laser manipulation and characterization of liquid …...laser manipulation and characterization of...

Laser manipulation and characterization of liquid crystaldroplets

Naoki Murazawa, Saulius Juodkazis, and Hiroaki Misawa

CREST-JST & Research Institute for Electronic Science, Hokkaido University, CRIS Bldg.,North 21 West 10, Sapporo 001-0021, Japan

ABSTRACT

We demonstrate laser manipulation of different nematic and smectic liquid crystal droplets in heavy water.Peculiarities of laser trapping and manipulation depending on the molecular structure of liquid crystal arediscussed. Possibility of molecular reordering inside the tweezed droplet is demonstrated. This phenomenoncan be used to induce the birefringence and to manipulate droplets, which have a small birefringence, e.g., aradial droplet of negligible birefringence can be turned into a birefringent one at high laser trapping power.This is a demonstration of the optical nonlinear effect being responsible for a micro-mechanical phenomenonsuch as spinning of the droplet in a circularly polarized laser tweezers. Three-photon absorption of MBAPB dyeat 1064 nm wavelength is demonstrated inside the liquid crystal droplet at comparatively low ∼ 60 MW/cm2

intensity.

Keywords: laser trapping/manipulation, laser-tweezers, two- and three-photon absorption, molecular reorder-ing, liquid crystals

1. INTRODUCTION

It has been recently demonstrated that the director orientation in liquid crystals has complex dynamics1 and thatthe laser trapping of spherical particles by tightly focused beams are, in fact, much more complex2,3 than usuallymodeled. These new theoretical developments could account for complex dynamical behavior of liquid crystaldroplets upon laser trapping.4–7 Better understanding and eventually control over the complex dynamic behaviorof liquid crystals can open new micro-photonic and photonic crystal applications where the liquid crystals areincorporated into complex three-dimensional (3D) structures and are subjected to high intensity irradiation ofexternally applied electric field. Molecular alignment of liquid crystals, though comparatively slow, yields in oneof the highest optical nonlinearities and can be used for optical switching applications.

There is a continuing interest in doping liquid crystals by dyes for optically active applications. Molecularalignment of dye inside liquid crystal might enhance absorption. The orientational average of dipoles orientedat angle θ with the chosen direction (e.g., a linear light polarization) depends on a factor:

γI ≡ 〈cos(θ)4〉 =14π

∫ 2π

0

∫ π

0

cos(θ)4 sin(θ)dθdϕ, (1)

where θ, ϕ are the angles of spherical coordinates. The fully linearly ordered dipoles result in the strongestabsorption according to γI = 1, which can be considered as 1D ordering. In a plane (2D ordering) of randomlyoriented dipoles the average is γI = 3/8, yet even smaller for the 3D case γI = 1/5.

Here, we report of difference of internal liquid crystal ordering inside droplets, when the different nematic andsmectic liquid crystals were dispersed in D2O. We demonstrate the effect of spontaneous re-ordering of liquidcrystals upon laser trapping. Also, the applicability of a simple model where the droplet of liquid crystal isdescribed by a wave-plate inserted into a plane wave (the laser trapping beam) is discussed. It is shown, thata three-photon absorption (3PA) has been achieved inside the laser trapped droplet doped with MBAPB dye(2PA is around 800 GM at ∼ 740 nm) at low ∼ 60 MW/cm2 intensity.

1Optical Trapping and Optical Micromanipulation III, edited by Kishan Dholakia, Gabriel C. Spalding,

Proc. of SPIE Vol. 6326, 632630, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.685058

Proc. of SPIE Vol. 6326 632630-1

Downloaded from SPIE Digital Library on 24 Jun 2011 to 136.186.80.71. Terms of Use: http://spiedl.org/terms

Figure 1. (a) Setup. (b) Polariscope image of a birefringent plate, the Maltese cross (eqn. 2). (c) Determination of thedroplet’s diameter by image processing. The background level is marked by line.

2. EXPERIMENTAL DETAILS

Figure 1 shows the principle setup. Laser manipulation was carried out by focused 1064 nm cw:YAG laserradiation. Liquid crystal droplets formed perfect spheres due to surface tension when dispersed in heavy water.D2O was used to avoid absorption at laser trapping wavelength (it is approximately by a factor of 10 smallerthan in the H2O). Polarization of the trapping beam at the focus was precisely controlled using combination ofλ/2 and λ/4 plates (Fig. 1(a)).

The polariscope image (obtained through the optically crossed polarizer and analyzer (see, Fig. 1(a))) ofnematic liquid crystal droplets dispersed in water resembles the Maltese cross. The Maltese cross (Fig. 1(b)) isgiven by the following intensity distribution (for details see the Appendix):

I(θ, ∆n) = I0 sin(2θ)2 sin(π∆nd/λ), (2)

where, θ is the angle between the polarizer and the fast axis of a birefringent sample, ∆n = ne − no is thebirefringence, d is the thickness of sample, and λ is the wavelength of light used for imaging (Fig. 1(b)). If thedroplets have polar structure, the polariscope image changes with droplets rotation (in respect to optical axisof setup). Therefore, a rotation frequency of the droplets can be measured by analyzing the polariscope imagesof droplets using photomultiplier as a detector. The measured frequency of optical transmission measured bydetector is fourfold of that of droplet’s rotation (due to the particular geometry of Maltese cross).

In the case of radial droplets, it is impossible to measure the rotation frequency by the described method.Due to symmetry of molecular alignment, the Maltese cross intensity distribution does not depend on droplet’srotation. In order to measure the rotation frequency, the polarization change of the laser trapping beam afterit passes through the droplet was analyzed (Fig. 1(a)). Here, we consider the left circularly polarized beamincident of a liquid crystal droplet, i.e., the polarization coefficient σin = +1 (an usual sign convention). Thebeam transmitted through the droplet has changed its polarization due to the transfer of the angular momentumto the droplet (+h per photon). As a result, polarization is changed to elliptical, in general, and can berepresented by the polarization coefficient σout = (IL − IR)/I ≡ (PL − PR)/P , here P = PL + PR is the fullpower, which is defined in terms of the difference of intenisty/power of the two orthogonal circular components.The corresponding field components of the transmitted light after the analyzer (set on optical axis in Fig. 1) canbe expressed by circularly polarized components: Ex = 1/

√2(EL + ER) and Ey = i/

√2(EL − ER). Thus, the

power amplitude after the analyzer is expressed as:

Px,y =12cε0n

∫A

|Ex,y|2dA = (1 ±√

1 − σ2out)

P

2, (3)

here, ‘+’ and ‘-’ correspond to the x- and y-components of the measured power, respectively; c is the velocity oflight, n the refractive index of at the focus, ε0 the vacuum permittivity, and A is the focal area. The amplitude of

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the power after the analyzer oscillates at the angular frequency twice higher than the actual rotation frequencyΩ of the particle, because the polarization plane is rotated onto itself after angle of π. Finally, the expression ofexperimentally measurable power transmission by analyzer is given as:

Px,y(t) = (1 ±√

1 − σ2out cos(2Ωt))

P

2. (4)

This measurement method does not depend on optical recognition of Maltese cross and can be used to dropletsof any molecular ordering. The same rotation frequency was obtained on polar nematic liquid crystal dropletsby using both methods (realized simultaneously in setup shown on Fig. 1).

Figure 1(c) shows the actual optical microscopic image of a liquid crystal droplet and the digitized transmissioncross-section. The diameter of liquid crystal droplet was determined by image processing of the optical imageusing Matlab 6.0 software package. The cross-section at a background intensity level was measured excludingdiffraction fringes at the rim of droplet.

3. RESULTS AND DISCUSSION

A model describing a liquid crystal droplet as a birefringent plate (wave-plate) inserted into plane wave was usedto determine the actual birefringence of the polar droplet and is given in Sec. 3.1. Section 3.2 shows differenceof polariscope imaging for different liquid crystal materials and possibility to modify the internal molecularordering in a step-like (spontaneous) fashion (Sec. 3.3). Three-photon absorption of dye-doped nematic liquidcrystal droplet is discussed in Sec. 3.4.

3.1. Birefringence determination of polar-5CB droplets

Figure 2 shows the method of the birefringence determination based on a wave-plate action of a droplet. Thepolarization angle φ = tan−1 ε (ε =

√Pmin/Pmax is the ellipticity of polarization determined from minimum

and maximum of transmitted power) is plotted for the onset of rotation according to:

φrot[degrees] = 45 − 90

λ∆nd, (5)

where λ is the wavelength of light, d and ∆n are the thickness and birefringence of the wave-plate (droplet),respectively. Once the optical path difference for ordinary and extraordinary rays throughout the droplet is equalto λ/2, droplet stops only when polarization is perfectly linear, i.e., φ = 0.

Figure 2(a) shows the dependence of laser power on polarization angle for droplets of different diameters (theellipticity of a laser trapping beam was determined without the droplet in the optical path before experimentswith droplets). With increasing laser power, the polarization angle increased and was fitted by a linear functionas would be expected for a wave-plate. In Fig. 2(b), we show the same dependence plotted against the diameter.It can be seen that the linear fits (in (b)) does not follow eqn. 5. The most important departure from theoryis the y-intercept angle, which is not 45 degrees (Fig. 2(c)). The slope (b), however, was approximately thesame. Figure 2(d) shows the effective birefringence of liquid crystal droplets determined from slopes in Fig. 2(b).Here, liquid crystal droplets were approximated by planar plates (disks) having the thickness equal to thedroplet’s diameter and the focused laser beam is assumed to be a plane wave. Obviously, it is an over simplifiedapproximation, especially for tightly focused laser beams. This is also evidenced by the line 0 mW (in Fig. 2(b))obtained from (a), which departs from the eqn. 5.

It is shown here that the wave-plate approximation is not quantitatively adequate for the bipolar-5CBdroplets, and increasingly so for the smallest droplets. The actual beam path and birefringence due to thespherical shape and specific internal molecular alignment should be taken into consideration in a view of treat-ment presented in ref. [2,3]. It is noteworthy, that the strongest departure form the wave-plate behavior hadhappened at the smallest laser trapping powers.

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Figure 2. (a) The polarization angle φ = tan−1 ε, where ε =√

Pmin/Pmax is the ellipticity of polarization, vs. lasertrapping power. (b) The same dependence plotted vs. diameter of polar-5CB droplets. The error bars mark the onset ofrotation when the polarization is changed from linear-to-circular (upper bound) and from circular-to-linear (lower bound)at different laser trapping powers. (c) The dependence of the intercept angle with y-axis (b) vs. laser power. (d) Thebirefringence determined as the slope of dependence shown in (b) vs. laser power.

3.2. Molecular alignment of liquid crystal droplets

Nematic liquid crystal is self-organized into droplets of 0.5-4 µm diameter when dispersed in water. Most of thedroplets possess a polar-like structure of internal molecular arrangement due to the an anchoring effect (shownschematically in Fig. 3(a)). The molecules of the outer regions tend to be oriented along the surface of thedroplet, while the inner regions tend to sustain their bulk-like orientation. This brings about the final polar-like structure of a droplet. However, some of LC droplets have a radial or irregular structure. When imagedthrough the pair of cross-polarized Nikol prisms, the iconoscopic picture, so-called ”Maltese cross”, is observed(Fig. 3). The dark regions correspond to those areas where the passing light was least scattered, and vice versa,the brightest ones where the scattering was strongest. However, the distinction between the polar and radialstructures is not straightforward from such imaging. As it is schematically shown in Fig. 3(a), the both molecularalignments cause similar iconoscopic images. Further distinction on the internal molecular arrangement can bedone on the basis of the response of a LC droplet to a laser manipulation. The underlaying mechanism of theresponse can be understood in terms of a birefringence of the droplet. If the structure of LC droplet is radialthe birefringence is negligible and the droplet will not acquire angular momentum from the circularly polarizedtrapping beam (a momentum of h is carried by a photon of circularly polarized light). The birefringent particleswith a polar internal structure can be efficiently laser manipulated. Sometimes, when laser beam is irradiatedon the droplet, its azimuthal orientation is such that the droplet is not polar in the focal plane, however, suchorientation is metastable and typically within a few tens-of-milliseconds the droplets of 2-5 µm are re-oriented toa stable trapping position with the director of the droplet aligned perpendicularly to the propagation of trappinglaser beam at the focal plane.

The particles with the polar orientation can be easily laser manipulated, orientated to a preset angle or spinedby, respectively, linearly or circularly polarized laser beam.8,9 Once the polarization of a laser trap is set to acircular, nematic LC droplet begins to spin as can be visualized by a viscous drag of adjacent LC droplets.

3.3. Texture control of liquid crystals via optical alignment

When LC droplets cannot be orientated by changing the polarization of the light due to their internal close-to-radial or irregular structure, the other phenomenon can be observed. Namely, an internal molecular re-orientationis taking place on a time scale of tens-of-minutes (Fig. 4). Since LC materials usually do not absorb at 1 µm thestructural changes observed are caused by dipolic re-orientation rather than by the absorption-induced heating.There is an direct proof of non-thermal character of the internal re-structuring of LC droplets. Most of the LCmaterials undergo the phase transition from ordered to isotropic state, which is optically isotropic, at 100C,

4



Figure 3. (a) The simplest polar and radial molecular alignments of a nematic LC. The darker regions corresponds to theMaltese cross when observed in polariscope. (b-g) Polariscope images of the laser-trapped LC droplets. (b) Typical imageof large LC droplets, which usually have complex internal molecular structure; nematic E-44 LC (c), smectic SmCA∗

CS-4001 LC (d), smectic SmC CS-1017 LC (e), SmC CS-1029 LC (f), and SmC CS-1023 LC (g). Scale bar, 10 µm.

µ

Figure 4. Texture manipulation of liquid crystal. Rearrangement of internal structure of a CS-1017 LC droplet in time.LC droplet was laser trapped by linearly polarized light of 1064 nm wavelength. (a) at 0-20 min, (b) 23 min, (c) 24 min,(d)25 min, (e) 26 min, and (f) 26-30 min. Trapping laser power on the particle was 0.4 W. Scale bar, 10 µm.

(for E-44 at 100C, CS-1017 - 68.7C, CS-1023 - 94C, CS-1029 - 92C, and CS-4001 - 86.6C). Once isotropic,the droplet do not rotate under circular polarization. However, for a nematic LC droplets partly ordered intoa polar structure, the experiments did not show any changes in the rotation frequency over the time scale ofmore than an hour. This exclude heating and convection inside the LC droplet as being the cause of the internalmolecular reorientation. The reorientation occurs as a result of dipole reordering in the electric field of the light.

Apparently, no causal dependence was found between the size of the LC droplets (2-5 µm) and the timerequired for their internal reordering. In SmC LC, the restructuring was found to take place non-monotonously(Fig. 4). This is most likely related to the restructuring of the domains in the droplet. Usually, SmC LCmaterial, which has a “book-shelf” order in the bulk, will preferentially self-arrange into a droplet with theradial-like internal structure in water. Droplets of such high symmetry have negligible birefringence and do notharness angular momentum when are laser-trapped by circularly polarized light. However, few droplets canspin in circularly polarized light, but usually at very low frequency ( 0.1 Hz10). Most probably, their internalstructure has domains, which were partly polar, hence, birefringent. Figure 4 shows how an internal molecularstructure is changing in a step-like fashion from disordered to the radial-like. The main change occurred duringthe 22 - 23 minute from irradiation. In different droplets even of the comparable size this reordering onset timewas random.

5



:

(a) (b) (c)

10m

Figure 5. (a) Polariscope image of a E44 droplet doped by MBAPB in D2O under condenser illumination. Same droplettrapped by circularly polarized laser tweezers with (b) and without (c) condenser illumination. Circle (in (c)) markscontour of the droplet.

300 400 500 600

0.0

0.5

1.0

In

ten

sity (

arb

. u

nits)

Wavelength / nm

1 2

Figure 6. The normalized spectral profiles of absorption (1) and emission (2) of MBAPB in toluene. The molecularMBAPB structure is schematically shown in the inset.

3.4. Three-photon absorption in dye-doped E-44 liquid crystal droplet

The hydrophobic two-photon absorbing dye C40H54N2O2 (MBAPB; molar weight 580.4155 g/M)11 was dopedinto E44 (Merck) nematic liquid crystal by ratio 0.3 mg to 20 µl (molar concentration 25.8 mM/l) at 100C.At this temperature E44 is isotropic and the dye was uniformly dispersed. Then the dye-doped E44 was putinto D2O (20 ml) under ultrasonic bath shacker conditions and droplets 2 – 12 µm in diameter were formed.The droplets appeared polar in polariscope imaging as an undoped E44 (Fig. 5(a)). Upon laser trapping in acircularly polarized light the droplets spined. Since the MBAPB is a strong two-photon absorber at around800 nm wavelength (2PA cross section is ∼ 1000 GM), it was interesting to explore a three photon absorbingproperty of this dye. Figure 5(c) shows a visible fluorescence of MBAPB from the focal region, which has cross-section comparable with the wavelength λ =1064 nm (a numerical aperture of the objective lens was NA = 1.3).This emission is excited by three-photon absorption when laser trapping power was 0.6 W (a recognizable emissionstarted at approximately 0.5 W). It should be noted, that there is negligible absorption of E44 and D2O at thiswavelength. No visible emission was observed from E44 nor D2O at the same conditions of focusing.

Let us estimate the difference in cross-sections of two- and three- photon absorption (2|3PA). Such scalingcan be estimated from the typical one-photon absorption cross-section, σ1, which is approximately equal tothe geometrical cross section of absorbing molecules, ∆S 10−16 cm−2, and lifetime of the virtual state,τ = 10−16 s (estimation based on the uncertainty principle). Then a N-photon absorption cross-section is givenby σN = σN

1 τN−1 [cm2N ·sN−1].12 The ratio of probabilities of 3PA and 2PA is σ1τ 10−32 cm2s.

Usually 3PA becomes significant at a 100 GW/cm2 or higher intensity, i.e., the optical density OD ≡ αd ∼ 1,here α is the absorption coefficient and d is the thickness of the sample. In the case of 2PA and 3PA, the absorptioncoefficient α = α0 +α2I +α3I

2, where α2,3 are the 2PA ([cm/W]) and 3PA ([cm3/W2]) coefficients, respectively,I the irradiance/intensity, and α0 the linear absorption coefficient. The nonlinear absorption coefficients can be

6



z

Figure 7. Geometry of experiment. A birefringent particle of thickness d oriented at angle θ with respect to its opticalaxis. θ = 0 corresponds to the “fast” axis of a birefringent material.

expressed via the corresponding absorption cross-sections:

α2[cm/W] =σ2[cm4s]NAd0 × 10−3

hω, (6)

where NA is the Avogadro number, d0 is the molar concentration (mol/l), and hω the photon energy. Similarly,the evaluation of 3PA coefficient is then:

α3[cm3/W2] (σ2[cm4s] × 10−32[cm2s])NAd0 × 10−3

(hω)2. (7)

In our experiments, the irradiance corresponding to the 0.5 W power focused by a NA = 1.3 objective lens(the diffraction limited focal spot is considered) was ∼ 60 MW/cm2. This was a threshold value at which fluo-rescence of MBAPB was observed. This value is an upper-bound estimate, since we assume a diffraction-limitedfocusing. This shows that the MBAPB has a large 3PA cross-section and can be excited at comparatively low∼ 102 MW/cm2 irradiance. The characteristic yellow emission of the MBAPB (Fig. 6) was clearly recognizable(Fig. 5(c)) in the center of the droplet. This demonstrates that MBAPB due can be used for multi-photonmicroscopy.

4. CONCLUSIONS

Liquid crystal droplets formed by self-organization inside water have complex internal molecular ordering and abirefringence very different from the bulk form of the same materials (can be called a “shape-altered” birefrin-gence). The internal molecular ordering can be altered by the high intensity laser trapping beam and was foundin some droplets occurring spontaneously in a switch-like pattern. Any change of molecular ordering inside thedroplets bring about the change of birefringence and can be used for optical applications.

Three-photon absorption at a low cw-laser trapping power was observed in dye-doped nematic liquid crystaldroplet. Control of 3D structure and doping of liquid crystal droplets is expected to open new applications inmicro-photonics and optically controlled photonic crystals.

We are grateful to Drs. Y. Tanamura and S. Matsuo for fruitful discussions about dye doping of liquid crystalsand laser trapping.

Appendix

Here, the determination method of the state of polarization of the light passed through the liquid crystal droplet,which is assumed to act as a wave-plate, is described and eqn. 2 is obtained. It is useful to employ a Jones calculus

7



for this aim. The Jones matrix of electrical field of light, which propagates along z-axis (Fig. 7) can be presentedas:

Ein =1√

E20,x + E2

0,y

(E0,xei(2πt−kz+ϕx)

E0,yei(2πt−kz+ϕy)

)(8)

where k is the wavevector of light, t is time, and ϕx,y are the phases. This matrix defines explicitly the polarization

and amplitude of the light, e.g., for a right and left circularly polarized light it is presented by E± = E0√2

(1±i

)

respectively, with “+” for a right-circular polarization (as viewed along the beam). For the linear polarization

E ‖ x Jones matrix is given by Ex =(

10

). The electric vector of the light Eout passed throughout a cascade

of n optical elements can be found by linear transformation:

Eout = Jn · Jn−1 · ... · J1 · Ein, (9)

where Ein is the incident field and Jn is the Jones matrix of the nth optical element. Transmission is then:

T =| Eout

x |2 + | Eouty |2

| Einx |2 + | Ein

y |2 . (10)

Jones matrix of analyzer oriented at an arbitrary angle θ is given by:

JA(θ) =(

cos(θ)2 cos(θ) sin(θ)cos(θ) sin(θ) sin(θ)2

)(11)

where J(0) and J(π/2) represents an analyzer whose transmission is maximum for the E-field oriented along xand y-axis, respectively.

In order to account for polarization changes when light is passing throughout a birefringent positive uniaxialmaterial like E44 and 5CB (the refractive index of extraordinary beam being larger than that of ordinary,ne > no), one needs to consider the orientation of a particle in the laboratory coordinate system xyz. Let usconsider a normal incidence (perpendicularly to the optical axis of uniaxial positive material) comprising an angleθ, which is between the x-axis of laboratory coordinates and the “fast” axis (referred to as an axis of ordinaryray) as shown in Fig.7. Jones matrix of a retarder in the crystal system of coordinates is given by:

JRet = e−i 2πλ ned

(1 00 eiδ

)(12)

where δ = 2πλ (ne − no)d is the phase difference introduced by retarder. In order to calculate the state of

polarization in the laboratory system of coordinates the following transformation is necessary Eout = R(−θ) ·JRet · R(θ) · Ein; i.e., the following calculus should be carried out: first, the incident light is transformed intocoordinates of the birefringent crystal by rotation at an angle θ using rotation matrix given below, then, thephase difference is introduced as beam passes the retarder, and, finally, the rotation back into the laboratorycoordinates should be accomplished (angle −θ) using the same rotation matrix:

R(θ) =(

cos θ sin θ− sin θ cos θ

)(13)

Now we can calculate an optical transmission through our setup. For an imaging of a rotating droplet hold ina circularly polarized laser tweezers we used condenser illumination. An auxiliary confocal pinhole was set tomeasure an optical transmission modulation by a rotating droplet (Fig. 1). Condenser illumination was passingthrough the polarizer, the droplet, and analyzer. Detected intensity can be calculated by:

| Eout |2=| JA(⊥) · [R(−θ) · JRet · R(θ)] · JA(‖) · Einnon−pol |2, (14)

where Einnon−pol represents a non-polarized incident light and ⊥, ‖ denotes the optically crossed angular positions

of retarders (polarizer-analyzer setup). In the case of a wave-plate (a birefringent plate as in Fig. 7) the eqn. 2can be obtained form eq. 14:

I(θ, ∆n) = I0 sin(2θ)2 sin(π∆nd/λ). (15)

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