Abstract

We demonstrate a theoretical model of channel mismatch effect in a mode-locked laser based time-wavelength interleaved optical clock generation system. The channel mismatch effect includes clock timing mismatch, amplitude mismatch, and pulse shape mismatch. An explicit expression of this model is derived for 2-channel simple system and a numerical simulation of multiple-channel complicated system is carried out. In comparison with the experimental measurement, the feasibility of the theoretical model is verified for calibration and compensation of the channel mismatches.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
  2. J. Azaña and M. A. Muriel, “Temporal self-imaging effects: theory and application for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron. 7(4), 728–744 (2001).
    [Crossref]
  3. T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion,” IEEE Photon. Technol. Lett. 11(9), 1168–1170 (1999).
    [Crossref]
  4. A. Yariv and R. G. M. P. Koumans, “Time interleaved optical sampling for ultra-high speed A/D conversion,” Electron. Lett. 34(21), 2012–2013 (1998).
    [Crossref]
  5. A. Khilo, S. J. Spector, M. E. Grein, A. H. Nejadmalayeri, C. W. Holzwarth, M. Y. Sander, M. S. Dahlem, M. Y. Peng, M. W. Geis, N. A. DiLello, J. U. Yoon, A. Motamedi, J. S. Orcutt, J. P. Wang, C. M. Sorace-Agaskar, M. A. Popović, J. Sun, G. R. Zhou, H. Byun, J. Chen, J. L. Hoyt, H. I. Smith, R. J. Ram, M. Perrott, T. M. Lyszczarz, E. P. Ippen, and F. X. Kärtner, “Photonic ADC: overcoming the bottleneck of electronic jitter,” Opt. Express 20(4), 4454–4469 (2012).
    [Crossref] [PubMed]
  6. X. Fu, H. Zhang, Y. Peng, and M. Yao, “40-Gbps time-and wavelength-interleaved pulse-train generation in wavelength-demultiplexing analog-to-digital conversion,” Opt. Eng. 48(10), 104302 (2009).
    [Crossref]
  7. K. L. Lee, C. Shu, and H. F. Liu, “10 Gsample/s photonic analog-to-digital converter constructed using 10- wavelength jitter-suppressed sampling pulses from a self-seeded laser diode,” CLEO 2001, pp. 67–68.
  8. G. Wu, S. Li, X. Li, and J. Chen, “18 wavelengths 83.9Gs/s optical sampling clock for photonic A/D converters,” Opt. Express 18(20), 21162–21168 (2010).
    [Crossref] [PubMed]
  9. N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48(3), 261–271 (2001).
  10. C. Vogel, “The impact of combined channel mismatch effects in time-interleaved ADCs,” IEEE Trans. Instrum. Meas. 54(1), 415–427 (2005).
    [Crossref]
  11. R. C. Williamson, P. W. Juodawlkis, J. L. Wasserman, G. E. Betts, and J. C. Twichell, “Effects of crosstalk in demultiplexers for photonic analog-to-digital converters,” J. Lightwave Technol. 19(2), 230–236 (2001).
    [Crossref]

2012 (1)

2010 (1)

2009 (1)

X. Fu, H. Zhang, Y. Peng, and M. Yao, “40-Gbps time-and wavelength-interleaved pulse-train generation in wavelength-demultiplexing analog-to-digital conversion,” Opt. Eng. 48(10), 104302 (2009).
[Crossref]

2007 (1)

2005 (1)

C. Vogel, “The impact of combined channel mismatch effects in time-interleaved ADCs,” IEEE Trans. Instrum. Meas. 54(1), 415–427 (2005).
[Crossref]

2001 (3)

R. C. Williamson, P. W. Juodawlkis, J. L. Wasserman, G. E. Betts, and J. C. Twichell, “Effects of crosstalk in demultiplexers for photonic analog-to-digital converters,” J. Lightwave Technol. 19(2), 230–236 (2001).
[Crossref]

J. Azaña and M. A. Muriel, “Temporal self-imaging effects: theory and application for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron. 7(4), 728–744 (2001).
[Crossref]

N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48(3), 261–271 (2001).

1999 (1)

T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion,” IEEE Photon. Technol. Lett. 11(9), 1168–1170 (1999).
[Crossref]

1998 (1)

A. Yariv and R. G. M. P. Koumans, “Time interleaved optical sampling for ultra-high speed A/D conversion,” Electron. Lett. 34(21), 2012–2013 (1998).
[Crossref]

Azaña, J.

J. Azaña and M. A. Muriel, “Temporal self-imaging effects: theory and application for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron. 7(4), 728–744 (2001).
[Crossref]

Betts, G. E.

Byun, H.

Chen, J.

Clark, T. R.

T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion,” IEEE Photon. Technol. Lett. 11(9), 1168–1170 (1999).
[Crossref]

Dahlem, M. S.

DiLello, N. A.

Esman, R. D.

T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion,” IEEE Photon. Technol. Lett. 11(9), 1168–1170 (1999).
[Crossref]

Fu, X.

X. Fu, H. Zhang, Y. Peng, and M. Yao, “40-Gbps time-and wavelength-interleaved pulse-train generation in wavelength-demultiplexing analog-to-digital conversion,” Opt. Eng. 48(10), 104302 (2009).
[Crossref]

Geis, M. W.

Grein, M. E.

Holzwarth, C. W.

Hoyt, J. L.

Ippen, E. P.

Juodawlkis, P. W.

Kang, J. U.

T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion,” IEEE Photon. Technol. Lett. 11(9), 1168–1170 (1999).
[Crossref]

Kärtner, F. X.

Khilo, A.

Kobayashi, H.

N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48(3), 261–271 (2001).

Kobayashi, K.

N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48(3), 261–271 (2001).

Koumans, R. G. M. P.

A. Yariv and R. G. M. P. Koumans, “Time interleaved optical sampling for ultra-high speed A/D conversion,” Electron. Lett. 34(21), 2012–2013 (1998).
[Crossref]

Kurosawa, N.

N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48(3), 261–271 (2001).

Li, S.

Li, X.

Lyszczarz, T. M.

Maruyama, K.

N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48(3), 261–271 (2001).

Motamedi, A.

Muriel, M. A.

J. Azaña and M. A. Muriel, “Temporal self-imaging effects: theory and application for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron. 7(4), 728–744 (2001).
[Crossref]

Nejadmalayeri, A. H.

Orcutt, J. S.

Peng, M. Y.

Peng, Y.

X. Fu, H. Zhang, Y. Peng, and M. Yao, “40-Gbps time-and wavelength-interleaved pulse-train generation in wavelength-demultiplexing analog-to-digital conversion,” Opt. Eng. 48(10), 104302 (2009).
[Crossref]

Perrott, M.

Popovic, M. A.

Ram, R. J.

Sander, M. Y.

Smith, H. I.

Sorace-Agaskar, C. M.

Spector, S. J.

Sugawara, H.

N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48(3), 261–271 (2001).

Sun, J.

Twichell, J. C.

Valley, G. C.

Vogel, C.

C. Vogel, “The impact of combined channel mismatch effects in time-interleaved ADCs,” IEEE Trans. Instrum. Meas. 54(1), 415–427 (2005).
[Crossref]

Wang, J. P.

Wasserman, J. L.

Williamson, R. C.

Wu, G.

Yao, M.

X. Fu, H. Zhang, Y. Peng, and M. Yao, “40-Gbps time-and wavelength-interleaved pulse-train generation in wavelength-demultiplexing analog-to-digital conversion,” Opt. Eng. 48(10), 104302 (2009).
[Crossref]

Yariv, A.

A. Yariv and R. G. M. P. Koumans, “Time interleaved optical sampling for ultra-high speed A/D conversion,” Electron. Lett. 34(21), 2012–2013 (1998).
[Crossref]

Yoon, J. U.

Zhang, H.

X. Fu, H. Zhang, Y. Peng, and M. Yao, “40-Gbps time-and wavelength-interleaved pulse-train generation in wavelength-demultiplexing analog-to-digital conversion,” Opt. Eng. 48(10), 104302 (2009).
[Crossref]

Zhou, G. R.

Electron. Lett. (1)

A. Yariv and R. G. M. P. Koumans, “Time interleaved optical sampling for ultra-high speed A/D conversion,” Electron. Lett. 34(21), 2012–2013 (1998).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

J. Azaña and M. A. Muriel, “Temporal self-imaging effects: theory and application for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron. 7(4), 728–744 (2001).
[Crossref]

IEEE Photon. Technol. Lett. (1)

T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion,” IEEE Photon. Technol. Lett. 11(9), 1168–1170 (1999).
[Crossref]

IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. (1)

N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48(3), 261–271 (2001).

IEEE Trans. Instrum. Meas. (1)

C. Vogel, “The impact of combined channel mismatch effects in time-interleaved ADCs,” IEEE Trans. Instrum. Meas. 54(1), 415–427 (2005).
[Crossref]

J. Lightwave Technol. (1)

Opt. Eng. (1)

X. Fu, H. Zhang, Y. Peng, and M. Yao, “40-Gbps time-and wavelength-interleaved pulse-train generation in wavelength-demultiplexing analog-to-digital conversion,” Opt. Eng. 48(10), 104302 (2009).
[Crossref]

Opt. Express (3)

Other (1)

K. L. Lee, C. Shu, and H. F. Liu, “10 Gsample/s photonic analog-to-digital converter constructed using 10- wavelength jitter-suppressed sampling pulses from a self-seeded laser diode,” CLEO 2001, pp. 67–68.

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Figures (9)

Fig. 1
Fig. 1 (a) Experimental configuration of time-wavelength interleaved optical clock generation based on mode locked laser. (b) Schematic of spectral slicing of mode locked laser and time-wavelength mapping of pulse trains, (c) A frequency domain measurement method. DMUX: de-multiplexer, TDL: tunable delay line, VOA: variable optical attenuator, WDM: wavelength division multiplexer, PD: photo-detector.
Fig. 2
Fig. 2 Schematic of the PADC clock in RF domain.
Fig. 3
Fig. 3 Schematic of pulse train mismatch (left) and the corresponding RF spectrum (right). Sampling rate fs = 40GHz. (a) Ideal clock. (b) Clock timing mismatch only. τ1 = −0.2ps and τ2 = 0.2ps. (c) Amplitude mismatch only. a1 = 1.01 and a2 = 0.99. (d) Pulse shape mismatch only. fc,1 = 73.66GHz and fc,2 = 69.06GHz.
Fig. 4
Fig. 4 Spectrum extinction ratio versus (a) only clock timing and amplitude mismatch and (b) only pulse shape mismatch (M = 2).
Fig. 5
Fig. 5 (a) Measured optical spectrum in each channel and (b) temporal pulse shapes normalized to the average amplitude for the calculation of normalized amplitude a ^ k .
Fig. 6
Fig. 6 (a) Normalized temporal pulse shapes and (b) u ˜ k ( f ) of all 4 channels. The inset in (b) is a full-scale plot.
Fig. 7
Fig. 7 (a) RF spectrum measured by R&S FSUP50 spectrum analyzer, (b) Comparison of the calculated and measured RF spectra.
Fig. 8
Fig. 8 (a)-(d): Comparison of simulated and measured RF spectrum after four adjustments of TDLs and VOAs.
Fig. 9
Fig. 9 (a) Dependence of spectrum extinction ratio on the timing and amplitude mismatches deduced from the experimental measurement (M = 4). (b) The contour of the surface in (a). Solid curves: theoretical analysis. Pentangle: the experimental measurement.

Tables (2)

Tables Icon

Table 1 Normalized amplitude, time skew and cutoff frequencies of all 4 channels evaluated from experimental data.

Tables Icon

Table 2 Mismatch parameters and spectrum extinction ratios after each adjustment.

Equations (36)

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I k ( t )= a k u k ( t τ k ) m= + δ[ tmM T s ( k1 ) T s ] k=1,2,,M,
s( t )= R PD k=1 M I k ( t ) ,
E( f )= | S ˜ ( f ) | 2 = | R PD M T s k=1 M a k u ˜ k ( f ) e j2πf τ k e j2π( k1 )f/ f s | 2 m= + δ( f m f s /M ) ,
E( f )= | R PD T s a 0 u ˜ 0 ( f ) | 2 m= + δ( fm f s ) .
E k =E( k f s /M )= ( R PD M T s ) 2 | l=1 M a l u ˜ l ( k f s /M ) e j2π( k f s /M ) τ l e j2π k( l1 ) /M | 2 k=1,2,,M.
η=10 log 10 ( E s / E n ),
E n = k=1 M1 E k , E s = E M .
τ ^ k = ( τ k τ ¯ ) / T s , a ^ k =( a k a ¯ ) / a ¯ ,
σ( τ ^ )= σ( τ ) / T s , σ( a ^ )= σ( a ) / a ¯ ,
u ˜ k ( f )1/ [ 1+ ( f/ f c,k ) 2 ] , f c,k 2 = [ δ( 1/ u ˜ k ) / δ( f 2 ) ] 1 | f= f s = 2 f s u ˜ k 2 ( f s ) / u ˜ k ( f s ) ,
f ^ k = ( f c, k f ¯ c ) / f ¯ c , σ( f ^ )= σ( f c ) / f ¯ c ,
ρ= f s / f ¯ c .
E k ( τ ^ , a ^ ; f ^ ,ρ )= ( R PD a ¯ / M T s ) 2 l,m=1 M u k ( f ^ l ,ρ ) u k ( f ^ m ,ρ )( 1+ a ^ l )( 1+ a ^ m )cos 2πk M [ ( τ ^ l τ ^ m )+( lm ) ] ,
η( τ ^ , a ^ ; f ^ ,ρ )=10 log 10 [ E M ( τ ^ , a ^ ; f ^ ,ρ ) / k=1 M1 E k ( τ ^ , a ^ ; f ^ ,ρ ) ].
S( x ): k=1 M x k 2 =M σ 2 ( x ) and k=1 M x k =0.
η[ σ( τ ^ ),σ( a ^ );σ( f ^ ),ρ ]= η( τ ^ , a ^ ; f ^ ,ρ )dS( τ ^ )dS( a ^ )dS( f ^ ) dS( τ ^ ) dS( a ^ ) dS( f ^ ) .
η[ σ( f ^ ),ρ ]= η( 0,0; f ^ ,ρ )dS( f ^ ) / dS( f ^ ) .
η[ σ( τ ^ ),σ( a ^ ) ]= η( τ ^ , a ^ ; f ^ ,ρ )dS( τ ^ )dS( a ^ ) / dS( τ ^ )dS( a ^ ) .
E s = ( R PD a ¯ / 2 T s ) 2 | u 2 [ σ( f ^ ),ρ ][ 1+σ( a ^ ) ] e j2πσ( τ ^ ) + u 2 [ σ( f ^ ),ρ ][ 1σ( a ^ ) ] e j2πσ( τ ^ ) | 2 . E n = ( R PD a ¯ / 2 T s ) 2 | u 1 [ σ( f ^ ),ρ ][ 1+σ( a ^ ) ] e jπσ( τ ^ ) u 1 [ σ( f ^ ),ρ ][ 1σ( a ^ ) ] e jπσ( τ ^ ) | 2
η[ σ( τ ^ ),σ( a ^ );0,0 ]=10 log 10 [ 2[ 1 σ 2 ( a ^ ) ][ 1cos4πσ( τ ^ ) ] 2 σ 2 ( a ^ )+[ 1 σ 2 ( a ^ ) ][ 1cos2πσ( τ ^ ) ] ].
η[ 0,0;σ( f ^ ),ρ ]=10 log 10 | u 2 [ σ( f ^ ),ρ ]+ u 2 [ σ( f ^ ),ρ ] u 1 [ σ( f ^ ),ρ ] u 1 [ σ( f ^ ),ρ ] | 2 .
{ 10 log 10 E 4 ( τ ^ , a ^ ; f ^ ,ρ ) E k ( τ ^ , a ^ ; f ^ ,ρ ) =P( 4 )P( k ) k=1,2,3 , k=1 4 τ ^ k =0
1/ u ˜ ( f ) c 0 + c 1 f+ c 2 f 2 +c.c..
1/ u ˜ ( f ) 1+ ( f/ f c ) 2 , 1 / f c 2 = δ( 1/ u ˜ ) / δ( f 2 ) | f=0 .
f c 2 = [ δ( 1/ u ˜ ) / δ( f 2 ) ] 1 | f=0 [ δ( 1/ u ˜ ) / δ( f 2 ) ] 1 | f= f s = 2 f s u ˜ 2 ( f s ) / u ˜ ( f s )
I= η( x )dS( x ) .
u=Ax, x= A T u .
S( u ): k=2 M u k 2 =M σ 2 ( x ), and u 1 =0.
v 1 =( 1/ M ) ( 1,1,,1,1 ) T v 2 =( 1/ 2 ) ( 1,0,,0,1 ) T v 3 =( 1/ 2 ) ( 0,1,,0,1 ) T . v M =( 1/ 2 ) ( 0,0,,1,1 ) T
e 1 = v 1 e 2 = v 2 ( v 2 e 1 ) e 1 e 3 = v 3 ( v 3 e 1 ) e 1 ( v 3 e 2 ) e 2 . e M = v M k=1 M1 ( v M e k ) e k
Α=( e 1 , e 2 ,, e M1 , e M ).
u 1 =0 u 2 =Rcos φ 1 u 3 =Rsin φ 1 cos φ 2 , u M1 =Rsin φ 1 sin φ 2 sin φ M3 cos φ M2 u M =Rsin φ 1 sin φ 2 sin φ M3 sin φ M2
dS[ u( R, φ 1 , φ 2 ,, φ M2 ) ]= R M2 k=1 M3 sin ( M2 )k φ k k=1 M2 d φ k .
I= 0 2π 0 π 0 π η[ A T u( R, φ 1 , φ 2 ,, φ M2 ) ]dS[ u( R, φ 1 , φ 2 ,, φ M2 ) ] .
dS = 0 2π 0 π 0 π R M2 k=1 M3 sin ( M2 )k φ k k=1 M2 d φ k = 2 π ( M1 )/2 R M2 Γ[ ( M1 )/2 ] ,
I=η{ [σ(x),σ(x)] }+η{ [ σ(x),σ(x) ] } .

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