Abstract

We propose a spectrum analyzer based on the properties of a hologram recorded with the field transmitted by a Fabry–Perot etalon. The spectral response of this holographic Fabry–Perot spectrometer (HFPS) is analytically investigated in the paraxial approximation and compared with a conventional Fabry–Perot etalon of similar characteristics. We demonstrate that the resolving power is twice increased and the free spectral range (FSR) is reduced to one-half. The proposed spectrometer could improve the operational performance of the etalon because it can exhibit high efficiency and it would be insensible to environmental conditions such as temperature and vibrations. Our analysis also extends to another variant of the HFPS based on holographic multiplexing of the transmitted field of a Fabry–Perot etalon. This device increases the FSR, keeping the same HFPS performance.

© 2011 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  2. J. M. Vaughan, The Fabry–Perot Interferometer: History, Theory, Practice and Applications (Taylor & Francis, 1989).
  3. Ch. Fabry and A. Perot, Ann. Chim. Phys. 7, 459 (1897).
  4. L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, London, 1981).
  5. O. Martinez-Matos, J. A. Rodrigo, M. P. Hernández-Garay, J. G. Izquierdo, R. Weigand, M. L. Calvo, P. Cheben, P. Vaveliuk, and L. Bañares, Opt. Lett. 35, 652 (2010).
    [PubMed]
  6. F. del Monte, O. Martínez-Matos, J. A. Rodrigo, M. L. Calvo, and P. Cheben, Adv. Mater. 18, 2014 (2006).

2010

2006

F. del Monte, O. Martínez-Matos, J. A. Rodrigo, M. L. Calvo, and P. Cheben, Adv. Mater. 18, 2014 (2006).

1897

Ch. Fabry and A. Perot, Ann. Chim. Phys. 7, 459 (1897).

Bañares, L.

Born, M.

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

Calvo, M. L.

Cheben, P.

Cooke, D. J.

L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, London, 1981).

del Monte, F.

F. del Monte, O. Martínez-Matos, J. A. Rodrigo, M. L. Calvo, and P. Cheben, Adv. Mater. 18, 2014 (2006).

Fabry, Ch.

Ch. Fabry and A. Perot, Ann. Chim. Phys. 7, 459 (1897).

Hernández-Garay, M. P.

Izquierdo, J. G.

Martinez-Matos, O.

Martínez-Matos, O.

F. del Monte, O. Martínez-Matos, J. A. Rodrigo, M. L. Calvo, and P. Cheben, Adv. Mater. 18, 2014 (2006).

Perot, A.

Ch. Fabry and A. Perot, Ann. Chim. Phys. 7, 459 (1897).

Rodrigo, J. A.

Solymar, L.

L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, London, 1981).

Vaughan, J. M.

J. M. Vaughan, The Fabry–Perot Interferometer: History, Theory, Practice and Applications (Taylor & Francis, 1989).

Vaveliuk, P.

Weigand, R.

Wolf, E.

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

Adv. Mater.

F. del Monte, O. Martínez-Matos, J. A. Rodrigo, M. L. Calvo, and P. Cheben, Adv. Mater. 18, 2014 (2006).

Ann. Chim. Phys.

Ch. Fabry and A. Perot, Ann. Chim. Phys. 7, 459 (1897).

Opt. Lett.

Other

L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, London, 1981).

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

J. M. Vaughan, The Fabry–Perot Interferometer: History, Theory, Practice and Applications (Taylor & Francis, 1989).

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Figures (2)

Fig. 1
Fig. 1

(a) Fabry–Perot etalon illuminated with two spectral components ( λ 1 and λ 2 ) emanating from A. (b) HFPS: top, upper part of the real etalon for holographic recording with λ r ; bottom, down part of the virtual etalon for reconstruction with λ; (c) multiplexing HFPS ( m = 2 ): top, upper part of the real etalon for the recording with λ r ; bottom, down part of the effective virtual etalon for reconstruction with λ.

Fig. 2
Fig. 2

Simulated transmittivity, Γ, for the yellow and red doublets of a low pressure sodium-vapor lamp analyzed using (a) conventional Fabry–Perot etalon, (b) HFPS, and (c) multiplexed HFPS with m = 4 . R = 0.85 , and d = 12 μm .

Equations (7)

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Γ = ( 1 + F sin 2 δ / 2 ) 1 ,
R P = λ / Δ λ = π d F / λ ,
Δ λ FSR = λ 2 / 2 d ,
F = Δ λ FSR / Δ λ = π F / 2.
RP h = λ r / Δ λ h = 2 π d F / λ r ,
Δ λ FSR , h = λ 2 / 4 d ,
Δ λ FSR , h / Δ λ h = F .

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