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.

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [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]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2010

2008

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]

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]

2007

2006

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]

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]

2005

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

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]

2004

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]

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

2003

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

2002

1998

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

1995

1989

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]

1987

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

1959

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]

Agarwal, R.

Arlt, J.

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

Ashkin, A.

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

Berg, H. C.

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]

Blair, D. F.

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]

Block, S. M.

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]

Booker, G. R.

Bryant, Z.

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

Bustamante, C.

C. Bustamante, Z. Bryant, and S. B. Smith, “Ten years of tension: single-molecule DNA mechanics,” Nature 421, 423–427 (2003).
[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, 1415–1419 (2004).
[CrossRef]

Carpenter, A. E.

Cižmár, T.

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

Dholakia, K.

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

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]

Dziedzic, J. M.

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

Golestanian, R.

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]

Grier, D. G.

Gu, M.

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

Guillon, M.

Hansen, T. M.

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]

Hossack, W. J.

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

Ke, P. C.

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

Khalesifard, H. R.

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]

Laczik, Z.

Ladavac, K.

Lieber, C. M.

Lopez, H. A.

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]

Mahmoudi, A.

Mazilu, M.

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

McGloin, D.

Oddershede, L. B.

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]

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]

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]

Perkins, T. T.

Ratner, M. A.

Reihani, N. S.

Reihani, S. N. S.

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

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]

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]

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]

Richards, B.

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]

Rohrbach, A.

Roichman, Y.

Samadi, A.

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]

Seol, Y.

Smith, S. B.

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

Sørensen, M. A.

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]

Stelzer, E. H. K.

Tan, S.

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]

Theofanidou, E.

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

Török, P.

Varga, P.

Wilson, L.

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

Wolf, E.

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]

Wong, V.

Yu, G.

Zhang, Y.

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]

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]

Appl. Opt.

J. Mod. Opt.

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

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nano Lett.

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]

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

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

Nature

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

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]

Opt. Commun.

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]

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

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

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

Proc. Natl. Acad. Sci. U.S.A.

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]

Proc. R. Soc. London Ser. A

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]

Science

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

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Figures (4)

Fig. 1
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.

Fig. 2
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.

Fig. 3
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.

Fig. 4
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.

Tables (2)

Tables Icon

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

Tables Icon

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

Equations (3)

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

E ( P ) = ik 2 π Ω a ( s x , s y ) s z exp ( ik [ Φ ( s x , s y ) + s ^ . r P ] ) d s 1 x d s 1 y
E 2 ( x , y , z I ) = i k 1 2 π Ω T 1 2 W e ( s ^ 1 ) exp ( i k 1 ( s 1 x x + s 1 y y s 1 z z I ) ) d s 1 x d s 1 y
E m ( x , y , z ) = i k 1 f 2 π E 0 n 1 n 2 0 α 0 2 π E sample s 1 z exp ( i k 0 [ n 1 ( t 2 + t 3 + ... + t m ) cos ϕ 1 n 2 t 2 cos ϕ 2 ... n m t m cos ϕ m ] ) exp [ i n m k 0 z cos ϕ m ] exp [ i n 1 k 0 sin ϕ 1 ( x cos θ + y sin θ ) ] sin ϕ 1 cos ϕ 1 1 / 2 d θ d ϕ 1

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