Abstract

In this paper we investigate the variation of free spectral range (FSR) for the Fabry-Perot interferometer (FPI) consisting of mirrors with phase shift dispersion. The reflection phase shift on a mirror has been calculated employing the Transfer-Matrix Method and the values of FSR have been calculated under the condition of normal incidence of light beam. Fabry-Perot (FP) cavities have been fabricated employing bulk micromachining technology, and silicon wafers coated with multilayer dielectric films were used as mirrors. FSR of these FP cavities have been experimentally measured. The experimental data match the calculated results very well. The conclusion is that FSR shortening effect must be taken into account for the FPIs with a small plate gap, as the finesse and the tunable range of tunable FPI can be affected by the shortening effect greatly.

© 2003 Optical Society of America

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References

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Appl. Opt. (4)

Appl. Phys. Lett. (1)

D. E. Wohlert, K. Y. Cheng, and S. T. Chou, �??Temperature invariant lasing and gain spectra in self-assembled GaInAs quantum wire Fabry--Perot lasers,�?? Appl. Phys. Lett. 78, 1047-1049 (2001)
[CrossRef]

Electr. Lett. (1)

S. R. Mallinson and J. H. Jerman, �??Miniature micromachined Fabry-Perot interferometer in silicon,�?? Electr. Lett. 23, 1041-1043 (1987).
[CrossRef]

IEEE Photo. Tech. Lett. (2)

A. T. T. D. Tran, Y. H. Lo, Z.H. Zhu, D. Haronian, and E. Mozdy, �??Surface micromachined Fabry-Perot tunable filter,�?? IEEE Photo. Tech. Lett. 8, 393-395 (1996).
[CrossRef]

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, �??A Tunable Dispersion Compensating MEMS All-Pass Filter,�?? IEEE Photo. Tech. Lett. 12, 651-653 (2000).
[CrossRef]

National Defence Industry Industry Press (1)

Y. C. Lin and W. Q. Lu, Principles of Optical thin films, (National Defence Industry Industry Press of China, 1990), Chap. 2.

Opt. Engr. (1)

P. D. Atherton, N. K. Reay, J. Ring, and T. R. Hicks, �??Tunable Fabry-Perot filters,�?? Opt. Engr. 20, 806-814 (1981).

Opt. Lett. (1)

Principles of Optics (1)

M. Born and E. Wolf, Principles of Optics, (Cambridge, 1999), Chap. 7.

Proc. SPIE (1)

M. Xiang, Y. M. Cai, Y. M. Wu, J. Y. Yang, and Y. L. Wang, �??A Novel Method of fabricating Fabry-Perot Cavity Employing MEMS Wet-Etching Process,�?? Asia-Pacific Optical and Wireless Communications Conference, Jim Hsieh, and Leping Wei, eds., Proc. SPIE 5279-58 (2003).

Sov. J. Quan. Elec. (1)

Yu. V. Troitskii, �??Interferometer for measuring ultramall displacements with a nonmonochromatic light source,�?? Sov. J. Quan. Elec. 22, 1051-1054 (1992).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

The structure of FP cavity in the experiment. (a) before bonding; (b) after bonding (1. top silicon wafer; 2. bottom silicon wafer with spacers; 3. spacers; 4. AR film; 5. HR film; 6. adhesive.)

Fig. 2.
Fig. 2.

Optical test system.

Fig. 3.
Fig. 3.

The phase shift dispersion on each plate.

Fig. 4.
Fig. 4.

The calculated and measured results of FSR.

Tables (1)

Tables Icon

Table. 1. FSR data for some FP cavity samples

Equations (10)

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τ = T 2 ( 1 R ) 2 { 1 + 4 R ( 1 R ) 2 sin 2 [ Φ ( λ ) ] } .
Φ ( λ ) = 2 π h μ cos ( θ ) λ ε ( λ ) .
FSR n = 2 h μ cos ( θ ) [ n ( n + 1 ) ] .
FSR n = 2 h μ cos ( θ ) [ 1 ε ( λ n ) π + ε ( λ n + 1 ) π ] [ ( n + ε ( λ n ) π ) ( n + 1 + ε ( λ n + 1 ) π ) ] .
ε ( λ ) = k λ + d .
FSR n = 1 2 k { π + ( n π + d ) 2 + 8 π h k μ [ ( n + 1 ) π + d ] 2 + 8 π h k μ } .
ε λ = 0.00564 λ 8.841.
k = 0.00564
d = 8.841
FSR n = 2 h μ cos ( θ ) [ ( n + ψ π ) ( n + 1 + ψ π ) ] .

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