Abstract

The NLFM waveform resulting from a tunable integrated optical ring resonator is simulated. The metrics of interest are the first sidelobe levels and FWHM times of the autocorrelation, as these directly relate to the long-range performance and fine range resolution of a LADAR system, and should ideally be as small as possible. Through simulation, the maximum sidelobe level of the autocorrelation of an NLFM waveform generated by a series of tunable integrated optical ring resonators is shown to be −20 to −30 dB or lower. A proof of concept experiment employing an off-the-shelf thermally tunable silicon-nitride optical ring resonator is shown to generate NLFM chirped waveforms with a bandwidth of 28 kHz.

©2010 Optical Society of America

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References

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  1. D. Youmans, “Coherent ladar imaging of the SEASAT satellite retro-reflector array using linear-FM chirp waveforms and pulse compression,” Proc. SPIE 6550, 655004 (2007).
    [Crossref]
  2. J. Buck, “High-resolution 3D coherent laser radar imaging,” Proc. SPIE 6550, 655002 (2007).
    [Crossref]
  3. D. Youmans, “Coherent lidar imaging of dust clouds: waveform comparisons with the poly-phase (P4) modulation waveform,” Proc. SPIE 6950, 695009 (2008).
    [Crossref]
  4. T. Collins and P. Atkins, “Nonlinear frequency modulation chirps for active sonar,” IEE Proc., Radar Sonar Navig. 146(6), 312–316 (1999).
    [Crossref]
  5. D. Youmans, “Waveform comparison for coherent ladar imaging using a helicopter facet model target,” Proc. SPIE 7323, 73230 (2009).
  6. Y. K. Chan, M. Y. Chua, and V. C. Koo, “Sidelobes reduction using simple two and tri-stages nonlinear frequency modulation (NLFM),” PIER PIER 98, 33–52 (2009) (PIER).
    [Crossref]
  7. J. A. Johnston and A. C. Fairhead, ““Waveform design and doppler sensitivity analysis for nonlinear FM chirp pulses,” IEE Proc,” Radar Sonar Navig. 133, 163–175 (1986).
  8. M. Luszczyk, “Numerical evaluation of ambiguity function for stepped non-linear FM radar waveform,” International Conference on Microwaves, Radar & Wireless Communications (2006) pp. 1164–1167.
  9. A. W. Doerry, “Generating precision nonlinear FM chirp waveforms,” Proc. SPIE 6547, 65470D (2007).
    [Crossref]
  10. C. K. Madsen, and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, (John Wiley, 1999).
  11. D. B. Adams, W. T. Snider, and C. K. Madsen, “A novel NLFM waveform generator using tunable integrated optical ring resonators: simulation and proof of concept experiment,” Proc. SPIE 7684, 76841A (2010).
    [Crossref]
  12. M. E. Solmaz, D. B. Adams, S. Grover, W.-C. Tan, X. Xia, O. Eknoyan, and C. K. Madsen, “First demonstration of an As2S3-on-LiNbO3 ring resonator,” Optical Fiber Communication Conference (OFC), (2009), pp. 1–3.

2010 (1)

D. B. Adams, W. T. Snider, and C. K. Madsen, “A novel NLFM waveform generator using tunable integrated optical ring resonators: simulation and proof of concept experiment,” Proc. SPIE 7684, 76841A (2010).
[Crossref]

2009 (2)

D. Youmans, “Waveform comparison for coherent ladar imaging using a helicopter facet model target,” Proc. SPIE 7323, 73230 (2009).

Y. K. Chan, M. Y. Chua, and V. C. Koo, “Sidelobes reduction using simple two and tri-stages nonlinear frequency modulation (NLFM),” PIER PIER 98, 33–52 (2009) (PIER).
[Crossref]

2008 (1)

D. Youmans, “Coherent lidar imaging of dust clouds: waveform comparisons with the poly-phase (P4) modulation waveform,” Proc. SPIE 6950, 695009 (2008).
[Crossref]

2007 (3)

D. Youmans, “Coherent ladar imaging of the SEASAT satellite retro-reflector array using linear-FM chirp waveforms and pulse compression,” Proc. SPIE 6550, 655004 (2007).
[Crossref]

J. Buck, “High-resolution 3D coherent laser radar imaging,” Proc. SPIE 6550, 655002 (2007).
[Crossref]

A. W. Doerry, “Generating precision nonlinear FM chirp waveforms,” Proc. SPIE 6547, 65470D (2007).
[Crossref]

1999 (1)

T. Collins and P. Atkins, “Nonlinear frequency modulation chirps for active sonar,” IEE Proc., Radar Sonar Navig. 146(6), 312–316 (1999).
[Crossref]

1986 (1)

J. A. Johnston and A. C. Fairhead, ““Waveform design and doppler sensitivity analysis for nonlinear FM chirp pulses,” IEE Proc,” Radar Sonar Navig. 133, 163–175 (1986).

Adams, D. B.

D. B. Adams, W. T. Snider, and C. K. Madsen, “A novel NLFM waveform generator using tunable integrated optical ring resonators: simulation and proof of concept experiment,” Proc. SPIE 7684, 76841A (2010).
[Crossref]

Atkins, P.

T. Collins and P. Atkins, “Nonlinear frequency modulation chirps for active sonar,” IEE Proc., Radar Sonar Navig. 146(6), 312–316 (1999).
[Crossref]

Buck, J.

J. Buck, “High-resolution 3D coherent laser radar imaging,” Proc. SPIE 6550, 655002 (2007).
[Crossref]

Chan, Y. K.

Y. K. Chan, M. Y. Chua, and V. C. Koo, “Sidelobes reduction using simple two and tri-stages nonlinear frequency modulation (NLFM),” PIER PIER 98, 33–52 (2009) (PIER).
[Crossref]

Chua, M. Y.

Y. K. Chan, M. Y. Chua, and V. C. Koo, “Sidelobes reduction using simple two and tri-stages nonlinear frequency modulation (NLFM),” PIER PIER 98, 33–52 (2009) (PIER).
[Crossref]

Collins, T.

T. Collins and P. Atkins, “Nonlinear frequency modulation chirps for active sonar,” IEE Proc., Radar Sonar Navig. 146(6), 312–316 (1999).
[Crossref]

Doerry, A. W.

A. W. Doerry, “Generating precision nonlinear FM chirp waveforms,” Proc. SPIE 6547, 65470D (2007).
[Crossref]

Fairhead, A. C.

J. A. Johnston and A. C. Fairhead, ““Waveform design and doppler sensitivity analysis for nonlinear FM chirp pulses,” IEE Proc,” Radar Sonar Navig. 133, 163–175 (1986).

Johnston, J. A.

J. A. Johnston and A. C. Fairhead, ““Waveform design and doppler sensitivity analysis for nonlinear FM chirp pulses,” IEE Proc,” Radar Sonar Navig. 133, 163–175 (1986).

Koo, V. C.

Y. K. Chan, M. Y. Chua, and V. C. Koo, “Sidelobes reduction using simple two and tri-stages nonlinear frequency modulation (NLFM),” PIER PIER 98, 33–52 (2009) (PIER).
[Crossref]

Madsen, C. K.

D. B. Adams, W. T. Snider, and C. K. Madsen, “A novel NLFM waveform generator using tunable integrated optical ring resonators: simulation and proof of concept experiment,” Proc. SPIE 7684, 76841A (2010).
[Crossref]

Snider, W. T.

D. B. Adams, W. T. Snider, and C. K. Madsen, “A novel NLFM waveform generator using tunable integrated optical ring resonators: simulation and proof of concept experiment,” Proc. SPIE 7684, 76841A (2010).
[Crossref]

Youmans, D.

D. Youmans, “Waveform comparison for coherent ladar imaging using a helicopter facet model target,” Proc. SPIE 7323, 73230 (2009).

D. Youmans, “Coherent lidar imaging of dust clouds: waveform comparisons with the poly-phase (P4) modulation waveform,” Proc. SPIE 6950, 695009 (2008).
[Crossref]

D. Youmans, “Coherent ladar imaging of the SEASAT satellite retro-reflector array using linear-FM chirp waveforms and pulse compression,” Proc. SPIE 6550, 655004 (2007).
[Crossref]

IEE Proc., Radar Sonar Navig. (1)

T. Collins and P. Atkins, “Nonlinear frequency modulation chirps for active sonar,” IEE Proc., Radar Sonar Navig. 146(6), 312–316 (1999).
[Crossref]

PIER (1)

Y. K. Chan, M. Y. Chua, and V. C. Koo, “Sidelobes reduction using simple two and tri-stages nonlinear frequency modulation (NLFM),” PIER PIER 98, 33–52 (2009) (PIER).
[Crossref]

Proc. SPIE (6)

A. W. Doerry, “Generating precision nonlinear FM chirp waveforms,” Proc. SPIE 6547, 65470D (2007).
[Crossref]

D. Youmans, “Waveform comparison for coherent ladar imaging using a helicopter facet model target,” Proc. SPIE 7323, 73230 (2009).

D. Youmans, “Coherent ladar imaging of the SEASAT satellite retro-reflector array using linear-FM chirp waveforms and pulse compression,” Proc. SPIE 6550, 655004 (2007).
[Crossref]

J. Buck, “High-resolution 3D coherent laser radar imaging,” Proc. SPIE 6550, 655002 (2007).
[Crossref]

D. Youmans, “Coherent lidar imaging of dust clouds: waveform comparisons with the poly-phase (P4) modulation waveform,” Proc. SPIE 6950, 695009 (2008).
[Crossref]

D. B. Adams, W. T. Snider, and C. K. Madsen, “A novel NLFM waveform generator using tunable integrated optical ring resonators: simulation and proof of concept experiment,” Proc. SPIE 7684, 76841A (2010).
[Crossref]

Radar Sonar Navig. (1)

J. A. Johnston and A. C. Fairhead, ““Waveform design and doppler sensitivity analysis for nonlinear FM chirp pulses,” IEE Proc,” Radar Sonar Navig. 133, 163–175 (1986).

Other (3)

M. Luszczyk, “Numerical evaluation of ambiguity function for stepped non-linear FM radar waveform,” International Conference on Microwaves, Radar & Wireless Communications (2006) pp. 1164–1167.

C. K. Madsen, and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, (John Wiley, 1999).

M. E. Solmaz, D. B. Adams, S. Grover, W.-C. Tan, X. Xia, O. Eknoyan, and C. K. Madsen, “First demonstration of an As2S3-on-LiNbO3 ring resonator,” Optical Fiber Communication Conference (OFC), (2009), pp. 1–3.

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Figures (5)

Fig. 1
Fig. 1 a) A basic integrated optical ring resonator to modulate the phase of an input signal. The modulators change the refractive index of the waveguide, the one internal to the ring creates a non-linear frequency chirp and the one outside the ring to create an approximately linear chirp b) The ring power coupling constant κ equates to the through and cross port transmission coefficients cos 2 ( θ ) and sin 2 ( θ ) respectively. c) The theoretical phase response of an optical ring resonator over one FSR (50GHz FSR, 0.2 π transmission coefficient). Rapidly changing the refractive index of the ring will shift the phase curve. If a narrow-band optical wave with a wavelength of 1549.75 nm (shown in black) were input to the ring, its phase would change correspondingly.
Fig. 2
Fig. 2 a) The time and frequency output of a ring resonator with a coupling constant of κ = 0.75 ( θ = 0.33 π ) whose refractive index is modulated with a 16.67 MHz cosine wave. Here a 110 MHz carrier was used as the narrow-band ring input for graphical purposes. The blue or solid line shows the output wave, and the red or dashed line shows the instantaneous frequency of the output wave. b) The output wave and instantaneous frequency of a straight waveguide refractive index modulator, modulated with the 16.67 MHz cosine wave.
Fig. 3
Fig. 3 Scatter plots of the mainlobe widths and sidelobe levels of simulated ACF’s of NLFM chirped waveforms generated by rings with a variety of coupling constants and phase offsets. In all cases bandwidth = 10 / T a) Green circles: two different rings θ = 0.3 π ...0.47 π ϕ = 0... π ; blue diamonds: two identical rings θ = 0.335 π ...0.365 π , and ϕ = 0...0.7 π ; red circles: two different rings θ = 0.35 π ...0.42 π and no phase variation. b) Green circles: three different rings θ = 0.3 π ...0.47 π ϕ = 0...0.75 π ; blue diamonds: three identical rings θ = 0.3775 π ...0.4025 π and ϕ = 0...0.45 π ; red circles three different rings θ = 0.415 π ...0.44 π and no phase variation.
Fig. 4
Fig. 4 The simulated ACF mainlobe widths and sidelobe levels of NLFM chirped waveforms generated by two lossless rings a) with identical coupling constants κ = 0.65 , ϕ = 0...0.25 π phase variation, and 1 / T ... 10 / T bandwidth of additional linear chirp b) with identical coupling constants κ = 0.85 , ϕ = 0...0.25 π phase variation, and 1 / T ... 10 / T bandwidth of additional linear chirp.
Fig. 5
Fig. 5 Instantaneous frequency chirp created by the Si3N4 tunable integrated ring resonator, reaching a peak frequency of 28kHz.

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