Abstract

The reflection Airy distribution (RAD) of a Fabry-Pérot (F-P) resonator is deduced with the consideration of the mode coupling between the cavity resonance field and the initial back-reflected field at the input F-P resonator facet, as well as the influence of the loss/gain factor. A waveguide loss/gain measurement method is proposed based on the measurement of the finesse of the RAD, which is intrinsically free from the influence of the coupling loss and the substrate scattering noise. The waveguide loss can be measured with a simple single-facet coupling setup, considerably reducing the coupling difficulty and the complexity of the measurement system while achieving the same or better measurement accuracy as that of the transmission F-P method.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  2. I. P. Kaminow and L. W. Stulz, “Loss in cleaved Ti‐diffused LiNbO3 waveguides,” Appl. Phys. Lett. 33(1), 62–64 (1978).
    [Crossref]
  3. T. Feuchter and C. Thirstrup, “High Precision Planar Waveguide Propagation Loss Measurement Technique Using a Fabry-Perot Cavity,” IEEE Photonics Technol. Lett. 6(10), 1244–1247 (1994).
    [Crossref]
  4. S. Taebi, M. Khorasaninejad, and S. S. Saini, “Modified Fabry-Perot interferometric method for waveguide loss measurement,” Appl. Opt. 47(35), 6625–6630 (2008).
    [Crossref] [PubMed]
  5. R. Regener and W. Sohler, “Loss in low-finesse Ti: LiNbO3 optical waveguide resonators,” Appl. Phys. B 36(3), 143–147 (1985).
    [Crossref]
  6. W. H. Guo, Q. Y. Lu, Y. Z. Huang, and L. J. Yu, “Fourier series expansion method for gain measurement from amplified spontaneous emission spectra of Fabry-Pérot semiconductor lasers,” IEEE J. Quantum Electron. 40(2), 123–129 (2004).
    [Crossref]
  7. G. Tittelbach, B. Richter, and W. Karthe, “Comparison of three transmission methods for integrated optical waveguide propagation loss measurement,” Pure Appl. Opt. 2(6), 683–700 (1993).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  16. Y. He, Z. Li, and D. Lu, “A waveguide loss measurement method based on the reflected interferometric pattern of a Fabry-Perot cavity,” Proc. SPIE 10535, 105351U (2018).

2018 (1)

Y. He, Z. Li, and D. Lu, “A waveguide loss measurement method based on the reflected interferometric pattern of a Fabry-Perot cavity,” Proc. SPIE 10535, 105351U (2018).

2016 (1)

2008 (2)

S. Taebi, M. Khorasaninejad, and S. S. Saini, “Modified Fabry-Perot interferometric method for waveguide loss measurement,” Appl. Opt. 47(35), 6625–6630 (2008).
[Crossref] [PubMed]

W. H. Guo, D. Byrne, Q. Y. Lu, and J. F. Donegan, “Waveguide Loss Measurement Using the Reflection Spectrum,” IEEE Photonics Technol. Lett. 20(16), 1423–1425 (2008).
[Crossref]

2004 (1)

W. H. Guo, Q. Y. Lu, Y. Z. Huang, and L. J. Yu, “Fourier series expansion method for gain measurement from amplified spontaneous emission spectra of Fabry-Pérot semiconductor lasers,” IEEE J. Quantum Electron. 40(2), 123–129 (2004).
[Crossref]

1994 (2)

T. Feuchter and C. Thirstrup, “High Precision Planar Waveguide Propagation Loss Measurement Technique Using a Fabry-Perot Cavity,” IEEE Photonics Technol. Lett. 6(10), 1244–1247 (1994).
[Crossref]

R. Adar, V. Mizrahi, and M. R. Serbin, “Less than 1 dB Per Meter Propagation Loss of Silica Waveguides Measured Using a Ring Resonator,” J. Lit. Technol. 12(8), 1369–1372 (1994).
[Crossref]

1993 (1)

G. Tittelbach, B. Richter, and W. Karthe, “Comparison of three transmission methods for integrated optical waveguide propagation loss measurement,” Pure Appl. Opt. 2(6), 683–700 (1993).
[Crossref]

1991 (1)

1990 (1)

1985 (1)

R. Regener and W. Sohler, “Loss in low-finesse Ti: LiNbO3 optical waveguide resonators,” Appl. Phys. B 36(3), 143–147 (1985).
[Crossref]

1983 (1)

I. P. Kaminow, G. Eisenstein, and L. W. Stulz, “Measurement of the Modal Reflectivity of an Antireflection Coating on a Superluminescent Diode,” IEEE J. Quantum Electron. 19(4), 493–495 (1983).
[Crossref]

1978 (1)

I. P. Kaminow and L. W. Stulz, “Loss in cleaved Ti‐diffused LiNbO3 waveguides,” Appl. Phys. Lett. 33(1), 62–64 (1978).
[Crossref]

Adar, R.

R. Adar, V. Mizrahi, and M. R. Serbin, “Less than 1 dB Per Meter Propagation Loss of Silica Waveguides Measured Using a Ring Resonator,” J. Lit. Technol. 12(8), 1369–1372 (1994).
[Crossref]

Byrne, D.

W. H. Guo, D. Byrne, Q. Y. Lu, and J. F. Donegan, “Waveguide Loss Measurement Using the Reflection Spectrum,” IEEE Photonics Technol. Lett. 20(16), 1423–1425 (2008).
[Crossref]

Clark, D. F.

Deri, R. J.

Donegan, J. F.

W. H. Guo, D. Byrne, Q. Y. Lu, and J. F. Donegan, “Waveguide Loss Measurement Using the Reflection Spectrum,” IEEE Photonics Technol. Lett. 20(16), 1423–1425 (2008).
[Crossref]

Eisenstein, G.

I. P. Kaminow, G. Eisenstein, and L. W. Stulz, “Measurement of the Modal Reflectivity of an Antireflection Coating on a Superluminescent Diode,” IEEE J. Quantum Electron. 19(4), 493–495 (1983).
[Crossref]

Feuchter, T.

T. Feuchter and C. Thirstrup, “High Precision Planar Waveguide Propagation Loss Measurement Technique Using a Fabry-Perot Cavity,” IEEE Photonics Technol. Lett. 6(10), 1244–1247 (1994).
[Crossref]

Geskus, D.

Guo, W. H.

W. H. Guo, D. Byrne, Q. Y. Lu, and J. F. Donegan, “Waveguide Loss Measurement Using the Reflection Spectrum,” IEEE Photonics Technol. Lett. 20(16), 1423–1425 (2008).
[Crossref]

W. H. Guo, Q. Y. Lu, Y. Z. Huang, and L. J. Yu, “Fourier series expansion method for gain measurement from amplified spontaneous emission spectra of Fabry-Pérot semiconductor lasers,” IEEE J. Quantum Electron. 40(2), 123–129 (2004).
[Crossref]

He, Y.

Y. He, Z. Li, and D. Lu, “A waveguide loss measurement method based on the reflected interferometric pattern of a Fabry-Perot cavity,” Proc. SPIE 10535, 105351U (2018).

Huang, Y. Z.

W. H. Guo, Q. Y. Lu, Y. Z. Huang, and L. J. Yu, “Fourier series expansion method for gain measurement from amplified spontaneous emission spectra of Fabry-Pérot semiconductor lasers,” IEEE J. Quantum Electron. 40(2), 123–129 (2004).
[Crossref]

Iqbal, M. S.

Ismail, N.

Kaminow, I. P.

I. P. Kaminow, G. Eisenstein, and L. W. Stulz, “Measurement of the Modal Reflectivity of an Antireflection Coating on a Superluminescent Diode,” IEEE J. Quantum Electron. 19(4), 493–495 (1983).
[Crossref]

I. P. Kaminow and L. W. Stulz, “Loss in cleaved Ti‐diffused LiNbO3 waveguides,” Appl. Phys. Lett. 33(1), 62–64 (1978).
[Crossref]

Karthe, W.

G. Tittelbach, B. Richter, and W. Karthe, “Comparison of three transmission methods for integrated optical waveguide propagation loss measurement,” Pure Appl. Opt. 2(6), 683–700 (1993).
[Crossref]

Khorasaninejad, M.

Kores, C. C.

Li, Z.

Y. He, Z. Li, and D. Lu, “A waveguide loss measurement method based on the reflected interferometric pattern of a Fabry-Perot cavity,” Proc. SPIE 10535, 105351U (2018).

Lu, D.

Y. He, Z. Li, and D. Lu, “A waveguide loss measurement method based on the reflected interferometric pattern of a Fabry-Perot cavity,” Proc. SPIE 10535, 105351U (2018).

Lu, Q. Y.

W. H. Guo, D. Byrne, Q. Y. Lu, and J. F. Donegan, “Waveguide Loss Measurement Using the Reflection Spectrum,” IEEE Photonics Technol. Lett. 20(16), 1423–1425 (2008).
[Crossref]

W. H. Guo, Q. Y. Lu, Y. Z. Huang, and L. J. Yu, “Fourier series expansion method for gain measurement from amplified spontaneous emission spectra of Fabry-Pérot semiconductor lasers,” IEEE J. Quantum Electron. 40(2), 123–129 (2004).
[Crossref]

Mizrahi, V.

R. Adar, V. Mizrahi, and M. R. Serbin, “Less than 1 dB Per Meter Propagation Loss of Silica Waveguides Measured Using a Ring Resonator,” J. Lit. Technol. 12(8), 1369–1372 (1994).
[Crossref]

Pollnau, M.

Regener, R.

R. Regener and W. Sohler, “Loss in low-finesse Ti: LiNbO3 optical waveguide resonators,” Appl. Phys. B 36(3), 143–147 (1985).
[Crossref]

Richter, B.

G. Tittelbach, B. Richter, and W. Karthe, “Comparison of three transmission methods for integrated optical waveguide propagation loss measurement,” Pure Appl. Opt. 2(6), 683–700 (1993).
[Crossref]

Saini, S. S.

Serbin, M. R.

R. Adar, V. Mizrahi, and M. R. Serbin, “Less than 1 dB Per Meter Propagation Loss of Silica Waveguides Measured Using a Ring Resonator,” J. Lit. Technol. 12(8), 1369–1372 (1994).
[Crossref]

Sohler, W.

R. Regener and W. Sohler, “Loss in low-finesse Ti: LiNbO3 optical waveguide resonators,” Appl. Phys. B 36(3), 143–147 (1985).
[Crossref]

Stulz, L. W.

I. P. Kaminow, G. Eisenstein, and L. W. Stulz, “Measurement of the Modal Reflectivity of an Antireflection Coating on a Superluminescent Diode,” IEEE J. Quantum Electron. 19(4), 493–495 (1983).
[Crossref]

I. P. Kaminow and L. W. Stulz, “Loss in cleaved Ti‐diffused LiNbO3 waveguides,” Appl. Phys. Lett. 33(1), 62–64 (1978).
[Crossref]

Taebi, S.

Thirstrup, C.

T. Feuchter and C. Thirstrup, “High Precision Planar Waveguide Propagation Loss Measurement Technique Using a Fabry-Perot Cavity,” IEEE Photonics Technol. Lett. 6(10), 1244–1247 (1994).
[Crossref]

Tittelbach, G.

G. Tittelbach, B. Richter, and W. Karthe, “Comparison of three transmission methods for integrated optical waveguide propagation loss measurement,” Pure Appl. Opt. 2(6), 683–700 (1993).
[Crossref]

Tomlinson, W. J.

Yu, L. J.

W. H. Guo, Q. Y. Lu, Y. Z. Huang, and L. J. Yu, “Fourier series expansion method for gain measurement from amplified spontaneous emission spectra of Fabry-Pérot semiconductor lasers,” IEEE J. Quantum Electron. 40(2), 123–129 (2004).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

R. Regener and W. Sohler, “Loss in low-finesse Ti: LiNbO3 optical waveguide resonators,” Appl. Phys. B 36(3), 143–147 (1985).
[Crossref]

Appl. Phys. Lett. (1)

I. P. Kaminow and L. W. Stulz, “Loss in cleaved Ti‐diffused LiNbO3 waveguides,” Appl. Phys. Lett. 33(1), 62–64 (1978).
[Crossref]

IEEE J. Quantum Electron. (2)

W. H. Guo, Q. Y. Lu, Y. Z. Huang, and L. J. Yu, “Fourier series expansion method for gain measurement from amplified spontaneous emission spectra of Fabry-Pérot semiconductor lasers,” IEEE J. Quantum Electron. 40(2), 123–129 (2004).
[Crossref]

I. P. Kaminow, G. Eisenstein, and L. W. Stulz, “Measurement of the Modal Reflectivity of an Antireflection Coating on a Superluminescent Diode,” IEEE J. Quantum Electron. 19(4), 493–495 (1983).
[Crossref]

IEEE Photonics Technol. Lett. (2)

T. Feuchter and C. Thirstrup, “High Precision Planar Waveguide Propagation Loss Measurement Technique Using a Fabry-Perot Cavity,” IEEE Photonics Technol. Lett. 6(10), 1244–1247 (1994).
[Crossref]

W. H. Guo, D. Byrne, Q. Y. Lu, and J. F. Donegan, “Waveguide Loss Measurement Using the Reflection Spectrum,” IEEE Photonics Technol. Lett. 20(16), 1423–1425 (2008).
[Crossref]

J. Lit. Technol. (1)

R. Adar, V. Mizrahi, and M. R. Serbin, “Less than 1 dB Per Meter Propagation Loss of Silica Waveguides Measured Using a Ring Resonator,” J. Lit. Technol. 12(8), 1369–1372 (1994).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Proc. SPIE (1)

Y. He, Z. Li, and D. Lu, “A waveguide loss measurement method based on the reflected interferometric pattern of a Fabry-Perot cavity,” Proc. SPIE 10535, 105351U (2018).

Pure Appl. Opt. (1)

G. Tittelbach, B. Richter, and W. Karthe, “Comparison of three transmission methods for integrated optical waveguide propagation loss measurement,” Pure Appl. Opt. 2(6), 683–700 (1993).
[Crossref]

Other (3)

A. Yariv, Photonics: Optical Electronics in Modern Communication, 6th edition (Oxford University Press, 2006).

E. Hecht and A. Zajac, Optics, 5th edition (Pearson, 2016).

A. E. Siegman, Lasers (University Science Books, 1986).

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Figures (7)

Fig. 1
Fig. 1 Schematic of the transmission, reflection and resonance electric fields in a Fabry-Perot resonator. E0 is the incidence field, E1 is the launching field from the input facet, E2-E4 are the electric fields inside the cavity, ET = EFT is the forward transmission field. EBT is the backward transmission field. EIBRF is the initial back-reflected field, and ER is the back-transmission field which combined contribution from the EIBRF and EBT.
Fig. 2
Fig. 2 Schematic diagram of the reflection spectrum as a function of phase. Three curves in this Fig. represent the reflection spectrum of the mode coupling factor ηm of 100%, 70%, and 40%, respectively. The FWHMs of the three curves are exactly the same for different coupling factors.
Fig. 3
Fig. 3 The reflection finesse as a function of the waveguide loss for several typical uncoated waveguide resonators based on different material systems, where high reflectivity (H-R) material such as GaAs and InP, medium reflectivity (M-R) material such as LiNbO3, and low reflectivity (L-R) material such as SiO2 are compared.
Fig. 4
Fig. 4 The random standard error caused by finesse ℱ measurement deviation and contrast K measurement deviation as a function of loss at different reflectivity.
Fig. 5
Fig. 5 The experimental system schematic diagram.
Fig. 6
Fig. 6 The measured transmission and reflection spectrum of a test sample. The upper half is the reflection spectrum and the lower half is the transmission spectrum. The dots are the experimental data, and the curves are the fitting curve of the experimental data.
Fig. 7
Fig. 7 The loss values based on the transmission contrast (TC) and reflection finesse (RF) waveguide measurement schemes for sample 1 and 2 under different coupling conditions. In the figure, from left to right, the distance between the tapered fiber and the sample waveguide gradually increases.

Tables (1)

Tables Icon

Table 1 Comparison of the loss values obtained using the transmission and the reflection spectrum schemes.

Equations (21)

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E 1 = η inccav t 1 1 r 1 r 2 G e iφ E 0
E FT = η inccav G t 1 t 2 e iφ/2 1 r 1 r 2 G e iφ E 0
E BT = η inccav G t 1 2 r 2 e iφ 1 r 1 r 2 G e iφ E 0
E IBRF,C = η IBRF r 1 E 0
E R,C = E IBRF,C + E BT = η IBRF r 1 E 0 + η inccav G t 1 2 r 2 e iφ 1 r 1 r 2 G e iφ E 0 = η IBRF ( r 1 + η m G t 1 2 r 2 e iφ 1 r 1 r 2 G e iφ ) E 0
I R =DC+ I R,C =DC+ E R,C E R,C * =DC+ η IBRF 2 [ ( r 1 + η m G t 1 2 r 2 e iφ 1 r 1 r 2 G e iφ )( r 1 + η m G t 1 2 r 2 e iφ 1 r 1 r 2 G e iφ ) ] I 0
A R I R,C I 0 = η IBRF 2 ( r+ η m G t 2 r e iφ 1 r 2 G e iφ )( r+ η m G t 2 r e iφ 1 r 2 G e iφ ) = η IBRF 2 R[ ( 1GU ) 2 +4GU sin 2 ( φ/2 ) ] ( 1GR ) 2 +4GR sin 2 ( φ/2 )
A R = η IBRF 2 R[ ( 1GU ) 2 +4GU sin 2 ( φ/2 ) ] A circ
A circ = 1 ( 1GR ) 2 +4GR sin 2 ( φ/2 )
A R ' = R[ ( 1G ) 2 +4G sin 2 ( φ/2 ) ] ( 1GR ) 2 +4GR sin 2 ( φ/2 ) = R[ ( 1G ) 2 +4G sin 2 ( φ/2 )] A circ
A R,max = η IBRF 2 R ( 1+GU ) 2 ( 1+GR ) 2
A R,min = η IBRF 2 R ( 1GU ) 2 ( 1GR ) 2
C R = I R,max I R,min = DC+ A R,max I 0 DC+ A R,min I 0
I R ( φ 1/2 )= I R,max + I R,min 2
φ 1/2 =arccos( 2RG G 2 R 2 +1 )
F= 2π 2 φ 1/2 = π arccos( 2RG G 2 R 2 +1 )
G= e αL = 1 R 1sin φ 1/2 cos φ 1/2 = 1 R 1sin( π/F ) cos( π/F )
α= 1 L ln( 1 R 1sin( π/F ) cos( π/F ) )
G F = e αL = 1 R 1sin( π/F ) cos( π/F )
G K = e αL = 1 R K 1 K +1
A T =DC+ η IBRF 2 G (1R) 2 ( 1GR ) 2 +4GR sin 2 ( φ/2 )

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