Abstract

A tunable asymmetrically-embedded-aperture interferometer configuration is proposed to enhance the measurement sensitivity of subwavelength variation. With this configuration, an aperture of reference was posited asymmetrically, relative to the test aperture, that exhibited subwavelength variation. By a shift in the relative position of the reference aperture, the detection sensitivity of measuring the subwavelength variation in the far field can be enhanced to a desired value at any specific detection width. We discuss the underlying mechanism of optimization and address the difference between the embedded-aperture interferometry and tunable asymmetrically-embedded-aperture interferometry with respect to tolerance.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Z. Bomzon, G. Biener, V. Kleiner, E. Hasman, “Real-time analysis of partially polarized light with a space-variant subwavelength dielectric grating,” Opt. Lett. 27, 188–190 (2002).
    [CrossRef]
  2. T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26, 1972–1974 (2001).
    [CrossRef]
  3. W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature (London) 424, 824–830 (2003).
    [CrossRef]
  4. P.-T. Lee, J. R. Cao, S.-J. Choi, Z.-J. Wei, J. D. O’Brien, P. D. Dapkus, “Operation of photonic crystal membrane lasers above room temperature,” Appl. Phys. Lett. 81, 3311–3313 (2002).
    [CrossRef]
  5. B. Niggemann, T. L. Drell, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, F. Entschladen, “Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix,” Exp. Cell Res. 298, 178–187 (2004).
    [CrossRef] [PubMed]
  6. S. Cooper, “Control and maintenance of mammalian cell size,” BMC Cell Biol. 5(35), (2004). (See http://www.biomedcentral.com/1471–2121/5/35.)
    [CrossRef] [PubMed]
  7. L. S. C. Pingree, M. C. Hersam, M. M. Kern, B. J. Scott, T. J. Marks, “Spatially-resolved electroluminescence of operating organic light-emitting diodes using conductive atomic force microscopy,” Appl. Phys. Lett. 85, 344–346 (2004).
    [CrossRef]
  8. A. A. Stekolnikov, J. Furthmüller, F. Bechstedt, “Structural elements on reconstructed Si and Ge(110) surfaces,” Phys. Rev. B 70(4), 045305 (2004).
    [CrossRef]
  9. K. Nakamoto, C. B. Mooney, S.-I. Kitamura, “AC mode feedback and gate pulse acquisition methods for scanning near-field optical microscope,” Jpn. J. Appl. Phys., Part 1 43, 2686–2689 (2004).
    [CrossRef]
  10. S. Selci, M. Righini, “Detection of subwavelength slit-width variation with irradiance measurements in the far field,” Opt. Lett. 27, 1971–1973 (2002).
    [CrossRef]
  11. S.-C. Chu, J.-L. Chern, “Characterization of the subwavelength variation signature from far-field irradiance,” Opt. Lett. 29, 1045–1047 (2004).
    [CrossRef] [PubMed]
  12. S.-C. Chu, J.-L. Chern, “Detection of subwavelength slit-width variation with measurements in the far field by use of an embedded-aperture interferometer configuration,” J. Opt. Soc. Am. A 22, 335–341 (2005).
    [CrossRef]
  13. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), p. 103.
  14. Ref. [13], p. 74.
  15. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965).

2005

2004

S.-C. Chu, J.-L. Chern, “Characterization of the subwavelength variation signature from far-field irradiance,” Opt. Lett. 29, 1045–1047 (2004).
[CrossRef] [PubMed]

B. Niggemann, T. L. Drell, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, F. Entschladen, “Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix,” Exp. Cell Res. 298, 178–187 (2004).
[CrossRef] [PubMed]

S. Cooper, “Control and maintenance of mammalian cell size,” BMC Cell Biol. 5(35), (2004). (See http://www.biomedcentral.com/1471–2121/5/35.)
[CrossRef] [PubMed]

L. S. C. Pingree, M. C. Hersam, M. M. Kern, B. J. Scott, T. J. Marks, “Spatially-resolved electroluminescence of operating organic light-emitting diodes using conductive atomic force microscopy,” Appl. Phys. Lett. 85, 344–346 (2004).
[CrossRef]

A. A. Stekolnikov, J. Furthmüller, F. Bechstedt, “Structural elements on reconstructed Si and Ge(110) surfaces,” Phys. Rev. B 70(4), 045305 (2004).
[CrossRef]

K. Nakamoto, C. B. Mooney, S.-I. Kitamura, “AC mode feedback and gate pulse acquisition methods for scanning near-field optical microscope,” Jpn. J. Appl. Phys., Part 1 43, 2686–2689 (2004).
[CrossRef]

2003

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature (London) 424, 824–830 (2003).
[CrossRef]

2002

2001

Barnes, W. L.

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature (London) 424, 824–830 (2003).
[CrossRef]

Bechstedt, F.

A. A. Stekolnikov, J. Furthmüller, F. Bechstedt, “Structural elements on reconstructed Si and Ge(110) surfaces,” Phys. Rev. B 70(4), 045305 (2004).
[CrossRef]

Biener, G.

Bomzon, Z.

Cao, J. R.

P.-T. Lee, J. R. Cao, S.-J. Choi, Z.-J. Wei, J. D. O’Brien, P. D. Dapkus, “Operation of photonic crystal membrane lasers above room temperature,” Appl. Phys. Lett. 81, 3311–3313 (2002).
[CrossRef]

Chern, J.-L.

Choi, S.-J.

P.-T. Lee, J. R. Cao, S.-J. Choi, Z.-J. Wei, J. D. O’Brien, P. D. Dapkus, “Operation of photonic crystal membrane lasers above room temperature,” Appl. Phys. Lett. 81, 3311–3313 (2002).
[CrossRef]

Chu, S.-C.

Cooper, S.

S. Cooper, “Control and maintenance of mammalian cell size,” BMC Cell Biol. 5(35), (2004). (See http://www.biomedcentral.com/1471–2121/5/35.)
[CrossRef] [PubMed]

Dapkus, P. D.

P.-T. Lee, J. R. Cao, S.-J. Choi, Z.-J. Wei, J. D. O’Brien, P. D. Dapkus, “Operation of photonic crystal membrane lasers above room temperature,” Appl. Phys. Lett. 81, 3311–3313 (2002).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature (London) 424, 824–830 (2003).
[CrossRef]

Drell, T. L.

B. Niggemann, T. L. Drell, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, F. Entschladen, “Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix,” Exp. Cell Res. 298, 178–187 (2004).
[CrossRef] [PubMed]

Ebbesen, T. W.

Entschladen, F.

B. Niggemann, T. L. Drell, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, F. Entschladen, “Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix,” Exp. Cell Res. 298, 178–187 (2004).
[CrossRef] [PubMed]

Furthmüller, J.

A. A. Stekolnikov, J. Furthmüller, F. Bechstedt, “Structural elements on reconstructed Si and Ge(110) surfaces,” Phys. Rev. B 70(4), 045305 (2004).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), p. 103.

Hasman, E.

Hersam, M. C.

L. S. C. Pingree, M. C. Hersam, M. M. Kern, B. J. Scott, T. J. Marks, “Spatially-resolved electroluminescence of operating organic light-emitting diodes using conductive atomic force microscopy,” Appl. Phys. Lett. 85, 344–346 (2004).
[CrossRef]

Joseph, J.

B. Niggemann, T. L. Drell, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, F. Entschladen, “Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix,” Exp. Cell Res. 298, 178–187 (2004).
[CrossRef] [PubMed]

Kern, M. M.

L. S. C. Pingree, M. C. Hersam, M. M. Kern, B. J. Scott, T. J. Marks, “Spatially-resolved electroluminescence of operating organic light-emitting diodes using conductive atomic force microscopy,” Appl. Phys. Lett. 85, 344–346 (2004).
[CrossRef]

Kitamura, S.-I.

K. Nakamoto, C. B. Mooney, S.-I. Kitamura, “AC mode feedback and gate pulse acquisition methods for scanning near-field optical microscope,” Jpn. J. Appl. Phys., Part 1 43, 2686–2689 (2004).
[CrossRef]

Kleiner, V.

Lang, K.

B. Niggemann, T. L. Drell, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, F. Entschladen, “Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix,” Exp. Cell Res. 298, 178–187 (2004).
[CrossRef] [PubMed]

Lee, P.-T.

P.-T. Lee, J. R. Cao, S.-J. Choi, Z.-J. Wei, J. D. O’Brien, P. D. Dapkus, “Operation of photonic crystal membrane lasers above room temperature,” Appl. Phys. Lett. 81, 3311–3313 (2002).
[CrossRef]

Lezec, H. J.

Linke, R. A.

Marks, T. J.

L. S. C. Pingree, M. C. Hersam, M. M. Kern, B. J. Scott, T. J. Marks, “Spatially-resolved electroluminescence of operating organic light-emitting diodes using conductive atomic force microscopy,” Appl. Phys. Lett. 85, 344–346 (2004).
[CrossRef]

Mooney, C. B.

K. Nakamoto, C. B. Mooney, S.-I. Kitamura, “AC mode feedback and gate pulse acquisition methods for scanning near-field optical microscope,” Jpn. J. Appl. Phys., Part 1 43, 2686–2689 (2004).
[CrossRef]

Nakamoto, K.

K. Nakamoto, C. B. Mooney, S.-I. Kitamura, “AC mode feedback and gate pulse acquisition methods for scanning near-field optical microscope,” Jpn. J. Appl. Phys., Part 1 43, 2686–2689 (2004).
[CrossRef]

Niggemann, B.

B. Niggemann, T. L. Drell, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, F. Entschladen, “Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix,” Exp. Cell Res. 298, 178–187 (2004).
[CrossRef] [PubMed]

O’Brien, J. D.

P.-T. Lee, J. R. Cao, S.-J. Choi, Z.-J. Wei, J. D. O’Brien, P. D. Dapkus, “Operation of photonic crystal membrane lasers above room temperature,” Appl. Phys. Lett. 81, 3311–3313 (2002).
[CrossRef]

Pellerin, K. M.

Pingree, L. S. C.

L. S. C. Pingree, M. C. Hersam, M. M. Kern, B. J. Scott, T. J. Marks, “Spatially-resolved electroluminescence of operating organic light-emitting diodes using conductive atomic force microscopy,” Appl. Phys. Lett. 85, 344–346 (2004).
[CrossRef]

Righini, M.

Scott, B. J.

L. S. C. Pingree, M. C. Hersam, M. M. Kern, B. J. Scott, T. J. Marks, “Spatially-resolved electroluminescence of operating organic light-emitting diodes using conductive atomic force microscopy,” Appl. Phys. Lett. 85, 344–346 (2004).
[CrossRef]

Selci, S.

Stekolnikov, A. A.

A. A. Stekolnikov, J. Furthmüller, F. Bechstedt, “Structural elements on reconstructed Si and Ge(110) surfaces,” Phys. Rev. B 70(4), 045305 (2004).
[CrossRef]

Thio, T.

Wei, Z.-J.

P.-T. Lee, J. R. Cao, S.-J. Choi, Z.-J. Wei, J. D. O’Brien, P. D. Dapkus, “Operation of photonic crystal membrane lasers above room temperature,” Appl. Phys. Lett. 81, 3311–3313 (2002).
[CrossRef]

Weidt, C.

B. Niggemann, T. L. Drell, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, F. Entschladen, “Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix,” Exp. Cell Res. 298, 178–187 (2004).
[CrossRef] [PubMed]

Zaenker, K. S.

B. Niggemann, T. L. Drell, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, F. Entschladen, “Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix,” Exp. Cell Res. 298, 178–187 (2004).
[CrossRef] [PubMed]

Appl. Phys. Lett.

P.-T. Lee, J. R. Cao, S.-J. Choi, Z.-J. Wei, J. D. O’Brien, P. D. Dapkus, “Operation of photonic crystal membrane lasers above room temperature,” Appl. Phys. Lett. 81, 3311–3313 (2002).
[CrossRef]

L. S. C. Pingree, M. C. Hersam, M. M. Kern, B. J. Scott, T. J. Marks, “Spatially-resolved electroluminescence of operating organic light-emitting diodes using conductive atomic force microscopy,” Appl. Phys. Lett. 85, 344–346 (2004).
[CrossRef]

BMC Cell Biol.

S. Cooper, “Control and maintenance of mammalian cell size,” BMC Cell Biol. 5(35), (2004). (See http://www.biomedcentral.com/1471–2121/5/35.)
[CrossRef] [PubMed]

Exp. Cell Res.

B. Niggemann, T. L. Drell, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, F. Entschladen, “Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix,” Exp. Cell Res. 298, 178–187 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys., Part 1

K. Nakamoto, C. B. Mooney, S.-I. Kitamura, “AC mode feedback and gate pulse acquisition methods for scanning near-field optical microscope,” Jpn. J. Appl. Phys., Part 1 43, 2686–2689 (2004).
[CrossRef]

Nature (London)

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature (London) 424, 824–830 (2003).
[CrossRef]

Opt. Lett.

Phys. Rev. B

A. A. Stekolnikov, J. Furthmüller, F. Bechstedt, “Structural elements on reconstructed Si and Ge(110) surfaces,” Phys. Rev. B 70(4), 045305 (2004).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), p. 103.

Ref. [13], p. 74.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

(a) Schematic diagram of the interferometer configuration, (b) relative position of the detected aperture, (c) relative position of the embedded aperture.

Fig. 2
Fig. 2

Normalized derivative intensity versus test aperture width. Reference aperture width 150 μ m , relative position (a) 50 μ m , (b) 150 μ m , and (c) 250 μ m . Relative position of the reference aperture 250 μ m , width (d) 50 μ m , (e) 150 μ m , and (f) 250 μ m .

Fig. 3
Fig. 3

Normalized derivative intensity versus test aperture width. The maximum sensitive detected-aperture width was optimized at (a) 100 μ m , (b) 300 μ m , and (c) 500 μ m .

Fig. 4
Fig. 4

Normalized derivative intensity versus test aperture width with amplitude ratio (a) γ = 1 , (b) γ = 5 .

Fig. 5
Fig. 5

(a)–(c) Differences in intensity, d I d a , on the detector at test aperture width of 150 μ m . (d)–(f) Additional irradiance variations, introduced by interference, compared with the directly detected cases of the three situations. (a), (b): Optimized conditions; (b), (e) and (c), (f): nonoptimized conditions: (b)(e) and (c)(f).

Fig. 6
Fig. 6

Normalized derivative intensity versus width of the test aperture under the three conditions: nonoptimized (dotted curves), optimized (thin solid curves), misalignment of a 4 (thick solid curves), and misalignment of a 2 (dashed curve). (a) Tunable asymmetrically-embedded-aperture interferometer configuration, (b) embedded-aperture interferometer configuration.

Equations (18)

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

U ( x , y ) = exp ( j k z ) exp [ j k 2 z ( x 2 + y 2 ) ] j λ z U ( ξ , η ) exp [ j 2 π λ z ( x ξ + y η ) ] d ξ d η ,
U 1 ( x , y ) = exp ( j k z ) exp [ j k 2 z ( x 2 + y 2 ) ] j λ z C 1 exp ( j π x a λ z ) sin ( π x a λ z ) π x λ z sin ( π y b λ z ) π y λ z ,
U 2 ( x , y ) = exp ( j k z ) exp [ j k 2 z ( x 2 + y 2 ) ] j λ z C 2 exp ( j π x ( β α ) λ z ) sin [ π x ( β α ) λ z ] π x λ z sin ( π y b λ z ) π y λ z .
f I ( x ) = C 1 exp ( j π x a λ z ) sin ( π x a λ z ) π x λ z + C 2 exp ( j π x ( β α ) λ z ) sin [ π x ( β α ) λ z ] π x λ z 2 .
f I ( x ) = C 1 2 [ sin 2 ( π x a λ z ) ( π x λ z ) 2 + 2 γ sin ( π x a λ z ) π x λ z sin [ π x ( β α ) λ z ] π x λ z cos [ π x λ z ( a α β ) ] + γ 2 sin [ π x ( β α ) λ z ] 2 ( π x λ z ) 2 ] .
f a ( a ) = 2 z k C 1 2 ( 2 Si ( k a X z ) γ { Si [ k ( a α ) X z ] Si [ k ( a β ) X z ] } ) ,
f a 1 ( a ) = 4 z k C 1 2 Si ( K a x z ) .
f a 2 ( a ) = 2 z k γ C 1 2 { Si [ K ( a α ) x z ] Si [ K ( a β ) x z ] } ,
f a 2 ( a ) = 2 z k γ { Si [ K ( a α ) x z ] + Si [ K ( β a ) x z ] } .
K ( a 0 α ) x z = π ,
K ( β a 0 ) x z = π .
α = a 0 λ z 2 X ,
a = β α = λ z X .
a 0 > λ z 2 X ;
a 0 2 = λ z 2 X ,
a 2 = λ z X .
α = a 0 λ z 2 X ,
a = β α = λ z X .

Metrics