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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    [CrossRef]
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    [CrossRef]

2006 (2)

2005 (4)

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]

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]

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 (1)

1995 (1)

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

1993 (1)

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.

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.

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.

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.

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.

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)

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, 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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