Spectral response of fiber-coupled Fabry&#x2013;Perot etalons

Pavel Ionov

doi:10.1364/JOSAA.31.000505

Abstract

In many remote sensing applications one or multiple Fabry–Perot etalons are used as high-spectral-resolution filter elements. These etalons are often coupled to a receiving telescope with a multimode fiber, leading to subtle effects of the fiber mode order on the overall spectral response of the system. A theoretical model is developed to treat the spectral response of the combined system: fiber, collimator, and etalon. The method is based on a closed-form expression of the diffracted mode in terms of a Hankel transform. In this representation, it is shown how the spectral effect of the fiber and collimator can be separated from the details of the etalon and can be viewed as a mode-dependent spectral broadening and shift.

Full Article | PDF Article

OSA Recommended Articles

Transmission characteristics of a Fabry-Perot etalon-microtoroid resonator coupled system

Wei Liang, Lan Yang, Joyce K. Poon, Yanyi Huang, Kerry J. Vahala, and Amnon Yariv
Opt. Lett. 31(4) 510-512 (2006)

Free spectral range measurement of a fiberized Fabry–Perot etalon with sub-Hz accuracy

Dimitrios Mandridis, Ibrahim Ozdur, Marcus Bagnell, and Peter J. Delfyett
Opt. Express 18(11) 11264-11269 (2010)

Ultraviolet high-spectral-resolution Rayleigh–Mie lidar with a dual-pass Fabry–Perot etalon for measuring atmospheric temperature profiles of the troposphere

Dengxin Hua, Masaru Uchida, and Takao Kobayashi
Opt. Lett. 29(10) 1063-1065 (2004)

References

View by:
Article Order
|
Year
|
Author
|
Publication

J. A. R. Rall, J. Campbell, J. B. Abshire, and J. D. Spinhirne, “Automatic weather station (AWS) lidar,” in IEEE 2001 International Geoscience and Remote Sensing Symposium (IEEE, 2001), Vol. 7, pp. 3065–3067.
B. M. Gentry, H. Chen, and S. X. Li, “Wind measurements with 355 nm molecular Doppler lidar,” Opt. Lett. 25, 1231–1233 (2000).
[Crossref]
C. J. Grund and E. W. Eloranta, “Fiber-optic scrambler reduces the bandpass range dependence of Fabry-Perot etalons used for spectral analysis of lidar backscatter,” Appl. Opt. 30, 2668–2670 (1991).
[Crossref]
D. Hua, M. Uchida, and T. Kobayashi, “Ultraviolet Rayleigh-Mie lidar with Mie-scattering correction by Fabry-Perot etalons for temperature profiling of the troposphere,” Appl. Opt. 44, 1305–1314 (2005).
[Crossref]
H. Xia, D. Sun, Y. Yang, F. Shen, J. Dong, and T. Kobayashi, “Fabry-Perot interferometer based Mie Doppler lidar for low tropospheric wind observation,” Appl. Opt. 46, 7120–7131 (2007).
[Crossref]
D. Su, A. A. P. Boechat, and J. D. C. Jones, “Beam delivery by large-core fibers: effect of launching conditions on near-field output profile,” Appl. Opt. 31, 5816–5821 (1992).
[Crossref]
A. Ghatak and K. Thyagarajan, An Introduction to Fiber Optics (Cambridge University, 1998).
J. Goodman, Introduction to Fourier Optics (Roberts, 2005), Chap. 3.
J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
[Crossref]
M. Guizar-Sicairos and J. C. Gutiérrez-Vega, “Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields,” J. Opt. Soc. Am. A 21, 53–58 (2004).
[Crossref]
H. Kihm and S.-W. Kim, “Nonparaxial free-space diffraction from oblique end faces of single-mode optical fibers,” Opt. Lett. 29, 2366–2368 (2004).
[Crossref]
L. Li and F. Guo, “An improved definition of divergence half-angle for the far-field of fiber,” Optik 123, 283–285 (2012).
[Crossref]
M. Young and R. C. Wittmann, “Vector theory of diffraction by a single-mode fiber: application to mode-field diameter measurements,” Opt. Lett. 18, 1715–1717 (1993).
[Crossref]
O. Svelto, Principles of Lasers (Plenum, 1998), Chaps. 4.5 and 4.7.
G. Arfken, Mathematical Methods for Physicists (Academic, 1985), Chaps. 2 and 11.
http://numpy.scipy.org/ .

2012 (1)

L. Li and F. Guo, “An improved definition of divergence half-angle for the far-field of fiber,” Optik 123, 283–285 (2012).
[Crossref]

1979 (1)

J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
[Crossref]

Abshire, J. B.

J. A. R. Rall, J. Campbell, J. B. Abshire, and J. D. Spinhirne, “Automatic weather station (AWS) lidar,” in IEEE 2001 International Geoscience and Remote Sensing Symposium (IEEE, 2001), Vol. 7, pp. 3065–3067.

Arfken, G.

G. Arfken, Mathematical Methods for Physicists (Academic, 1985), Chaps. 2 and 11.

Boechat, A. A. P.

D. Su, A. A. P. Boechat, and J. D. C. Jones, “Beam delivery by large-core fibers: effect of launching conditions on near-field output profile,” Appl. Opt. 31, 5816–5821 (1992).
[Crossref]

Campbell, J.

J. A. R. Rall, J. Campbell, J. B. Abshire, and J. D. Spinhirne, “Automatic weather station (AWS) lidar,” in IEEE 2001 International Geoscience and Remote Sensing Symposium (IEEE, 2001), Vol. 7, pp. 3065–3067.

Chen, H.

B. M. Gentry, H. Chen, and S. X. Li, “Wind measurements with 355 nm molecular Doppler lidar,” Opt. Lett. 25, 1231–1233 (2000).
[Crossref]

Dong, J.

H. Xia, D. Sun, Y. Yang, F. Shen, J. Dong, and T. Kobayashi, “Fabry-Perot interferometer based Mie Doppler lidar for low tropospheric wind observation,” Appl. Opt. 46, 7120–7131 (2007).
[Crossref]

Eloranta, E. W.

C. J. Grund and E. W. Eloranta, “Fiber-optic scrambler reduces the bandpass range dependence of Fabry-Perot etalons used for spectral analysis of lidar backscatter,” Appl. Opt. 30, 2668–2670 (1991).
[Crossref]

Gentry, B. M.

B. M. Gentry, H. Chen, and S. X. Li, “Wind measurements with 355 nm molecular Doppler lidar,” Opt. Lett. 25, 1231–1233 (2000).
[Crossref]

Ghatak, A.

A. Ghatak and K. Thyagarajan, An Introduction to Fiber Optics (Cambridge University, 1998).

Goodman, J.

J. Goodman, Introduction to Fourier Optics (Roberts, 2005), Chap. 3.

Grund, C. J.

C. J. Grund and E. W. Eloranta, “Fiber-optic scrambler reduces the bandpass range dependence of Fabry-Perot etalons used for spectral analysis of lidar backscatter,” Appl. Opt. 30, 2668–2670 (1991).
[Crossref]

Guizar-Sicairos, M.

M. Guizar-Sicairos and J. C. Gutiérrez-Vega, “Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields,” J. Opt. Soc. Am. A 21, 53–58 (2004).
[Crossref]

Guo, F.

L. Li and F. Guo, “An improved definition of divergence half-angle for the far-field of fiber,” Optik 123, 283–285 (2012).
[Crossref]

Gutiérrez-Vega, J. C.

M. Guizar-Sicairos and J. C. Gutiérrez-Vega, “Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields,” J. Opt. Soc. Am. A 21, 53–58 (2004).
[Crossref]

Harvey, J. E.

J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
[Crossref]

Hua, D.

D. Hua, M. Uchida, and T. Kobayashi, “Ultraviolet Rayleigh-Mie lidar with Mie-scattering correction by Fabry-Perot etalons for temperature profiling of the troposphere,” Appl. Opt. 44, 1305–1314 (2005).
[Crossref]

Jones, J. D. C.

D. Su, A. A. P. Boechat, and J. D. C. Jones, “Beam delivery by large-core fibers: effect of launching conditions on near-field output profile,” Appl. Opt. 31, 5816–5821 (1992).
[Crossref]

Kihm, H.

H. Kihm and S.-W. Kim, “Nonparaxial free-space diffraction from oblique end faces of single-mode optical fibers,” Opt. Lett. 29, 2366–2368 (2004).
[Crossref]

Kim, S.-W.

H. Kihm and S.-W. Kim, “Nonparaxial free-space diffraction from oblique end faces of single-mode optical fibers,” Opt. Lett. 29, 2366–2368 (2004).
[Crossref]

Kobayashi, T.

H. Xia, D. Sun, Y. Yang, F. Shen, J. Dong, and T. Kobayashi, “Fabry-Perot interferometer based Mie Doppler lidar for low tropospheric wind observation,” Appl. Opt. 46, 7120–7131 (2007).
[Crossref]

D. Hua, M. Uchida, and T. Kobayashi, “Ultraviolet Rayleigh-Mie lidar with Mie-scattering correction by Fabry-Perot etalons for temperature profiling of the troposphere,” Appl. Opt. 44, 1305–1314 (2005).
[Crossref]

Li, L.

L. Li and F. Guo, “An improved definition of divergence half-angle for the far-field of fiber,” Optik 123, 283–285 (2012).
[Crossref]

Li, S. X.

B. M. Gentry, H. Chen, and S. X. Li, “Wind measurements with 355 nm molecular Doppler lidar,” Opt. Lett. 25, 1231–1233 (2000).
[Crossref]

Rall, J. A. R.

J. A. R. Rall, J. Campbell, J. B. Abshire, and J. D. Spinhirne, “Automatic weather station (AWS) lidar,” in IEEE 2001 International Geoscience and Remote Sensing Symposium (IEEE, 2001), Vol. 7, pp. 3065–3067.

Shen, F.

H. Xia, D. Sun, Y. Yang, F. Shen, J. Dong, and T. Kobayashi, “Fabry-Perot interferometer based Mie Doppler lidar for low tropospheric wind observation,” Appl. Opt. 46, 7120–7131 (2007).
[Crossref]

Spinhirne, J. D.

J. A. R. Rall, J. Campbell, J. B. Abshire, and J. D. Spinhirne, “Automatic weather station (AWS) lidar,” in IEEE 2001 International Geoscience and Remote Sensing Symposium (IEEE, 2001), Vol. 7, pp. 3065–3067.

Su, D.

D. Su, A. A. P. Boechat, and J. D. C. Jones, “Beam delivery by large-core fibers: effect of launching conditions on near-field output profile,” Appl. Opt. 31, 5816–5821 (1992).
[Crossref]

Sun, D.

H. Xia, D. Sun, Y. Yang, F. Shen, J. Dong, and T. Kobayashi, “Fabry-Perot interferometer based Mie Doppler lidar for low tropospheric wind observation,” Appl. Opt. 46, 7120–7131 (2007).
[Crossref]

Svelto, O.

O. Svelto, Principles of Lasers (Plenum, 1998), Chaps. 4.5 and 4.7.

Thyagarajan, K.

A. Ghatak and K. Thyagarajan, An Introduction to Fiber Optics (Cambridge University, 1998).

Uchida, M.

D. Hua, M. Uchida, and T. Kobayashi, “Ultraviolet Rayleigh-Mie lidar with Mie-scattering correction by Fabry-Perot etalons for temperature profiling of the troposphere,” Appl. Opt. 44, 1305–1314 (2005).
[Crossref]

Wittmann, R. C.

M. Young and R. C. Wittmann, “Vector theory of diffraction by a single-mode fiber: application to mode-field diameter measurements,” Opt. Lett. 18, 1715–1717 (1993).
[Crossref]

Xia, H.

H. Xia, D. Sun, Y. Yang, F. Shen, J. Dong, and T. Kobayashi, “Fabry-Perot interferometer based Mie Doppler lidar for low tropospheric wind observation,” Appl. Opt. 46, 7120–7131 (2007).
[Crossref]

Yang, Y.

H. Xia, D. Sun, Y. Yang, F. Shen, J. Dong, and T. Kobayashi, “Fabry-Perot interferometer based Mie Doppler lidar for low tropospheric wind observation,” Appl. Opt. 46, 7120–7131 (2007).
[Crossref]

Young, M.

M. Young and R. C. Wittmann, “Vector theory of diffraction by a single-mode fiber: application to mode-field diameter measurements,” Opt. Lett. 18, 1715–1717 (1993).
[Crossref]

Am. J. Phys. (1)

J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
[Crossref]

Appl. Opt. (4)

C. J. Grund and E. W. Eloranta, “Fiber-optic scrambler reduces the bandpass range dependence of Fabry-Perot etalons used for spectral analysis of lidar backscatter,” Appl. Opt. 30, 2668–2670 (1991).
[Crossref]

D. Su, A. A. P. Boechat, and J. D. C. Jones, “Beam delivery by large-core fibers: effect of launching conditions on near-field output profile,” Appl. Opt. 31, 5816–5821 (1992).
[Crossref]

D. Hua, M. Uchida, and T. Kobayashi, “Ultraviolet Rayleigh-Mie lidar with Mie-scattering correction by Fabry-Perot etalons for temperature profiling of the troposphere,” Appl. Opt. 44, 1305–1314 (2005).
[Crossref]

H. Xia, D. Sun, Y. Yang, F. Shen, J. Dong, and T. Kobayashi, “Fabry-Perot interferometer based Mie Doppler lidar for low tropospheric wind observation,” Appl. Opt. 46, 7120–7131 (2007).
[Crossref]

J. Opt. Soc. Am. A (1)

M. Guizar-Sicairos and J. C. Gutiérrez-Vega, “Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields,” J. Opt. Soc. Am. A 21, 53–58 (2004).
[Crossref]

Opt. Lett. (3)

H. Kihm and S.-W. Kim, “Nonparaxial free-space diffraction from oblique end faces of single-mode optical fibers,” Opt. Lett. 29, 2366–2368 (2004).
[Crossref]

M. Young and R. C. Wittmann, “Vector theory of diffraction by a single-mode fiber: application to mode-field diameter measurements,” Opt. Lett. 18, 1715–1717 (1993).
[Crossref]

B. M. Gentry, H. Chen, and S. X. Li, “Wind measurements with 355 nm molecular Doppler lidar,” Opt. Lett. 25, 1231–1233 (2000).
[Crossref]

Optik (1)

L. Li and F. Guo, “An improved definition of divergence half-angle for the far-field of fiber,” Optik 123, 283–285 (2012).
[Crossref]

Other (6)

O. Svelto, Principles of Lasers (Plenum, 1998), Chaps. 4.5 and 4.7.

G. Arfken, Mathematical Methods for Physicists (Academic, 1985), Chaps. 2 and 11.

http://numpy.scipy.org/ .

J. A. R. Rall, J. Campbell, J. B. Abshire, and J. D. Spinhirne, “Automatic weather station (AWS) lidar,” in IEEE 2001 International Geoscience and Remote Sensing Symposium (IEEE, 2001), Vol. 7, pp. 3065–3067.

A. Ghatak and K. Thyagarajan, An Introduction to Fiber Optics (Cambridge University, 1998).

J. Goodman, Introduction to Fourier Optics (Roberts, 2005), Chap. 3.

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.

Click here to see a list of articles that cite this paper

Fig. 1. Optical configuration under study: multimode fiber, collimator, and Fabry–Perot etalon.

Download Full Size | PPT Slide | PDF

Fig. 2. (a) Geometry used in the derivation of the Rayleigh–Sommerfeld diffraction integral [see Eq. (1)]. Initial conditions are given on the surface

Σ_{0}

by

U (P_{0})

, and the field

U (P_{1})

is calculated at a point

P_{1}

. (b) Coordinate systems adopted to derive Eq. (9), (c) geometrical construct used to obtain Eq. (2).

Download Full Size | PPT Slide | PDF

Fig. 3. Gaussian beam propagation with Eq. (9) for 3 and 10 Rayleigh ranges.

Download Full Size | PPT Slide | PDF

Fig. 4. Fiber–collimator instrumental function

T_{f}

, for high-order mode in

NA = 0.22

fiber.

Download Full Size | PPT Slide | PDF

Fig. 5. Fiber–collimator instrumental function

T_{f}

, for high-order mode in

NA = 0.12

fiber.

Download Full Size | PPT Slide | PDF

Equations (26)

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

U (P_{1}) = \frac{1}{j λ} \iint_{Σ_{0}} U (P_{0}) \cos (n⃗, {r⃗}_{01}) \frac{\exp (j k r_{01})}{r_{01}} d s .

\cos (n⃗, {r⃗}_{01}) = \frac{z}{r_{01}} = \frac{ρ \cos (θ)}{r_{01}} .

U (P_{0}) = \exp (j n φ_{0}) u_{0} (r_{0}),

U (P_{1}) = \frac{ρ \exp (j n φ_{1}) \cos (θ)}{j λ} \int_{0}^{\infty} u_{0} (r_{0}) r_{0} d r_{0} \int_{0}^{2 π} \frac{\exp (j n Δ φ + j k r_{01})}{r_{01}^{2}} d Δ φ .

r_{01} = {(ρ^{2} + r_{0}^{2} - 2 ρ r_{0} \sin (θ) \cos (Δ φ))}^{1 / 2} .

r_{01} \approx ρ - r_{0} \sin (θ) \cos (Δ φ), in the phase

r_{01} \approx ρ, in the amplitude term .

U (P_{1}) = \frac{\exp (j n φ_{1} + j k ρ) \cos (θ)}{j λ ρ} \int_{0}^{\infty} u_{0} (r_{0}) r_{0} d r_{0} \int_{0}^{2 π} \exp (j n Δ φ + j k r_{0} \sin (θ) \cos (Δ φ)) d Δ φ .

U (P_{1}) = \frac{\exp (j n φ_{1} - j n π / 2 + j k ρ) \cos (θ)}{j λ ρ} 2 π \int_{0}^{\infty} u_{0} (r_{0}) J_{n} (k r_{0} \sin (θ)) r_{0} d r_{0} .

U (P_{1}) = \frac{\exp (j n φ_{1} - j n π / 2 + j k ρ) \cos (θ)}{j λ ρ} H_{n} {u_{0}} (\frac{\sin (θ)}{λ}),

H_{n} {f} (ν) = 2 π \int_{0}^{\infty} f (r) J_{n} (2 π ν r) r d r,

H_{n}^{- 1} {f} (r) = 2 π \int_{0}^{\infty} f (ν) J_{n} (2 π ν r) ν d ν .

U (P_{1}) = \exp (j n φ_{1}) \frac{\exp (j k ρ)}{λ ρ} u_{1} (θ) .

u_{1} (θ) = \cos (θ) H_{n} {u_{0}} (\frac{\sin (θ)}{λ}) .

U (Σ_{2}) = \exp (j n φ_{2}) u_{2} (r_{2}),

u_{2} (r_{2}) = \frac{F}{λ (F^{2} + r_{2}^{2})} H_{n} {u_{0}} (\frac{r_{2}}{λ {(F^{2} + r_{2}^{2})}^{0.5}}) .

U (Σ_{2}) \approx \exp (j n φ_{2}) H_{n} {u_{0}} (r_{2} / λ F) / λ F .

u_{3} (θ) = H_{n} {u_{2}} (\frac{θ}{λ}) .

g_{n} (k_{r}) = \exp (j ω t + j n φ + j k_{z} z) J_{n} (k_{r} r), where

k_{z}^{2} + k_{r}^{2} = k^{2} = {(\frac{2 π}{λ})}^{2} .

T_{e} (k_{z}) = {| \frac{t_{1} t_{2}}{1 - r_{1} r_{2} \exp (2 j k_{z} L)} |}^{2} .

I_{t} (L_{nm}) = \int_{0}^{\infty} {| H {u_{2}} (ν) |}^{2} T_{e} (2 π \sqrt{λ^{- 2} - ν^{2}}) ν d ν .

I_{t} (L_{nm}) = \int_{0}^{\infty} {| H {u_{2}} (ν) |}^{2} T_{e} (2 π (λ^{- 1} - 0.5 λ ν^{2})) ν d ν .

I_{t} / I = \int_{0}^{\infty} T_{f} (Δ f) T_{e} (2 π (f - Δ f) / c) d Δ f, where

T_{f} (Δ f) = {| H {u_{2}} (\sqrt{2 Δ f / λ c}) |}^{2} / \int_{0}^{\infty} {| H {u_{2}} (\sqrt{2 Δ f / λ c}) |}^{2} d Δ f .

T_{f} (Δ f) \approx {| u_{0} (F \sqrt{2 Δ f / f}) |}^{2} / \int_{0}^{\infty} {| u_{0} (F \sqrt{2 Δ f / f}) |}^{2} d Δ f, for NA ≪ 1 .

Abstract

References

2012 (1)

2007 (1)

2005 (1)

2004 (2)

2000 (1)

1993 (1)

1992 (1)

1991 (1)

1979 (1)

Abshire, J. B.

Arfken, G.

Boechat, A. A. P.

Campbell, J.

Chen, H.

Dong, J.

Eloranta, E. W.

Gentry, B. M.

Ghatak, A.

Goodman, J.

Grund, C. J.

Guizar-Sicairos, M.

Guo, F.

Gutiérrez-Vega, J. C.

Harvey, J. E.

Hua, D.

Jones, J. D. C.

Kihm, H.

Kim, S.-W.

Kobayashi, T.

Li, L.

Li, S. X.

Rall, J. A. R.

Shen, F.

Spinhirne, J. D.

Su, D.

Sun, D.

Svelto, O.

Thyagarajan, K.

Uchida, M.

Wittmann, R. C.

Xia, H.

Yang, Y.

Young, M.

Am. J. Phys. (1)

Appl. Opt. (4)

J. Opt. Soc. Am. A (1)

Opt. Lett. (3)

Optik (1)

Other (6)

Cited By

Figures (5)

Equations (26)

Metrics

Login or Create Account