Abstract

The direct temporal domain approach can be applied for arbitrary optical waveform generation using 2D ring resonator arrays (RRAs). To demonstrate the approach, we provide numerical examples which show the generation of two very different waveforms from the same input pulse. In particular, we consider a hyperbolic secant input pulse with 8 ps full width half maximum and generate (1) a 50 ps square-like waveform with 5 ps rising and falling times and a 40 ps flat-top as well as (2) a 60 ps triangular waveform with 30 ps rising and falling times, both with a 5×5 RRA. Simulations show that the generated waveforms are well-matched to their targets.

© 2006 Optical Society of America

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  1. A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
    [CrossRef]
  2. J. Azana and M. A. Muriel, “Temporal self-imaging effects: Theory and application for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron. 7, 728–744 (2001).
    [CrossRef]
  3. D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high-repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Technol. Lett. 13, 221–223 (2001).
    [CrossRef]
  4. Z. Jiang, D. E. Leaird, and A. M. Weiner, “Line-by-line pulse shaping control for optical arbitrary waveform generation,” Opt. Express 13, 10431–10439 (2005).
    [CrossRef] [PubMed]
  5. J. D. McKinney, D. Seo, D. E. Leaird, and A. M. Weiner, “Photonically assisted generation of arbitrary millimeter-wave and microwave electromagnetic waveforms via direct space-to-time optical pulse shaping,” J. Lightwave Technol. 21, 3020–3028 (2003).
    [CrossRef]
  6. F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “All-optical pulse reshaping and retiming systems incorporating pulse shaping fiber Bragg grating,” J. Lightwave Technol,  24, 357–364 (2006).
    [CrossRef]
  7. P. Petropoulos, M. Ibsen, A. D. Ellis, and D. J. Richardson, “Rectangular pulse generation based on pulse reshaping using a superstructured fiber Bragg grating,” J. Lightwave Technol. 19, 746–752 (2001).
    [CrossRef]
  8. A. Rundquist, A. Efimov, and D. H. Reitze, “Pulse shaping with the Gerchberg-Saxton algorithm,” J. Opt. Soc. Am. B 19, 2468–2478 (2002).
    [CrossRef]
  9. A. M. Weiner, S. Oudin, D. E. Leaird, and D. H. Reitze, “Shaping of femtosecond pulses using phase-only filters designed by simulated annealing,” J. Opt. Soc. Am. A. 10, 1112–1120 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2006 (2)

2005 (4)

Y. M. Landobasa, S. Darmawan, and M. K. Chin, “Matrix analysis of 2-D microresonator lattice optical filters,” IEEE J. Quantum Electron. 41, 1410–1418 (2005).
[CrossRef]

B. Xia and L. R. Chen, “A direct temporal domain approach for pulse-repetition rate multiplication with arbitrary envelope shaping,” IEEE J. Sel. Top. Quantum Electron. 1, 165–172 (2005).

A. Rostami and G. Rostami, “All-optical implementation of tunable low-pass, high-pass, and band-pass optical fitlers using ring resonators,” J. Lightwave Technol. 23, 446–460 (2005).
[CrossRef]

Z. Jiang, D. E. Leaird, and A. M. Weiner, “Line-by-line pulse shaping control for optical arbitrary waveform generation,” Opt. Express 13, 10431–10439 (2005).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

2001 (4)

P. Petropoulos, M. Ibsen, A. D. Ellis, and D. J. Richardson, “Rectangular pulse generation based on pulse reshaping using a superstructured fiber Bragg grating,” J. Lightwave Technol. 19, 746–752 (2001).
[CrossRef]

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

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high-repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Technol. Lett. 13, 221–223 (2001).
[CrossRef]

T. Sakamoto, F. Futami, K. Kikuchi, S. Takeda, Y. Sugaya, and S. Watanabe, “All-optical wavelength conversion of 500-fs pulse trains by using a nonlinear-optical loop mirror composed of a highly nonlinear DSF,” IEEE Photon. Technol. Lett. 13, 502–504 (2001).
[CrossRef]

1999 (2)

1995 (1)

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[CrossRef]

1993 (1)

A. M. Weiner, S. Oudin, D. E. Leaird, and D. H. Reitze, “Shaping of femtosecond pulses using phase-only filters designed by simulated annealing,” J. Opt. Soc. Am. A. 10, 1112–1120 (1993).
[CrossRef]

Agarwal, A.

Azana, J.

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

Banwell, T.

Brener, I.

Bruce, A. J.

Capuzzo, M. A.

Chen, L. R.

B. Xia and L. R. Chen, “A direct temporal domain approach for pulse-repetition rate multiplication with arbitrary envelope shaping,” IEEE J. Sel. Top. Quantum Electron. 1, 165–172 (2005).

Chen, W.

Chin, M. K.

Y. M. Landobasa, S. Darmawan, and M. K. Chin, “Matrix analysis of 2-D microresonator lattice optical filters,” IEEE J. Quantum Electron. 41, 1410–1418 (2005).
[CrossRef]

Chu, S. T.

Darmawan, S.

Y. M. Landobasa, S. Darmawan, and M. K. Chin, “Matrix analysis of 2-D microresonator lattice optical filters,” IEEE J. Quantum Electron. 41, 1410–1418 (2005).
[CrossRef]

Davidson, R.

Delfyett, P. J.

Donovan, K.

Efimov, A.

Ellis, A. D.

Etemad, S.

Futami, F.

T. Sakamoto, F. Futami, K. Kikuchi, S. Takeda, Y. Sugaya, and S. Watanabe, “All-optical wavelength conversion of 500-fs pulse trains by using a nonlinear-optical loop mirror composed of a highly nonlinear DSF,” IEEE Photon. Technol. Lett. 13, 502–504 (2001).
[CrossRef]

Gill, D.

Gomez, L. T.

Hryniewicz, J.

Ibsen, M.

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “All-optical pulse reshaping and retiming systems incorporating pulse shaping fiber Bragg grating,” J. Lightwave Technol,  24, 357–364 (2006).
[CrossRef]

P. Petropoulos, M. Ibsen, A. D. Ellis, and D. J. Richardson, “Rectangular pulse generation based on pulse reshaping using a superstructured fiber Bragg grating,” J. Lightwave Technol. 19, 746–752 (2001).
[CrossRef]

Ishii, M.

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high-repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Technol. Lett. 13, 221–223 (2001).
[CrossRef]

Jackel, J.

Jiang, Z.

Johnson, F.

Kamei, S.

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high-repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Technol. Lett. 13, 221–223 (2001).
[CrossRef]

Kikuchi, K.

T. Sakamoto, F. Futami, K. Kikuchi, S. Takeda, Y. Sugaya, and S. Watanabe, “All-optical wavelength conversion of 500-fs pulse trains by using a nonlinear-optical loop mirror composed of a highly nonlinear DSF,” IEEE Photon. Technol. Lett. 13, 502–504 (2001).
[CrossRef]

King, O.

Landobasa, Y. M.

Y. M. Landobasa, S. Darmawan, and M. K. Chin, “Matrix analysis of 2-D microresonator lattice optical filters,” IEEE J. Quantum Electron. 41, 1410–1418 (2005).
[CrossRef]

Leaird, D. E.

Z. Jiang, D. E. Leaird, and A. M. Weiner, “Line-by-line pulse shaping control for optical arbitrary waveform generation,” Opt. Express 13, 10431–10439 (2005).
[CrossRef] [PubMed]

J. D. McKinney, D. Seo, D. E. Leaird, and A. M. Weiner, “Photonically assisted generation of arbitrary millimeter-wave and microwave electromagnetic waveforms via direct space-to-time optical pulse shaping,” J. Lightwave Technol. 21, 3020–3028 (2003).
[CrossRef]

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high-repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Technol. Lett. 13, 221–223 (2001).
[CrossRef]

A. M. Weiner, S. Oudin, D. E. Leaird, and D. H. Reitze, “Shaping of femtosecond pulses using phase-only filters designed by simulated annealing,” J. Opt. Soc. Am. A. 10, 1112–1120 (1993).
[CrossRef]

Lenz, C.

Little, B.E.

Madsen, C. K.

McKinney, J. D.

Menendez, R.

Muriel, M. A.

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

Nielsen, T. N.

Okamoto, K.

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high-repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Technol. Lett. 13, 221–223 (2001).
[CrossRef]

Oudin, S.

A. M. Weiner, S. Oudin, D. E. Leaird, and D. H. Reitze, “Shaping of femtosecond pulses using phase-only filters designed by simulated annealing,” J. Opt. Soc. Am. A. 10, 1112–1120 (1993).
[CrossRef]

Parmigiani, F.

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “All-optical pulse reshaping and retiming systems incorporating pulse shaping fiber Bragg grating,” J. Lightwave Technol,  24, 357–364 (2006).
[CrossRef]

Petropoulos, P.

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “All-optical pulse reshaping and retiming systems incorporating pulse shaping fiber Bragg grating,” J. Lightwave Technol,  24, 357–364 (2006).
[CrossRef]

P. Petropoulos, M. Ibsen, A. D. Ellis, and D. J. Richardson, “Rectangular pulse generation based on pulse reshaping using a superstructured fiber Bragg grating,” J. Lightwave Technol. 19, 746–752 (2001).
[CrossRef]

Reitze, D. H.

A. Rundquist, A. Efimov, and D. H. Reitze, “Pulse shaping with the Gerchberg-Saxton algorithm,” J. Opt. Soc. Am. B 19, 2468–2478 (2002).
[CrossRef]

A. M. Weiner, S. Oudin, D. E. Leaird, and D. H. Reitze, “Shaping of femtosecond pulses using phase-only filters designed by simulated annealing,” J. Opt. Soc. Am. A. 10, 1112–1120 (1993).
[CrossRef]

Richardson, D. J.

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “All-optical pulse reshaping and retiming systems incorporating pulse shaping fiber Bragg grating,” J. Lightwave Technol,  24, 357–364 (2006).
[CrossRef]

P. Petropoulos, M. Ibsen, A. D. Ellis, and D. J. Richardson, “Rectangular pulse generation based on pulse reshaping using a superstructured fiber Bragg grating,” J. Lightwave Technol. 19, 746–752 (2001).
[CrossRef]

Rostami, A.

Rostami, G.

Rundquist, A.

Sakamoto, T.

T. Sakamoto, F. Futami, K. Kikuchi, S. Takeda, Y. Sugaya, and S. Watanabe, “All-optical wavelength conversion of 500-fs pulse trains by using a nonlinear-optical loop mirror composed of a highly nonlinear DSF,” IEEE Photon. Technol. Lett. 13, 502–504 (2001).
[CrossRef]

Seo, D.

Shen, S.

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high-repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Technol. Lett. 13, 221–223 (2001).
[CrossRef]

Sugaya, Y.

T. Sakamoto, F. Futami, K. Kikuchi, S. Takeda, Y. Sugaya, and S. Watanabe, “All-optical wavelength conversion of 500-fs pulse trains by using a nonlinear-optical loop mirror composed of a highly nonlinear DSF,” IEEE Photon. Technol. Lett. 13, 502–504 (2001).
[CrossRef]

Sugita, A.

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high-repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Technol. Lett. 13, 221–223 (2001).
[CrossRef]

Takeda, S.

T. Sakamoto, F. Futami, K. Kikuchi, S. Takeda, Y. Sugaya, and S. Watanabe, “All-optical wavelength conversion of 500-fs pulse trains by using a nonlinear-optical loop mirror composed of a highly nonlinear DSF,” IEEE Photon. Technol. Lett. 13, 502–504 (2001).
[CrossRef]

Toliver, P.

Watanabe, S.

T. Sakamoto, F. Futami, K. Kikuchi, S. Takeda, Y. Sugaya, and S. Watanabe, “All-optical wavelength conversion of 500-fs pulse trains by using a nonlinear-optical loop mirror composed of a highly nonlinear DSF,” IEEE Photon. Technol. Lett. 13, 502–504 (2001).
[CrossRef]

Weiner, A. M.

Z. Jiang, D. E. Leaird, and A. M. Weiner, “Line-by-line pulse shaping control for optical arbitrary waveform generation,” Opt. Express 13, 10431–10439 (2005).
[CrossRef] [PubMed]

J. D. McKinney, D. Seo, D. E. Leaird, and A. M. Weiner, “Photonically assisted generation of arbitrary millimeter-wave and microwave electromagnetic waveforms via direct space-to-time optical pulse shaping,” J. Lightwave Technol. 21, 3020–3028 (2003).
[CrossRef]

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high-repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Technol. Lett. 13, 221–223 (2001).
[CrossRef]

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[CrossRef]

A. M. Weiner, S. Oudin, D. E. Leaird, and D. H. Reitze, “Shaping of femtosecond pulses using phase-only filters designed by simulated annealing,” J. Opt. Soc. Am. A. 10, 1112–1120 (1993).
[CrossRef]

Xia, B.

B. Xia and L. R. Chen, “A direct temporal domain approach for pulse-repetition rate multiplication with arbitrary envelope shaping,” IEEE J. Sel. Top. Quantum Electron. 1, 165–172 (2005).

Yong, J.

Zhao, J. H.

C. K. Madsen and J. H. Zhao, Optical filter design and analysis-A signal processing approach (John Wiley & Sons, 1999), Chap.5.

IEEE J. Quantum Electron. (1)

Y. M. Landobasa, S. Darmawan, and M. K. Chin, “Matrix analysis of 2-D microresonator lattice optical filters,” IEEE J. Quantum Electron. 41, 1410–1418 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

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

B. Xia and L. R. Chen, “A direct temporal domain approach for pulse-repetition rate multiplication with arbitrary envelope shaping,” IEEE J. Sel. Top. Quantum Electron. 1, 165–172 (2005).

IEEE Photon. Technol. Lett. (2)

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high-repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Technol. Lett. 13, 221–223 (2001).
[CrossRef]

T. Sakamoto, F. Futami, K. Kikuchi, S. Takeda, Y. Sugaya, and S. Watanabe, “All-optical wavelength conversion of 500-fs pulse trains by using a nonlinear-optical loop mirror composed of a highly nonlinear DSF,” IEEE Photon. Technol. Lett. 13, 502–504 (2001).
[CrossRef]

J. Lightwave Technol (1)

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “All-optical pulse reshaping and retiming systems incorporating pulse shaping fiber Bragg grating,” J. Lightwave Technol,  24, 357–364 (2006).
[CrossRef]

J. Lightwave Technol. (4)

J. Opt. Soc. Am. A. (1)

A. M. Weiner, S. Oudin, D. E. Leaird, and D. H. Reitze, “Shaping of femtosecond pulses using phase-only filters designed by simulated annealing,” J. Opt. Soc. Am. A. 10, 1112–1120 (1993).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Opt. Lett. (1)

Prog. Quantum Electron. (1)

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[CrossRef]

Other (1)

C. K. Madsen and J. H. Zhao, Optical filter design and analysis-A signal processing approach (John Wiley & Sons, 1999), Chap.5.

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of arbitrary waveform generation using the direct temporal domain approach; (a) PRRM output with a uniform envelope from an input pulse train with narrow pulse widths; (b) PRRM output from an input pulse train with wide pulse widths; (c) waveform generation with an optimized SP filter and an input pulse train with wide pulse widths.

Fig. 2.
Fig. 2.

(a) General configuration of an M×N RRA and (b) detailed view of the individual rings, r is the radius of the ring resonator, κ is the coupling coefficient and φ is an additional phase shift.

Fig. 3.
Fig. 3.

(a) Input and target waveform in one repetition period; (b) The generated square-like waveform; (c) The generated waveform in dB scale.

Fig. 4.
Fig. 4.

Spectrum of the 10 GHz pulse train at the RRA input and of the square-like waveform at he output. Amplitude (a) and (c); phase (b) and (d).

Fig. 5.
Fig. 5.

(a) The input hyperbolic secant pulse train at 10 GHz and the target waveform; (b) the target waveform and the generated triangular waveform form. the RRA.

Fig. 6.
Fig. 6.

Contour plots for fabrication errors in the RRA for the square waveform generation; (a) the average extinction ratio; (b) peak-to-peak intensity variation in the flat-top portion.

Tables (1)

Tables Icon

Table 1. Parameters of the RRA configuration for generation of a square waveform and a triangular waveform from a 10 GHz hyperbolic secant pulse train.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

[ I 1 O 1 ] = θ 1 . θ 2 θ m + 1 [ I 2 O 2 ] = [ θ 11 θ 12 θ 21 θ 22 ] [ I 2 O 2 ]
= ( Π p = 1 m j ( 1 t p 2 ) γ e p e 2 πR [ 1 t p γ e j φ p e 2 πR t p γ e −j φ p e 2 πR ] ) j 1 t m + 1 2 [ 1 t m + 1 t m + 1 1 ] [ I 2 O 2 ]
[ O 1 O 2 ] = Φ n [ I 1 I 2 ] = 1 θ 12 [ θ 22 ( θ 11 θ 22 θ 12 θ 21 ) 1 θ 11 ] [ I 1 I 2 ]

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