1. Introduction

Since the inception of laser tweezers based on a single highly focused laser beam [1], this technology has been used to manipulate erythrocytes or red blood cells (RBCs) [2,5] because they play important roles in drug therapy [3] and disease diagnostics [4]. Rotation of a trapped RBC was first demonstrated by the use of a doughnut laser beam [6] and recently achieved by using a polarized laser beam [7 – 10]. Although laser tweezers were used to pull on bead-handles attached to an RBC for introducing deformations in the range of 15 – 50% [11, 12], optical stretching of RBCs has also been obtained by using two counter propagating laser beams of slight divergence with an achieved deformation of less than 15% [13]. Efforts have been made to fold an RBC with laser tweezers [8,9], although the mechanism for folding an RBC in a single beam trap is arguable [14].

One of the recent developments in near-field optics is the generation and application of the focused evanescent wave by a centrally obstructed high numerical aperture (NA) objective [15, 16]. It has been demonstrated both experimentally and theoretically that the focal spot distributions produced by an objective lens of NA=1.65 under the total internal condition becomes evanescent. Due to its highly confined nature, the strength of the evanescent focal spot is so strong that nonlinear near-field excitation becomes possible [15]. Unlike evanescent wave manipulation on a prism surface [17], focused evanescent illumination makes near-field laser tweezing possible [18], which has been confirmed by the ray optics and electromagnetic wave models [19, 20]. In the near-field trapping case, the axial trapping volume is only a few tens of nanometers. The field distribution in an evanescent focal region of an objective of NA=1.65 is depicted in Fig. 1(a), showing the two peaks produced due to the strong depolarization effect in a ring beam illumination under the total internal reflection condition [15, 16, 18]. These two localized evanescent wave peaks form a directional trap and can be used to trap an RBC both horizontally and vertically. We demonstrate in this article that biconcave shaped RBCs can be trapped, stretched, folded and rotated by a focused evanescent focal spot.

2. Modeling of focused evanescent trapping using finite difference time domain (FDTD) method

It should be pointed out that the trapping position in the near-field tweezers shown in Fig. 1(a) is always located on the surface due to the evanescent nature of illumination. This feature is different from the far-field laser tweezers in which case the trapping position can be moved within an object, and thus provides a balanced trapping position near the centre of the object. In other words, a near-field trap produces an axially asymmetrical force distribution and can effectively “stick” an object in various orientations on the surface where total internal reflection occurs.

 

Fig. 1. (Color online) (a) Distribution of an evanescent wave focal spot at the interface between the cover slip (n=1.78) and water (n=1.33), produced by a high NA objective (NA=1.65) obstructed by a circular opaque disk. The 3D distribution represents the calculated modulus squared of the electric field in the focal region. The strength of the evanescent wave decays rapidly with the distance d. The evanescent focal spot exhibits two peaks that play a critical role in near-field trapping, rotation and folding. (b) Stress profile on a biconcave RBC oriented horizontally. (c) Stress profile on a biconcave RBC oriented vertically.

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Distributions of optical stress on a biconcave RBC oriented in horizontal and vertical planes in the focal region of the objective (NA=1.65) at wavelength 1.06 μm, calculated using the finite domain time difference (FDTD) [21] and Maxwell stress tensor [23] methods, are shown in the insets of Figs. 1(b) and 1(c), respectively. The size of the RBC is the same as that used elsewhere [10]. The simulation confirms that both horizontal (Fig. 1(b)) and vertical (Fig. 1(c)) orientations are stable trapping positions, as demonstrated by Supplementary Movie 1 and Supplementary Movie 2 (the experimental details are given in Section 3). This feature is fundamentally different from far-field laser tweezers in which case an RBC can be trapped only in the vertical plane [10, 14].

3. Experiment

The experimental setup of the near-field laser trapping system under focused evanescent wave illumination was the same as that reported elsewhere [18]. The trapping laser beam of wavelength 1.06 μm was generated from a 2W diode-pumped solid state continuous wave Nd:YAG laser (Spectra-Physics). The video capturing through the CCD camera was controlled by the PC, using a movie capturing software (Avermedia). The red blood cells were diluted (1:10000) and suspended in phosphate buffered saline (PBS) which ensured the isotonicity of the suspension. The bottom central portion of a Petri dish was drilled away, and the special high index cover glass was attached. One drop of RBC suspension was carefully pippetted on to the high index cover glass, and the Petri dish was sealed partly so as to ensure the complete illumination of the sample with white light. The Petri dish was then attached to the PC controlled piezo-electric scanning stage, and the entire sample stage was aligned tilt free horizontally using the vertically aligned laser beam. A half wave plate was inserted in the beam path in order to rotate the plane of polarization of the laser.

4. Rotation of a trapped erythrocyte

The focused evanescent trapping geometry capable of trapping RBC in the horizontal and vertical planes provides a mechanism for rotating a trapped RBC. Figures 2(a-c) (Supplementary Movie 3) show the rotation of an RBC trapped in the horizontal plane.

 

Fig. 2. Optical rotation of a trapped RBC in near-field laser tweezers. (a) - (c) Successive frames taken from the video (Supplementary Movie 3) show the rotation of an RBC trapped in the horizontal plane. (d) The rotation speed ω as a function of the trapping power in the horizontal plane. The arrow indicates the change in the direction of the incident laser polarization. [Media 3]

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The time required for rotating a trapped RBC towards the polarization direction of the trapping beam is dependent on the trapping power. This in turn gives rise to the measurement of rotation speed ω as a function of the trapped power, as depicted in Fig. 2(d). It is noted that the rotation speed increases linearly with the trapping power, and reaches approximately 1.5 rpm at the power of 18.6 mW. This speed is considerably slower compared with that achieved in the far-field optical tweezers, which is approximately 8.5 rpm at the power of 17 mW for an RBC of similar size [7]. However, it should be noted from Fig. 2(d) that the rate of increment of the rotating speed with the optical trapping power is approximately 30% higher than that in the far-field case. Since the RBC membrane is “stuck” on the cover-glass surface under the near-field trapping condition, it requires more optical force to overcome the extra friction between the RBC and the cover glass surface. Therefore, the threshold for optical rotation is significantly higher in the near-field trapping case. The high rate of increment of rotating speed above the threshold value indicates that the trapping force maxima at the two intensity peaks along the polarization direction provides effective optical rotation.

5. Stretching of a trapped erythrocyte

The fact that an RBC can be trapped in the horizontal and vertical planes allows for the measurement of the deformation property of an RBC in the three directions. To this end, we first trap an RBC in the horizontal plane at the trapping power of 12 mW. Increasing the power from this level to 14 mW can deform the circular shape of a trapped RBC. The dynamic deformation of a trapped RBC can be achieved in the power range of 14 to 18 mW (Figs. 3(a-c) and Supplementary Movie 4). While the size of a trapped RBC in the x direction, ρ^h_x, is stretched, the size in the y direction, ρ^h_y, is squeezed. Figure 3(g) shows that the dependence of the deformation on the trapping power is linear. A further increase in the trapping power leads to the folding of the trapped RBC, which is discussed in Section 6.

The near-field optical stretcher using focused evanescent wave has a few unique features. Firstly, the ratio of the deformation of the RBC from its original size is as large as approximately ± 23% (Fig. 3(c)), which is half the ratio achieved using bead-handles attached to an RBC [12]. However, the trapping power in near-field optical stretching is less than 18 mW, which is one order of magnitude less than that in the bead-handle method [12]. Secondly, the single beam near-field stretcher results in a deformation ratio of approximately 53% larger than that measured with the two-beam optical stretching method, while the trapping power in the near-field trap is one tenth of the latter [13]. The physical reason for this feature is that the focused evanescent wave generates a highly confined distribution of optical stress on the RBC membrane as illustrated in Figs. 1(b) and 1(c). Therefore, at a given level of total trapping force, this confined “sticking” force distribution becomes more effective in deforming an RBC membrane. Thirdly, it is noted from Fig. 3(g) that the amount of stretching and squeezing is almost the same in the two orthogonal directions, which is different from that in the bead-handle method [12] and implies that stretching in the direction perpendicular to the primary plane (the RBC plane) should be negligible.

 

Fig. 3. (Color online) Optical squeezing and stretching of a trapped RBC in near-field laser tweezers. (a) - (c) Successive frames taken from the video (Supplementary Movie 4) show the squeezing and stretching of an RBC trapped in the horizontal plane. (d) - (f) Successive frames taken from the video (Supplementary Movie 5) show the squeezing of an RBC trapped in the vertical plane. (g) The dependence of the RBC size as a function of the trapping power in the horizontal and vertical planes, where the conditions corresponding to (a) - (f) are marked. [Media 4][Media 5]

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To confirm this feature, we trap an RBC in the vertical plane. By increasing the trapping power to the same range as that in Figs. 3(a - c), we can obtain the deformation property of a trapped RBC (Figs. 3(d-f) and Supplementary Movie 5). It can be seen from Fig. 3(g), that as expected, the size of a trapped RBC in the x (polarization) direction, ρ_x^v, is stretched while the size in the perpendicular direction, ρ_y^v, is almost unchanged with a deformation ratio of approximately 1%. The change of ρ_x^v accounts for a deformation of approximately 8%, but is only one third of the change of ρ_x^h within the same power range. This feature can be understood because the trapping spot in the near-field trap is located on the surface of the cover glass [18]. Thus, the centre of an RBC trapped in the vertical plane is far away from the trapping spot, as demonstrated in Fig. 1(c), which leads to the significant reduction in the deformation. The observation that the deformation in the perpendicular direction is negligible is consistent with the fact that the deformation in the two orthogonal directions in the primary plane is the same. This result is understandable as an RBC has been understood as an incompressible neo-Hookean form continuum whose volume remains unchanged in the linear deformation region. [12, 22].

6. Folding a trapped erythrocyte

Let us now turn our attention to the RBC trapped in the horizontal plane when the trapping power is larger than 18 mW.

 

Fig. 4. Optical folding of a trapped RBC in near-field laser tweezers. (a) - (c) Successive frames taken from the video (Supplementary Movie 6) show the folding of an RBC trapped in the horizontal plane. (d) The dependence of the folding angle of an RBC trapped in the horizontal plane as a function of the trapping power, where the conditions corresponding to (a) - (c) are marked. [Media 6]

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In this case, we observed that the trapped RBC exhibits folding with respect to the x - z plane as illustrated in Fig. 4. Such a folding effect (Figs. 4(a-c) and Supplementary Movie 6) is caused by the trapping force maxima at the two intensity peaks along the x axis. It can be seen from Fig. 1(b), that the direction of the trapping force at the peak intensity positions is downwards (i.e. towards the negative direction of the z - axis). These two force peaks act as two optical handles that eventually fold the trapped RBC. The measured folding angle α as a function of the trapping power is shown in Fig. 4(d), which exhibits a linear characteristic. The maximum folding angle achieved in the experiment is approximately 60 degrees for a trapping power of 19.3 mW.

7. Conclusion

In conclusion, a focused evanescent field can perform cell folding and high ratio optical stretching/squeezing at a power level of at least one order of magnitude less than that by other methods, as well as can exhibit a unique feature of trapping an RBC in both orientations. The linear dependence of deformation (e.g. stretching/squeezing) and folding on the trapping power in a single beam near-field laser trap provides a new tool to investigate, quantitatively and simultaneously, the cell mechanical properties such as Young’s modulus, shear modulus and bulk modulus.