Abstract

By measuring the excitation efficiency of an optical waveguide on a diffraction grating one can accurately register the changes in the incidence angle of the exciting light beam. This phenomenon was applied to detect ultrasmall deflections of silicon dioxide cantilevers of submicrometer thickness that were fabricated with corrugation on top to act as diffraction grating couplers. The power of light coupled into the cantilevers was monitored with a conventional photodetector and modulated using mechanical vibration of the cantilever, thus changing the spatial orientation of the coupler with respect to the incident light beam. The technique can be considered as an alternative to the methods known for detection of cantilever deflection.

© 2006 Optical Society of America

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  1. R. McKendry, J. Zhang, Y. Arntz, T. Strunz, M. Hegner, H. P. Lang, M. K. Baller, U. Certa, E. Meyer, H.-J. Güntherodt, and C. Gerber, "Multiple label free biodetection and quantitative DNA-binding assays on a nanomechanical cantilever array," Proc. Natl. Acad. Sci. USA 99, 9783-9788 (2002).
    [CrossRef] [PubMed]
  2. J. Thaysen, A. Boisen, O. Hansen, and S. Bouwstra, "Atomic force microscopy probe with piezoresistive read-out and a highly symmetrical Wheatstone bridge arrangement," Sens. Actuators B 83, 47-53 (2000).
    [CrossRef]
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    [CrossRef]
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2005

2002

R. McKendry, J. Zhang, Y. Arntz, T. Strunz, M. Hegner, H. P. Lang, M. K. Baller, U. Certa, E. Meyer, H.-J. Güntherodt, and C. Gerber, "Multiple label free biodetection and quantitative DNA-binding assays on a nanomechanical cantilever array," Proc. Natl. Acad. Sci. USA 99, 9783-9788 (2002).
[CrossRef] [PubMed]

R. Budakian and S. J. Putterman, "Force detection using a fiber-optic cantilever," Appl. Phys. Lett. 81, 2100-2102 (2002).
[CrossRef]

2001

B. N. Zvonkov, K. E. Zinoviev, D. Kh. Nurligareev, I. F. Salakhutdinov, V. V. Svetikov, and V. A. Sychugov, "Tunable wide-aperture semiconductor laser with an external waveguide-grating mirror," Quantum Electron. 31, 35-38 (2001).
[CrossRef]

2000

R. Orobtchouk, A. Layadi, H. Gualous, D. Pascal, A. Koster, and S. Laval, "High-efficiency light coupling in a submicrometric silicon-on-insulator waveguide," Appl. Opt. 39, 5773-5777 (2000).
[CrossRef]

J. Thaysen, A. Boisen, O. Hansen, and S. Bouwstra, "Atomic force microscopy probe with piezoresistive read-out and a highly symmetrical Wheatstone bridge arrangement," Sens. Actuators B 83, 47-53 (2000).
[CrossRef]

1999

1996

N. Ericsson, M. Hagberg, and A. Larsson, "Highly directional grating outcouplers with tailorable radiation characteristics," IEEE J. Quantum Electron. 32, 1038-1047 (1996).
[CrossRef]

O. Parriaux, V. A. Sychugov, and A. V. Tishchenko, "Coupling gratings as waveguide functional element," Pure Appl. Opt. 5, 453-469 (1996).
[CrossRef]

1995

1994

D. Sarid, Scanning Force Microscopy with Applications to Electric, Magnetic and Atomic Forces (Oxford U. Press, 1994).

1992

E. Anemogiannis and E. N. Glytsis, "Multilayer waveguides: efficient numerical analysis of general structures," J. Lightwave Technol. 10, 1344-1351 (1992).
[CrossRef]

1990

1985

M. T. Wlodarczyk and S. R. Seshadri, "Analysis of grating couplers for planar dielectric waveguides," J. Appl. Phys. 58, 69-87 (1985).
[CrossRef]

1980

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, 1980).
[CrossRef]

1976

W. Streifer, R. D. Burnham, and D. R. Scifres, "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron. QE-12, 422-428 (1976).
[CrossRef]

1975

S. T. Peng and T. Tamir, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123-133 (1975).
[CrossRef]

1973

K. Ogawa, W. S. C. Chang, B. L. Sopori, and F. J. Rosenbaum, "A theoretical analysis of etched grating couplers for integrated optics," IEEE J. Quantum Electron. QE-9, 29-42 (1973).
[CrossRef]

Ahmed, M. Abdou

Anemogiannis, E.

E. Anemogiannis and E. N. Glytsis, "Multilayer waveguides: efficient numerical analysis of general structures," J. Lightwave Technol. 10, 1344-1351 (1992).
[CrossRef]

Arntz, Y.

R. McKendry, J. Zhang, Y. Arntz, T. Strunz, M. Hegner, H. P. Lang, M. K. Baller, U. Certa, E. Meyer, H.-J. Güntherodt, and C. Gerber, "Multiple label free biodetection and quantitative DNA-binding assays on a nanomechanical cantilever array," Proc. Natl. Acad. Sci. USA 99, 9783-9788 (2002).
[CrossRef] [PubMed]

Baller, M. K.

R. McKendry, J. Zhang, Y. Arntz, T. Strunz, M. Hegner, H. P. Lang, M. K. Baller, U. Certa, E. Meyer, H.-J. Güntherodt, and C. Gerber, "Multiple label free biodetection and quantitative DNA-binding assays on a nanomechanical cantilever array," Proc. Natl. Acad. Sci. USA 99, 9783-9788 (2002).
[CrossRef] [PubMed]

Boisen, A.

J. Thaysen, A. Boisen, O. Hansen, and S. Bouwstra, "Atomic force microscopy probe with piezoresistive read-out and a highly symmetrical Wheatstone bridge arrangement," Sens. Actuators B 83, 47-53 (2000).
[CrossRef]

Bouwstra, S.

J. Thaysen, A. Boisen, O. Hansen, and S. Bouwstra, "Atomic force microscopy probe with piezoresistive read-out and a highly symmetrical Wheatstone bridge arrangement," Sens. Actuators B 83, 47-53 (2000).
[CrossRef]

Brazas, J. C.

Budakian, R.

R. Budakian and S. J. Putterman, "Force detection using a fiber-optic cantilever," Appl. Phys. Lett. 81, 2100-2102 (2002).
[CrossRef]

Burnham, R. D.

W. Streifer, R. D. Burnham, and D. R. Scifres, "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron. QE-12, 422-428 (1976).
[CrossRef]

Certa, U.

R. McKendry, J. Zhang, Y. Arntz, T. Strunz, M. Hegner, H. P. Lang, M. K. Baller, U. Certa, E. Meyer, H.-J. Güntherodt, and C. Gerber, "Multiple label free biodetection and quantitative DNA-binding assays on a nanomechanical cantilever array," Proc. Natl. Acad. Sci. USA 99, 9783-9788 (2002).
[CrossRef] [PubMed]

Chang, W. S. C.

K. Ogawa, W. S. C. Chang, B. L. Sopori, and F. J. Rosenbaum, "A theoretical analysis of etched grating couplers for integrated optics," IEEE J. Quantum Electron. QE-9, 29-42 (1973).
[CrossRef]

Destouches, N.

Ericsson, N.

N. Ericsson, M. Hagberg, and A. Larsson, "Highly directional grating outcouplers with tailorable radiation characteristics," IEEE J. Quantum Electron. 32, 1038-1047 (1996).
[CrossRef]

Fujii, T.

Gerber, C.

R. McKendry, J. Zhang, Y. Arntz, T. Strunz, M. Hegner, H. P. Lang, M. K. Baller, U. Certa, E. Meyer, H.-J. Güntherodt, and C. Gerber, "Multiple label free biodetection and quantitative DNA-binding assays on a nanomechanical cantilever array," Proc. Natl. Acad. Sci. USA 99, 9783-9788 (2002).
[CrossRef] [PubMed]

Glytsis, E. N.

E. Anemogiannis and E. N. Glytsis, "Multilayer waveguides: efficient numerical analysis of general structures," J. Lightwave Technol. 10, 1344-1351 (1992).
[CrossRef]

Gualous, H.

Güntherodt, H.-J.

R. McKendry, J. Zhang, Y. Arntz, T. Strunz, M. Hegner, H. P. Lang, M. K. Baller, U. Certa, E. Meyer, H.-J. Güntherodt, and C. Gerber, "Multiple label free biodetection and quantitative DNA-binding assays on a nanomechanical cantilever array," Proc. Natl. Acad. Sci. USA 99, 9783-9788 (2002).
[CrossRef] [PubMed]

Gupta, M. C.

Hagberg, M.

N. Ericsson, M. Hagberg, and A. Larsson, "Highly directional grating outcouplers with tailorable radiation characteristics," IEEE J. Quantum Electron. 32, 1038-1047 (1996).
[CrossRef]

Hansen, O.

J. Thaysen, A. Boisen, O. Hansen, and S. Bouwstra, "Atomic force microscopy probe with piezoresistive read-out and a highly symmetrical Wheatstone bridge arrangement," Sens. Actuators B 83, 47-53 (2000).
[CrossRef]

Hegner, M.

R. McKendry, J. Zhang, Y. Arntz, T. Strunz, M. Hegner, H. P. Lang, M. K. Baller, U. Certa, E. Meyer, H.-J. Güntherodt, and C. Gerber, "Multiple label free biodetection and quantitative DNA-binding assays on a nanomechanical cantilever array," Proc. Natl. Acad. Sci. USA 99, 9783-9788 (2002).
[CrossRef] [PubMed]

Koster, A.

Lang, H. P.

R. McKendry, J. Zhang, Y. Arntz, T. Strunz, M. Hegner, H. P. Lang, M. K. Baller, U. Certa, E. Meyer, H.-J. Güntherodt, and C. Gerber, "Multiple label free biodetection and quantitative DNA-binding assays on a nanomechanical cantilever array," Proc. Natl. Acad. Sci. USA 99, 9783-9788 (2002).
[CrossRef] [PubMed]

Larsson, A.

N. Ericsson, M. Hagberg, and A. Larsson, "Highly directional grating outcouplers with tailorable radiation characteristics," IEEE J. Quantum Electron. 32, 1038-1047 (1996).
[CrossRef]

Laval, S.

Layadi, A.

Li, L.

McKendry, R.

R. McKendry, J. Zhang, Y. Arntz, T. Strunz, M. Hegner, H. P. Lang, M. K. Baller, U. Certa, E. Meyer, H.-J. Güntherodt, and C. Gerber, "Multiple label free biodetection and quantitative DNA-binding assays on a nanomechanical cantilever array," Proc. Natl. Acad. Sci. USA 99, 9783-9788 (2002).
[CrossRef] [PubMed]

Meyer, E.

R. McKendry, J. Zhang, Y. Arntz, T. Strunz, M. Hegner, H. P. Lang, M. K. Baller, U. Certa, E. Meyer, H.-J. Güntherodt, and C. Gerber, "Multiple label free biodetection and quantitative DNA-binding assays on a nanomechanical cantilever array," Proc. Natl. Acad. Sci. USA 99, 9783-9788 (2002).
[CrossRef] [PubMed]

Nishihara, H.

Nurligareev, D. Kh.

B. N. Zvonkov, K. E. Zinoviev, D. Kh. Nurligareev, I. F. Salakhutdinov, V. V. Svetikov, and V. A. Sychugov, "Tunable wide-aperture semiconductor laser with an external waveguide-grating mirror," Quantum Electron. 31, 35-38 (2001).
[CrossRef]

Ogawa, K.

K. Ogawa, W. S. C. Chang, B. L. Sopori, and F. J. Rosenbaum, "A theoretical analysis of etched grating couplers for integrated optics," IEEE J. Quantum Electron. QE-9, 29-42 (1973).
[CrossRef]

Orobtchouk, R.

Parriaux, O.

Pascal, D.

Peng, S. T.

S. T. Peng and T. Tamir, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123-133 (1975).
[CrossRef]

Petit, R.

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, 1980).
[CrossRef]

Pommier, J. C.

Putterman, S. J.

R. Budakian and S. J. Putterman, "Force detection using a fiber-optic cantilever," Appl. Phys. Lett. 81, 2100-2102 (2002).
[CrossRef]

Reynaud, S.

Rosenbaum, F. J.

K. Ogawa, W. S. C. Chang, B. L. Sopori, and F. J. Rosenbaum, "A theoretical analysis of etched grating couplers for integrated optics," IEEE J. Quantum Electron. QE-9, 29-42 (1973).
[CrossRef]

Salakhutdinov, I. F.

B. N. Zvonkov, K. E. Zinoviev, D. Kh. Nurligareev, I. F. Salakhutdinov, V. V. Svetikov, and V. A. Sychugov, "Tunable wide-aperture semiconductor laser with an external waveguide-grating mirror," Quantum Electron. 31, 35-38 (2001).
[CrossRef]

Sarid, D.

D. Sarid, Scanning Force Microscopy with Applications to Electric, Magnetic and Atomic Forces (Oxford U. Press, 1994).

Scifres, D. R.

W. Streifer, R. D. Burnham, and D. R. Scifres, "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron. QE-12, 422-428 (1976).
[CrossRef]

Seshadri, S. R.

M. T. Wlodarczyk and S. R. Seshadri, "Analysis of grating couplers for planar dielectric waveguides," J. Appl. Phys. 58, 69-87 (1985).
[CrossRef]

Sopori, B. L.

K. Ogawa, W. S. C. Chang, B. L. Sopori, and F. J. Rosenbaum, "A theoretical analysis of etched grating couplers for integrated optics," IEEE J. Quantum Electron. QE-9, 29-42 (1973).
[CrossRef]

Streifer, W.

W. Streifer, R. D. Burnham, and D. R. Scifres, "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron. QE-12, 422-428 (1976).
[CrossRef]

Strunz, T.

R. McKendry, J. Zhang, Y. Arntz, T. Strunz, M. Hegner, H. P. Lang, M. K. Baller, U. Certa, E. Meyer, H.-J. Güntherodt, and C. Gerber, "Multiple label free biodetection and quantitative DNA-binding assays on a nanomechanical cantilever array," Proc. Natl. Acad. Sci. USA 99, 9783-9788 (2002).
[CrossRef] [PubMed]

Suhara, T.

Svetikov, V. V.

B. N. Zvonkov, K. E. Zinoviev, D. Kh. Nurligareev, I. F. Salakhutdinov, V. V. Svetikov, and V. A. Sychugov, "Tunable wide-aperture semiconductor laser with an external waveguide-grating mirror," Quantum Electron. 31, 35-38 (2001).
[CrossRef]

Sychugov, V. A.

B. N. Zvonkov, K. E. Zinoviev, D. Kh. Nurligareev, I. F. Salakhutdinov, V. V. Svetikov, and V. A. Sychugov, "Tunable wide-aperture semiconductor laser with an external waveguide-grating mirror," Quantum Electron. 31, 35-38 (2001).
[CrossRef]

O. Parriaux, V. A. Sychugov, and A. V. Tishchenko, "Coupling gratings as waveguide functional element," Pure Appl. Opt. 5, 453-469 (1996).
[CrossRef]

Tamir, T.

S. T. Peng and T. Tamir, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123-133 (1975).
[CrossRef]

Thaysen, J.

J. Thaysen, A. Boisen, O. Hansen, and S. Bouwstra, "Atomic force microscopy probe with piezoresistive read-out and a highly symmetrical Wheatstone bridge arrangement," Sens. Actuators B 83, 47-53 (2000).
[CrossRef]

Tishchenko, A. V.

Tonchev, S.

Ura, S.

Wlodarczyk, M. T.

M. T. Wlodarczyk and S. R. Seshadri, "Analysis of grating couplers for planar dielectric waveguides," J. Appl. Phys. 58, 69-87 (1985).
[CrossRef]

Zhang, J.

R. McKendry, J. Zhang, Y. Arntz, T. Strunz, M. Hegner, H. P. Lang, M. K. Baller, U. Certa, E. Meyer, H.-J. Güntherodt, and C. Gerber, "Multiple label free biodetection and quantitative DNA-binding assays on a nanomechanical cantilever array," Proc. Natl. Acad. Sci. USA 99, 9783-9788 (2002).
[CrossRef] [PubMed]

Zinoviev, K. E.

B. N. Zvonkov, K. E. Zinoviev, D. Kh. Nurligareev, I. F. Salakhutdinov, V. V. Svetikov, and V. A. Sychugov, "Tunable wide-aperture semiconductor laser with an external waveguide-grating mirror," Quantum Electron. 31, 35-38 (2001).
[CrossRef]

Zvonkov, B. N.

B. N. Zvonkov, K. E. Zinoviev, D. Kh. Nurligareev, I. F. Salakhutdinov, V. V. Svetikov, and V. A. Sychugov, "Tunable wide-aperture semiconductor laser with an external waveguide-grating mirror," Quantum Electron. 31, 35-38 (2001).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

R. Budakian and S. J. Putterman, "Force detection using a fiber-optic cantilever," Appl. Phys. Lett. 81, 2100-2102 (2002).
[CrossRef]

IEEE J. Quantum Electron.

K. Ogawa, W. S. C. Chang, B. L. Sopori, and F. J. Rosenbaum, "A theoretical analysis of etched grating couplers for integrated optics," IEEE J. Quantum Electron. QE-9, 29-42 (1973).
[CrossRef]

N. Ericsson, M. Hagberg, and A. Larsson, "Highly directional grating outcouplers with tailorable radiation characteristics," IEEE J. Quantum Electron. 32, 1038-1047 (1996).
[CrossRef]

W. Streifer, R. D. Burnham, and D. R. Scifres, "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron. QE-12, 422-428 (1976).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

S. T. Peng and T. Tamir, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123-133 (1975).
[CrossRef]

J. Appl. Phys.

M. T. Wlodarczyk and S. R. Seshadri, "Analysis of grating couplers for planar dielectric waveguides," J. Appl. Phys. 58, 69-87 (1985).
[CrossRef]

J. Lightwave Technol.

E. Anemogiannis and E. N. Glytsis, "Multilayer waveguides: efficient numerical analysis of general structures," J. Lightwave Technol. 10, 1344-1351 (1992).
[CrossRef]

Opt. Express

Proc. Natl. Acad. Sci. USA

R. McKendry, J. Zhang, Y. Arntz, T. Strunz, M. Hegner, H. P. Lang, M. K. Baller, U. Certa, E. Meyer, H.-J. Güntherodt, and C. Gerber, "Multiple label free biodetection and quantitative DNA-binding assays on a nanomechanical cantilever array," Proc. Natl. Acad. Sci. USA 99, 9783-9788 (2002).
[CrossRef] [PubMed]

Pure Appl. Opt.

O. Parriaux, V. A. Sychugov, and A. V. Tishchenko, "Coupling gratings as waveguide functional element," Pure Appl. Opt. 5, 453-469 (1996).
[CrossRef]

Quantum Electron.

B. N. Zvonkov, K. E. Zinoviev, D. Kh. Nurligareev, I. F. Salakhutdinov, V. V. Svetikov, and V. A. Sychugov, "Tunable wide-aperture semiconductor laser with an external waveguide-grating mirror," Quantum Electron. 31, 35-38 (2001).
[CrossRef]

Sens. Actuators B

J. Thaysen, A. Boisen, O. Hansen, and S. Bouwstra, "Atomic force microscopy probe with piezoresistive read-out and a highly symmetrical Wheatstone bridge arrangement," Sens. Actuators B 83, 47-53 (2000).
[CrossRef]

Other

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, 1980).
[CrossRef]

D. Sarid, Scanning Force Microscopy with Applications to Electric, Magnetic and Atomic Forces (Oxford U. Press, 1994).

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Figures (9)

Fig. 1
Fig. 1

(a) Excitation of the guided wave by an out-of-plane incident beam on the DG, (b) cantilever in vibration mode.

Fig. 2
Fig. 2

Image of the fabricated cantilevers obtained with a confocal microscope.

Fig. 3
Fig. 3

Profiles of the cantilevers presented in Fig. 2 and the derivatives of the profiles representing the tangent angles to the profile curves.

Fig. 4
Fig. 4

Angular spectra of the incident beam with a waist of 40 µm and of the grating intrinsic acceptance for the second mode. The coupling efficiency is proportional to the overlap of the curves (the shaded area).

Fig. 5
Fig. 5

Dependence of the coupling factor on the size of the incident beam for three different propagation modes.

Fig. 6
Fig. 6

Noise floor for deflection measurements required for detection of 1 µrad cantilever deflection versus detuning angle Θ d . The noise floor was calculated with respect to the normalized coupling efficiency, which is unity if the detuning angle is zero.

Fig. 7
Fig. 7

Schematic view of the experimental setup. PSD, position-sensitive photodetector.

Fig. 8
Fig. 8

Intensity distributions of the waveguide modes exiting the cantilever. Light exiting from the waveguide was projected to the screen located 2 cm off from the cantilever end. The images were taken with a digital camera.

Fig. 9
Fig. 9

Results of the experimental measurements of the coupling efficiencies for different spot sizes. The dependence of the coupling factor on the excitation length for three different modes is presented on the background for comparison.

Tables (1)

Tables Icon

Table 1 Experimental Results

Equations (6)

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

Δ z = 2 3 Δ Θ 0 L cant ,
β i = n 2 π λ 0 sin ( Θ 0 , i ) + m 2 π Λ ,
Δ Θ gr = 2 α rad λ 0 n 2 π cos ( Θ 0 ) ,
Δ Θ i = tan - 1 ( λ 0 π w 0 ) .
FC = [ exp ( α rad L g ) 0 L g exp ( α rad L g ) f ( x ) d x ] 2 ,
δ = 10 log [ Δ V out ( Θ d ) V out ( Θ d = 0 ) ] ,

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