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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 16 — Aug. 1, 2011
  • pp: 14794–14800
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The effect of immersion oil in optical tweezers

Ali Mahmoudi and S. Nader S. Reihani  »View Author Affiliations


Optics Express, Vol. 19, Issue 16, pp. 14794-14800 (2011)
http://dx.doi.org/10.1364/OE.19.014794


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Abstract

Optimized optical tweezers are of great importance for biological micromanipulation. In this paper, we present a detailed electromagnetic-based calculation of the spatial intensity distribution for a laser beam focused through a high numerical aperture objective when there are several discontinuities in the optical pathway of the system. For a common case of 3 interfaces we have shown that 0.01 increase in the refractive index of the immersion medium would shift the optimal trapping depth by 3–4μm (0.2–0.6μm) for aqueous (air) medium. For the first time, We have shown that the alteration of the refractive index of the immersion medium can be also used in aerosol trapping provided that larger increase in the refractive index is considered.

© 2011 OSA

1. Introduction

Optical Tweezers are widely used as non-invasive micromanipulation tools in many scientific areas, from biology [1

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

4

4. T. M. Hansen, S. N. S. Reihani, L. B. Oddershede, and M. A. Sørensen, “Correlation between mechanical strength of messenger RNA pseudoknots and ribosomal frameshifting,” Proc. Natl. Acad. Sci. U.S.A. 104, 5830–5835 (2007). [CrossRef] [PubMed]

] to nanotechnology [5

5. R. Agarwal, K. Ladavac, Y. Roichman, G. Yu, C. M. Lieber, and D. G. Grier, “Manipulation and assembly of nanowires with holographic optical traps,” Opt. Express 13, 8906–8912 (2005). [CrossRef] [PubMed]

8

8. Y. Seol, A. E. Carpenter, and T. T. Perkins, “Gold nanoparticles: enhanced optical trapping and sensitivity coupled with significant heating,” Opt. Lett. 31, 2429–2431(2006). [CrossRef] [PubMed]

]. Typical Optical tweezers (OT) consist of a Gaussian laser beam tightly focused through a high Numerical Aperture (NA) objective lens producing a 3-D intensity gradient at the focus. An object with the refractive index greater than that of the surrounding medium experiences a Hookean restoring force toward the focus [1

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

] for which the strength of the trap can be regarded as the spring constant. A micron (and nano)-sized sphere trapped by OT is widely used as a handle of a non-contact micromanipulator. Nanometer spatial resolution along with sub-Megahertz temporal resolution have turned OT to a widely desired tool in many scientific areas. OT are normally implemented into an optical microscope in order to visualize the specimen under manipulation. Oil immersion objective lenses are commonly used for OT-based micromanipulation due to their high NA which provides stronger trap along with more detailed visualization of the sample. A significant problem of using oil immersion objectives is the Spherical Abberation (SA) induced by the refractive index mismatch between the immersion (oil) and sample (water) media. It is well known that the SA dramatically increases as the trapping (and visualization) depth increases which limits the trapping depth range. For example, a 1μm polystyrene bead can only be trapped up to depth of ∼ 10μm. The situation becomes even worse when trapping of nanoparticles is on demand. Therefore, finding a method for optimized nanoparticle trapping deep inside the sample chamber would be of great interest for in-depth micromanipulation. Different methods are proposed [9

9. S. N. S. Reihani and L. B. Oddershede, “Optimizing immersion media refractive index improves optical trapping by compensating spherical aberrations,” Opt. Lett. 32, 1998–2000 (2007). [CrossRef] [PubMed]

13

13. T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010). [CrossRef]

] to compensate for the SA introduced by oil immersion objectives among which the changing the refractive index of the immersion medium [9

9. S. N. S. Reihani and L. B. Oddershede, “Optimizing immersion media refractive index improves optical trapping by compensating spherical aberrations,” Opt. Lett. 32, 1998–2000 (2007). [CrossRef] [PubMed]

] seems to be more feasible. Reihani et al. has shown that, first, for an immersion oil with a given refractive index, there would be a depth (so-called optimal depth) at which the stiffest trap occurs, second, by increasing the Refractive Index of the Immersion Medium (RIIM) the optimal depth shifts toward the deeper positions. In this letter, we present a detailed electromagnetic-based calculation of the intensity profile around the focus of the objective as well as the restoring force of the optical trap in presence of several refractive index discontinuities in the optical pathway of typical OT. Considering the case of 3 interfaces (very common case in OT applications), we have theoretically confirmed that for trapping inside water, 0.01 increase in RIIM would shift the optimal trapping depth by 3 – 4μm which is in very good agreement with the previously reported experimental results [9

9. S. N. S. Reihani and L. B. Oddershede, “Optimizing immersion media refractive index improves optical trapping by compensating spherical aberrations,” Opt. Lett. 32, 1998–2000 (2007). [CrossRef] [PubMed]

]. We also have shown that for the case of trapping in air, 0.01 increase in RIIM would shift the optimal trapping depth only by 0.2 – 0.6μm which implies that the alteration of the RIIM can also be used for aerosol trapping, provided that larger increase in the RIIM is considered. For example, we have shown that an immersion medium with refractive index of 2.11 would provide the optimal depth of ∼ 36μm which could be of great interest for aerosol trapping community.

2. Calculation of optimal RIIM for OT

Fig. 1 The optical pathway of a typical ray. The dotted line defines the optical path of the ray as if there is no refractive index mismatch in the optical pathway. The solid line represents the path of the same ray when nim > ng = nobjective > ns. Δz defines the shift of the ray in the axial direction.

2.1. Trapping in water

Trapping inside an aqueous medium using an oil immersion objective is very common in OT applications for which ns = 1.33, and nim = 1.518. Figure 2 shows the resulted axial (Fig. (2a)) and typical lateral (Fig. (2c)) intensity profiles produced by an oil immersion objective (NA=1.3, working distance=200μm) through a coverglass of 170μm thick. Note that the lateral intensity profile varies at different depths. The calculated average intensity gradients acting on a 1μm polystyrene bead trapped in such intensity profiles are shown in Figs. 2(b) and 2(d), for the lateral and axial directions, respectively.

Fig. 2 Trapping inside water: intensity distribution in the axial (a) and lateral (c) directions for different immersion oils. Calculated axial (b) and lateral (d) Average Intensity Gradient (AIG) for a 1μm dielectric microsphere trapped using an objective with NA=1.3 and working distance of 200μm. The electric field beam waist of the incident laser beam was considered to be w 0 = 3mm.

Table 1. The Effect of the RIIM (nim) on the Axial and Lateral Trap Inside Water1,2

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Table 1 implies that 0.01 increment in nim results in 3 – 4μm shift for the depth at which the optimal axial trap occurs. This is in very good agreement with the previously reported experimental results [9

9. S. N. S. Reihani and L. B. Oddershede, “Optimizing immersion media refractive index improves optical trapping by compensating spherical aberrations,” Opt. Lett. 32, 1998–2000 (2007). [CrossRef] [PubMed]

]. For the lateral direction, our results suggest 3.5 – 4.2μm shift for the depth at which the optimal lateral trap occurs. Note that due to the refractive index mismatch, the real focus of the laser differs from the probe depth which is defined as the distance traveled by the objective. This calculation would be of great importance when the exact position of the trap inside the sample or the distance from the chamber wall is required.

2.2. Trapping in air

Optical tweezers have also been widely used for aerosol trapping [21

21. M. Guillon, K. Dholakia, and D. McGloin, “Optical trapping and spectral analysis of aerosols with a supercontiuum laser source,” Opt. Express 16, 7655–7664 (2008). [CrossRef] [PubMed]

]. For this case, same calculations can be repeated using m = 4 and nsample = 1 to find the optimal conditions for aerosol trapping. It is worth mentioning that the total internal reflection may limit the effective NA of the system. For example, in the case of trapping inside water, the upper limit for effective NA would be 1.33 while for the case of aerosol trapping it can not exceed 1 due to the total internal reflection at the glass-air interface. Figure 3 shows typical axial (Fig. (3a)) and lateral (Fig. (3c)) intensity distributions as well as the calculated average intensity gradient in both axial (Fig. (3b)) and lateral (Fig. (3d)) directions.

Fig. 3 Trapping in air: intensity distribution in the axial (a) and lateral (c) directions for different immersion oils. Calculated axial (b) and lateral (d) Average Intensity Gradient (AIG) for a 1μm dielectric microsphere trapped using an objective with effective numerical aperture of 1 and working distance of 200μm. The electric field beam waist of the incident laser beam was considered to be w 0 = 3mm.

Figure 3 shows that: (1) The maximum of the intensity graphs is considerably lower compared to the case of trapping in water. This is mainly due to the decreased transmission coefficient for the current case. (2) The intensity distributions are wider compared to the water case. These considerations explains why the restoring force of the trap both in the axial (Fig. (3b)) and lateral (Fig. (3d)) directions is considerably lower compared to the water case. Considering the larger refractive index contrast when the object is trapped in air (compared to water) and the fact that the trapped object would has larger wiggling due to the lower viscosity of the air (compared to water), it can be explained that why trapping in air is always harder than in water. Table 2 quantitatively summarizes the results for trapping in air using an objective with effective NA of 1.

Table 2. The Effect of the RIIM (nim) on the Axial and Lateral Trap in Air1,2

table-icon
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From Table 2 it can be deduced that 0.01 increment in nim shifts the optimal depth for the axial (lateral) trap by 0.2 – 0.6μm (0.4 – 0.6μm). Note that the shift is very small compared to the case of trapping in water. Therefore, changing the refraction index of the immersion medium may not be very helpful for aerosol trapping unless a considerably larger increase in nim is considered. As an example, the axial intensity distribution as well as the axial AIG for the immersion medium with nim = 2.11 is shown in Fig. 4. Note that the optimal depth is shifted to d = 36μm using nim = 2.11 which could be of great importance for aerosol trapping applications.

Fig. 4 The axial intensity distribution (a) and AIG (b) for a 1μm dielectric sphere trapped using an objective with NA=1 and nim = 2.11. It is worth mentioning that the transmission coefficient for this case is reduced by %51 compared to the case of nim = 1.518.

3. Conclusion

References and links

1.

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

2.

C. Bustamante, Z. Bryant, and S. B. Smith, “Ten years of tension: single-molecule DNA mechanics,” Nature 421, 423–427 (2003). [CrossRef] [PubMed]

3.

S. M. Block, D. F. Blair, and H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature 338, 514–518 (1989). [CrossRef] [PubMed]

4.

T. M. Hansen, S. N. S. Reihani, L. B. Oddershede, and M. A. Sørensen, “Correlation between mechanical strength of messenger RNA pseudoknots and ribosomal frameshifting,” Proc. Natl. Acad. Sci. U.S.A. 104, 5830–5835 (2007). [CrossRef] [PubMed]

5.

R. Agarwal, K. Ladavac, Y. Roichman, G. Yu, C. M. Lieber, and D. G. Grier, “Manipulation and assembly of nanowires with holographic optical traps,” Opt. Express 13, 8906–8912 (2005). [CrossRef] [PubMed]

6.

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

7.

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]

8.

Y. Seol, A. E. Carpenter, and T. T. Perkins, “Gold nanoparticles: enhanced optical trapping and sensitivity coupled with significant heating,” Opt. Lett. 31, 2429–2431(2006). [CrossRef] [PubMed]

9.

S. N. S. Reihani and L. B. Oddershede, “Optimizing immersion media refractive index improves optical trapping by compensating spherical aberrations,” Opt. Lett. 32, 1998–2000 (2007). [CrossRef] [PubMed]

10.

P. C. Ke and M. Gu, “Characterization of trapping force in the presence of spherical aberration,” J. Mod. Opt. 45, 2159–2168 (1998). [CrossRef]

11.

S. N. S. Reihani, H. R. Khalesifard, and R. Golestanian, “Measuring lateral efficiency of optical traps: the effect of tube length,” Opt. Commun. 259, 204–211 (2006). [CrossRef]

12.

E. Theofanidou, L. Wilson, W. J. Hossack, and J. Arlt, “Spherical aberration correction for optical tweezers,” Opt. Commun. 236, 145–150 (2004). [CrossRef]

13.

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010). [CrossRef]

14.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959). [CrossRef]

15.

P. Török, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A , 12, 325–332 (1995). [CrossRef]

16.

A. Rohrbach, “Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95, 168102 (2005). [CrossRef] [PubMed]

17.

A. Rohrbach and E. H. K. Stelzer, “Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations,” Appl. Opt. 41, 2494–2507 (2002). [CrossRef] [PubMed]

18.

V. Wong and M. A. Ratner, “Size dependence of gradient and nongradient optical forces in silver nanoparticles,” J. Opt. Soc. Am. B 24, 106–112 (2007). [CrossRef]

19.

A. Samadi and N. S. Reihani, “Optimal beam diameter for optical tweezers,” Opt. Lett. 35, 1494–1496 (2010). [CrossRef] [PubMed]

20.

A. Mahmoudi and S. N. S. Reihani, “Phase contrast optical tweezers,” Opt. Express 18, 17983–17996 (2010). [CrossRef] [PubMed]

21.

M. Guillon, K. Dholakia, and D. McGloin, “Optical trapping and spectral analysis of aerosols with a supercontiuum laser source,” Opt. Express 16, 7655–7664 (2008). [CrossRef] [PubMed]

OCIS Codes
(140.7010) Lasers and laser optics : Laser trapping
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(220.1000) Optical design and fabrication : Aberration compensation
(350.4855) Other areas of optics : Optical tweezers or optical manipulation

ToC Category:
Optical Trapping and Manipulation

History
Original Manuscript: April 4, 2011
Revised Manuscript: May 15, 2011
Manuscript Accepted: May 15, 2011
Published: July 18, 2011

Virtual Issues
Vol. 6, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Ali Mahmoudi and S. Nader S. Reihani, "The effect of immersion oil in optical tweezers," Opt. Express 19, 14794-14800 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-16-14794


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References

  1. A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987). [CrossRef] [PubMed]
  2. C. Bustamante, Z. Bryant, and S. B. Smith, “Ten years of tension: single-molecule DNA mechanics,” Nature 421, 423–427 (2003). [CrossRef] [PubMed]
  3. S. M. Block, D. F. Blair, and H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature 338, 514–518 (1989). [CrossRef] [PubMed]
  4. T. M. Hansen, S. N. S. Reihani, L. B. Oddershede, and M. A. Sørensen, “Correlation between mechanical strength of messenger RNA pseudoknots and ribosomal frameshifting,” Proc. Natl. Acad. Sci. U.S.A. 104, 5830–5835 (2007). [CrossRef] [PubMed]
  5. R. Agarwal, K. Ladavac, Y. Roichman, G. Yu, C. M. Lieber, and D. G. Grier, “Manipulation and assembly of nanowires with holographic optical traps,” Opt. Express 13, 8906–8912 (2005). [CrossRef] [PubMed]
  6. S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, “Optical trapping of single-walled carbon nanotubes,” Nano Lett. 4, 1415–1419 (2004). [CrossRef]
  7. 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]
  8. Y. Seol, A. E. Carpenter, and T. T. Perkins, “Gold nanoparticles: enhanced optical trapping and sensitivity coupled with significant heating,” Opt. Lett. 31, 2429–2431(2006). [CrossRef] [PubMed]
  9. S. N. S. Reihani and L. B. Oddershede, “Optimizing immersion media refractive index improves optical trapping by compensating spherical aberrations,” Opt. Lett. 32, 1998–2000 (2007). [CrossRef] [PubMed]
  10. P. C. Ke and M. Gu, “Characterization of trapping force in the presence of spherical aberration,” J. Mod. Opt. 45, 2159–2168 (1998). [CrossRef]
  11. S. N. S. Reihani, H. R. Khalesifard, and R. Golestanian, “Measuring lateral efficiency of optical traps: the effect of tube length,” Opt. Commun. 259, 204–211 (2006). [CrossRef]
  12. E. Theofanidou, L. Wilson, W. J. Hossack, and J. Arlt, “Spherical aberration correction for optical tweezers,” Opt. Commun. 236, 145–150 (2004). [CrossRef]
  13. T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010). [CrossRef]
  14. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959). [CrossRef]
  15. P. Török, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A , 12, 325–332 (1995). [CrossRef]
  16. A. Rohrbach, “Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95, 168102 (2005). [CrossRef] [PubMed]
  17. A. Rohrbach and E. H. K. Stelzer, “Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations,” Appl. Opt. 41, 2494–2507 (2002). [CrossRef] [PubMed]
  18. V. Wong and M. A. Ratner, “Size dependence of gradient and nongradient optical forces in silver nanoparticles,” J. Opt. Soc. Am. B 24, 106–112 (2007). [CrossRef]
  19. A. Samadi and N. S. Reihani, “Optimal beam diameter for optical tweezers,” Opt. Lett. 35, 1494–1496 (2010). [CrossRef] [PubMed]
  20. A. Mahmoudi and S. N. S. Reihani, “Phase contrast optical tweezers,” Opt. Express 18, 17983–17996 (2010). [CrossRef] [PubMed]
  21. M. Guillon, K. Dholakia, and D. McGloin, “Optical trapping and spectral analysis of aerosols with a supercontiuum laser source,” Opt. Express 16, 7655–7664 (2008). [CrossRef] [PubMed]

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