Abstract

Spurious reflections can preclude the accurate experimental characterization of integrated optical devices. This is particularly important for facet reflections in high refractive index platforms such as Indium Phosphide (InP) or Silicon-on-Insulator (SOI) when no anti-reflective (AR) coating is used. In this paper we present a novel method to recover the original device characteristics from the measured power transmission in the presence of such reflections. Our approach uses minimum phase techniques to reconstruct time domain information which is filtered to remove the reflection artifacts. A criterion to assess if a certain device exhibits the minimum phase characteristics required to apply the technique is given. Simulated and experimental results for multi-mode interference couplers (MMICs) in SOI without AR coating validate the technique.

©2009 Optical Society of America

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References

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2008 (1)

2007 (1)

A. Ozcan, M. Digonnet, and G. Kino, “Quasi-phase-matched grating characterization using minimum-phase functions,” Opt. Commun. 269, 199–205 (2007).
[Crossref]

2006 (2)

2005 (1)

2004 (2)

2001 (1)

J. McDaniel and C. Clarke, “Interpretation and identification of minimum phase reflection coefficients,” J. Acoust. Soc. Am. 110, 3003–3010 (2001).
[Crossref]

1999 (2)

K. Rochford and S. Dyer, “Reconstruction of minimum-phase group delay from fibre Bragg grating transmittance/reflectance measurements,” Electron. Lett. 35, 838–839 (1999).
[Crossref]

J. Skaar and H. Engan, “Phase reconstruction from reflectivity in fiber Bragg gratings,” Opt. Lett. 24, 136–138 (1999).
[Crossref]

1997 (3)

M. Muriel and A. Carballar, “Phase reconstruction from reflectivity in uniform fiber Bragg gratings,” Opt. Express 22, 93–95 (1997).

A. Carballar and M. Muriel, “Phase reconstruction from reflectivity in fiber Bragg gratings,” J. Lightwave Tech-nol. 15, 1314–1322 (1997).
[Crossref]

L. Poladian, “Group-delay reconstruction for fiber Bragg gratings in reflection and transmission,” Opt. Lett. 22, 1571–1573 (1997).
[Crossref]

1995 (1)

1991 (1)

1989 (1)

1985 (1)

R. G. Walker, “Simple and accurate loss measurement technique for semiconductor optical waveguides,” Electron. Lett. 21, 581–583 (1985).
[Crossref]

1978 (1)

1956 (1)

S. J. Mason, “Feedback Theory — Further Properties of Singal Flow Graphs,” Proc. IRE 44, 920–926 (1956).
[Crossref]

Baquero, P.

Brown, J. W.

R. V. Churchill and J. W. Brown, Variable Compleja y Aplicaciones (McGraw-Hill, 1990).

Carballar, A.

M. Muriel and A. Carballar, “Phase reconstruction from reflectivity in uniform fiber Bragg gratings,” Opt. Express 22, 93–95 (1997).

A. Carballar and M. Muriel, “Phase reconstruction from reflectivity in fiber Bragg gratings,” J. Lightwave Tech-nol. 15, 1314–1322 (1997).
[Crossref]

Cheben, P.

Churchill, R. V.

R. V. Churchill and J. W. Brown, Variable Compleja y Aplicaciones (McGraw-Hill, 1990).

Clarke, C.

J. McDaniel and C. Clarke, “Interpretation and identification of minimum phase reflection coefficients,” J. Acoust. Soc. Am. 110, 3003–3010 (2001).
[Crossref]

Deri, R. J.

Digonnet, M.

Dyer, S.

K. Rochford and S. Dyer, “Reconstruction of minimum-phase group delay from fibre Bragg grating transmittance/reflectance measurements,” Electron. Lett. 35, 838–839 (1999).
[Crossref]

Engan, H.

Fienup, J.

Froggatt, M. E.

Gifford, D. K.

Gottesman, Y.

Halir, R.

Hernández-Gil, F.

Janz, S.

Kino, G.

Mason, S. J.

S. J. Mason, “Feedback Theory — Further Properties of Singal Flow Graphs,” Proc. IRE 44, 920–926 (1956).
[Crossref]

McDaniel, J.

J. McDaniel and C. Clarke, “Interpretation and identification of minimum phase reflection coefficients,” J. Acoust. Soc. Am. 110, 3003–3010 (2001).
[Crossref]

Molina-Fernández, I.

Muriel, M.

A. Carballar and M. Muriel, “Phase reconstruction from reflectivity in fiber Bragg gratings,” J. Lightwave Tech-nol. 15, 1314–1322 (1997).
[Crossref]

M. Muriel and A. Carballar, “Phase reconstruction from reflectivity in uniform fiber Bragg gratings,” Opt. Express 22, 93–95 (1997).

Oppenheim, A. V.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall International, 1989).

A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice Hall, 1975).

Ortega-Moñux, A.

Ozcan, A.

Poladian, L.

Rabus, D.

Rao, E.

Rochford, K.

K. Rochford and S. Dyer, “Reconstruction of minimum-phase group delay from fibre Bragg grating transmittance/reflectance measurements,” Electron. Lett. 35, 838–839 (1999).
[Crossref]

Schafer, R. W.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall International, 1989).

A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice Hall, 1975).

Shahar, A.

Skaar, J.

Soller, B. J.

Tomlinson, W. J.

Vázquez, C.

Victor, J.

Walker, R. G.

R. G. Walker, “Simple and accurate loss measurement technique for semiconductor optical waveguides,” Electron. Lett. 21, 581–583 (1985).
[Crossref]

Wangüemert-Pérez, J. G.

Wolfe, M. S.

Xu, D.-X.

Appl. Opt. (2)

Electron. Lett. (2)

R. G. Walker, “Simple and accurate loss measurement technique for semiconductor optical waveguides,” Electron. Lett. 21, 581–583 (1985).
[Crossref]

K. Rochford and S. Dyer, “Reconstruction of minimum-phase group delay from fibre Bragg grating transmittance/reflectance measurements,” Electron. Lett. 35, 838–839 (1999).
[Crossref]

J. Acoust. Soc. Am. (1)

J. McDaniel and C. Clarke, “Interpretation and identification of minimum phase reflection coefficients,” J. Acoust. Soc. Am. 110, 3003–3010 (2001).
[Crossref]

J. Lightwave Tech-nol. (1)

A. Carballar and M. Muriel, “Phase reconstruction from reflectivity in fiber Bragg gratings,” J. Lightwave Tech-nol. 15, 1314–1322 (1997).
[Crossref]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

A. Ozcan, M. Digonnet, and G. Kino, “Quasi-phase-matched grating characterization using minimum-phase functions,” Opt. Commun. 269, 199–205 (2007).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Proc. IRE (1)

S. J. Mason, “Feedback Theory — Further Properties of Singal Flow Graphs,” Proc. IRE 44, 920–926 (1956).
[Crossref]

Other (3)

A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice Hall, 1975).

R. V. Churchill and J. W. Brown, Variable Compleja y Aplicaciones (McGraw-Hill, 1990).

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall International, 1989).

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Figures (8)

Fig. 1.
Fig. 1. Measured transmittance of a 2×3 MMIC in SOI without AR coating.
Fig. 2.
Fig. 2. (a) Physical model of a device inside a Fabry-Perot cavity with signal flow graph. (b) Schematic representation of the impulse response m(t). (c) Minimum phase signal flow graph.
Fig. 3.
Fig. 3. 2×2 coupler with signal flow graph. The two forward paths are shown as blue and red lines.
Fig. 4.
Fig. 4. (a) Simulated power transmission of a 2 × 2 MMIC in SOI without AR coating. The device layout is shown schematically in the inset of Fig. 4(b). (b) Computed minimum phase impulse response. The length of the input and output waveguides shown in the inset are L 1 = 1mm, L 2 = 2 mm, L 3 = 3 mm and L 4 = 4 mm. The length of the MMIC is 0.256mm [22].
Fig. 5.
Fig. 5. Recovered coupler parameters for (a) a 2 × 2 MMIC and (b) a 2 × 3 MMIC.
Fig. 6.
Fig. 6. Measurement setup (not to scale).
Fig. 7.
Fig. 7. (a) MPTF processed calibration data. (b) Minimum phase impulse response (c) Recovered coupler response.
Fig. 8.
Fig. 8. Discrete time representation of a sequence of impulses.

Equations (20)

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m(t)=+M(ν)exp(jM(ν))exp(j2πνt)dν.
Di(ν)=exp(αLi)exp(j2πνneffLi/c),
M˜0(ν)2=C12C22exp(2α(L1+L2))S21(ν)2.
M(s)=+m(t)exp(st)dt,
M(s)=C1D1(s)S21(s)D2(s)C2Δ(s) .
M˜(s)=C1D˜1(s)S˜21(s)D˜2(s)C2Δ(s)
M¯(s)=D¯1(s)S¯21(s)D¯2(s).
m˜0(t)=C1C2exp(α(L1+L2))s˜21(t),
M˜0(ν)2=C12C22exp(2α(L1+L2))S21(ν)2 ,
M(s)=1Δ(s) [k=0NFk(s)[1+qkPqk(s)]] ,
F0>k=1NFk+k=0NFkqkPqk,
Lminλ02BWDUTng,
BWmeasλ02LDUTng.
Λλ02Lmaxng ,
M(s)=1Δ(s) [k=0NFk(s)[1+qkPqk(s)]] .
V(s)=exp(sτ0)[F0+k=1NFkexp(sτk)+k=0NFkexp(sτk)qkPqkexp(sτqk)],
U(z)=F0zmM+k=1NFkzmMmk+k=0NFkzmMmkqkPqkzmqk.
f(z)=F0zmM
g(z)=U(z)f(z).
F0>k=1NFk+k=0NFkqkPqk,

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