Abstract

A micro displacement sensor and its sensing technique based on line-defect resonant cavity in photonic crystals (PhCs) are presented. The line-defect resonant cavity is formed by a fixed and a mobile PhC segments. With a proper operating frequency, a quasi-linear measurement of micro-displacement is achieved with sensitivity of 1.15 a -1 (a is the lattice constant) and Q factor of 40. The sensitivity can be adjusted easily by varying either Q factor or operating frequency of the sensing system. In addition, the sensing range can be broadened to -0.55 a ~0.60 a by using multiple operating frequencies. The properties of the micro displacement sensor are analyzed theoretically and simulated using finite-difference time-domain (FDTD) method.

© 2006 Optical Society of America

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References

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Appl. Phys. Lett. (3)

J. Topolancik, P. Bhattacharya, J. Sabarinathan, and P.-C. Yu, "Fluid detection with photonic crystal-based multichannel waveguides," Appl. Phys. Lett. 82, 1143-1145, (2003).
[CrossRef]

O. Levy, B. Z. Steinberg, M. Nathan, and A. Boag, "Ultrasensitive displacement sensing using photonic crystal waveguides," Appl. Phys. Lett. 86, 104102, (2005).
[CrossRef]

Wonjoo Suh, M. F. Yanik, Olav Solgaard, and Shanhui Fan, "Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs," Appl. Phys. Lett. 82, 1999-2001, (2003).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

Youngmin Kim, and Dean P. Neikirk, "Micromachined Fabry-Perot Cavity Pressure Transducer," IEEE Photonics Technol. Lett. 7, 1471-1473 (1995).
[CrossRef]

J. Appl. Phys. (1)

Wonjoo Suh, Olav Solgaard, and Shanhui Fan, "Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs," J. Appl. Phys. 98, 033102, (2005).
[CrossRef]

Opt. Eng. (1)

J. Zhou, S. Dasgupta, H. Kobayashi, J. M. Wolff, H. E. Jackson, and J. T. Boyd, "Optically interrogated MEMS pressure sensors for propulsion applications," Opt. Eng. 40, 598-604, (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

S. G. Johnson, P.. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

Other (2)

H. A. Haus, Waves and Felds in Optoelectronics (Prentice-Hall, Englewood Cliffs, USA, 1985).

J. Joannopoulos, R, Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 1995).

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Figures (7)

Fig. 1.
Fig. 1.

Layout of the linear displacement sensor based on 2D PhC with square lattice of dielectric rods. This structure is composed of a fixed PhC segment, a mobile PhC segment, a coherent light source and a photo detector. The radius of blued rods can be tuned to adjust the Q factor of PhC cavity.

Fig. 2.
Fig. 2.

(a) Lorentzian curves of normalized intensity for different displacements of moving PhC segment, the peak frequency moves from 0.335(2πc/a) to 0.333(2πc/a) when the displacement shifts from 0.00 a to 0.20 a, and the operating frequency is chosen near 0.332(2πc/a); (b) Variation of normalized intensity as a linear function of displacement, the blue square dots present the simulation values, and the red line is the linear regression result.

Fig. 3.
Fig. 3.

Electric-field distribution when a PCWG perpendicular to the line-defect cavity is formed: (a) The displacement is -0.60 a, the adjacent two columns of rods of fixed and moving segments form a PCWG; (b) The displacement is 0.70 a, an air PCWG is introduced between these two adjacent two columns of rods.

Fig. 4.
Fig. 4.

(a) M L 0 and theoretical sensitivity for each resonant frequency, the length of PhC cavity is 7 a; (b) Lorentzian curves of normalized intensity for the displacements shifting from 0.00 a to 0.10 a, and the operating frequency is chosen near 0.361(2πc/a).

Fig.5.
Fig.5.

(a)M L 0 and Q factor for different lengths of PhC cavity, the length increases from 7 a to 17 a, and the operating frequency is nearly 0.361(2πc/a); (b) Theoretical sensitivity as a function of the cavity length.

Fig. 6.
Fig. 6.

(a) Lorentzian curves of normalized intensity for the displacements shifting from 0.00 a to 0.075 a, the Q factor of sensor’s PhC cavity is enhanced to ~200 by increasing the radius of blued rods from 0.10 a to 0.15 a; (b) Variation of normalized intensity as a linear function of displacement, and the operating frequency is chosen near 0.332(2πc/a).

Fig. 7.
Fig. 7.

Sensing performances of the micro displacement sensor in the cases of (1) the moving PhC segment shifts 0.05 a in the perpendicular direction; (2) random errors are introduced in the radius and locations of dielectric rods; (3) error-free structure. The initial radius of blued rods in Fig.2 is 0.20 a, and L 0 =7a.

Tables (1)

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Table 1. Operating frequency, regression coefficient and sensitivity for different displacement regions

Equations (4)

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T ( ω , ω 0 ) = ( ω 0 2 Q ) 2 ( ω ω 0 ) 2 + ( ω 0 2 Q ) 2 ,
Δ T ( Δ L ) = T ( L 0 + Δ L ) T ( L 0 ) = T ( ω 0 + Δ ω , ω 1 ) T ( ω 0 , ω 1 ) ,
Δ T ( Δ L ) = T ( ω 0 , ω 1 ) Δ ω + T ( ω 0 , ω 1 ) 2 Δ ω 2 + O ( Δ ω ) ,
Δ T ( Δ L ) 3 3 Q 4 ω 0 Δ ω = 3 3 Q M L 0 4 ω 0 Δ L .

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