Abstract

We propose and demonstrate that a conventional multimode fiber can function as a high-resolution, low-loss spectrometer. The proposed spectrometer consists only of the fiber and a camera that images the speckle pattern generated by interference among the fiber modes. Although this speckle pattern is detrimental to many applications, it encodes information about the spectral content of the input signal, which can be recovered using calibration data. We achieve a spectral resolution of 0.15 nm over 25 nm bandwidth using 1 m long fiber, and 0.03 nm resolution over 5 nm bandwidth with a 5 m fiber. The insertion loss is less than 10%, and the signal-to-noise ratio in the reconstructed spectra is more than 1000.

© 2012 Optical Society of America

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References

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  1. Z. Xu, Z. Wang, M. E. Sullivan, D. J. Brady, S. H. Foulger, and A. Adibi, Opt. Express 11, 2126 (2003).
    [CrossRef]
  2. T. Kohlgraf-Owens and A. Dogariu, Opt. Lett. 352236 (2010).
    [CrossRef]
  3. Q. Hang, B. Ung, I. Syed, N. Guo, and M. Skorobogatiy, Appl. Opt. 49, 4791 (2010).
    [CrossRef]
  4. J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2007).

2010 (2)

2003 (1)

Adibi, A.

Brady, D. J.

Dogariu, A.

Foulger, S. H.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2007).

Guo, N.

Hang, Q.

Kohlgraf-Owens, T.

Skorobogatiy, M.

Sullivan, M. E.

Syed, I.

Ung, B.

Wang, Z.

Xu, Z.

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Figures (3)

Fig. 1.
Fig. 1.

(a–c) Images of the intensity distribution at the end of a 5 m long multimode fiber with varying input wavelength. Although the speckle pattern in (a) shows some resemblance to that in (b), it looks very different from that in (c), illustrating that the speckle pattern decorrelates quickly with wavelength; (d) Spectral correlation function C(Δλ) normalized to unity at Δλ=0 for fibers of varying length; (e) The spectral correlation width δλ, as a function of the inverse of the fiber length L. The crosses represent the experimental data points, and the straight line is a linear fit showing that δλ scales as 1/L.

Fig. 2.
Fig. 2.

(a) Close-up of a speckle pattern imaged at the end of a 1 m fiber. The transmission matrix was sampled at spatial positions separated by 3.8 μm (lc/2), indicated by “+” symbols; (b) Part of the transmission matrix for a 1 m fiber describing the intensity generated at varying spatial positions by different wavelengths. The wavelength spacing of adjacent spectral channels is 0.05 nm (δλ/4).

Fig. 3.
Fig. 3.

(a, c) Reconstructed spectra of single lines centered between the wavelengths sampled for the T matrix calibration. The average linewidth for the 1 m fiber spectrometer [(a) 25 nm bandwidth, 0.05 nm channel spacing] is 0.12 nm, and for the 5 m fiber [(c) 5 nm bandwidth, 0.01 nm channel spacing] is 0.021 nm. (b, d) Reconstructed spectra (black solid lines with crosses marking the sampled wavelengths λi) of two closely spaced lines. Red dotted lines mark the center wavelengths of the input lines. The 1 m fiber spectrometer (b) can clearly resolve two lines separated by 0.15 nm, and the 5 m fiber (d) can resolve lines separated by 0.03 nm.

Tables (1)

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Table 1. Summary of Spectrometer Performance

Equations (2)

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E(r,θ,λ,L)=m Amψm(r,θ,λ)exp[i(βm(λ)Lωt)],
I(r,θ)=T(r,θ,λ)S(λ)dλ,

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