Abstract

We report on a novel cancellation technique, for reducing the nonlinearity associated with the tracking phase-modulator in recently proposed phase-locked coherent demodulator for phase modulated analog optical links. The proposed cancellation technique is input RF signal power and frequency independent leading to a significant increase in dynamic range of the coherent demodulator. Furthermore, this technique demonstrates that large values of the signal-to-intermodulation ratio of the demodulated signal can be obtained even though the tracking phase modulator is fairly nonlinear, and thereby relaxing the linearity requirements for the tracking phase modulator. A new model is developed and the calculated results are in good agreement with measurements.

© 2007 Optical Society of America

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  1. C. H. Cox, E. I. Ackerman, G. E. Bets and J. L. Prince,"Limits on performance of RF-over-fibre links and their impact on device design," IEEE Trans. on Microwave Theory Tech. 54, Part 2, 906-920 (2006)
    [CrossRef]
  2. AlwynJ. Seeds,"Microwave photonics," IEEE Trans. on Microwave Theory Tech. 50, 877-887 (2002)
    [CrossRef]
  3. R.F. Kalman, J.C. Fan and L.G. Kazovsky, "Dynamic range of coherent analog fiber-optic links," IEEE J. Lightwave Technol. 12, 1263-1277 (1994)
    [CrossRef]
  4. H. F. Chou, A. Ramaswamy, D. Zibar, L.A. Johansson, L. Coldren and J. Bowers, "SFDR Improvement of a Coherent Receiver Using Feedback," in Optical Amplifiers and Their Applications/Coherent Optical Technologies and Applications, Technical Digest (CD) (Optical Society of America, 2006), paper CFA3.
  5. <jrn>H. F. Chou, A. Ramaswamy, D. Zibar, L.A. Johansson, J. E. Bowers, M. Rodwell and L. Coldren,"Highly-linear coherent receiver with feeback," submitted to IEEE Photon. Technol. Lett.</jrn>
  6. H. F Chou, L.A. Johansson, Darko Zibar, A.  Ramaswamy, M. Rodwell and J.E. Bowers, "All-Optical Coherent Receiver with Feedback and Sampling," in proceedings of IEEE International Topical Meeting on Microwave Photonics (MWP) 2006, Grenoble France, paper W3.2, (2006)
  7. D. Zibar, L. A. Johansson, H. F. Chou, A. Ramaswamy and J. E. Bowers, "Time Domain Analysis of a Novel Phase-Locked Coherent Optical Demodulator," in Optical Amplifiers and Their Applications/Coherent Optical Technologies and Applications, Technical Digest (CD) (Optical Society of America, 2006), paper JWB11.
  8. C. Cox, Analog optical links, (Cambridge, U.K. Cambidge Univ. Press, 2004)
    [CrossRef]
  9. M. N. Sysak, L. A. Johannson, J. Klamkin, L. A. Coldren, J. E. Bowers,"Characterization of Distortion in In- GaAsP Optical Phase Modulators Monolithically Integrated with Balanced UTC Photodetector", in Proceedings of IEEE Lasers and Electro-Optics Society (LEOS) 19th Annual Meeting 2006, Montreal, Canada, paper TuU2, (2006)
  10. David M.  Pozar, Microwave engineering, 2nd edition (John Wiley and sons, USA, 1998)

2006

C. H. Cox, E. I. Ackerman, G. E. Bets and J. L. Prince,"Limits on performance of RF-over-fibre links and their impact on device design," IEEE Trans. on Microwave Theory Tech. 54, Part 2, 906-920 (2006)
[CrossRef]

2002

AlwynJ. Seeds,"Microwave photonics," IEEE Trans. on Microwave Theory Tech. 50, 877-887 (2002)
[CrossRef]

1994

R.F. Kalman, J.C. Fan and L.G. Kazovsky, "Dynamic range of coherent analog fiber-optic links," IEEE J. Lightwave Technol. 12, 1263-1277 (1994)
[CrossRef]

Ackerman, E. I.

C. H. Cox, E. I. Ackerman, G. E. Bets and J. L. Prince,"Limits on performance of RF-over-fibre links and their impact on device design," IEEE Trans. on Microwave Theory Tech. 54, Part 2, 906-920 (2006)
[CrossRef]

Alwyn,

AlwynJ. Seeds,"Microwave photonics," IEEE Trans. on Microwave Theory Tech. 50, 877-887 (2002)
[CrossRef]

Bets, G. E.

C. H. Cox, E. I. Ackerman, G. E. Bets and J. L. Prince,"Limits on performance of RF-over-fibre links and their impact on device design," IEEE Trans. on Microwave Theory Tech. 54, Part 2, 906-920 (2006)
[CrossRef]

Cox, C. H.

C. H. Cox, E. I. Ackerman, G. E. Bets and J. L. Prince,"Limits on performance of RF-over-fibre links and their impact on device design," IEEE Trans. on Microwave Theory Tech. 54, Part 2, 906-920 (2006)
[CrossRef]

Fan, J.C.

R.F. Kalman, J.C. Fan and L.G. Kazovsky, "Dynamic range of coherent analog fiber-optic links," IEEE J. Lightwave Technol. 12, 1263-1277 (1994)
[CrossRef]

Kalman, R.F.

R.F. Kalman, J.C. Fan and L.G. Kazovsky, "Dynamic range of coherent analog fiber-optic links," IEEE J. Lightwave Technol. 12, 1263-1277 (1994)
[CrossRef]

Kazovsky, L.G.

R.F. Kalman, J.C. Fan and L.G. Kazovsky, "Dynamic range of coherent analog fiber-optic links," IEEE J. Lightwave Technol. 12, 1263-1277 (1994)
[CrossRef]

Prince, J. L.

C. H. Cox, E. I. Ackerman, G. E. Bets and J. L. Prince,"Limits on performance of RF-over-fibre links and their impact on device design," IEEE Trans. on Microwave Theory Tech. 54, Part 2, 906-920 (2006)
[CrossRef]

IEEE J. Lightwave Technol.

R.F. Kalman, J.C. Fan and L.G. Kazovsky, "Dynamic range of coherent analog fiber-optic links," IEEE J. Lightwave Technol. 12, 1263-1277 (1994)
[CrossRef]

IEEE Trans. on Microwave Theory Tech.

C. H. Cox, E. I. Ackerman, G. E. Bets and J. L. Prince,"Limits on performance of RF-over-fibre links and their impact on device design," IEEE Trans. on Microwave Theory Tech. 54, Part 2, 906-920 (2006)
[CrossRef]

AlwynJ. Seeds,"Microwave photonics," IEEE Trans. on Microwave Theory Tech. 50, 877-887 (2002)
[CrossRef]

Other

H. F. Chou, A. Ramaswamy, D. Zibar, L.A. Johansson, L. Coldren and J. Bowers, "SFDR Improvement of a Coherent Receiver Using Feedback," in Optical Amplifiers and Their Applications/Coherent Optical Technologies and Applications, Technical Digest (CD) (Optical Society of America, 2006), paper CFA3.

<jrn>H. F. Chou, A. Ramaswamy, D. Zibar, L.A. Johansson, J. E. Bowers, M. Rodwell and L. Coldren,"Highly-linear coherent receiver with feeback," submitted to IEEE Photon. Technol. Lett.</jrn>

H. F Chou, L.A. Johansson, Darko Zibar, A.  Ramaswamy, M. Rodwell and J.E. Bowers, "All-Optical Coherent Receiver with Feedback and Sampling," in proceedings of IEEE International Topical Meeting on Microwave Photonics (MWP) 2006, Grenoble France, paper W3.2, (2006)

D. Zibar, L. A. Johansson, H. F. Chou, A. Ramaswamy and J. E. Bowers, "Time Domain Analysis of a Novel Phase-Locked Coherent Optical Demodulator," in Optical Amplifiers and Their Applications/Coherent Optical Technologies and Applications, Technical Digest (CD) (Optical Society of America, 2006), paper JWB11.

C. Cox, Analog optical links, (Cambridge, U.K. Cambidge Univ. Press, 2004)
[CrossRef]

M. N. Sysak, L. A. Johannson, J. Klamkin, L. A. Coldren, J. E. Bowers,"Characterization of Distortion in In- GaAsP Optical Phase Modulators Monolithically Integrated with Balanced UTC Photodetector", in Proceedings of IEEE Lasers and Electro-Optics Society (LEOS) 19th Annual Meeting 2006, Montreal, Canada, paper TuU2, (2006)

David M.  Pozar, Microwave engineering, 2nd edition (John Wiley and sons, USA, 1998)

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Figures (6)

Fig. 1.
Fig. 1.

General outline of phase-modulated optical link and phase-locked optical demodulator at the receiver unit.

Fig. 2.
Fig. 2.

(a) One tone measurement. Output of the balanced photodetector, Vpd (t), as a function of loop gain. (b) Two tone measurement. SIR as a function of input signal modulation depth, Min .

Fig. 3.
Fig. 3.

RF input signal modulation depth Min =π/2. (a) SIR of the demodulated signal as a function of normalized loop gain for selected values of the ratio fLF /f 1. (b) SIR of the demodulated signal as a function of the ratio c 1/c 3 of the LO phase-modulator. Quadratic term c 2=0.

Fig. 4.
Fig. 4.

SIR of the demodulated signal as a function of c 1/c 3. The ratio c 1/c 2 takes values: 80,60,40,20. (b) SIR of the demodulated signal as a function of loop gain, K. c 1/c 2=40 and c 1/c 3=20+Δ offset .

Fig. 5.
Fig. 5.

(a) SIR of the demodulated signal as a function of Dx for x=1,2,3. (c2, c3)=0. (b) SIR of the demodulated signal as a function of c 1/c 3 for selected values of the quadratic term, D 2, of the residual amplitude modulation. c 1/c 2=40 and D 1=0.03 1/V.

Fig. 6.
Fig. 6.

c 1/c 3=10, c 1/c 2=40, D 1=0.03 1/V and D 2=0.05 1/V. (a) Amplitude of the fundamental and 3rd order mixing product (IM3 curve) of the demodulated signal as a function of input signal voltage, Vin . (b) SIR of the demodulated signal as a function of input signal frequency for selected values of modulation depth Min

Equations (26)

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E in ( t ) = P in e j ( ω 0 t + ϕ in ( t ) )
ϕ in ( t ) = π V in ( t ) V π , in ( 1 + a 2 a 1 V π , in V in ( t ) + a 3 a 1 V π , in 2 V in 2 ( t ) )
V in ( t ) = V 1 sin [ ω 1 t ] + V 2 sin [ ω 2 t ]
E LO ( t ) = P LO ( t ) e j ( ω 0 t + ϕ LO ( t ) )
E 1 ( t ) = 1 2 P in e j ( ω 0 t + ϕ in ( t ) π 2 ) + 1 2 P LO ( t ) e j ( ω 0 t + ϕ LO ( t ) π )
E 2 ( t ) = 1 2 P in e j ( ω 0 t + ϕ in ( t ) π ) + 1 2 P LO ( t ) e j ( ω 0 t + ϕ LO ( t ) π 2 )
I 1 ( t ) = R pd E 1 ( t ) 2 ( 1 + b 2 E 1 ( t ) 2 b 1 + b 3 E 1 ( t ) 3 b 1 )
= R pd n = 1 3 b n b 1 ( 1 2 P in + 1 2 P LO ( t ) P in P LO ( t ) sin [ ϕ in ( t ) ϕ LO ( t ) ] ) n
I 2 ( t ) = R pd E 2 ( t ) 2 ( 1 + b 2 E 2 ( t ) 2 b 1 + b 3 E 2 ( t ) 3 b 1 )
= R pd n = 1 3 b n b 1 ( 1 2 P in + 1 2 P LO ( t ) + P in P LO ( t ) sin [ ϕ in ( t ) ϕ LO ( t ) ] ) n
V pd ( t ) = R L ( I 2 ( t ) I 1 ( t ) )
dV out dt = A [ V pd ( t ) V out ( t ) τ LF ]
ϕ LO ( t ) = πV out ( t ) V π , LO ( 1 + c 2 c 1 V π , LO V out ( t ) + c 3 c 1 V π , LO 2 V out 2 ( t ) )
P LO ( t ) P 0 = A LO ( t ) A 0 = 1 + D 1 V out ( t ) + D 2 V out 2 ( t ) + D 3 V out 3 ( t )
ϕ e ( t ) = ϕ in ( t ) ϕ LO ( t )
e dt = π V π , in ( ω 1 V 1 cos [ ω 1 t ] + ω 2 V 2 cos [ ω 2 t ] )
( 1 + 2 a 2 a 1 V π , in ( V 1 sin [ ω 1 t ] + V 2 sin [ ω 2 t ] ) + 3 a 3 a 1 V π , in 2 ( V 1 sin [ ω 1 t ] + V 2 sin [ ω 2 t ] ) 2 )
A π τ LF V π , LO ( 1 + 2 c 2 c 1 V π , LO V out ( t ) + 3 c 3 c 1 V π , LO 2 V out 2 ( t ) ) ( V pd ( t ) V out ( t ) )
V ref ( t ) = 2 R pd P in P LO R L A sin [ π V π , LO V in ( t ) π V π , LO ( V out ( t ) + c′ 2 V out 2 ( t ) + c′ 3 V out 3 ( t ) ) + ϕ 0 ]
2 R pd P in P LO R L A sin [ ϕ 0 ] + G 1 [ V in ( t ) V out ( t ) c′ 2 V out 2 ( t ) c′ 3 V out 3 ( t ) ]
G 2 [ V in ( t ) V out ( t ) c′ 2 V out 2 ( t ) c′ 3 V out 3 ( t ) ] 2
G 3 [ V in ( t ) V out ( t ) c′ 2 V out 2 ( t ) c′ 3 V out 3 ( t ) ] 3
V out ( t ) = A 1 V in ( t ) + A 2 V in 2 ( t ) + A 3 V in 3 ( t )
V out ( t ) = G 1 1 + G 1 V in ( t ) ( c′ 3 G 1 4 + G 3 2 G 2 c′ 2 G 1 2 ) ( 1 + G 1 ) 4 V in 3 ( t )
V out ( t ) = G 1 1 + G 1 V in ( t ) ( 2 G 2 c′ 2 G 1 2 + D 1 G 1 4 c′ 2 + G 3 + c′ 3 G 1 4 D 2 G 1 3 D 1 G 1 G 2 ( 1 + G 1 ) 4 ) V in 3 ( t )
SIR = 20 log [ 8 ( 1 + G 1 ) 3 M in 2 ]

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