Abstract

Novel fluorescence microscopy techniques and two-color laser direct imaging photolithography methods that enable resolution an order of magnitude beyond the diffraction limit require Laguerre–Gaussian beams and a fast and precise laser beam steering device to obtain images and produce microstructures. An acousto-optic deflector (AOD) is a suitable choice and provides high-speed random access beam positioning with subnanometer precision as well as beam intensity control in a single element. In high-resolution applications, the impact of an AOD on beam quality plays a major role. We study the transfer function of an AOD for a fundamental Gaussian and a doughnut-shaped Laguerre–Gaussian beam by measuring the beam quality as a function of the diffraction angle after passing through the device. It is demonstrated that an AOD introduces negligible distortion and degradation to the beam profile and is therefore highly suitable for use in super-resolution imaging and photolithography techniques where manipulation of Laguerre–Gaussian doughnut-shaped beams is required.

© 2013 Optical Society of America

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References

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  1. E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
    [CrossRef]
  2. E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. mikrosk. Anat. Entwichlungsmech. 9, 413–468 (1873).
  3. S. W. Hell, “Toward fluorescence nanoscopy,” Nat. Biotechnol. 21, 1347–1355 (2003).
    [CrossRef]
  4. S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6, 24–32 (2009).
    [CrossRef]
  5. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780–782 (1994).
    [CrossRef]
  6. B. Harke, J. Keller, C. K. Ullal, V. Westphal, A. Schönle, and S. W. Hell, “Resolution scaling in STED microscopy,” Opt. Express 16, 4154–4162 (2008).
    [CrossRef]
  7. T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
    [CrossRef]
  8. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).
  9. B. Kavčič, D. Babić, N. Osterman, B. Podobnik, and I. Poberaj, “Rapid prototyping system with sub-micrometer resolution for microfluidic applications,” Microsys. Technol. 18, 191–198 (2012).
  10. J. Kotar, M. Vilfan, N. Osterman, D. Babič, M. Čopič, and I. Poberaj, “Interparticle potential and drag coefficient in nematic colloids,” Phys. Rev. Lett. 96, 207801 (2006).
    [CrossRef]
  11. N. Draper and H. Smith, Applied Regression Analysis (Wiley, 1998).
  12. Laser and laser-related equipment—test methods for laser beam widths, divergence angles and beam propagation ratios—part 1: stigmatic and simple astigmatic beam, (ISO, 2005).
  13. M. Hazewinkel, Encyclopedia of Mathematics (Kluwer, 1988).

2012

B. Kavčič, D. Babić, N. Osterman, B. Podobnik, and I. Poberaj, “Rapid prototyping system with sub-micrometer resolution for microfluidic applications,” Microsys. Technol. 18, 191–198 (2012).

2009

E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[CrossRef]

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6, 24–32 (2009).
[CrossRef]

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[CrossRef]

2008

2006

J. Kotar, M. Vilfan, N. Osterman, D. Babič, M. Čopič, and I. Poberaj, “Interparticle potential and drag coefficient in nematic colloids,” Phys. Rev. Lett. 96, 207801 (2006).
[CrossRef]

2003

S. W. Hell, “Toward fluorescence nanoscopy,” Nat. Biotechnol. 21, 1347–1355 (2003).
[CrossRef]

1994

1873

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. mikrosk. Anat. Entwichlungsmech. 9, 413–468 (1873).

Abbe, E.

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. mikrosk. Anat. Entwichlungsmech. 9, 413–468 (1873).

Babic, D.

B. Kavčič, D. Babić, N. Osterman, B. Podobnik, and I. Poberaj, “Rapid prototyping system with sub-micrometer resolution for microfluidic applications,” Microsys. Technol. 18, 191–198 (2012).

J. Kotar, M. Vilfan, N. Osterman, D. Babič, M. Čopič, and I. Poberaj, “Interparticle potential and drag coefficient in nematic colloids,” Phys. Rev. Lett. 96, 207801 (2006).
[CrossRef]

Bowman, C. N.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[CrossRef]

Copic, M.

J. Kotar, M. Vilfan, N. Osterman, D. Babič, M. Čopič, and I. Poberaj, “Interparticle potential and drag coefficient in nematic colloids,” Phys. Rev. Lett. 96, 207801 (2006).
[CrossRef]

Draper, N.

N. Draper and H. Smith, Applied Regression Analysis (Wiley, 1998).

Eggeling, C.

E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[CrossRef]

Han, K. Y.

E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[CrossRef]

Harke, B.

Hazewinkel, M.

M. Hazewinkel, Encyclopedia of Mathematics (Kluwer, 1988).

Hell, S. W.

E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[CrossRef]

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6, 24–32 (2009).
[CrossRef]

B. Harke, J. Keller, C. K. Ullal, V. Westphal, A. Schönle, and S. W. Hell, “Resolution scaling in STED microscopy,” Opt. Express 16, 4154–4162 (2008).
[CrossRef]

S. W. Hell, “Toward fluorescence nanoscopy,” Nat. Biotechnol. 21, 1347–1355 (2003).
[CrossRef]

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780–782 (1994).
[CrossRef]

Irvine, S. E.

E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[CrossRef]

Kavcic, B.

B. Kavčič, D. Babić, N. Osterman, B. Podobnik, and I. Poberaj, “Rapid prototyping system with sub-micrometer resolution for microfluidic applications,” Microsys. Technol. 18, 191–198 (2012).

Keller, J.

Kotar, J.

J. Kotar, M. Vilfan, N. Osterman, D. Babič, M. Čopič, and I. Poberaj, “Interparticle potential and drag coefficient in nematic colloids,” Phys. Rev. Lett. 96, 207801 (2006).
[CrossRef]

Kowalski, B. A.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[CrossRef]

McLeod, R. R.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[CrossRef]

Osterman, N.

B. Kavčič, D. Babić, N. Osterman, B. Podobnik, and I. Poberaj, “Rapid prototyping system with sub-micrometer resolution for microfluidic applications,” Microsys. Technol. 18, 191–198 (2012).

J. Kotar, M. Vilfan, N. Osterman, D. Babič, M. Čopič, and I. Poberaj, “Interparticle potential and drag coefficient in nematic colloids,” Phys. Rev. Lett. 96, 207801 (2006).
[CrossRef]

Poberaj, I.

B. Kavčič, D. Babić, N. Osterman, B. Podobnik, and I. Poberaj, “Rapid prototyping system with sub-micrometer resolution for microfluidic applications,” Microsys. Technol. 18, 191–198 (2012).

J. Kotar, M. Vilfan, N. Osterman, D. Babič, M. Čopič, and I. Poberaj, “Interparticle potential and drag coefficient in nematic colloids,” Phys. Rev. Lett. 96, 207801 (2006).
[CrossRef]

Podobnik, B.

B. Kavčič, D. Babić, N. Osterman, B. Podobnik, and I. Poberaj, “Rapid prototyping system with sub-micrometer resolution for microfluidic applications,” Microsys. Technol. 18, 191–198 (2012).

Rittweger, E.

E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

Schönle, A.

Scott, T. F.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[CrossRef]

Smith, H.

N. Draper and H. Smith, Applied Regression Analysis (Wiley, 1998).

Sullivan, A. C.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

Ullal, C. K.

Vilfan, M.

J. Kotar, M. Vilfan, N. Osterman, D. Babič, M. Čopič, and I. Poberaj, “Interparticle potential and drag coefficient in nematic colloids,” Phys. Rev. Lett. 96, 207801 (2006).
[CrossRef]

Westphal, V.

Wichmann, J.

Arch. mikrosk. Anat. Entwichlungsmech.

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. mikrosk. Anat. Entwichlungsmech. 9, 413–468 (1873).

Microsys. Technol.

B. Kavčič, D. Babić, N. Osterman, B. Podobnik, and I. Poberaj, “Rapid prototyping system with sub-micrometer resolution for microfluidic applications,” Microsys. Technol. 18, 191–198 (2012).

Nat. Biotechnol.

S. W. Hell, “Toward fluorescence nanoscopy,” Nat. Biotechnol. 21, 1347–1355 (2003).
[CrossRef]

Nat. Methods

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6, 24–32 (2009).
[CrossRef]

Nat. Photonics

E. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

J. Kotar, M. Vilfan, N. Osterman, D. Babič, M. Čopič, and I. Poberaj, “Interparticle potential and drag coefficient in nematic colloids,” Phys. Rev. Lett. 96, 207801 (2006).
[CrossRef]

Science

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[CrossRef]

Other

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

N. Draper and H. Smith, Applied Regression Analysis (Wiley, 1998).

Laser and laser-related equipment—test methods for laser beam widths, divergence angles and beam propagation ratios—part 1: stigmatic and simple astigmatic beam, (ISO, 2005).

M. Hazewinkel, Encyclopedia of Mathematics (Kluwer, 1988).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Spiral phase plate thickness profile. The beam phase is continuously varied from 0 to 2π delay to generate a phase profile typical for TEM01 Laguerre–Gaussian beam. (b) Schematic diagram of the experimental setup.

Fig. 2.
Fig. 2.

Radial beam intensity profile and its cross section (a) for the TEM00 beam and (b) upon passing through the spiral phase plate for the TEM01 beam.

Fig. 3.
Fig. 3.

(a) Deflection efficiency for both AOD crystals (orthogonal directions 1 and 2). (b) Deflection efficiency results from (a) with the beam conversion losses taken into account. The plot shows results for both the TEM00 (solid and empty squares) and TEM01 (solid and empty triangles) beams.

Fig. 4.
Fig. 4.

Beam ellipticity ε as a function of frequency (deflection angle) for both AOD crystals (circles and triangles), with the reference beam ellipticity (solid black line). Results are shown for (a) TEM00 and (b) TEM01 beams.

Fig. 5.
Fig. 5.

Beam quality factor M2 as a function of frequency (deflection angle) for both AOD crystals (circles and triangles), with the reference beam quality (solid black line). Results are shown for (a) TEM00 and (b) TEM01 beams.

Equations (8)

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

Ep,l(r,φ,z)=E0wow(z)(2rw(z))lLpl(2r2w2(z))e±ilφiηp,leikr22R(z)er2w2(z)eikz,
2Λsin(θ)=λ.
η=I01I00=0.77±0.01,
I00er2w00,I01r2er2w01,
R2=1SSESST.
SSE=i(yifi)2,
SST=i(yiy¯)2,
[σxx2σxy2σyx2σyy2];σij2=(iic)(jjc)I(x,y)dxdyI(x,y)dxdy,

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