Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Theoretical investigation on nonlinear optical effects in laser trapping of dielectric nanoparticles with ultrafast pulsed excitation

Open Access Open Access

Abstract

The use of low-power high-repetition-rate ultrafast pulsed excitation in stable optical trapping of dielectric nanoparticles has been demonstrated in the recent past; the high peak power of each pulse leads to instantaneous trapping of a nanoparticle with fast inertial response and the high repetition-rate ensures repetitive trapping by successive pulses However, with such high peak power pulsed excitation under a tight focusing condition, nonlinear optical effects on trapping efficiency also become significant and cannot be ignored. Thus, in addition to the above mentioned repetitive instantaneous trapping, trapping efficiency under pulsed excitation is also influenced by the optical Kerr effect, which we theoretically investigate here. Using dipole approximation we show that with an increase in laser power the radial component of the trapping potential becomes progressively more stable but the axial component is dramatically modulated due to increased Kerr nonlinearity. We justify that the relevant parameter to quantify the trapping efficiency is not the absolute depth of the highly asymmetric axial trapping potential but the height of the potential barrier along the beam propagation direction. We also discuss the optimal excitation parameters leading to the most stable dipole trap. Our results show excellent agreement with previous experiments.

© 2016 Optical Society of America

1. Introduction

In spite of its vast application in measuring nanoscale mechanical forces driving fundamental life processes in nature [1–5], laser tweezers (i.e. gradient optical trap created by a tightly focused laser beam with Gaussian transverse intensity profile [6, 7]) so far have very limited application in trapping and manipulation of dielectric nanoparticles [8–11] compared with metallic nanoparticles [12–16]. Direct optical trapping of a single macromolecule (as opposed to widely used indirect optical trapping of a micron-sized dielectric particle tethered to the single molecule [1–5]) is yet to be achieved.

In recent years the role of low-power high-repetition-rate ultrafast pulsed excitation on trapping efficiency of larger dielectric particles with diameter ≥ 0.5µm has been investigated [17–23] and it has been demonstrated that such excitation results in stable trapping of individual dielectric nanoparticles with diameter ≤ 0.1µm (which is confirmed by sensitive measurement of precise step-wise rise in two-photon fluorescence and/or scattering signal), for example, trapping of 100nm diameter latex nanospheres [24,25] and 10-20nm diameter Cd-Se quantum dots [25,26]. The high pulse peak power leads to a fleeting but steep trapping potential required to circumvent the difficulties associated with small dimension of nanoparticles leading to more erratic Brownian motion as well as with low polarizability of dielectrics (compared with metals) whereas the high pulse repetition-rate restricts diffusion of the trapped particle out of focus during the dead-time between consecutive pulses [24–26]. A phenomenological description has been put forward by one of us which captures the underlying physics of the origin of enhanced trapping efficiency with such excitation [26]: Stable trapping is facilitated due to repetitive instantaneous momentum transfer by a train of pulses with typically 100fs pulse-width at 100MHz repetition-rate (i.e. with 10ns time lag between consecutive pulses) but the trapped particle’s inertial time (which decreases with decreasing particle size) dictates the response of the particle to an instantaneous momentum transfer. A smaller particle with diameter ≤ 0.1µm can respond to this impulsive force. However, for a larger particle with diameter ≥ 0.5µm the typical inertial time is several tens of nano-seconds; therefore, 1) the particle always responds to cumulative momentum transfer by several pulses in the pulse train such that the trapping efficiencies turn out to be the same under pulsed and continuous-wave (CW) excitation [17,22] and 2) even after chirping the pulse-width remains too small to have any effect such that the trapping efficiency turns out to be independent of femto- to pico-second pulse-chirping [18].

In spite of the growing body of work along this direction, nonlinear optical effects on trapping efficiency under pulsed excitation has hitherto been explored in detail although these effects are non-negligible for such high peak-power pulsed excitation combined with tight-focusing condition. In this paper, we theoretically show that for a dipolar particle (having diameter much less that the wavelength of the trapping beam, i.e.dλ) optical Kerr effect always has a stabilizing effect on the radial component of trapping potential but it significantly modulates the axial component. At lower power level the fine balance between the gradient force and the scattering force along axial direction renders the trap progressively more stable upon increasing the power; however, above a critical power level the trend is reversed leading to an unstable trap along axial direction. With increase in power the trapping potential along axial direction becomes more asymmetric and in order to quantify the trapping efficiency the appropriate quantity is the height of the potential barrier along beam propagation direction and not the absolute depth of the trapping potential which is contrary to the common understanding in exsisting literature regarding the stability of an optical trap. We also discuss under what optimal excitation parameters the dipole trap is most stable.

Finally, although the explicit nature of the force (and potential) differs with particle size the essential physics remains unchanged and, our model nicely explains few puzzling observations that were found experimentally: 1) for larger colloidal particles (diameter ≥ 0.5µm), if we keep on increasing the power under pulsed excitation trapping is destabilized around few tens of milli-Watt power level (the particle first moves laterally toward trap center and then is ejected out of the trap axially, as observed by video microscopy) but this is not observed under CW excitation at similar power level [18,22,23] and 2) 100nm polystyrene beads were reported to be optically trapped for few seconds under pulsed excitation at power levels slightly over 30mW but no stable trapping was observed at higher power level [24,25].

2. General discussion

In this paper, we discuss the trapping of polystyrene nanoparticles in water. For a focused Gaussian beam, the intensity is given by [27]:

I(r,z)=(2Pπw02)11+(2z˜)2exp[2r˜21+(2z˜)2]
where P is the average power (for CW excitation) or the peak power (for pulsed excitation), w0=0.82*λNA is the spot-size (i.e. Gaussian beam radius at focus) with NA the numerical aperture and the reduced coordinates are given by: r˜=rw0, z˜=  zk*w02. Under tight focusing, the radial component of the total force is contributed only by (radial component of) the gradient force while the axial component of the total force is contributed by both (axial component of) the gradient force as well as the scattering force [6,7]. We compute the magnitudes of the total force around the geometrical focus (r=z=0) which, for dipolar particles (dλ), can be analytically expressed as [27]:
Fradial(r; z=0)= 2πnwa3c(m21m2+2)4r˜w0(Pπw02)exp[2(r˜2)]Faxial,gradient(z; r=0)= 2πnwa3c(m21m2+2)8z˜/(kw02)1+(2z˜)2(2Pπw02)11+(2z˜)2Faxial,  scatter(z; r=0)= 8πnw(ka)4a23c(m21m2+2)2(2Pπw02)11+(2z˜)2
where nw is the refractive index of medium (here, water), a=d2 is the radius of the trapped particle, k=2π*nwλ is wave-vector inside the medium, c is the speed of light in vacuum, m=npnw is the ratio of refractive index of the material the particle is made of (here, polystyrene) to that of surrounding medium (here, water). Numerical integration of the analytical expressions for force yields the corresponding expressions for potential:

Uradial(r; z=0)= Fradial(r; z=0)drUaxial,gradient/scatter(z; r=0)= Faxial,gradient/scatter(z; r=0)dz

2.1 Excitation parameters

Here, we take wavelength of trapping to be 800nm and, for pulsed excitation, the pulse-width is chosen as 120fs (τ) while repetition-rate (f, i.e. the inverse of the time lag between consecutive pulses, T) is chosen as 76MHz; these are typical values for a commercial Titanium:sapphire oscillator for which the peak-power/-intensity to average-power/-intensity ratio turns out to be:

PpeakPaverageIpeakIaverage=1f*τ105
Note that such a definition assumes the peak-power/-intensity to be constant over the duration of the pulse, neglecting the explicit time dependence of the envelope of the pulse (which is equivalent to saying that the pulse has a rectangular temporal envelope).

2.2 Dipole approximation

Harada and Asakura [27] discussed the conditions for the validity of the dipole limit; they compared the numerical simulation results using the Rayleigh scattering expression with that using the generalized Lorentz-Mie theorem (GLMT) and found excellent agreement for particles with diameters an order of magnitude smaller than the wavelength. Following their work, we chose the particle sizes to be 80nm and 70nm (i.e. d=2aλ10). Although GLMT is a more rigorous method for estimating trapping force (or potential), in what follows we show that the simpler theoretical treatment under dipole approximation yields very accurate estimates of trapping force (or potential) reported in earlier experiments. Also, in this size limit, Rayleigh scattering expression is more useful as there is, in principle, no restriction on the NA of the focusing objective which is often a problem to deal with in GLMT. For realistic estimation, we consider typical values for commercial oil-immersion objectives as NA=1.4, 1.3 & 1.45 (with typical refractive index of immersion oil being 1.515); these values are 0.924, 0.858 & 0.957 and 1.228, 1.140, & 1.272 in air and water, respectively.

2.3 Kerr effect

The (linear) refractive indices of water and polystyrene are taken to be 1.329 and 1.578, respectively [28]. Taking into account for the intensity-dependent nonlinear refractive indices of both polystyrene and water, we have the expression:

nw/p=n0w/p+ n2w/p*I(r,z)
The values of n2w and n2p are taken as 2.7x10−20m2W−1 [29] and 5.9x10−17m2W−1 [30–32], respectively. Note that these values were reported at 532nm and we ignore the wavelength dependence of these quantities since, at 800nm, these values are expected to change but only slightly (and certainly not by an order of magnitude); so this is an reasonable approximation.

Let us now carefully examine the magnitudes of the nonlinear terms (n2w/p*I) with respect to the linear terms (n0w/p) considering intensity around geometric focus, I(r=z=0)=2Pπw02 under tight-focusing condition (NA=1.4). Under CW excitation, the terms n2p/w*Iaverage are much smaller than n0w/p such that nw/pn0w/p; for example, even at average power level as high as 100mW the values for n2p/w*Iaverage are only 1.3x10−5 and 6.0x10−9, respectively, for polystyrene and water. Contrary to this, under pulsed excitation, n2p*Ipeak is non-negligible compared with n0p; for example, at 100mW average power n2p*Ipeak1.4 which is comparable with n0p=1.578. However, even at this high peak intensity n2w*Ipeak is only about 6.6x10−4. So nwn0w for all excitation conditions and non-linear beam propagation effects inside water can be ignored (k=2π*nwλ2π*n0wλ).

2.4 Time averaged force (or potential)

Under pulsed excitation, the force (or potential) corresponds to the instantaneous force (or potential) acting on the particle for which time-averaging over one duty cycle yields:

Fpulsed=1Tτ2τ2Fpulseddt=Fpulsed1Tτ2τ2dt=Fpulsed*(1T*τ)=Fpulsed*(f*τ)
Here, the instantaneous force is independent of time since the peak intensity is assumed to be constant over the duration of the pulse. If we ignore Kerr effect the instantaneous force is only linearly proportionl to the peak intensity (as the terms involving m=npnw=n0pn0w do not depend on peak intensity) for which we have:
Fpulsed=constant*Ipeak*(f*τ)=constant*IaverageFCW
which means trapping efficiency would be the same under pulsed and CW excitation; this has been observed under low power excitation [17,22] for which the Kerr effect may be neglected. However, the same result does not hold if we take into account of Kerr effect because the instantaneous force has now nonlinear dependence on peak power (as the terms involving m=npnw=(n0p+n2p*Ipeak)(n0w+n2w*Ipeak)depend on peak intensity) for which we have:
FpulsedFCW
and very different results are obtained; the pulse-chirping experiment on silica microspheres [18] did not reveal this owing to the very low Kerr nonlinearity of silica (2x10−20m2W−1 [33]).

3. Results and discussion

Since nonlinear optical effects are instantaneous, to include the Kerr effect under pulsed excitation we first calculate the instantaneous force (or potential) which readily yields the time averaged force (or potential) just after multiplication by (f*τ). The NA is chosen as 1.4 and the particle diameter as 80nm unless otherwise mentioned.

3.1 Radial force and potential

In Fig. 1, the radial components of the trapping force are plotted. Introduction of Kerr effect increases the maximum of (radial component of) the gradient force under pulsed excitation by a factor of ~4. As a result of Kerr effect, the maxima shift a bit from the classical turning points (r=±w02). This results in more stable (~3 times) lateral trapping which is evident from the corresponding plots of trapping potential along radial direction as shown in Fig. 2.

 figure: Fig. 1

Fig. 1 Plots of trapping force along radial direction at 100mW average power under CW and pulsed excitation ignoring and including Kerr effect.

Download Full Size | PPT Slide | PDF

 figure: Fig. 2

Fig. 2 Plots of trapping potential along radial direction at 100mW average power under CW and pulsed excitation ignoring and including Kerr effect.

Download Full Size | PPT Slide | PDF

3.2 Axial force and potential

In Fig. 3, the axial components of the trapping force are plotted. As before, introduction of Kerr effect increases the maximum of (axial component of) the gradient force under pulsed excitation by a factor of ~4.2; however, maximum of the scattering force is increased by a factor of ~23.4. Here also the maxima shift a bit from the classical turning points for the gradient force (z=±kw0223) and away from the focal plane for the scattering force (z=0). The corresponding plots of trapping potential along axial direction are shown in Fig. 4.

 figure: Fig. 3

Fig. 3 Plots of trapping force along axial direction at 100mW average power under CW and pulsed excitation ignoring and including Kerr effect. The blue lines correspond to scattering force, the green to gradient force and the red to total force.

Download Full Size | PPT Slide | PDF

 figure: Fig. 4

Fig. 4 Plots of trapping potential along axial direction at 100mW average power under CW and pulsed excitation ignoring and including Kerr effect. The blue lines correspond to scattering potential, the green to gradient potential and the red to total potential.

Download Full Size | PPT Slide | PDF

3.3 Dependence on power

From now on, let us restrict our discussion on trapping along axial direction under pulsed excitation only for which Kerr effect significantly modulates the potential. The influence of Kerr effect on total trapping potential needs a special attention. As shown in Fig. 4, there is an absolute depth of the global potential minimum, Umin (longer double-headed arrow in Fig. 4). However, the potential well is highly asymmetric and there is a potential barrier, Uesc (smaller double-headed arrow in Fig. 4), along beam propagation direction (i.e. positive z direction) to come out of this potential well. Introduction of Kerr effect increases Umin by a factor of ~15.7 while it increases Uesc by a factor of ~1.1 only.

Upon increasing the power, a point is reached when there is no restoring force along beam propagation direction; as shown is Fig. 5, this condition is already reached at 500mW power. At this power level, although Umin is very high, Uesc=0 i.e. the axial trapping potential becomes unbound; this is depicted in Fig. 6. So the particle is initially dragged toward the trap center but eventually propelled along axial direction which is consistent with the well known observation of axial ejection for larger colloidal particles (diameter ≥ 0.5µm) upon increasing the power under pulsed excitation only [18,22,23]. Therefore, the more relevant parameter to quantify the trapping efficiency is Uesc and not Umin.

 figure: Fig. 5

Fig. 5 Plots of trapping force along axial direction at different average power levels. The blue lines correspond to scattering force, the green to gradient force and the red to total force.

Download Full Size | PPT Slide | PDF

 figure: Fig. 6

Fig. 6 Plots of trapping potential along axial direction at different average power levels. The blue lines correspond to scattering potential, the green to gradient potential and the red to total potential.

Download Full Size | PPT Slide | PDF

To have a better insight into the nature of these two types of potential, Umin and Uesc, we plotted them separately with increasing power. Quite interestingly, as shown in Fig. 7, we see that although Umin monotonically increases with power, Uesc increases reaching a maximum before dropping off. This means there is an optimal average power for which the dipolar trap is most stable which is about 150mW for the 80nm particle using 1.4 NA objective. This is a very important finding as we can theoretically predict the optimal excitation parameters for having most stable dipole trap.

 figure: Fig. 7

Fig. 7 Plots of absolute depth of the trapping potential (left) and escape potential (right) along axial direction at different average power levels.

Download Full Size | PPT Slide | PDF

When we further investigate the shift in axial equilibrium position with increasing power, we note that the most stable trap around 150mW corresponds to a trap center away from the geometrical focus (z=0); this is shown in left panel of Fig. 8. As shown in middle panel of Fig. 8, when we plot the gradient and the scattering potential at the location corresponding to this axial equilibrium position, we notice an initial dominance of the gradient potential which, upon increasing power, is reversed around 40mW (zoomed within inset); also note that the gradient potential goes through a maximum around 250mW. So, contrary to the common understanding, the trap is neither destabilized due to pushing the particle away from focus by scattering potential nor it is stabilized by maximizing gradient potential alone.

 figure: Fig. 8

Fig. 8 Plots of position of the minima for absolute trapping potential along axial direction (Left) and the gradient and the scattering potential (green and blue lines, respectively) corresponding to this minima (Middle) at different average power levels. Right: Plots of the absolute depth of the trapping potential and the asymptotic scattering potential (red and blue lines, respectively) for the same.

Download Full Size | PPT Slide | PDF

In right panel of Fig. 8, we plot sum of these two potential at axial equilibrium position, i.e. Umin, alongwith its asymptotic value, i.e. Uasymp=U (z)Uscatter (z) since Ugradient (z)=0. We notice the separation between these two potential, i.e. Uesc, is maximum around 150mW when the trap is most stable (zoomed within inset) and there is a merging near 400mW when the potential is unbound, i.e. Uesc=0. So trapping efficiency is in fact subtly controlled by a delicate balance between Umin and Uasymp.

Quite interestingly, the above results indicate that for particles having linear refractive indices less than the surrounding medium, which are repelled by single beam trapping potential, there is a possibility of observing Kerr effect assisted stable trapping (depending on the strength of Kerr nonlinearity). We note an earlier theoretical work in literature [34] that discussed the role of Kerr effect resulting only in slight increase in trapping force under CW excitation, however for an idealized nanoparticle with quite high Kerr nonlinearity (1.8x10−12 m2W−1) and without any detailed analysis on the exact nature of trapping force and potential.

3.4 Dependence on numerical aperture

Let us now compare the trapping efficiencies under different focusing conditions. From Fig. 9 we see that Uesc is decreased/increased by a factor of about 1.5/1.2 when the NA is switched from 1.4 to 1.3/1.45; the power corresponding to maximum Uesc is also changed but only slightly. Tighter focusing leads to more stable trap as the relative contributions of gradient and scattering potential are changed. For stable trapping a ‘rule of thumb’ is that a minimum of 10 kBT barrier height is required; so the trap is thermally unstable when NA is changed to 1.3.

 figure: Fig. 9

Fig. 9 Plots of escape potential with NA = 1.3, 1.4 and 1.45 (black, red and grey lines respectively) at different average power levels.

Download Full Size | PPT Slide | PDF

3.5 Dependence on particle size

It is interesting to explore the optimal average power and the corresponding Uesc for particles with different diameters (each satisfying the criterion, d=2aλ10), for example, 80nm and 70nm without changing the focusing condition (NA=1.4). As shown in the left panel of Fig. 10, while the optimal average power is 150mW for the 80nm particle, it is around 500mW for the 70nm particle which means it requires more power for stable trapping of the smaller particle. The maximum height of the potential barrier is also increased by a factor of about 2.6 for the smaller particle which means the smaller particle can be trapped with more stability. This is a very promising finding considering the direct trapping of dielectric nanoparticles. Also, the threshold power (Uesc=0) decreses with increasing particle size. A small change in particle size results in a significant change in the optimal average power level which is a consequence of third-/sixth-power dependence of force on radius of the particle.

 figure: Fig. 10

Fig. 10 Left: Plots of escape potential on an 80nm particle (red line) and on a 70nm particle (black line) at different average power levels. Right: The same for a 100nm particle.

Download Full Size | PPT Slide | PDF

Although 100nm polystyrene beads do not strictly satisfy the dipole limit, we are still intrigued to find the optimal power level for such particles. As shown in right panel of Fig. 10, the optimal power is ~40mW for which Uesc is just about 2.7kBT; this means the particle is trapped but only for a while (considering the ‘rule of thumb’ of minimum 10kBT barrier height for stable trap). All these quantitatively agree with the experimental findings [24,25].

4. Conclusion

We have shown how the efficiency of laser trapping of dielectric nanoparticles under high-repetition-rate ultrafast pulsed excitation is dramatically modulated by optical Kerr effect. We have thoroughly analyzed the results of such effect. Considering trapping efficiency, the height of the potential barrier along beam propagation direction has been identified to be the most relevant quantity which nicely explains previous experimental results. Our analysis have shown how to estimate optimal average power level for most stable dipole trap which is extremely important in direct trapping of individual nanoparticles. We have also predicted Kerr effect assisted stable trapping of nanoparticles that are difficult to trap otherwise.

Funding

This work is supported by SERB, DST (Grant No: ECR/2016/000467) and IISER Mohali (Start-up Grant). We thank IISER mohali for providing graduate fellowship to AD.

Acknowledgment

This paper is dedicated to Prof. N. Sathyamurthy on 65.

References and links

1. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004). [CrossRef]   [PubMed]  

2. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994). [CrossRef]   [PubMed]  

3. A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-molecule biomechanics with optical methods,” Science 283(5408), 1689–1695 (1999). [CrossRef]   [PubMed]  

4. C. Bustamante, Y. R. Chemla, N. R. Forde, and D. Izhaky, “Mechanical processes in biochemistry,” Annu. Rev. Biochem. 73(1), 705–748 (2004). [CrossRef]   [PubMed]  

5. J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008). [CrossRef]   [PubMed]  

6. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288–290 (1986). [CrossRef]   [PubMed]  

7. A. Ashkin, Optical Trapping and Manipulation of Neutral Particles Using Lasers: A Reprint Volume with Commentaries (World Scientific, 2006).

8. A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987). [CrossRef]   [PubMed]  

9. S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, “Optical trapping of single-walled carbon nanotubes,” Nano Lett. 4(8), 1415–1419 (2004). [CrossRef]  

10. L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008). [CrossRef]   [PubMed]  

11. L. Jauffred and L. B. Oddershede, “Two-photon quantum dot excitation during optical trapping,” Nano Lett. 10(5), 1927–1930 (2010). [CrossRef]   [PubMed]  

12. K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19(13), 930–932 (1994). [CrossRef]   [PubMed]  

13. P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005). [CrossRef]   [PubMed]  

14. L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008). [CrossRef]   [PubMed]  

15. C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sönnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8(9), 2998–3003 (2008). [CrossRef]   [PubMed]  

16. F. Hajizadeh and S. N. S. Reihani, “Optimized optical trapping of gold nanoparticles,” Opt. Express 18(2), 551–559 (2010). [CrossRef]   [PubMed]  

17. B. Agate, C. Brown, W. Sibbett, and K. Dholakia, “Femtosecond optical tweezers for in-situ control of two-photon fluorescence,” Opt. Express 12(13), 3011–3017 (2004). [CrossRef]   [PubMed]  

18. J. C. Shane, M. Mazilu, W. M. Lee, and K. Dholakia, “Effect of pulse temporal shape on optical trapping and impulse transfer using ultrashort pulsed lasers,” Opt. Express 18(7), 7554–7568 (2010). [CrossRef]   [PubMed]  

19. L. G. Wang and C. L. Zhao, “Dynamic radiation force of a pulsed gaussian beam acting on rayleigh dielectric sphere,” Opt. Express 15(17), 10615–10621 (2007). [CrossRef]   [PubMed]  

20. L. G. Wang and H. S. Chai, “Revisit on dynamic radiation forces induced by pulsed Gaussian beams,” Opt. Express 19(15), 14389–14402 (2011). [CrossRef]   [PubMed]  

21. A. K. De, D. Roy, B. Saha, and D. Goswami, “A simple method for constructing and calibrating an optical tweezer,” Curr. Sci. 95, 723–724 (2008).

22. A. K. De, D. Roy, and D. Goswami, “Towards stable trapping of single macromolecules in solution,” Proc SPIE Int Soc Opt Eng 7762, 776203 (2010). [CrossRef]   [PubMed]  

23. T.-H. Liu, W.-Y. Chiang, A. Usman, and H. Masuhara, “Optical trapping dynamics of a single polystyrene sphere: Continuous wave versus femtosecond lasers,” J. Phys. Chem. C 120(4), 2392–2399 (2016). [CrossRef]  

24. A. K. De, D. Roy, A. Dutta, and D. Goswami, “Stable optical trapping of latex nanoparticles with ultrashort pulsed illumination,” Appl. Opt. 48(31), G33–G37 (2009). [CrossRef]   [PubMed]  

25. A. K. De and D. Goswami, “Towards controlling molecular motions in fluorescence microscopy and optical trapping: a spatiotemporal approach,” Int. Rev. Phys. Chem. 30(3), 275–299 (2011). [CrossRef]   [PubMed]  

26. D. Roy, D. Goswami, and A. K. De, “Exploring the physics of efficient optical trapping of dielectric nanoparticles with ultrafast pulsed excitation,” Appl. Opt. 54(23), 7002–7006 (2015). [CrossRef]   [PubMed]  

27. Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996). [CrossRef]  

28. http://refractiveindex.info/

29. J. M. Weber, CRC Handbook of Optical Material, Vol. III (CRC Press, 2003).

30. M. Jahja, “On nonlinear optical constants of polystyrene,” International Symposium on Modern Optics and Its Applications-2011 (2011).

31. X. Y. Hu, Q. H. Gong, Y. H. Liu, B. Cheng, and D. Zhang, “All-optical switching of defect mode in two-dimensional nonlinear organic photonic crystals,” Appl. Phys. Lett. 87(23), 231111 (2005). [CrossRef]  

32. X. Y. Hu, P. Jiang, C. Y. Ding, H. Yang, and Q. H. Gong, “Picosecond and low power all-optical switching based on an organic photonic bandgap microcavity,” Nat. Photonics 2(3), 185–189 (2008). [CrossRef]  

33. K. Tanaka, “Optical nonlinearity in photonic glasses,” J. Mater. Sci. Mater. Electron. 16(10), 633–643 (2005). [CrossRef]  

34. R. Pobre and C. Saloma, “Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam,” Opt. Commun. 267(2), 295–304 (2006). [CrossRef]  

References

  • View by:

  1. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
    [Crossref] [PubMed]
  2. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
    [Crossref] [PubMed]
  3. A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-molecule biomechanics with optical methods,” Science 283(5408), 1689–1695 (1999).
    [Crossref] [PubMed]
  4. C. Bustamante, Y. R. Chemla, N. R. Forde, and D. Izhaky, “Mechanical processes in biochemistry,” Annu. Rev. Biochem. 73(1), 705–748 (2004).
    [Crossref] [PubMed]
  5. J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
    [Crossref] [PubMed]
  6. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288–290 (1986).
    [Crossref] [PubMed]
  7. A. Ashkin, Optical Trapping and Manipulation of Neutral Particles Using Lasers: A Reprint Volume with Commentaries (World Scientific, 2006).
  8. A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
    [Crossref] [PubMed]
  9. S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, “Optical trapping of single-walled carbon nanotubes,” Nano Lett. 4(8), 1415–1419 (2004).
    [Crossref]
  10. L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008).
    [Crossref] [PubMed]
  11. L. Jauffred and L. B. Oddershede, “Two-photon quantum dot excitation during optical trapping,” Nano Lett. 10(5), 1927–1930 (2010).
    [Crossref] [PubMed]
  12. K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19(13), 930–932 (1994).
    [Crossref] [PubMed]
  13. P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005).
    [Crossref] [PubMed]
  14. L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008).
    [Crossref] [PubMed]
  15. C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sönnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8(9), 2998–3003 (2008).
    [Crossref] [PubMed]
  16. F. Hajizadeh and S. N. S. Reihani, “Optimized optical trapping of gold nanoparticles,” Opt. Express 18(2), 551–559 (2010).
    [Crossref] [PubMed]
  17. B. Agate, C. Brown, W. Sibbett, and K. Dholakia, “Femtosecond optical tweezers for in-situ control of two-photon fluorescence,” Opt. Express 12(13), 3011–3017 (2004).
    [Crossref] [PubMed]
  18. J. C. Shane, M. Mazilu, W. M. Lee, and K. Dholakia, “Effect of pulse temporal shape on optical trapping and impulse transfer using ultrashort pulsed lasers,” Opt. Express 18(7), 7554–7568 (2010).
    [Crossref] [PubMed]
  19. L. G. Wang and C. L. Zhao, “Dynamic radiation force of a pulsed gaussian beam acting on rayleigh dielectric sphere,” Opt. Express 15(17), 10615–10621 (2007).
    [Crossref] [PubMed]
  20. L. G. Wang and H. S. Chai, “Revisit on dynamic radiation forces induced by pulsed Gaussian beams,” Opt. Express 19(15), 14389–14402 (2011).
    [Crossref] [PubMed]
  21. A. K. De, D. Roy, B. Saha, and D. Goswami, “A simple method for constructing and calibrating an optical tweezer,” Curr. Sci. 95, 723–724 (2008).
  22. A. K. De, D. Roy, and D. Goswami, “Towards stable trapping of single macromolecules in solution,” Proc SPIE Int Soc Opt Eng 7762, 776203 (2010).
    [Crossref] [PubMed]
  23. T.-H. Liu, W.-Y. Chiang, A. Usman, and H. Masuhara, “Optical trapping dynamics of a single polystyrene sphere: Continuous wave versus femtosecond lasers,” J. Phys. Chem. C 120(4), 2392–2399 (2016).
    [Crossref]
  24. A. K. De, D. Roy, A. Dutta, and D. Goswami, “Stable optical trapping of latex nanoparticles with ultrashort pulsed illumination,” Appl. Opt. 48(31), G33–G37 (2009).
    [Crossref] [PubMed]
  25. A. K. De and D. Goswami, “Towards controlling molecular motions in fluorescence microscopy and optical trapping: a spatiotemporal approach,” Int. Rev. Phys. Chem. 30(3), 275–299 (2011).
    [Crossref] [PubMed]
  26. D. Roy, D. Goswami, and A. K. De, “Exploring the physics of efficient optical trapping of dielectric nanoparticles with ultrafast pulsed excitation,” Appl. Opt. 54(23), 7002–7006 (2015).
    [Crossref] [PubMed]
  27. Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
    [Crossref]
  28. http://refractiveindex.info/
  29. J. M. Weber, CRC Handbook of Optical Material, Vol. III (CRC Press, 2003).
  30. M. Jahja, “On nonlinear optical constants of polystyrene,” International Symposium on Modern Optics and Its Applications-2011 (2011).
  31. X. Y. Hu, Q. H. Gong, Y. H. Liu, B. Cheng, and D. Zhang, “All-optical switching of defect mode in two-dimensional nonlinear organic photonic crystals,” Appl. Phys. Lett. 87(23), 231111 (2005).
    [Crossref]
  32. X. Y. Hu, P. Jiang, C. Y. Ding, H. Yang, and Q. H. Gong, “Picosecond and low power all-optical switching based on an organic photonic bandgap microcavity,” Nat. Photonics 2(3), 185–189 (2008).
    [Crossref]
  33. K. Tanaka, “Optical nonlinearity in photonic glasses,” J. Mater. Sci. Mater. Electron. 16(10), 633–643 (2005).
    [Crossref]
  34. R. Pobre and C. Saloma, “Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam,” Opt. Commun. 267(2), 295–304 (2006).
    [Crossref]

2016 (1)

T.-H. Liu, W.-Y. Chiang, A. Usman, and H. Masuhara, “Optical trapping dynamics of a single polystyrene sphere: Continuous wave versus femtosecond lasers,” J. Phys. Chem. C 120(4), 2392–2399 (2016).
[Crossref]

2015 (1)

2011 (2)

A. K. De and D. Goswami, “Towards controlling molecular motions in fluorescence microscopy and optical trapping: a spatiotemporal approach,” Int. Rev. Phys. Chem. 30(3), 275–299 (2011).
[Crossref] [PubMed]

L. G. Wang and H. S. Chai, “Revisit on dynamic radiation forces induced by pulsed Gaussian beams,” Opt. Express 19(15), 14389–14402 (2011).
[Crossref] [PubMed]

2010 (4)

J. C. Shane, M. Mazilu, W. M. Lee, and K. Dholakia, “Effect of pulse temporal shape on optical trapping and impulse transfer using ultrashort pulsed lasers,” Opt. Express 18(7), 7554–7568 (2010).
[Crossref] [PubMed]

A. K. De, D. Roy, and D. Goswami, “Towards stable trapping of single macromolecules in solution,” Proc SPIE Int Soc Opt Eng 7762, 776203 (2010).
[Crossref] [PubMed]

L. Jauffred and L. B. Oddershede, “Two-photon quantum dot excitation during optical trapping,” Nano Lett. 10(5), 1927–1930 (2010).
[Crossref] [PubMed]

F. Hajizadeh and S. N. S. Reihani, “Optimized optical trapping of gold nanoparticles,” Opt. Express 18(2), 551–559 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (6)

A. K. De, D. Roy, B. Saha, and D. Goswami, “A simple method for constructing and calibrating an optical tweezer,” Curr. Sci. 95, 723–724 (2008).

X. Y. Hu, P. Jiang, C. Y. Ding, H. Yang, and Q. H. Gong, “Picosecond and low power all-optical switching based on an organic photonic bandgap microcavity,” Nat. Photonics 2(3), 185–189 (2008).
[Crossref]

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008).
[Crossref] [PubMed]

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sönnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8(9), 2998–3003 (2008).
[Crossref] [PubMed]

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008).
[Crossref] [PubMed]

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (1)

R. Pobre and C. Saloma, “Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam,” Opt. Commun. 267(2), 295–304 (2006).
[Crossref]

2005 (3)

X. Y. Hu, Q. H. Gong, Y. H. Liu, B. Cheng, and D. Zhang, “All-optical switching of defect mode in two-dimensional nonlinear organic photonic crystals,” Appl. Phys. Lett. 87(23), 231111 (2005).
[Crossref]

K. Tanaka, “Optical nonlinearity in photonic glasses,” J. Mater. Sci. Mater. Electron. 16(10), 633–643 (2005).
[Crossref]

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005).
[Crossref] [PubMed]

2004 (4)

B. Agate, C. Brown, W. Sibbett, and K. Dholakia, “Femtosecond optical tweezers for in-situ control of two-photon fluorescence,” Opt. Express 12(13), 3011–3017 (2004).
[Crossref] [PubMed]

S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, “Optical trapping of single-walled carbon nanotubes,” Nano Lett. 4(8), 1415–1419 (2004).
[Crossref]

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[Crossref] [PubMed]

C. Bustamante, Y. R. Chemla, N. R. Forde, and D. Izhaky, “Mechanical processes in biochemistry,” Annu. Rev. Biochem. 73(1), 705–748 (2004).
[Crossref] [PubMed]

1999 (1)

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-molecule biomechanics with optical methods,” Science 283(5408), 1689–1695 (1999).
[Crossref] [PubMed]

1996 (1)

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[Crossref]

1994 (2)

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[Crossref] [PubMed]

K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19(13), 930–932 (1994).
[Crossref] [PubMed]

1987 (1)

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
[Crossref] [PubMed]

1986 (1)

Aabo, T.

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008).
[Crossref] [PubMed]

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008).
[Crossref] [PubMed]

Agate, B.

Asakura, T.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[Crossref]

Ashkin, A.

Bendix, P. M.

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008).
[Crossref] [PubMed]

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008).
[Crossref] [PubMed]

Bhatia, V. K.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005).
[Crossref] [PubMed]

Bjorkholm, J. E.

Block, S. M.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[Crossref] [PubMed]

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[Crossref] [PubMed]

K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19(13), 930–932 (1994).
[Crossref] [PubMed]

Bosanac, L.

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008).
[Crossref] [PubMed]

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008).
[Crossref] [PubMed]

Brown, C.

Bustamante, C.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

C. Bustamante, Y. R. Chemla, N. R. Forde, and D. Izhaky, “Mechanical processes in biochemistry,” Annu. Rev. Biochem. 73(1), 705–748 (2004).
[Crossref] [PubMed]

Cai, C. W.

S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, “Optical trapping of single-walled carbon nanotubes,” Nano Lett. 4(8), 1415–1419 (2004).
[Crossref]

Chai, H. S.

Chemla, Y. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

C. Bustamante, Y. R. Chemla, N. R. Forde, and D. Izhaky, “Mechanical processes in biochemistry,” Annu. Rev. Biochem. 73(1), 705–748 (2004).
[Crossref] [PubMed]

Cheng, B.

X. Y. Hu, Q. H. Gong, Y. H. Liu, B. Cheng, and D. Zhang, “All-optical switching of defect mode in two-dimensional nonlinear organic photonic crystals,” Appl. Phys. Lett. 87(23), 231111 (2005).
[Crossref]

Chiang, W.-Y.

T.-H. Liu, W.-Y. Chiang, A. Usman, and H. Masuhara, “Optical trapping dynamics of a single polystyrene sphere: Continuous wave versus femtosecond lasers,” J. Phys. Chem. C 120(4), 2392–2399 (2016).
[Crossref]

Chu, S.

De, A. K.

D. Roy, D. Goswami, and A. K. De, “Exploring the physics of efficient optical trapping of dielectric nanoparticles with ultrafast pulsed excitation,” Appl. Opt. 54(23), 7002–7006 (2015).
[Crossref] [PubMed]

A. K. De and D. Goswami, “Towards controlling molecular motions in fluorescence microscopy and optical trapping: a spatiotemporal approach,” Int. Rev. Phys. Chem. 30(3), 275–299 (2011).
[Crossref] [PubMed]

A. K. De, D. Roy, and D. Goswami, “Towards stable trapping of single macromolecules in solution,” Proc SPIE Int Soc Opt Eng 7762, 776203 (2010).
[Crossref] [PubMed]

A. K. De, D. Roy, A. Dutta, and D. Goswami, “Stable optical trapping of latex nanoparticles with ultrashort pulsed illumination,” Appl. Opt. 48(31), G33–G37 (2009).
[Crossref] [PubMed]

A. K. De, D. Roy, B. Saha, and D. Goswami, “A simple method for constructing and calibrating an optical tweezer,” Curr. Sci. 95, 723–724 (2008).

Dholakia, K.

Ding, C. Y.

X. Y. Hu, P. Jiang, C. Y. Ding, H. Yang, and Q. H. Gong, “Picosecond and low power all-optical switching based on an organic photonic bandgap microcavity,” Nat. Photonics 2(3), 185–189 (2008).
[Crossref]

Dutta, A.

Dziedzic, J. M.

Forde, N. R.

C. Bustamante, Y. R. Chemla, N. R. Forde, and D. Izhaky, “Mechanical processes in biochemistry,” Annu. Rev. Biochem. 73(1), 705–748 (2004).
[Crossref] [PubMed]

Gong, Q. H.

X. Y. Hu, P. Jiang, C. Y. Ding, H. Yang, and Q. H. Gong, “Picosecond and low power all-optical switching based on an organic photonic bandgap microcavity,” Nat. Photonics 2(3), 185–189 (2008).
[Crossref]

X. Y. Hu, Q. H. Gong, Y. H. Liu, B. Cheng, and D. Zhang, “All-optical switching of defect mode in two-dimensional nonlinear organic photonic crystals,” Appl. Phys. Lett. 87(23), 231111 (2005).
[Crossref]

Goswami, D.

D. Roy, D. Goswami, and A. K. De, “Exploring the physics of efficient optical trapping of dielectric nanoparticles with ultrafast pulsed excitation,” Appl. Opt. 54(23), 7002–7006 (2015).
[Crossref] [PubMed]

A. K. De and D. Goswami, “Towards controlling molecular motions in fluorescence microscopy and optical trapping: a spatiotemporal approach,” Int. Rev. Phys. Chem. 30(3), 275–299 (2011).
[Crossref] [PubMed]

A. K. De, D. Roy, and D. Goswami, “Towards stable trapping of single macromolecules in solution,” Proc SPIE Int Soc Opt Eng 7762, 776203 (2010).
[Crossref] [PubMed]

A. K. De, D. Roy, A. Dutta, and D. Goswami, “Stable optical trapping of latex nanoparticles with ultrashort pulsed illumination,” Appl. Opt. 48(31), G33–G37 (2009).
[Crossref] [PubMed]

A. K. De, D. Roy, B. Saha, and D. Goswami, “A simple method for constructing and calibrating an optical tweezer,” Curr. Sci. 95, 723–724 (2008).

Hajizadeh, F.

Hansen, P. M.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005).
[Crossref] [PubMed]

Harada, Y.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[Crossref]

Harrit, N.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005).
[Crossref] [PubMed]

Hu, X. Y.

X. Y. Hu, P. Jiang, C. Y. Ding, H. Yang, and Q. H. Gong, “Picosecond and low power all-optical switching based on an organic photonic bandgap microcavity,” Nat. Photonics 2(3), 185–189 (2008).
[Crossref]

X. Y. Hu, Q. H. Gong, Y. H. Liu, B. Cheng, and D. Zhang, “All-optical switching of defect mode in two-dimensional nonlinear organic photonic crystals,” Appl. Phys. Lett. 87(23), 231111 (2005).
[Crossref]

Izhaky, D.

C. Bustamante, Y. R. Chemla, N. R. Forde, and D. Izhaky, “Mechanical processes in biochemistry,” Annu. Rev. Biochem. 73(1), 705–748 (2004).
[Crossref] [PubMed]

Jahja, M.

M. Jahja, “On nonlinear optical constants of polystyrene,” International Symposium on Modern Optics and Its Applications-2011 (2011).

Jauffred, L.

L. Jauffred and L. B. Oddershede, “Two-photon quantum dot excitation during optical trapping,” Nano Lett. 10(5), 1927–1930 (2010).
[Crossref] [PubMed]

Jiang, P.

X. Y. Hu, P. Jiang, C. Y. Ding, H. Yang, and Q. H. Gong, “Picosecond and low power all-optical switching based on an organic photonic bandgap microcavity,” Nat. Photonics 2(3), 185–189 (2008).
[Crossref]

Lee, W. M.

Liu, T.-H.

T.-H. Liu, W.-Y. Chiang, A. Usman, and H. Masuhara, “Optical trapping dynamics of a single polystyrene sphere: Continuous wave versus femtosecond lasers,” J. Phys. Chem. C 120(4), 2392–2399 (2016).
[Crossref]

Liu, Y. H.

X. Y. Hu, Q. H. Gong, Y. H. Liu, B. Cheng, and D. Zhang, “All-optical switching of defect mode in two-dimensional nonlinear organic photonic crystals,” Appl. Phys. Lett. 87(23), 231111 (2005).
[Crossref]

Lopez, H. A.

S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, “Optical trapping of single-walled carbon nanotubes,” Nano Lett. 4(8), 1415–1419 (2004).
[Crossref]

Masuhara, H.

T.-H. Liu, W.-Y. Chiang, A. Usman, and H. Masuhara, “Optical trapping dynamics of a single polystyrene sphere: Continuous wave versus femtosecond lasers,” J. Phys. Chem. C 120(4), 2392–2399 (2016).
[Crossref]

Mazilu, M.

Mehta, A. D.

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-molecule biomechanics with optical methods,” Science 283(5408), 1689–1695 (1999).
[Crossref] [PubMed]

Moffitt, J. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Neuman, K. C.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[Crossref] [PubMed]

Oddershede, L.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005).
[Crossref] [PubMed]

Oddershede, L. B.

L. Jauffred and L. B. Oddershede, “Two-photon quantum dot excitation during optical trapping,” Nano Lett. 10(5), 1927–1930 (2010).
[Crossref] [PubMed]

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008).
[Crossref] [PubMed]

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008).
[Crossref] [PubMed]

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sönnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8(9), 2998–3003 (2008).
[Crossref] [PubMed]

Pobre, R.

R. Pobre and C. Saloma, “Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam,” Opt. Commun. 267(2), 295–304 (2006).
[Crossref]

Reihani, S. N. S.

Rief, M.

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-molecule biomechanics with optical methods,” Science 283(5408), 1689–1695 (1999).
[Crossref] [PubMed]

Roy, D.

D. Roy, D. Goswami, and A. K. De, “Exploring the physics of efficient optical trapping of dielectric nanoparticles with ultrafast pulsed excitation,” Appl. Opt. 54(23), 7002–7006 (2015).
[Crossref] [PubMed]

A. K. De, D. Roy, and D. Goswami, “Towards stable trapping of single macromolecules in solution,” Proc SPIE Int Soc Opt Eng 7762, 776203 (2010).
[Crossref] [PubMed]

A. K. De, D. Roy, A. Dutta, and D. Goswami, “Stable optical trapping of latex nanoparticles with ultrashort pulsed illumination,” Appl. Opt. 48(31), G33–G37 (2009).
[Crossref] [PubMed]

A. K. De, D. Roy, B. Saha, and D. Goswami, “A simple method for constructing and calibrating an optical tweezer,” Curr. Sci. 95, 723–724 (2008).

Saha, B.

A. K. De, D. Roy, B. Saha, and D. Goswami, “A simple method for constructing and calibrating an optical tweezer,” Curr. Sci. 95, 723–724 (2008).

Saloma, C.

R. Pobre and C. Saloma, “Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam,” Opt. Commun. 267(2), 295–304 (2006).
[Crossref]

Schubert, O.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sönnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8(9), 2998–3003 (2008).
[Crossref] [PubMed]

Selhuber-Unkel, C.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sönnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8(9), 2998–3003 (2008).
[Crossref] [PubMed]

Shane, J. C.

Sibbett, W.

Simmons, R. M.

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-molecule biomechanics with optical methods,” Science 283(5408), 1689–1695 (1999).
[Crossref] [PubMed]

Smith, D. A.

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-molecule biomechanics with optical methods,” Science 283(5408), 1689–1695 (1999).
[Crossref] [PubMed]

Smith, S. B.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Sönnichsen, C.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sönnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8(9), 2998–3003 (2008).
[Crossref] [PubMed]

Spudich, J. A.

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-molecule biomechanics with optical methods,” Science 283(5408), 1689–1695 (1999).
[Crossref] [PubMed]

Svoboda, K.

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[Crossref] [PubMed]

K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19(13), 930–932 (1994).
[Crossref] [PubMed]

Tan, S.

S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, “Optical trapping of single-walled carbon nanotubes,” Nano Lett. 4(8), 1415–1419 (2004).
[Crossref]

Tanaka, K.

K. Tanaka, “Optical nonlinearity in photonic glasses,” J. Mater. Sci. Mater. Electron. 16(10), 633–643 (2005).
[Crossref]

Usman, A.

T.-H. Liu, W.-Y. Chiang, A. Usman, and H. Masuhara, “Optical trapping dynamics of a single polystyrene sphere: Continuous wave versus femtosecond lasers,” J. Phys. Chem. C 120(4), 2392–2399 (2016).
[Crossref]

Wang, L. G.

Yang, H.

X. Y. Hu, P. Jiang, C. Y. Ding, H. Yang, and Q. H. Gong, “Picosecond and low power all-optical switching based on an organic photonic bandgap microcavity,” Nat. Photonics 2(3), 185–189 (2008).
[Crossref]

Zhang, D.

X. Y. Hu, Q. H. Gong, Y. H. Liu, B. Cheng, and D. Zhang, “All-optical switching of defect mode in two-dimensional nonlinear organic photonic crystals,” Appl. Phys. Lett. 87(23), 231111 (2005).
[Crossref]

Zhang, Y.

S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, “Optical trapping of single-walled carbon nanotubes,” Nano Lett. 4(8), 1415–1419 (2004).
[Crossref]

Zhao, C. L.

Zins, I.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sönnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8(9), 2998–3003 (2008).
[Crossref] [PubMed]

Annu. Rev. Biochem. (2)

C. Bustamante, Y. R. Chemla, N. R. Forde, and D. Izhaky, “Mechanical processes in biochemistry,” Annu. Rev. Biochem. 73(1), 705–748 (2004).
[Crossref] [PubMed]

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Annu. Rev. Biophys. Biomol. Struct. (1)

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

X. Y. Hu, Q. H. Gong, Y. H. Liu, B. Cheng, and D. Zhang, “All-optical switching of defect mode in two-dimensional nonlinear organic photonic crystals,” Appl. Phys. Lett. 87(23), 231111 (2005).
[Crossref]

Curr. Sci. (1)

A. K. De, D. Roy, B. Saha, and D. Goswami, “A simple method for constructing and calibrating an optical tweezer,” Curr. Sci. 95, 723–724 (2008).

Int. Rev. Phys. Chem. (1)

A. K. De and D. Goswami, “Towards controlling molecular motions in fluorescence microscopy and optical trapping: a spatiotemporal approach,” Int. Rev. Phys. Chem. 30(3), 275–299 (2011).
[Crossref] [PubMed]

J. Mater. Sci. Mater. Electron. (1)

K. Tanaka, “Optical nonlinearity in photonic glasses,” J. Mater. Sci. Mater. Electron. 16(10), 633–643 (2005).
[Crossref]

J. Phys. Chem. C (1)

T.-H. Liu, W.-Y. Chiang, A. Usman, and H. Masuhara, “Optical trapping dynamics of a single polystyrene sphere: Continuous wave versus femtosecond lasers,” J. Phys. Chem. C 120(4), 2392–2399 (2016).
[Crossref]

Nano Lett. (6)

S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, “Optical trapping of single-walled carbon nanotubes,” Nano Lett. 4(8), 1415–1419 (2004).
[Crossref]

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008).
[Crossref] [PubMed]

L. Jauffred and L. B. Oddershede, “Two-photon quantum dot excitation during optical trapping,” Nano Lett. 10(5), 1927–1930 (2010).
[Crossref] [PubMed]

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005).
[Crossref] [PubMed]

L. Bosanac, T. Aabo, P. M. Bendix, and L. B. Oddershede, “Efficient optical trapping and visualization of silver nanoparticles,” Nano Lett. 8(5), 1486–1491 (2008).
[Crossref] [PubMed]

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sönnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8(9), 2998–3003 (2008).
[Crossref] [PubMed]

Nat. Photonics (1)

X. Y. Hu, P. Jiang, C. Y. Ding, H. Yang, and Q. H. Gong, “Picosecond and low power all-optical switching based on an organic photonic bandgap microcavity,” Nat. Photonics 2(3), 185–189 (2008).
[Crossref]

Opt. Commun. (2)

R. Pobre and C. Saloma, “Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam,” Opt. Commun. 267(2), 295–304 (2006).
[Crossref]

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Proc SPIE Int Soc Opt Eng (1)

A. K. De, D. Roy, and D. Goswami, “Towards stable trapping of single macromolecules in solution,” Proc SPIE Int Soc Opt Eng 7762, 776203 (2010).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[Crossref] [PubMed]

Science (2)

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
[Crossref] [PubMed]

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-molecule biomechanics with optical methods,” Science 283(5408), 1689–1695 (1999).
[Crossref] [PubMed]

Other (4)

A. Ashkin, Optical Trapping and Manipulation of Neutral Particles Using Lasers: A Reprint Volume with Commentaries (World Scientific, 2006).

http://refractiveindex.info/

J. M. Weber, CRC Handbook of Optical Material, Vol. III (CRC Press, 2003).

M. Jahja, “On nonlinear optical constants of polystyrene,” International Symposium on Modern Optics and Its Applications-2011 (2011).

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1 Plots of trapping force along radial direction at 100mW average power under CW and pulsed excitation ignoring and including Kerr effect.
Fig. 2
Fig. 2 Plots of trapping potential along radial direction at 100mW average power under CW and pulsed excitation ignoring and including Kerr effect.
Fig. 3
Fig. 3 Plots of trapping force along axial direction at 100mW average power under CW and pulsed excitation ignoring and including Kerr effect. The blue lines correspond to scattering force, the green to gradient force and the red to total force.
Fig. 4
Fig. 4 Plots of trapping potential along axial direction at 100mW average power under CW and pulsed excitation ignoring and including Kerr effect. The blue lines correspond to scattering potential, the green to gradient potential and the red to total potential.
Fig. 5
Fig. 5 Plots of trapping force along axial direction at different average power levels. The blue lines correspond to scattering force, the green to gradient force and the red to total force.
Fig. 6
Fig. 6 Plots of trapping potential along axial direction at different average power levels. The blue lines correspond to scattering potential, the green to gradient potential and the red to total potential.
Fig. 7
Fig. 7 Plots of absolute depth of the trapping potential (left) and escape potential (right) along axial direction at different average power levels.
Fig. 8
Fig. 8 Plots of position of the minima for absolute trapping potential along axial direction (Left) and the gradient and the scattering potential (green and blue lines, respectively) corresponding to this minima (Middle) at different average power levels. Right: Plots of the absolute depth of the trapping potential and the asymptotic scattering potential (red and blue lines, respectively) for the same.
Fig. 9
Fig. 9 Plots of escape potential with NA = 1.3, 1.4 and 1.45 (black, red and grey lines respectively) at different average power levels.
Fig. 10
Fig. 10 Left: Plots of escape potential on an 80nm particle (red line) and on a 70nm particle (black line) at different average power levels. Right: The same for a 100nm particle.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

I ( r , z ) = ( 2 P π w 0 2 ) 1 1 + ( 2 z ˜ ) 2 exp [ 2 r ˜ 2 1 + ( 2 z ˜ ) 2 ]
F r a d i a l ( r ;   z = 0 ) =   2 π n w a 3 c ( m 2 1 m 2 + 2 ) 4 r ˜ w 0 ( P π w 0 2 ) exp [ 2 ( r ˜ 2 ) ] F a x i a l , g r a d i e n t ( z ;   r = 0 ) =   2 π n w a 3 c ( m 2 1 m 2 + 2 ) 8 z ˜ / ( k w 0 2 ) 1 + ( 2 z ˜ ) 2 ( 2 P π w 0 2 ) 1 1 + ( 2 z ˜ ) 2 F a x i a l ,     s c a t t e r ( z ;   r = 0 ) =   8 π n w ( k a ) 4 a 2 3 c ( m 2 1 m 2 + 2 ) 2 ( 2 P π w 0 2 ) 1 1 + ( 2 z ˜ ) 2
U r a d i a l ( r ;   z = 0 ) =   F r a d i a l ( r ;   z = 0 ) d r U a x i a l , g r a d i e n t / s c a t t e r ( z ;   r = 0 ) =   F a x i a l , g r a d i e n t / s c a t t e r ( z ;   r = 0 ) d z
P p e a k P a v e r a g e I p e a k I a v e r a g e = 1 f * τ 10 5
n w / p = n 0 w / p +   n 2 w / p * I ( r , z )
F p u l s e d = 1 T τ 2 τ 2 F p u l s e d d t = F p u l s e d 1 T τ 2 τ 2 d t = F p u l s e d * ( 1 T * τ ) = F p u l s e d * ( f * τ )
F p u l s e d = c o n s t a n t * I p e a k * ( f * τ ) = c o n s t a n t * I a v e r a g e F C W
F p u l s e d F C W

Metrics

Select as filters


Select Topics Cancel
© Copyright 2022 | Optica Publishing Group. All Rights Reserved