Abstract

A new technique to cancel photodiode-induced even-order distortion in microwave photonic links is demonstrated. A single Mach-Zehnder modulator, biased slightly away from the quadrature point, is shown to suppress photodiode second-order intermodulation distortion in excess of 40 dB without affecting the fundamental power. The technique is theoretically described with supporting experimental results.

©2013 Optical Society of America

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References

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  1. V. J. Urick, J. F. Diehl, M. N. Draa, J. D. McKinney, and K. J. Williams, “Wideband analog photonic links: some performance limits and considerations for multi-octave limitations,” Proc. SPIE 8259, 1–14 (2012).
    [Crossref]
  2. V. J. Urick, A. S. Hastings, J. D. McKinney, P. S. Devgan, K. J. Williams, C. Sunderman, J. F. Diehl, and K. Colladay, “Photodiode linearity requirements for radio-frequency photonics and demonstration of increased performance using photodiode arrays,” in 2008IEEE International Meeting on Microwave Photonics Digest, pp. 86–89.
    [Crossref]
  3. A. Joshi, “Highly linear dual photodiodes for Ku-Band applications,” in 2009IEEE Avionics Fiber Optics and Photonics Conference Digest, pp. 9–10.
  4. Y. Fu, H. Pan, and J. C. Campbell, “Photodiodes with monolithically integrated Wilkinson power combiner,” IEEE J. Quantum Electron. 46(4), 541–545 (2010).
    [Crossref]
  5. S. Itakura, K. Sakai, T. Nagatsuka, E. Ishimura, M. Nakaji, H. Otsuka, K. Mori, and Y. Hirano, “High-current backside-illuminated photodiode array module for optical analog links,” J. Lightwave Technol. 28(6), 965–971 (2010).
    [Crossref]
  6. Y. Fu, H. Pan, Z. Li, and J. Campbell, “High linearity photodiode array with monolithically integrated Wilkinson power combiner,” in 2010IEEE International Meeting on Microwave Photonics Digest, pp. 111–113.
    [Crossref]
  7. A. S. Hastings, V. J. Urick, C. Sunderman, J. F. Diehl, J. D. McKinney, D. A. Tulchinsky, P. S. Devgan, and K. J. Williams, “Suppression of even-order photodiode nonlinearities in multioctave photonic links,” J. Lightwave Technol. 26(15), 2557–2562 (2008).
    [Crossref]
  8. B. H. Kolner and D. W. Dolfi, “Intermodulation distortion and compression in an integrated electrooptic modulator,” Appl. Opt. 26(17), 3676–3680 (1987).
    [Crossref] [PubMed]
  9. K. J. Williams and R. D. Esman, “Design considerations for high-current photodetectors,” J. Lightwave Technol. 17(8), 1443–1454 (1999).
    [Crossref]
  10. Y. Fu, H. Pan, Z. Li, A. Beling, and J. C. Campbell, “Characterizing and modeling nonlinear intermodulation distortions in modified uni-traveling carrier photodiodes,” IEEE J. Quantum Electron. 47(10), 1312–1319 (2011).
    [Crossref]
  11. A. Ramaswamy, N. Nunoya, K. J. Williams, J. Klamkin, M. Piels, L. A. Johansson, A. S. Hastings, L. A. Coldren, and J. E. Bowers, “Measurement of intermodulation distortion in high-linearity photodiodes,” Opt. Express 18(3), 2317–2324 (2010).
    [Crossref] [PubMed]
  12. M. N. Draa, A. S. Hastings, and K. J. Williams, “Comparison of photodiode nonlinearity measurement systems,” Opt. Express 19(13), 12635–12645 (2011).
    [Crossref] [PubMed]

2012 (1)

V. J. Urick, J. F. Diehl, M. N. Draa, J. D. McKinney, and K. J. Williams, “Wideband analog photonic links: some performance limits and considerations for multi-octave limitations,” Proc. SPIE 8259, 1–14 (2012).
[Crossref]

2011 (2)

Y. Fu, H. Pan, Z. Li, A. Beling, and J. C. Campbell, “Characterizing and modeling nonlinear intermodulation distortions in modified uni-traveling carrier photodiodes,” IEEE J. Quantum Electron. 47(10), 1312–1319 (2011).
[Crossref]

M. N. Draa, A. S. Hastings, and K. J. Williams, “Comparison of photodiode nonlinearity measurement systems,” Opt. Express 19(13), 12635–12645 (2011).
[Crossref] [PubMed]

2010 (3)

2008 (1)

1999 (1)

1987 (1)

Beling, A.

Y. Fu, H. Pan, Z. Li, A. Beling, and J. C. Campbell, “Characterizing and modeling nonlinear intermodulation distortions in modified uni-traveling carrier photodiodes,” IEEE J. Quantum Electron. 47(10), 1312–1319 (2011).
[Crossref]

Bowers, J. E.

Campbell, J. C.

Y. Fu, H. Pan, Z. Li, A. Beling, and J. C. Campbell, “Characterizing and modeling nonlinear intermodulation distortions in modified uni-traveling carrier photodiodes,” IEEE J. Quantum Electron. 47(10), 1312–1319 (2011).
[Crossref]

Y. Fu, H. Pan, and J. C. Campbell, “Photodiodes with monolithically integrated Wilkinson power combiner,” IEEE J. Quantum Electron. 46(4), 541–545 (2010).
[Crossref]

Coldren, L. A.

Devgan, P. S.

Diehl, J. F.

V. J. Urick, J. F. Diehl, M. N. Draa, J. D. McKinney, and K. J. Williams, “Wideband analog photonic links: some performance limits and considerations for multi-octave limitations,” Proc. SPIE 8259, 1–14 (2012).
[Crossref]

A. S. Hastings, V. J. Urick, C. Sunderman, J. F. Diehl, J. D. McKinney, D. A. Tulchinsky, P. S. Devgan, and K. J. Williams, “Suppression of even-order photodiode nonlinearities in multioctave photonic links,” J. Lightwave Technol. 26(15), 2557–2562 (2008).
[Crossref]

Dolfi, D. W.

Draa, M. N.

V. J. Urick, J. F. Diehl, M. N. Draa, J. D. McKinney, and K. J. Williams, “Wideband analog photonic links: some performance limits and considerations for multi-octave limitations,” Proc. SPIE 8259, 1–14 (2012).
[Crossref]

M. N. Draa, A. S. Hastings, and K. J. Williams, “Comparison of photodiode nonlinearity measurement systems,” Opt. Express 19(13), 12635–12645 (2011).
[Crossref] [PubMed]

Esman, R. D.

Fu, Y.

Y. Fu, H. Pan, Z. Li, A. Beling, and J. C. Campbell, “Characterizing and modeling nonlinear intermodulation distortions in modified uni-traveling carrier photodiodes,” IEEE J. Quantum Electron. 47(10), 1312–1319 (2011).
[Crossref]

Y. Fu, H. Pan, and J. C. Campbell, “Photodiodes with monolithically integrated Wilkinson power combiner,” IEEE J. Quantum Electron. 46(4), 541–545 (2010).
[Crossref]

Hastings, A. S.

Hirano, Y.

Ishimura, E.

Itakura, S.

Johansson, L. A.

Klamkin, J.

Kolner, B. H.

Li, Z.

Y. Fu, H. Pan, Z. Li, A. Beling, and J. C. Campbell, “Characterizing and modeling nonlinear intermodulation distortions in modified uni-traveling carrier photodiodes,” IEEE J. Quantum Electron. 47(10), 1312–1319 (2011).
[Crossref]

McKinney, J. D.

V. J. Urick, J. F. Diehl, M. N. Draa, J. D. McKinney, and K. J. Williams, “Wideband analog photonic links: some performance limits and considerations for multi-octave limitations,” Proc. SPIE 8259, 1–14 (2012).
[Crossref]

A. S. Hastings, V. J. Urick, C. Sunderman, J. F. Diehl, J. D. McKinney, D. A. Tulchinsky, P. S. Devgan, and K. J. Williams, “Suppression of even-order photodiode nonlinearities in multioctave photonic links,” J. Lightwave Technol. 26(15), 2557–2562 (2008).
[Crossref]

Mori, K.

Nagatsuka, T.

Nakaji, M.

Nunoya, N.

Otsuka, H.

Pan, H.

Y. Fu, H. Pan, Z. Li, A. Beling, and J. C. Campbell, “Characterizing and modeling nonlinear intermodulation distortions in modified uni-traveling carrier photodiodes,” IEEE J. Quantum Electron. 47(10), 1312–1319 (2011).
[Crossref]

Y. Fu, H. Pan, and J. C. Campbell, “Photodiodes with monolithically integrated Wilkinson power combiner,” IEEE J. Quantum Electron. 46(4), 541–545 (2010).
[Crossref]

Piels, M.

Ramaswamy, A.

Sakai, K.

Sunderman, C.

Tulchinsky, D. A.

Urick, V. J.

V. J. Urick, J. F. Diehl, M. N. Draa, J. D. McKinney, and K. J. Williams, “Wideband analog photonic links: some performance limits and considerations for multi-octave limitations,” Proc. SPIE 8259, 1–14 (2012).
[Crossref]

A. S. Hastings, V. J. Urick, C. Sunderman, J. F. Diehl, J. D. McKinney, D. A. Tulchinsky, P. S. Devgan, and K. J. Williams, “Suppression of even-order photodiode nonlinearities in multioctave photonic links,” J. Lightwave Technol. 26(15), 2557–2562 (2008).
[Crossref]

Williams, K. J.

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

Y. Fu, H. Pan, and J. C. Campbell, “Photodiodes with monolithically integrated Wilkinson power combiner,” IEEE J. Quantum Electron. 46(4), 541–545 (2010).
[Crossref]

Y. Fu, H. Pan, Z. Li, A. Beling, and J. C. Campbell, “Characterizing and modeling nonlinear intermodulation distortions in modified uni-traveling carrier photodiodes,” IEEE J. Quantum Electron. 47(10), 1312–1319 (2011).
[Crossref]

J. Lightwave Technol. (3)

Opt. Express (2)

Proc. SPIE (1)

V. J. Urick, J. F. Diehl, M. N. Draa, J. D. McKinney, and K. J. Williams, “Wideband analog photonic links: some performance limits and considerations for multi-octave limitations,” Proc. SPIE 8259, 1–14 (2012).
[Crossref]

Other (3)

V. J. Urick, A. S. Hastings, J. D. McKinney, P. S. Devgan, K. J. Williams, C. Sunderman, J. F. Diehl, and K. Colladay, “Photodiode linearity requirements for radio-frequency photonics and demonstration of increased performance using photodiode arrays,” in 2008IEEE International Meeting on Microwave Photonics Digest, pp. 86–89.
[Crossref]

A. Joshi, “Highly linear dual photodiodes for Ku-Band applications,” in 2009IEEE Avionics Fiber Optics and Photonics Conference Digest, pp. 9–10.

Y. Fu, H. Pan, Z. Li, and J. Campbell, “High linearity photodiode array with monolithically integrated Wilkinson power combiner,” in 2010IEEE International Meeting on Microwave Photonics Digest, pp. 111–113.
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Intensity-modulation direct-detection link employing an external Mach-Zehnder Modulator (MZM).

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Fig. 2
Fig. 2 Apparatus for characterization of photodiode linearity, where two lasers are both intensity modulated via an external Mach-Zehnder modulator (MZM). Variable optical attenuators (VOA) are employed to balance the output power between MZMs.

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Fig. 3
Fig. 3 Measured OIP2 due to intermodulation distortion for the photodiode at 3 mA average photocurrent. Shown are the measured fundamentals (circles), the measured IMD2 (squares), and the first- and second-order fits with slopes m = 1 and m = 2, respectively.

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Fig. 4
Fig. 4 (a) Measured OIP2s for the link at quadrature and at the cancellation point. Shown are the measured fundamentals (circles), the measured IMD2 at quadrature (squares), the measured IMD2 at the cancellation condition (triangles), and the first and second order fits with slopes m = 1 and m = 2, respectively. (b) The CIR at quadrature (squares) and at the cancellation condition (triangles).

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Fig. 5
Fig. 5 Measured fundamental output power (open circles), measured IMD2 (triangles) and measured DC photocurrent (gray circles) as a function of MZM bias for the link at −20 dBm input power to the fundamentals. The solid lines show the calculated fundamental power, IMD2 power and average photocurrent.

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Equations (14)

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[ E 1 ( t ) E 2 ( t ) ]= 1 2 [ 1 i i 1 ][ e iφ( t ) /2 0 0 e −iφ( t ) /2 ][ 1 i i 1 ][ E in ( t ) 0 ],
I dc,mzm = I dc,q − I dc,q J 0 ( ϕ 1 ) J 0 ( ϕ 2 )cos( ϕ dc )
I odd,mzm =2sin( ϕ dc ) I dc,q                       ×{ J 0 ( ϕ 2 ) ∑ j=0 ∞ J 2j+1 ( ϕ 1 )sin[ ( 2j+1 ) Ω 1 t ]                               + J 0 ( ϕ 1 ) ∑ k=0 ∞ J 2k+1 ( ϕ 2 )sin[ ( 2k+1 ) Ω 2 t ]                               − ∑ j=0 ∞ ∑ m=1 ∞ J 2j+1 ( ϕ 1 ) J 2m ( ϕ 2 )sin[ ( 2m Ω 2 −( 2j+1 ) Ω 1 )t ]                               − ∑ k=0 ∞ ∑ h=1 ∞ J 2k+1 ( ϕ 2 ) J 2h ( ϕ 1 )sin[ ( 2h Ω 1 −( 2k+1 ) Ω 2 )t ]                               + ∑ j=0 ∞ ∑ m=1 ∞ J 2j+1 ( ϕ 1 ) J 2m ( ϕ 2 )sin[ ( 2m Ω 2 +( 2j+1 ) Ω 1 )t ]                                + ∑ k=0 ∞ ∑ h=1 ∞ J 2k+1 ( ϕ 2 ) J 2h ( ϕ 1 )sin[ ( 2h Ω 1 +( 2k+1 ) Ω 2 )t ] }
I even,mzm =2cos( ϕ dc ) I dc,q                        ×{ − J 0 ( ϕ 2 ) ∑ k=1 ∞ J 2k ( ϕ 1 )cos( 2k Ω 1 t )                              − J 0 ( ϕ 1 ) ∑ m=1 ∞ J 2m ( ϕ 2 )cos( 2m Ω 2 t )                              + ∑ n=0 ∞ ∑ p=0 ∞ J 2n+1 ( ϕ 1 ) J 2p+1 ( ϕ 2 )cos[ ( ( 2p+1 ) Ω 2 −( 2n+1 ) Ω 1 )t ]                              − ∑ n=0 ∞ ∑ p=0 ∞ J 2n+1 ( ϕ 1 ) J 2p+1 ( ϕ 2 )cos[ ( ( 2p+1 ) Ω 2 +( 2n+1 ) Ω 1 )t ]                             − ∑ k=1 ∞ ∑ m=1 ∞ J 2k ( ϕ 1 ) J 2m ( ϕ 2 )cos[ 2( m Ω 2 −k Ω 1 )t ]                              − ∑ k=1 ∞ ∑ m=1 ∞ J 2k ( ϕ 1 ) J 2m ( ϕ 2 )cos[ 2( m Ω 2 +k Ω 1 )t ] }
I fund,mzm =ϕ I dc,q sin( ϕ dc )[ sin( Ω 1 t )+sin( Ω 2 t ) ].
I imd2,mzm =± ϕ 2 I dc,q cos( ϕ dc ) 2 cos[ ( Ω 2 ∓ Ω 1 )t ].
OIP 2 mzm = 2 sin 4 ( ϕ dc ) cos 2 ( ϕ dc ) I dc,q 2 R.
I pd = a 0 + a 1 ( I in − I dc )+ a 2 ( I in − I dc ) 2 +⋯
a m = 1 m! ⋅ d m I pd d I in m | I in = I dc .
I pd =( a 0 + a 2 I 2 )+ a 1 Isin( Ω 1 t )+ a 1 Isin( Ω 2 t )               − a 2 I 2 2 cos( 2 Ω 1 t )− a 2 I 2 2 cos( 2 Ω 2 t )               + a 2 I 2 cos[ ( Ω 1 − Ω 2 )t ]− a 2 I 2 cos[ ( Ω 1 + Ω 2 )t ]+⋯
I imd2,pd =± a 2 ϕ 2 I dc,q 2 sin 2 ( ϕ dc )cos[ ( Ω 2 ∓ Ω 1 )t ].
OIP 2 pd = a 1 4 R 2 a 2 2 .
I imd2,peak =± ϕ 2 I dc,q [ cos( ϕ dc ) 2 + a 2 I dc,q sin 2 ( ϕ dc ) ],
cos( ϕ dc ) sin 2 ( ϕ dc ) =−2 a 2 I dc,q .

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