the focal length of local micro lens. As the pump power increase, the absorption energy increases. As a consequence, the rate of decreasing of
|Pump power, mW||1 ~ 8|
|Pump beam diameter, mm||0.8|
|Probe power, mW||10|
|Probe beam diameter, mm||0.8|
|Absorption coefficient, cm-1||2.0|
|Phase front curvature radius, ||320|
4. Tunable fluidic lens
Fluidic lenses are well known to present significant advantages for wide range of applications from mobile phone to laboratory on a chip. Fluidic lenses have a number of apparent advantages such as tunable refractive index and reconfigurable geometry. Several approaches to design the liquid lens have been developed based on the microfluidic techniques to modify the liquid lens shape by using: out-of-plane micro-optofluidic [25-26], in-plane micro-optofluidic [27-28], electron wetting , dielectrophoresis  and hydrodynamic force . Other approach bases on turning the refractive index of the liquid by different means such as pressure control, optical control, magnetic control, thermo-optic control, and electro-optic control.
4.1. Principle of fluidic lens
When the liquid medium is irradiated, local heating near the beam axis produces a radially dependent temperature variation, which changes the liquid refractive index in which the lower refractive index is in the region near to the beam center. As a consequence, the radius of curvature of the wave front at the region near the beam center is shorter than one at the beam wing. The liquid medium behaviors as a convergence GRIN-L with focal length depends on the radial position of the incident ray relative to the optical axis of the cuvette. The ray equation that is calculated numerically to obtain the path of an incident beam, which is given by:
4.2. Influences of the pump beam profile
Influences of the pump beam profile to the focal length of the GRIN-L were investigated numerically with the calculation conditions in Table. 3. The intensity profile of the pump is applied with the Gaussian beam and the quasi-flat-top beam (a super-Gaussian distribution of order
Here Γ is the Gamma function,
|Pump power, mW||10|
|Pump beam diameter, mm||1.5|
|Absorption coefficient, cm-1||2.0|
The effect of the pump beam profile to the focal length of the GRIN-L lens is shown in Fig. 16. The vertical and horizontal axes show focal length and distance from laser axis respectively. The solid and dashed lines represent the plot of the focal length again the radial position of the incident ray relative to the optical axis of the cuvette in the case of Gaussian pump beam and quasi flat-top pump beam respectively. As shown in Fig. 16, for the Gaussian pump beam the focal length of the GRIN-L increases sharply with increasing of the distance from laser axis, which means larger spherical aberration. It means that, the beam center which passes through shorter focal length is spread out more rapidly than the beam wing. As a consequence, the further the propagation distance of the probe beam, the laser beam profile changes from Gaussian to the doughnut beam profile , which should cause some undesirable results in laser processing . In contrast, with the quasi flat-top pump beam, the focal length of the GRIN-L varies lightly with increasing of the distance from laser axis smaller than beam waist of the flat-top pump beam. The area smaller than the beam waist of the flat-top pump beam acts as a divergent lens with small spherical aberration. Therefore, for the purpose of designing the GRIN-L lens the uniform pump beam shows the advance in reducing the spherical aberration.
4.3. Experimental set-up
In order to confirm the qualities of the GRIN-L, an experiment with the quasi flat-top pump beam is carried out as shown in Fig. 17. A CW diode blue laser is used as pump laser (
Figure 19(a) shows the change along the propagation direction in the beam profile. The vertical and horizontal axes show the intensity and distance from the laser axis respectively. By using the quasi flat-top pump beam, the beam profile of probe laser can remain in Gaussian distribution during its propagation. Figure 19(b) shows the plot of probe beam waist again propagation distance. As shown in Fig. 19(b), the beam waist of probe laser varies linearly with propagation distance. In other words, cuvette 2 acts as a divergence lens with focal length of f = -424 mm (this value has been calculated by considering the divergence angle of probe laser
Next, the pump power is changed from
In this research, a novel idea of fluidic optical devices which includes laser beam shaper and fluidic divergent lens are demonstrated. The fluidic optical devices are based on controlling some parameters in the thermal lens system. The interaction among the intensity distribution, power of the pump beam, the absorption coefficient, the propagation distance and the intensity profile of the probe beam have been investigated experimentally and theoretically. It is found that
By controlling the pump power and the absorption coefficient, the input Gaussian beam can be converted into a flat-top beam profile. The distance to get the flat-top beam profile can be controlled easily by adjusting the pump power and the absorption coefficient. In actual applications, single-beam shaper has another role, which is as an attenuator. This laser beam shaper/attenuator can be applied in practical laser drilling technology. In the case of applying on only laser beam shaper, the double-beam system is recommended. In this case, it is needed to select a dye whose absorbance of the probe-beam is negligible small.
The uniform pump beam shows the advance in reducing the spherical aberration. And by adjusting the pump power, the focal length can be controlled
With some merits such as flexiblility, versatility and low cost, these fluidic optical devices will be promising tools in many fields of laser application.
Part of this work has been supported by the Grant-in-Aid for JSPS Fellows and Grant-in-Aid for Scientific Research of MEXT/JSPS. The authors also would like to acknowledge Mr. Akamine Yoshihiko.
Appl. Phys. 36 ( Gordon J. P. Leite R. C. C. Moore R. S. Porto S. P. S. Whinnery J. R. Long-Transient . effects in. lasers with. inserted liquid. samples J. 1965 3 8
Quantum Electronics QE- Akhmanov S. A. Krindach D. P. Migulin A. V. Sukhorukov A. P. Khokhlov R. V. Thermal self-actions. of laser. beams I. E. E. E. J. 4 1968 1968 568
Opt. Livingston P. M. Thermally induced. modifications of. a. high power. C. W. laser beam. Appl 10 1971 1971 426 436
Opt. Power J. F. Pulsed mode. thermal lens. effect detection. in the. near field. via thermally. induced probe. beam spatial. phase modulation. a. theory Appl. 29 1990 1990 52
Opt. Soc. Am. B Banerjee P. P. Misra R. M. Maghraoui M. Theoretical experimental studies. of propagation. of beams. through a. finite sample. of a. cubically nonlinear. material J. 8 1991 1991 1072 1080
Rev. Lett. Hickmann J. M. Gomes A. S. L. de Araújo C. B. Observation of. spatial cross-phase. modulation effects. in a. self-defocusing nonlinear. medium Phys. 68 1992 1992 3547 3550
Opt. Soc. Am. B Govind P. Agrawal Transverse. modulation instability. of copropagating. optical beams. in nonlinear. Kerr media. J. 7 1990 1990 1072 1078
Rosenberg C. J. et al. Analysis of. the dynamics. of high. intensity Gaussian. laser beams. in nonlinear. de-focusing Kerr. media Optics. Communications 2. 2007
lett. 29 (13) ( Sakakura M. Terazima M. Oscillation of. the refractive. index at. the focal. region of. a. femtosecond laser. pulse inside. a. glass Opt. 2004
Phys. France Sakakura M. Terazima M. Real-time observation. of photothermal. effect after. photo-irradiation of. femtosecond laser. pulse inside. a. glass J. 125 2005 2005 355 360
Terazima M. Hirota N. Braslavsky S. E. Mandelis A. Bialkowski S. E. Diebold G. J. Miller R. J. D. Fournier D. Palmer R. A. Tam A. Quantities terminology. symbols in. photothermal related spectroscopies. . I. U. P. A. C. Recommendations 2004Pure Appl.Chem., 76, 1083
Kudou Uehara 1990Basic Optics (Kougaku Kiso) Gendaikougaku, Tokyo, Japan, 45 47Japanese)
Phys. Lett. 88, 06112, Tang S. K. Y. Mayers B. T. Vezenov D. V. Whitesides G. M. Optical waveguiding. using thermal. gradients across. homogeneous liquids. in microﬂuidic. channels Appl. 2006
ITherm Doan H. D. Fushinobu K. Okazaki K. Investigation on. the interaction. among light. material temperature field. in the. transient lens. effect transmission. characteristics in. . D. temperature field. Proc I. 2010 127
Phys. B: At. Mol. Opt. Phys. 42 ( Yang J. Wang Y. Zhang X. Li C. Jin X. Shui M. Song Y. Characterization of. the transient. thermal-lens effect. using flat-top. beam Z-scan. J. 2009pp)
SPIE, Ebata K. Fuse K. Hirai T. Kurisu K. Advanced laser. optics for. laser material. processing Proc. S. P. I. 5063 2003
Govil E. B. S. Longtin J. P. Gouldstone A. Frame M. D. Uniform-intensity visible. light source. for in. situ imaging. Journal of. Biomedical Optics. 14( 2009
Shealy ‘Laser Beam Shaping Applications’, Taylor & Francis, Dickey F. M. Holswade S. C. D. L. 2006
Opt. Eismann M. T. Tai A. M. Cederquist J. N. Iterative design. of a. holographic beam. former Appl. 28 1998 1998 2641 1650
York, Dickey F. M. Holswade S. C. Laser beam. shaping Theory. Techniques Marcel. Dekker New. 2000
Opt. 20 (9) ( Scott P. Reflective optics. for irradiance. redistribution of. laser beam. design Appl. 1981
Opt. Zhang S. Zhang Q. Lupke G. Spatial beam. shaping of. ultrashort laser. pulse theory. experiment Appl. 44 2005 2005 5818 5823
Mercier B. Rousseau J. P. Jullien A. Antonucci L. Nonlinear beam. shaper for. femtosecond laser. pulses from. Gaussian to. ﬂat-top proﬁle. Optics Communications. 2. 2010
J. Heat Mass Transfer ( Doan H. D. Akamine Y. Fushinobu K. Fluidic laser. beam shaper. by using. thermal lens. effect Int. 2012
Actuators ( Ahn S. H. Kim Y. K. Proposal of. human eye’s. crystalline lens-like. variable focusing. lens Sens. 1999A 78, 48
Phys. Lett. 82 ( Zhang D. Y. Lien V. Berdichevsky Y. Choi J. H. Lo Y. H. Fluidic adaptive. lens with. high focal. length tenability. Appl 2003
Hsiung S. K. Lee C. H. Lee G. B. Microcapillary electrophoresis. chips utilizing. controllable micro-lens. structures buried optical. fibers for. on-line optical. detection Electrophoresis. 2008
Phys. Lett. ( Lien V. Berdichevsky Y. Lo Y. H. Microspherical surfaces. with predefined. focal lengths. fabricated using. microfluidic capillaries. Appl 2003
Gorman C. B. Biebuyck H. A. Whitesides G. M. Control of. the Shape. of Liquid. Lenses on. a. Modified Gold. Surface Using. an Applied. Electrical Potential. across a. Self-Assembled Monolayer. Langmuir 1995
Express ( Cheng C. C. Chang C. A. Yeh H. A. Variable focus. dielectric liquid. droplet lens. Opt 2006
Tang S. K. Y. Stan C. A. Whitesides G. M. Dynamically reconfigurable. liquid-core liquid-cladding. lens in. a. microfluidic channel. Lab Chip. 2008
National Heat Transfer Symposium Doan D. H. Yin Y. Iwatani N. Fushinobu K. Laser processing. by using. fluidic laser. beam shaper. Proc 2012Inpress