Abstract

We present a method for measuring the complete linear response, including amplitude, phase, and polarization, of a fiber-optic component or assembly that requires only a single scan of a tunable laser source. The method employs polarization-diverse swept-wavelength interferometry to measure the matrix transfer function of a device under test. We outline the theory of operation to establish how the transfer function is obtained. We demonstrate the enhanced accuracy, precision, and dynamic range of the technique through measurements of several components.

© 2005 Optical Society of America

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  1. The linear transfer function is the two-by-two matrix, H¯¯(ω), that relates the input and output electric field vectors of an optical system in the spectral domain according to E→out(ω)=H¯¯(ω)E→in(ω). We use the transfer function nomenclature because, whereas the Jones matrix describes only the transfer of the polarization state, the transfer function also contains the average loss (insertion loss) and phase (chromatic dispersion).
  2. D. Sandel, N. Reinhold, G. Heise, B. Borchert, “Optical network analysis and longitudinal structure characterization of fiber Bragg grating,” J. Lightwave Technol. 16, 2435–2442 (1998).
    [CrossRef]
  3. G. D. VanWiggeren, A. R. Motamedi, D. M. Baney, “Singlescan interferometric component analyzer,” IEEE Photon Technol Lett. 15, 263–265 (2003).
    [CrossRef]
  4. U. Glombitza, E. Brinkmeyer, “Coherent frequency domain reflectometry for characterization of single-mode integrated optical waveguides,” J. Lightwave Technol. 11, 1377–1384 (1993).
    [CrossRef]
  5. M. Froggatt, T. Erdogan, J. Moore, S. Shenk, “Optical frequency domain characterization (OFDC) of dispersion in optical fiber Bragg gratings,” in Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper FF2.
  6. R. Passy, N. Gisin, J. P. von der Wide, H. H. Gilden, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12, 1622–1630 (1994).
    [CrossRef]
  7. Misalignment of either polarization controller such that the proper orthogonality conditions are not met can lead to errors in the measurement. However, for these experiments the polarization alignment was maintained such that any errors due to misalignment were much less than other sources of error in the measurement.
  8. B. L. Heffner, “Automated measurement of polarization mode dispersion and using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
    [CrossRef]
  9. A. Motamedi, B. Szafraniec, P. Robrish, D. M. Baney, “Group delay reference artifact based on molecular gas absorption,” in Optical Fiber Communication, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2001), paper ThC8-l.
  10. B. L. Heffner, “Deterministic, analytically complete measurement of polarization dependent transmission through optical devices,” IEEE Photon. Technol. Lett. 4, 451–454 (1992).
    [CrossRef]

2003 (1)

G. D. VanWiggeren, A. R. Motamedi, D. M. Baney, “Singlescan interferometric component analyzer,” IEEE Photon Technol Lett. 15, 263–265 (2003).
[CrossRef]

1998 (1)

1994 (1)

R. Passy, N. Gisin, J. P. von der Wide, H. H. Gilden, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12, 1622–1630 (1994).
[CrossRef]

1993 (1)

U. Glombitza, E. Brinkmeyer, “Coherent frequency domain reflectometry for characterization of single-mode integrated optical waveguides,” J. Lightwave Technol. 11, 1377–1384 (1993).
[CrossRef]

1992 (2)

B. L. Heffner, “Automated measurement of polarization mode dispersion and using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
[CrossRef]

B. L. Heffner, “Deterministic, analytically complete measurement of polarization dependent transmission through optical devices,” IEEE Photon. Technol. Lett. 4, 451–454 (1992).
[CrossRef]

Baney, D. M.

G. D. VanWiggeren, A. R. Motamedi, D. M. Baney, “Singlescan interferometric component analyzer,” IEEE Photon Technol Lett. 15, 263–265 (2003).
[CrossRef]

A. Motamedi, B. Szafraniec, P. Robrish, D. M. Baney, “Group delay reference artifact based on molecular gas absorption,” in Optical Fiber Communication, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2001), paper ThC8-l.

Borchert, B.

Brinkmeyer, E.

U. Glombitza, E. Brinkmeyer, “Coherent frequency domain reflectometry for characterization of single-mode integrated optical waveguides,” J. Lightwave Technol. 11, 1377–1384 (1993).
[CrossRef]

Erdogan, T.

M. Froggatt, T. Erdogan, J. Moore, S. Shenk, “Optical frequency domain characterization (OFDC) of dispersion in optical fiber Bragg gratings,” in Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper FF2.

Froggatt, M.

M. Froggatt, T. Erdogan, J. Moore, S. Shenk, “Optical frequency domain characterization (OFDC) of dispersion in optical fiber Bragg gratings,” in Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper FF2.

Gilden, H. H.

R. Passy, N. Gisin, J. P. von der Wide, H. H. Gilden, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12, 1622–1630 (1994).
[CrossRef]

Gisin, N.

R. Passy, N. Gisin, J. P. von der Wide, H. H. Gilden, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12, 1622–1630 (1994).
[CrossRef]

Glombitza, U.

U. Glombitza, E. Brinkmeyer, “Coherent frequency domain reflectometry for characterization of single-mode integrated optical waveguides,” J. Lightwave Technol. 11, 1377–1384 (1993).
[CrossRef]

Heffner, B. L.

B. L. Heffner, “Automated measurement of polarization mode dispersion and using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
[CrossRef]

B. L. Heffner, “Deterministic, analytically complete measurement of polarization dependent transmission through optical devices,” IEEE Photon. Technol. Lett. 4, 451–454 (1992).
[CrossRef]

Heise, G.

Moore, J.

M. Froggatt, T. Erdogan, J. Moore, S. Shenk, “Optical frequency domain characterization (OFDC) of dispersion in optical fiber Bragg gratings,” in Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper FF2.

Motamedi, A.

A. Motamedi, B. Szafraniec, P. Robrish, D. M. Baney, “Group delay reference artifact based on molecular gas absorption,” in Optical Fiber Communication, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2001), paper ThC8-l.

Motamedi, A. R.

G. D. VanWiggeren, A. R. Motamedi, D. M. Baney, “Singlescan interferometric component analyzer,” IEEE Photon Technol Lett. 15, 263–265 (2003).
[CrossRef]

Passy, R.

R. Passy, N. Gisin, J. P. von der Wide, H. H. Gilden, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12, 1622–1630 (1994).
[CrossRef]

Reinhold, N.

Robrish, P.

A. Motamedi, B. Szafraniec, P. Robrish, D. M. Baney, “Group delay reference artifact based on molecular gas absorption,” in Optical Fiber Communication, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2001), paper ThC8-l.

Sandel, D.

Shenk, S.

M. Froggatt, T. Erdogan, J. Moore, S. Shenk, “Optical frequency domain characterization (OFDC) of dispersion in optical fiber Bragg gratings,” in Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper FF2.

Szafraniec, B.

A. Motamedi, B. Szafraniec, P. Robrish, D. M. Baney, “Group delay reference artifact based on molecular gas absorption,” in Optical Fiber Communication, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2001), paper ThC8-l.

VanWiggeren, G. D.

G. D. VanWiggeren, A. R. Motamedi, D. M. Baney, “Singlescan interferometric component analyzer,” IEEE Photon Technol Lett. 15, 263–265 (2003).
[CrossRef]

von der Wide, J. P.

R. Passy, N. Gisin, J. P. von der Wide, H. H. Gilden, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12, 1622–1630 (1994).
[CrossRef]

IEEE Photon Technol Lett. (1)

G. D. VanWiggeren, A. R. Motamedi, D. M. Baney, “Singlescan interferometric component analyzer,” IEEE Photon Technol Lett. 15, 263–265 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

B. L. Heffner, “Automated measurement of polarization mode dispersion and using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
[CrossRef]

B. L. Heffner, “Deterministic, analytically complete measurement of polarization dependent transmission through optical devices,” IEEE Photon. Technol. Lett. 4, 451–454 (1992).
[CrossRef]

J. Lightwave Technol. (3)

R. Passy, N. Gisin, J. P. von der Wide, H. H. Gilden, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12, 1622–1630 (1994).
[CrossRef]

U. Glombitza, E. Brinkmeyer, “Coherent frequency domain reflectometry for characterization of single-mode integrated optical waveguides,” J. Lightwave Technol. 11, 1377–1384 (1993).
[CrossRef]

D. Sandel, N. Reinhold, G. Heise, B. Borchert, “Optical network analysis and longitudinal structure characterization of fiber Bragg grating,” J. Lightwave Technol. 16, 2435–2442 (1998).
[CrossRef]

Other (4)

The linear transfer function is the two-by-two matrix, H¯¯(ω), that relates the input and output electric field vectors of an optical system in the spectral domain according to E→out(ω)=H¯¯(ω)E→in(ω). We use the transfer function nomenclature because, whereas the Jones matrix describes only the transfer of the polarization state, the transfer function also contains the average loss (insertion loss) and phase (chromatic dispersion).

M. Froggatt, T. Erdogan, J. Moore, S. Shenk, “Optical frequency domain characterization (OFDC) of dispersion in optical fiber Bragg gratings,” in Bragg Gratings, Photosensitivity and Poling in Glass Waveguides, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper FF2.

Misalignment of either polarization controller such that the proper orthogonality conditions are not met can lead to errors in the measurement. However, for these experiments the polarization alignment was maintained such that any errors due to misalignment were much less than other sources of error in the measurement.

A. Motamedi, B. Szafraniec, P. Robrish, D. M. Baney, “Group delay reference artifact based on molecular gas absorption,” in Optical Fiber Communication, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2001), paper ThC8-l.

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Figures (5)

Fig. 1
Fig. 1

Optical vector network analyzer.

Fig. 2
Fig. 2

FFT of raw data from detector P. The DUT is a fiber Bragg grating. The peaks at τD − τ and τD + τ are associated with two elements of the DUT TF. The dashed boxes represent the location of windows used to “slice out” these impulses to extract the DUT TF elements. The 6 ns width of these windows limits the measurable GD or PMD to 6 ns.

Fig. 3
Fig. 3

Group delay of an acetylene gas cell as measured (solid curve) using the technique described in this paper and as calculated (dashed curve) from the loss of the same cell. The inset shows five representative data sets illustrating measurement repeatability.

Fig. 4
Fig. 4

Measured PMD of a PMD artifact (solid curve) and a 7 m length of SMF28 fiber (dotted curve) using the network shown in Fig. 1.

Fig. 5
Fig. 5

Measured IL, GD, and PMD of a thin-film filter using the network shown in Fig. 1. The two IL curves represent the maximum and minimum IL as a function of input polarization state and wavelength.

Equations (10)

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E 1 = ( M ¯ ¯ 0 + M ¯ ¯ 1 ) ρ ̂ exp ( i ω t ) = m ̂ exp [ i ω ( t τ 0 ) ] + n ̂ exp [ i ω ( t τ 1 ) ] .
M ¯ ¯ D 0 P ¯ ¯ 2 m ̂ = 1 2 ( ŝ + p ̂ ) exp ( i ω τ D 0 ) ,
M ¯ ¯ D 0 P ¯ ¯ 2 n ̂ = 1 2 ( ŝ p ̂ ) exp ( i ω τ D 0 ) ,
E R , out = M ¯ ¯ D 0 P ¯ ¯ 2 E 1 = 1 2 ( ŝ + p ̂ ) exp [ i ω ( t τ 0 τ D 0 ) ] + 1 2 ( ŝ p ̂ ) exp [ i ω ( t τ 1 τ D 0 ) ] .
E D , out = H ¯ ¯ P ¯ ¯ 2 m ̂ exp [ i ω ( t τ 0 τ D 1 ) ] + H ¯ ¯ P ¯ ¯ 2 n ̂ exp [ i ω ( t τ 1 τ D 1 ) ] ,
E s ŝ = ( E out · ŝ ) ŝ = ( 1 2 { exp [ i ω ( t τ 0 τ D 0 ) ] + exp [ i ω ( t τ 1 τ D 0 ) ] } + [ ( H ¯ ¯ P ¯ ¯ 2 m ̂ ) · ŝ ] × exp [ i ω ( t τ 0 τ D 1 ) ] + [ ( H ¯ ¯ P ¯ ¯ 2 n ̂ ) · ŝ ] × exp [ i ω ( t τ 1 τ D 1 ) ] ) ŝ
E p p ̂ = ( E out · p ̂ ) p ̂ = ( 1 2 { exp [ i ω ( t τ 0 τ D 0 ) ] exp [ i ω ( t τ 1 τ D 0 ) ] } + [ ( H ¯ ¯ P ¯ ¯ 2 m ̂ ) · p ̂ ] × exp [ i ω ( t τ 0 τ D 1 ) ] + [ ( H ¯ ¯ P ¯ ¯ 2 n ̂ ) · p ̂ ] × exp [ i ω ( t τ 1 τ D 1 ) ] ) p ̂
I p ( ω ) = E p E p * Re { H p p exp [ i ω ( τ D + τ ) ] H s p exp [ i ω ( τ D τ ) ] } + ,
I s ( ω ) = E s E s * Re { H p s exp [ i ω ( τ D + τ ) ] + H s s exp [ i ω ( τ D τ ) ] } + .
G D ( ω ) = arg { H i j ( ω ) H ij * ( ω Δ ω ) } Δ ω ,

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