1. Introduction

Since Ashkin and associates first demonstrated the utility of a tightly focused laser beam to trap micrometer-sized dielectric particles [1], optical traps (optical tweezers) have been successfully used in a variety of biological applications [2–4] including, for example, the trapping of viruses, bacteria, cells and organelles [5–7]. Typical laser powers used in such applications of optical tweezers lie in the range 10-100 mW, leading to focal intensities that lie in the MW/cm² range. The potential for thermal and non-thermal damage caused by these high intensities to biological samples has been a matter of continuing concern and investigation [7–10]. One way of reducing non-thermal photodamage to many biological materials is to use near-infrared lasers (such as Nd:YAG, Nd:YLF, diode or Ti:Sapphire lasers) rather than visible lasers.

Hitherto, optical trap studies have been carried out on transparent materials in a transparent medium, and on absorbing material in a transparent medium. However, there seems to be no information in the literature on how optical traps behave in the case of a transparent material in an absorbing medium. The importance of thermal effects in optical traps and their direct and indirect impact on motile and non-motile cell function and behavior was initially studied by Liu and associates [11]. Optical damage to bacterial cells trapped for an extended period and the influence of laser power, bacterial species, and growth conditions has also been studied [12]. Using an interferometric technique, localized heating distribution in water at the focus of an infrared optical trap has been inferred and peak temperatures of ~4 K have been reported for average heating time of 250 ms at 55 mW laser power at 985 nm [13]. The increase in temperature in such instances has been rationalized using a simple model that involves heat generation by light absorption in the laser focal volume and subsequent heat dissipation to the bulk solution. A more elaborate model has been developed by Schönle and Hell [14] in which heat generation by absorption and conduction in the entire light cone is taken into account and the effect of different focusing geometries has been numerically calculated for objectives of different numerical apertures (NA). Subsequent experiments showed that for NA = 1.2 (water immersion objective), irradiation of water for 1 second with 100 mW of 850 nm light raises the local temperature by 0.2 K [15]. However, it has been shown that even though the heating effect in water may be considered to be rather small, it can have non-negligible effects on trap calibration in typical biophysical experimental circumstances and needs to be taken into consideration when laser powers of more than 100 mW are used [15]. This is even more the case in non-transparent media like glycerol [15].

Non-transparent media, in particular metallic objects, are generally regarded as poor candidates for optical trap studies. However, such materials, in particular metallic nanoparticles, are now finding wide applicability as heat transducers in photothermal applications and they hold great promise in drug delivery assays or photothermal therapy. The temperature increase of individual gold nanoparticles trapped in three dimensions exhibits temperature sensitive permeability, with increase in surface temperature being as large as hundreds of degrees Celsius even at moderate laser powers being demonstrated [16]. It is precisely for this reason that gold beads are not considered to be good handles for applying forces to biological molecules in optical tweezers as there is significant heating (266 C/W, more than 20 times higher than heating of water within the laser focal volume [15]) that can result in damage to biomaterials such as enzymes [17]. Carbon nanotubes (CNTs) constitute another class of material that have interesting applicability in diverse biological and biomedical environments. As in the case of metallic objects, CNTs are also non-transparent to infra-red light that is conventionally used in optical tweezers. Consequently, single walled CNT bundles have been shown to be repelled from the focal volume in an optical trap [18]. However, we have recently demonstrated that CNTs can, indeed, be optically trapped using a low power (5 mW) infrared (1064 nm) laser [18]. Moreover, we showed that trapping of CNTs is accompanied by concomitant formation of microbubbles. Such bubbles arise from the localized heating at the tweezer focal volume due to the efficient absorption of near-infrared light by the CNTs. The elevated temperatures at the CNT location result in expulsion of gases (dissolved atmospheric gases) in the liquid and vaporization of the surrounding liquid. This volume of hot gas is trapped by the cooler liquid to form bubbles. The CNT bundles that are normally repelled by the tweezer [18] display completely the opposite behavior in the presence of bubbles—they are, in this case, invariably attracted towards the tweezer focus. Experiments have demonstrated that in an optical trap coupled to a fluid flow system bubbles are formed by laser heating of CNT bundles in the flowing fluid. It is found that the surface of these bubbles become encrusted by the CNT bundles and such encrusted bubbles experience strong attraction towards the laser focal volume, even when the fluid velocity is large [18]. Such attraction is a consequence of the steep temperature gradient in the liquid and the resulting steep surface tension gradient that sets up convection currents that, in turn, induce temperature-driven movement of matter in their vicinity [18–20]. It is these convective currents that propel the CNT-encrusted bubbles towards the laser focus, overcoming the dipole repulsion of the bundle by the tweezer light [19]. There are other (different) contexts in which laser-induced heating in optical traps has also been experimentally studied [15, 21, 22].

In the present study we trap a transparent polystyrene bead suspended in an absorbing medium, hemin dissolved in NaOH. We use two different methods for calculating the trap strength: one which relies on the equipartition theorem and the other that uses the conventional power spectrum method [2]. The concentration of hemin in NaOH provides us with an experimental handle on the amount of optical energy that is absorbed. We observe that increase of hemin concentration converts a normal optical trap into a thermal trap. We are readily able to differentiate between the optical trapping and thermal trapping regimes by estimating the trap strength. We also deduce the rise in temperature that occurs within the laser focal volume: temperature changes of 5-24 K are observed for laser power values of 10-90 mW for hemin concentrations of 0-50 mg/ml. At intermediate values of hemin concentration a transition regime between optical trapping and thermal trapping is observed.

2. Experimental details

Our optical trap is formed by focusing a Nd-YAG (1064 nm) laser beam with the 100X objective (N.A = 1.3) onto a sample. Detailed descriptions of our apparatus have been published earlier [23, 24]. In brief, the light transmitted through our optical tweezers set-up is collected by a 60X condenser lens and is allowed to fall on a quadrant photodiode (QPD). The QPD signal is then amplified and recorded on an oscilloscope. Initially the QPD is calibrated by fixing a polystyrene bead, of 2 µm diameter, onto a cover slip and moving it by a known displacement to record the change in voltage. Our QPD was measured to have a sensitivity of

6 mV/nm. A typical power spectrum (Fig. 1 ) is obtained by recording the displacement of a trapped bead dispersed in plain NaOH as a function of time and taking a Fourier transform of the displacement-time graph. The corner frequency, f_c, is obtained by fitting to the data the function [2]

 

Fig. 1 Typical power spectral density (PSD) deduced from a recording of the displacement of a trapped 2 µm diameter polystyrene bead in NaOH. The inset shows the bead’s displacement over a period of 2 s. Measurements were made at a rate of 250 kilosamples per second.

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3. Results and discussion

3.1 Absorption measurements

We made absorption measurements at different concentrations of hemin in NaOH. As can be seen in Fig. 2(a) , the absorbance increases with hemin concentration at the trapping wavelength of 1064 nm; it rises from 1.13 to 6.3 cm⁻¹ as the concentration increases from 6.5 mM to 100 mM. The inset to Fig. 2(a) shows the transmission change as a function of concentration for a fixed laser power of (539 mW), with the scatter plot showing the experimental data and the red line depicting an exponential fit to y = A + Be^Cx (where A = 0.694, B = 0.307, and C = −0.014) that confirms adherence to the Beers-Lambert law. In Fig. 2(b) we show how the normalized transmission varies as a function of intensity for different incident laser powers at 100 mM concentration. The intensity variation in this case is obtained by focusing the 1064 nm laser (2 mm beam) with a lens and translating the sample across the laser focal zone. The size of the focused laser beam was determined in a separate experiment by CCD imaging and taking the full-width at half-maximum of the measured Gaussian profile. The diameter at the beam waist was measured to be 52.0 ± 0.4 µm. Measurement of the laser power was by means of an integrating sphere coupled to a calibrated Si photodiode. The intensity at a distance z from the beam focus is calculated by using the equation I(z) = P/[πω(z)²], where ω(z) is given by ω(z) = ω₀[1 + (z/z₀)²]^1/2 with ω₀ being the radius at the beam waist and z₀ = πω₀²/λ; z is the distance from the beam waist.

 

Fig. 2 (a). Concentration-dependent absorption spectrum of hemin in NaOH. Inset shows the variation in transmission of 1064 nm light as a function of hemin concentration. (b) Normalized transmission of at incident power levels of 207 mW, 412 mW, and 509 mW.

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As can be seen for a laser power of 207 mW (intensity 9.7 × 10³ W/cm²) the change is transmission is very negligible. As the power is increased the transmission decreases to ~95% at a laser power of 412 mW (intensity 1.9 × 10⁵ W/cm²). At 509 mW (intensity 2.4 × 10⁵ W/cm²) the transmission decreases to 90%.

3.2 Power spectra

In order to determine the trap strength variation in absorbing media, we made measurements of power spectra at different values of hemin concentration, and some typical results are shown in Fig. 3 .

 

Fig. 3 Power spectra measured for three different hemin concentrations, all at a laser power of 83 mW. f_c denotes the corner frequency deduced from fitting Eq. (1) to each of the measured spectra; the appropriate fitting parameters are shown in the equations below each of the power spectra.

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These power spectra enabled deduction of the corner frequency, f_c, which, in turn, allowed us to use well-established methodology [2] to estimate the trap strength in each case. These results are discussed in the following.

3.3 Trap strength measurements

We have utilized the data obtained from our absorption measurements in conjunction with the theoretical model developed by Peterman et al. [15] to deduce the change in temperature. This model is realistic in that it accounts for heat that is generated because of light absorption in the vicinity of the laser focus, balanced by heat flow outward from the laser focal volume, as well as heat sinking at the glass microscope slide used in our experiments. The model relates the change in temperature to experimentally-accessible parameters [15]:

We took the thermal conductivity of NaOH to be 0.65 W/mK. Our bead was trapped at a distance of 25 µm above the coverslip. We estimated the temperatures as a function of laser power for different concentrations of hemin in NaOH, and some typical results are shown in Fig. 4 . As is seen, in case of NaOH without hemin, the change in temperature, ΔT, is miniscule (1-5 K). Upon addition of the absorber, the value of ΔT almost doubles, even at the lowest concentration; ΔT is seen to increase four-fold at hemin concentration of 50 mg/ml.

 

Fig. 4 Temperature change as a function of incident laser power for different hemin concentrations.

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The amplitude of the Brownian motion of trapped beads is a direct indication of temperature, T: as T rises in our case due to the presence of absorbing solvent, the Brownian motion also increases. In order to probe this effect of temperature in the laser focal volume we have used two methods to estimate trap stiffness, k: we have utilized the equipartition theorem to deduce k_eq and the measured power spectrum to deduce k_ps. We note that k_eq (k_eq = k_BT/ ‹x²›) depends linearly on T whereas k_ps ( = 12π²R_bηf₀) is not explicitly dependent on T but, rather, depends linearly on the fluid viscosity, η. Earlier work has experimentally established [17] that mutually diverging k_ps and k_eq values as a function of incident laser power is a signature of significant heating. Figure 5 shows the variation of k with laser power using two different methods. As is seen, the two curves for k overlap very well in case of pure NaOH, indicating that there is no heating. With addition of small quantities of hemin (12 mg/ml) the two trap strengths start to deviate at higher values of laser power (~60 mW). As the hemin concentration is raised to 25 mg/ml the laser power at which the two k-values begin to deviate reduces to ~40 mW. With further increase in hemin concentration (50 mg/ml) the two curves become distinctly separate, even at the lowest laser power (10 mW).

 

Fig. 5 Variation of trap strength, k, with incident laser power in NaOH and for different concentrations of hemin. k_ps and k_eq denote, respectively, the trap strength deduced from the power spectrum and the equipartition theorem.

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As already noted, k_eq depends linearly on T. The fact that in the case of pure NaOH we do not observe any deviation in the two k values offers an experimental indication that temperature begins to play a role when even a small quantity of hemin is added. What is the cause of the temperature rise that is observed? In earlier experiments it has been shown that for a transparent bead placed in a non-absorbing liquid, a rise in laser power produces minimal heating effect and the localized temperature is not significantly affected. But if there is even slight absorption of optical energy, either by the surrounding medium or by the trapped particle itself, the localized temperature increases dramatically [15, 17]. In the present work, the absorber that we have used has significant linear absorption at 1064 nm [Fig. 2(a)]; moreover it has a strong intensity dependent absorption [Fig. 2(b)]. The intensity in the focal volume is very large since we are using a 100X objective with large NA (intensity = 1.3 - 13 × 10⁶ W/cm² for power = 10 - 100 mW).

If we compare these values with the intensity at which we observe significant nonlinear absorption [see Fig. 2(b)], it is clear that 10 mW power is sufficient to cause nonlinear absorption in the medium. Interestingly, we note that for concentration up to 25 mg/ml, k_ps< k_eq at low power levels. This may be due to hemin absorption at 1064 nm resulting in lowering the effective power that reaches the trapped bead. As the laser power rises, the focused intensity also increases, resulting in more non-linear absorption. This, in turn, would be expected to lead to decrease in trap stiffness. But we do not see such a behavior (Fig. 5): upto a certain laser power k_ps and k_eq remain more or less constant, indicative of a saturation kind of behavior (particularly at 12 and 25 mg/ml concentrations). This “saturation” behavior deviates at 60 mW (for 12 mg/ml) and 40 mW (for 25 mg/ml), indicating the onset of a rise in temperature. The “saturation” of k upto a certain power level can be attributed to the saturation of absorption and may, indeed, be compared with the optical limiting that is routinely observed in porphyrins [25]. At 50 mg/ml we see the deviation of two curves even at a lower laser power (10 mW). At this high value of hemin concentration, we believe that the higher levels of optical energy being absorbed leads to a transition in the trapping regime wherein thermal effects begin to dominate. The laser-induced temperature gradient in the medium results in a pressure gradient via thermal expansion that, in turn, drives a localized convective current in the vicinity of the laser focus [21, 22]. This is the regime that we refer to as thermal tweezing.

We also note that data presented in Fig. 5 indicate that the trap strength increases with hemin concentration. For instance, at incident laser power of 60 mW, the value of k_ps increases from ~1.5 x 10⁻² at a concentration of 12 mg/ml to ~2.0 x 10⁻² at a concentration of 25 mg/ml and to 2.4 x 10⁻² at 50 mg/ml concentration. This observation is at variance with the simplest possible rationalization of our observations, namely that convective currents caused by thermal heating give rise to positional fluctuations that lower the value of the apparent trap strength deduced via the equipartition theorem. It is also noteworthy that changes in trap strength do not manifest themselves for low values of incident laser power. For instance, at 30 mW laser power, the trap strength remains essentially invariant as the hemin concentration is doubled from 12 to 25 mg/ml whereas it rises as soon as the concentration is large enough to access the thermal tweezing regime.

The estimated rise in temperature due to absorption was earlier used to correct both for temperature and viscosity in deducing the trap strength. These results showed quantitative agreement [17] in the case of heating caused by gold nanoparticles. In our experiments, on the other hand, by accounting for the rise in temperature and the consequent viscosity change, we do not account for the observed discrepancy in the two trap strengths. This may be due to the nonlinear absorption of the solvent that will result in a higher rise in temperature than estimated using only the linear absorption term, α.

Our results now enable us to reconcile earlier observations made in experiments carried out with carbon nanotube bundles in various liquids [18–20]. In these experiments it was observed that even with 5 mW laser power bubble formation readily occurs, indicating large localized rises in temperature. With hemin as the absorber, we estimated localized temperature increases of 24 K at modest laser power levels. However, further work clearly needs to be undertaken to gain better insights. For instance, the role of non-linear absorption by the absorber needs to be properly quantified. Also, the role of thermal conductivity needs to be explicitly accounted for in future work.