Abstract

We provide analytical modeling and the detailed procedure that is used in recently proposed arbitrary waveform generation technique by using MEMS digital micro-mirror arrays. We estimate the achievable temporal resolution, repetition rate, modulation index and the rise/fall times of the final waveform as figure of merit in the proposed systems. We show that reducing the diffraction limit via increasing the ratio of beam size to lens focal length (>0.075) and the spatial modulation down to single mirror pitch size (10.8μm), waveforms up to 18GHz repetition rates with >90% modulation index and <100ps rise times are achievable. Theoretical calculations are compared with experimental generation of 120MHz square waves and 160MHz sawtooth waves and obtained good agreement.

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. C. Wang and J. Yao, “Large time-bandwidth product microwave arbitrary waveform generation using a spatially discrete chirped fiber Bragg grating,” J. Lightwave Technol.28(11), 1652–1660 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  17. S. K. Kalyoncu, Y. Huang, Q. Song and O. Boyraz, “Fast arbitrary waveform generation by using digital micro mirror arrays,” IEEE Photon. Technol. Lett. (To be Appear In Photonics Technology Letters).
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    [CrossRef]
  19. O. Boyraz, J. Kim, M. N. Islam, and B. Jalali, “10 Gb/s multiple wavelength, coherent short pulse source based on spectral carving of supercontinuum generated in fibers,” J. Lightwave Technol.18(12), 2167–2175 (2000).
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2011 (1)

M. Bolea, J. Mora, B. Ortega, and J. Capmany, “Optical arbitrary waveform generator using incoherent microwave photonic filtering,” IEEE Photon. Technol. Lett.23(10), 618–620 (2011).
[CrossRef]

2010 (1)

2007 (2)

H. Chi and J. Yao, “Symmetrical waveform generation based on temporal pulse shaping using amplitude-only modulator,” Electron. Lett.43(7), 415–417 (2007).
[CrossRef]

I. W. Jung, J. S. Wang, and O. Solgaard, “Optical pattern generation using a spatial light modulator for maskless lithography,” IEEE J. Sel. Top. Quantum Electron.13(2), 147–154 (2007).
[CrossRef]

2006 (1)

M. L. Hsieh, “Modulation transfer function of Digital Micromirror Device,” Opt. Eng.45(3), 034001 (2006).
[CrossRef]

2003 (2)

D. Dudley, W. Duncan, and J. Slaughter, “Emerging Digital Micromirror Device (DMD) applications,” Proc. SPIE4985, 14–25 (2003).
[CrossRef]

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-Photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett.15(4), 581–583 (2003).
[CrossRef]

2002 (3)

2000 (1)

1999 (1)

R. S. Nesbitt, S. L. Smith, R. A. Molnar, and S. A. Benton, “Holographic recording using a digital micromirror device,” Proc. SPIE3637, 12–20 (1999).
[CrossRef]

1995 (2)

L. J. Mullen, A. J. C. Vieira, P. R. Herezfeld, and V. M. Contarino, “Application of RADAR technology to aerial LIDAR systems for enhancement of shallow underwater target detection,” IEEE Trans. Microw. Theory Tech.43(9), 2370–2377 (1995).
[CrossRef]

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron.19(3), 161–237 (1995).
[CrossRef]

Abeles, J. H.

T. Yilmaz, C. M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, “Toward a photonic arbitrary waveform generator using modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett.14(11), 1608–1610 (2002).
[CrossRef]

Benton, S. A.

R. S. Nesbitt, S. L. Smith, R. A. Molnar, and S. A. Benton, “Holographic recording using a digital micromirror device,” Proc. SPIE3637, 12–20 (1999).
[CrossRef]

Bolea, M.

M. Bolea, J. Mora, B. Ortega, and J. Capmany, “Optical arbitrary waveform generator using incoherent microwave photonic filtering,” IEEE Photon. Technol. Lett.23(10), 618–620 (2011).
[CrossRef]

Boussert, B.

Boyraz, O.

Capmany, J.

M. Bolea, J. Mora, B. Ortega, and J. Capmany, “Optical arbitrary waveform generator using incoherent microwave photonic filtering,” IEEE Photon. Technol. Lett.23(10), 618–620 (2011).
[CrossRef]

Chi, H.

H. Chi and J. Yao, “Symmetrical waveform generation based on temporal pulse shaping using amplitude-only modulator,” Electron. Lett.43(7), 415–417 (2007).
[CrossRef]

Chou, J.

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-Photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett.15(4), 581–583 (2003).
[CrossRef]

Contarino, V. M.

L. J. Mullen, A. J. C. Vieira, P. R. Herezfeld, and V. M. Contarino, “Application of RADAR technology to aerial LIDAR systems for enhancement of shallow underwater target detection,” IEEE Trans. Microw. Theory Tech.43(9), 2370–2377 (1995).
[CrossRef]

Delfyett, P. J.

T. Yilmaz, C. M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, “Toward a photonic arbitrary waveform generator using modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett.14(11), 1608–1610 (2002).
[CrossRef]

DePriest, C. M.

T. Yilmaz, C. M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, “Toward a photonic arbitrary waveform generator using modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett.14(11), 1608–1610 (2002).
[CrossRef]

Dudley, D.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging Digital Micromirror Device (DMD) applications,” Proc. SPIE4985, 14–25 (2003).
[CrossRef]

Duncan, W.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging Digital Micromirror Device (DMD) applications,” Proc. SPIE4985, 14–25 (2003).
[CrossRef]

Goedgebuer, J.-P.

Han, Y.

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-Photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett.15(4), 581–583 (2003).
[CrossRef]

Herezfeld, P. R.

L. J. Mullen, A. J. C. Vieira, P. R. Herezfeld, and V. M. Contarino, “Application of RADAR technology to aerial LIDAR systems for enhancement of shallow underwater target detection,” IEEE Trans. Microw. Theory Tech.43(9), 2370–2377 (1995).
[CrossRef]

Hsieh, M. L.

M. L. Hsieh, “Modulation transfer function of Digital Micromirror Device,” Opt. Eng.45(3), 034001 (2006).
[CrossRef]

Islam, M. N.

Jalali, B.

Jung, I. W.

I. W. Jung, J. S. Wang, and O. Solgaard, “Optical pattern generation using a spatial light modulator for maskless lithography,” IEEE J. Sel. Top. Quantum Electron.13(2), 147–154 (2007).
[CrossRef]

Kim, J.

Leaird, D. E.

McKinney, J. D.

Molnar, R. A.

R. S. Nesbitt, S. L. Smith, R. A. Molnar, and S. A. Benton, “Holographic recording using a digital micromirror device,” Proc. SPIE3637, 12–20 (1999).
[CrossRef]

Mora, J.

M. Bolea, J. Mora, B. Ortega, and J. Capmany, “Optical arbitrary waveform generator using incoherent microwave photonic filtering,” IEEE Photon. Technol. Lett.23(10), 618–620 (2011).
[CrossRef]

Mullen, L. J.

L. J. Mullen, A. J. C. Vieira, P. R. Herezfeld, and V. M. Contarino, “Application of RADAR technology to aerial LIDAR systems for enhancement of shallow underwater target detection,” IEEE Trans. Microw. Theory Tech.43(9), 2370–2377 (1995).
[CrossRef]

Nesbitt, R. S.

R. S. Nesbitt, S. L. Smith, R. A. Molnar, and S. A. Benton, “Holographic recording using a digital micromirror device,” Proc. SPIE3637, 12–20 (1999).
[CrossRef]

Ortega, B.

M. Bolea, J. Mora, B. Ortega, and J. Capmany, “Optical arbitrary waveform generator using incoherent microwave photonic filtering,” IEEE Photon. Technol. Lett.23(10), 618–620 (2011).
[CrossRef]

Poinsot, S.

Porte, H.

Rhodes, W. T.

Slaughter, J.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging Digital Micromirror Device (DMD) applications,” Proc. SPIE4985, 14–25 (2003).
[CrossRef]

Smith, S. L.

R. S. Nesbitt, S. L. Smith, R. A. Molnar, and S. A. Benton, “Holographic recording using a digital micromirror device,” Proc. SPIE3637, 12–20 (1999).
[CrossRef]

Solgaard, O.

I. W. Jung, J. S. Wang, and O. Solgaard, “Optical pattern generation using a spatial light modulator for maskless lithography,” IEEE J. Sel. Top. Quantum Electron.13(2), 147–154 (2007).
[CrossRef]

Turpin, T.

T. Yilmaz, C. M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, “Toward a photonic arbitrary waveform generator using modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett.14(11), 1608–1610 (2002).
[CrossRef]

Vieira, A. J. C.

L. J. Mullen, A. J. C. Vieira, P. R. Herezfeld, and V. M. Contarino, “Application of RADAR technology to aerial LIDAR systems for enhancement of shallow underwater target detection,” IEEE Trans. Microw. Theory Tech.43(9), 2370–2377 (1995).
[CrossRef]

Wang, C.

Wang, J. S.

I. W. Jung, J. S. Wang, and O. Solgaard, “Optical pattern generation using a spatial light modulator for maskless lithography,” IEEE J. Sel. Top. Quantum Electron.13(2), 147–154 (2007).
[CrossRef]

Weiner, A. M.

Yao, J.

C. Wang and J. Yao, “Large time-bandwidth product microwave arbitrary waveform generation using a spatially discrete chirped fiber Bragg grating,” J. Lightwave Technol.28(11), 1652–1660 (2010).
[CrossRef]

H. Chi and J. Yao, “Symmetrical waveform generation based on temporal pulse shaping using amplitude-only modulator,” Electron. Lett.43(7), 415–417 (2007).
[CrossRef]

Yilmaz, T.

T. Yilmaz, C. M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, “Toward a photonic arbitrary waveform generator using modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett.14(11), 1608–1610 (2002).
[CrossRef]

Electron. Lett. (1)

H. Chi and J. Yao, “Symmetrical waveform generation based on temporal pulse shaping using amplitude-only modulator,” Electron. Lett.43(7), 415–417 (2007).
[CrossRef]

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

I. W. Jung, J. S. Wang, and O. Solgaard, “Optical pattern generation using a spatial light modulator for maskless lithography,” IEEE J. Sel. Top. Quantum Electron.13(2), 147–154 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-Photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett.15(4), 581–583 (2003).
[CrossRef]

M. Bolea, J. Mora, B. Ortega, and J. Capmany, “Optical arbitrary waveform generator using incoherent microwave photonic filtering,” IEEE Photon. Technol. Lett.23(10), 618–620 (2011).
[CrossRef]

T. Yilmaz, C. M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, “Toward a photonic arbitrary waveform generator using modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett.14(11), 1608–1610 (2002).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

L. J. Mullen, A. J. C. Vieira, P. R. Herezfeld, and V. M. Contarino, “Application of RADAR technology to aerial LIDAR systems for enhancement of shallow underwater target detection,” IEEE Trans. Microw. Theory Tech.43(9), 2370–2377 (1995).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Eng. (1)

M. L. Hsieh, “Modulation transfer function of Digital Micromirror Device,” Opt. Eng.45(3), 034001 (2006).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (2)

R. S. Nesbitt, S. L. Smith, R. A. Molnar, and S. A. Benton, “Holographic recording using a digital micromirror device,” Proc. SPIE3637, 12–20 (1999).
[CrossRef]

D. Dudley, W. Duncan, and J. Slaughter, “Emerging Digital Micromirror Device (DMD) applications,” Proc. SPIE4985, 14–25 (2003).
[CrossRef]

Prog. Quantum Electron. (1)

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron.19(3), 161–237 (1995).
[CrossRef]

Other (5)

D. L. P. Texas Instruments, “DLP 0.55XGA Chipset,” (Texas Instruments 2010). http://www.ti.com/lit/ml/dlpb003/dlpb003.pdf

S. K. Nayar, V. Branzoi, and T. E. Boult, “Programmable imaging using a digital micromirror array,” In Proc. of IEEE Conference on Computer Vision and Pattern Recognition (CVPR) I, 436–443 (2004).

S. K. Kalyoncu, Y. Huang, Q. Song, and O. Boyraz, “Fast arbitrary waveform generation by using digital micro mirror arrays,” IEEE Photonics Conference, paper TuK 4, San Francisco, Sept. 2012.

S. K. Kalyoncu, Y. Huang, Q. Song and O. Boyraz, “Fast arbitrary waveform generation by using digital micro mirror arrays,” IEEE Photon. Technol. Lett. (To be Appear In Photonics Technology Letters).

B. Jalali, P. Kelkar, and V. Saxena, “Photonic arbitrary waveform generator,” in Proc. 14th Annu. Meeting IEEE Lasers Electro-Optics Soc. 1, 253–254 (2001).

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Figures (11)

Fig. 1
Fig. 1

Functional block diagram for all-optical arbitrary waveform generation by using micro-mirror arrays. SC: Supercontinuum, DCM: Dispersion compensating module, DMD: Digital micro-mirror device, PC: Personal computer, OSC: Oscilloscope.

Fig. 2
Fig. 2

The spatial resolution (a) of the focusing system depends on the diffraction limit and is improved by increasing diffraction parameter, r. The spectral and temporal resolution (calculated for D = −675ps/nm) mainly depends on the beam size, d and the effective groove density, Gβ (b).

Fig. 3
Fig. 3

The micro mirrors inbuilted on DMD with having 10.8 microns pitch size and ~1micron gap in between (a) can be oriented with high precision and speed at + 12 or + 12 degrees [13]. A sample (b) implemented ON-OFF modulation pattern on DMD [19].

Fig. 4
Fig. 4

The sample binary image patterns created on DMD to generate square waveforms with different spatial frequencies. Patterns with spatial period of 60mirrors/period (a), 120mirrors/period (b) and 200mirrors/period (c).

Fig. 5
Fig. 5

The spectral modulation and the corresponding temporal frequency (calculated for D = −675ps/nm) of the RF waveforms depends on the spatial modulation period and the effective groove density (a). Analytically generated square waveforms for different spatial modulation periods, P are illustrated in (b).

Fig. 6
Fig. 6

The modulation index (m) with respect to spatial modulation period and the diffraction parameter (r) is calculated for both Gaussian (a) and Plane (c) beams. Due to the difference in the definition of the beam size, which is the aperture diameter if the plane wave is considered and the spatial FWHM width if the Gaussian wave is considered, the plane beam becomes comparably narrower and cause the modulation index to be dropped abruptly. The inset figures shows the required modulation period to obtain m>90%. Analytically generated waveforms for different diffraction parameters are illustrated in (b-d)

Fig. 7
Fig. 7

The spectral (δλR) and the temporal (τR) rise at the waveform edges due to spatial modulation period (a-c) and the beam size (b-d) for Gaussian and Plane beams, respectively. The inset figures shows that the effect of lens focal length on δλR and τR is almost negligible.

Fig. 8
Fig. 8

The 2-D amplitude quantization model for sawtooth waveform generation. The sample modulation scheme employed on DMD with 128 horizontal mirrors/period and 8 amplitude quantization levels (a). The sample binary image pattern with 128 horizontal mirrors/period and 320 vertical mirrors (40 mirrors /each level) created on DMD to generate sawtooth waveform (b).

Fig. 9
Fig. 9

The so-called pulse width modulation model for sawtooth waveform generation. The sample modulation scheme employed on DMD with 128 mirrors/period and 8 amplitude quantization levels (a). The sample binary image pattern with 128 horizontal mirrors/period created on DMD to generate sawtooth waveform (b).

Fig. 10
Fig. 10

The experimental setup of all optical arbitrary waveform generator (AWG). MLL: Mode locked laser, EDFA: Erbium doped fiber amplifier, SC: Supercontinuum, BPF: Band pass filter.

Fig. 11
Fig. 11

The analytical and experimental results for the generated square waveform at 120MHz (a) and for the sawtooth waveform at 160MHz (b). The weak high frequency modulation appears on the analytically generated sawtooth waveform (b) results from the individual square type modulation of the sub-periods of the pattern used to generate sawtooth waveforms (Fig. 9). This weak modulation on the sawtooth waveform and the sharp edges of the square waveform are slightly smoothened due to the 1GHz LPF used in the experimental setup.

Equations (2)

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I( x,λ, d f ){ exp 2 [ π 2 ( x x pi ) 2 2ln( 2 ) λ 2 ( d f ) 2 ],Gaussianwave sin c 2 [ ( x x pi ) λ ( d f ) ],Planewave }
Δx{ 2λf dπ ln( 2 ),Gaussianwave 2×1.39156λf dπ ,Planewave },Δλ Δx G β f ={ 2λ G β dπ ln( 2 ),Gaussianwave 2×1.39156λ G β dπ ,Planewave }

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