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Single-arm three-wave interferometer for measuring dispersion of short lengths of fiber

Michael A. Galle, Waleed Mohammed, Li Qian, and Peter W. E. Smith

Open Access Open Access

Abstract

We present a simple fiber-based single-arm spectral interferometer to measure directly the second-order dispersion parameter of short lengths of fiber (<50 cm). The standard deviation of the measured dispersion on a 39.5-cm-long SMF28™ fiber is 1×10-4 ps/nm, corresponding to 1% relative error, without employing any curve fitting. Our technique measures the second-order dispersion by examining the envelope of the interference pattern produced by three reflections: two from the facets of the test fiber and one from a mirror placed away from the fiber facet at a distance that introduces the same group delay as the test fiber at the measured wavelength. The operational constraints on system parameters, such as required bandwidth, wavelength resolution, and fiber length, are discussed in detail. Experimental verification of this technique is carried out via comparison of measurements of single mode fiber (SMF28™) with published data and via comparison of measurements of a dispersion compensating fiber with those taken using conventional techniques. Moreover, we used this new technique to measure the dispersion coefficient of a 45-cm-long twin-hole fiber over a 70 nm bandwidth. It is the first time dispersion measurement on this specialty fiber is reported.

©2007 Optical Society of America

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Figures (6)
Fig. 1.
Fig. 1. (a). General dual-arm balanced Michelson interferometer. The spectral interferogram is produced by two reflected waves U1 and U2 . (b) Single-arm interferometer where the spectral interferogram is produced by three reflected waves; Uo , U1 and U2 .

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Fig. 2.
Fig. 2. Simulated spectral interferogram produced by the setup in Fig. 1(b) for a 30-cm-long SMF28™ as the test fiber, with α=γ=1. The parameters used for the SMF28™ fiber are given in [27]. The thick green line represents the function calculated by Eq. (3), which is a close approximation of the upper envelope. Bmin denotes the minimum required bandwidth, and Bsource is the source bandwidth, which determines the extent of the interferogram. λ0 is the balanced wavelength. λ1 and λ2 are wavelengths corresponding to two adjacent troughs on one side of λ0.

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Fig. 3.
Fig. 3. (a). The dependence of wavelength resolution on the dispersion-length product (DLf). (b) The dependence of the minimum required bandwidth (Bmin) and the measurable bandwidth (Bmea), on the DLf product. Note we assume the values λo=1550nm and δLair=5µm and Bsource=130nm for these figures.

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Fig. 4.
Fig. 4. (a). Experimentally obtained spectral envelope for a 39.5cm SMF-28 fiber. (b) Measured dispersion compared to published dispersion [27] for the same fiber.

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Fig. 5.
Fig. 5. Comparison of dispersion values measured by two methods. The red points are obtained on a 100-m-long DCF using the Agilent 83427A Chromatic Dispersion Measurement System. The black points are obtained on a 15.5cm DCF using the SAI.

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Fig. 6.
Fig. 6. Dispersion measured using a 45-cm long Twin Hole Fiber

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Equations (24)

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U 1 = α U 0 e − j 2 β L f
U 2 = γ U 0 e − j 2 β L f − j 2 k 0 L air
I o = ∣ U 0 + U 1 + U 2 ∣ 2 = U 0 2 ∣ 1 + α e − i 2 β L f + γ e − i 2 β L f − i 2 k o L a ∣ 2
= U 0 2 { 1 + α 2 + γ 2 − 2 γ + 4 γ cos 2 ( β L f + k o L a ) + 2 α ( 1 − γ ) cos ( 2 β L f )
+ 4 α γ cos ( β L f + k o L a ) cos ( β L f − k o L a ) }
I upper _ env ≈ U o 2 ( 1 + α 2 + γ 2 + 2 α ( γ − 1 ) + 2 γ + 4 α ∣ cos ( ϕ envelope ) ∣ )
ϕ envelope ( λ ) = 2 π { 1 λ [ ( n eff ( λ o ) − λ o d n eff d λ ∣ λ o ) L f − L air ] + L f d n eff d λ ∣ λ o
+ L f ( λ − λ o ) 2 2 ! λ d 2 n eff d λ 2 ∣ λ o + L f ( λ − λ o ) 3 3 ! λ d 3 n eff d λ 3 ∣ λ o + ⋯ }
Δ ϕ envelope = ∣ ϕ envelope ( λ 2 ) − ϕ envelope ( λ 1 ) ∣
= 2 π ( [ ( λ 2 − λ 0 ) 2 2 ! λ 2 − ( λ 1 − λ 0 ) 2 2 ! λ 1 ] d 2 n eff d λ 2 ∣ λ 0 + [ ( λ 2 − λ 0 ) 3 3 ! λ 2 − ( λ 1 − λ 0 ) 3 3 ! λ 1 ] d 3 n eff d λ 3 ∣ λ 0 ) L f
D ( λ o ) = − λ o c d 2 n eff d λ 2 ∣ λ o
L air = ( n eff ( λ o ) − λ o d n eff d λ ∣ λ o ) L f
d L air d λ ∣ λ o = ( − λ o d 2 n eff d λ 2 ∣ λ o ) L f = cD ( λ o ) L f
δ λ o = δ L air c L f D
∣ ϕ envelope ( λ 1 ) − ϕ envelope ( λ 0 ) ∣ = 2 π ( λ 1 − λ 0 ) 2 2 ! λ 1 d 2 n eff d λ 2 ∣ λ 0 L f ≤ π
λ 1 − λ 0 ≤ λ 0 cD L f
( λ 2 − λ 0 ) 2 − ( λ 1 − λ 0 ) 2 ≈ λ o 2 cD L f
( λ 2 − λ 0 ) 2 = [ ( λ 2 − λ 1 ) + ( λ 1 − λ 0 ) ] 2 ≤ 2 λ o 2 cD L f
B min = 2 2 λ 0 cD L f
B mea = B source − B min ≥ B source − 2 2 λ 0 cD L f
B mea = B source − 2 ( λ 1 − λ 0 ) ≥ B source − 2 λ 0 cD L f
B min ≤ B source
L f ≥ 8 λ o 2 cD B source 2
L f ≤ λ o 2 4 n eff Δ λ
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