Abstract

We propose and demonstrate a linear time-to-space mapping system, which is based on two times electrooptic sinusoidal beam deflection. The direction of each deflection is set to be mutually orthogonal with the relative deflection phase of π/2 rad so that the circular optical beam trajectory can be achieved. The beam spot at the observation plane moves with an uniform velocity and as a result linear time-to-space mapping (an uniform temporal resolution through the mapping) can be realized. The proof-of-concept experiment are carried out and the temporal resolution of 5 ps has been demonstrated using traveling-wave type quasi-velosity-matched electrooptic beam deflectors. The developed system is expected to be applied to characterization of ultrafast optical signal or optical arbitrary waveform shaping for modulated microwave/millimeter-wave generation.

© 2008 Optical Society of America

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References

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  1. J. Capmany and D. Novak, "Microwave photonics combines two worlds," Nature Photon. 1, 319-330 (2007).
    [CrossRef]
  2. C -Bin Huang, Z. Jiang, D. E. Leaird, J. Caraquitena, and A. M.Weiner, "Spectral line-by-line shaping for optical and microwave arbitrary waveform generations," Laser Photon Rev 2, 227-248 (2008).
    [CrossRef]
  3. A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
    [CrossRef]
  4. J. Desbois, F. Gires, and P. Tournois, "A new approach to picosecond laser pulse analysis shaping and coding," IEEE J. Quantum Electron. QE-9, 213-218 (1973).
    [CrossRef]
  5. T. Kobayashi and T. Sueta, "Picosecond electrooptic devices," in. Tech. Dig., Conf. on Lasers and Electro-Opt. Washington, DC: Opt. Soc. Amer., 94- 95 (1984).
  6. Z. Jiang,C -B Huang, D. E. Leaird, and A. W. Weiner,"Optical arbitrary waveform processing of more than 100 spectral comb lines," Nature Photon. 1, 463-467 (2007).
    [CrossRef]
  7. S. Hisatake, Y. Nakase, K. Shibuya, and T. Kobayashi, "Generation of flat power-envelope terahertz-wide modulation sidebands from a continuous-wave laser based on an external electro-optic phase modulator," Opt. Lett. 30, 777-779 (2005).
    [CrossRef] [PubMed]
  8. V. Torres-Company, J. Lancis, and P. Andres, "Lossless equalization of frequency combs," Opt. Lett. 33, 1822-1824 (2008).
    [CrossRef] [PubMed]
  9. S. Hisatake and T. Kobayashi, "Time-to-space mapping of a continuous light wave with picosecond time resolution based on an electrooptic beam deflection," Opt. Express 14, 12704-12711 (2006).
    [CrossRef] [PubMed]
  10. S. Hisatake, K. Shibuya, and T. Kobayashi, "Ultrafast traveling-wave electro-optic deflector using domainengineered LiTaO3 crystal," Appl. Phys. Lett. 87, 081101 (2005).
    [CrossRef]

2008 (2)

C -Bin Huang, Z. Jiang, D. E. Leaird, J. Caraquitena, and A. M.Weiner, "Spectral line-by-line shaping for optical and microwave arbitrary waveform generations," Laser Photon Rev 2, 227-248 (2008).
[CrossRef]

V. Torres-Company, J. Lancis, and P. Andres, "Lossless equalization of frequency combs," Opt. Lett. 33, 1822-1824 (2008).
[CrossRef] [PubMed]

2007 (2)

J. Capmany and D. Novak, "Microwave photonics combines two worlds," Nature Photon. 1, 319-330 (2007).
[CrossRef]

Z. Jiang,C -B Huang, D. E. Leaird, and A. W. Weiner,"Optical arbitrary waveform processing of more than 100 spectral comb lines," Nature Photon. 1, 463-467 (2007).
[CrossRef]

2006 (1)

2005 (2)

2000 (1)

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

1973 (1)

J. Desbois, F. Gires, and P. Tournois, "A new approach to picosecond laser pulse analysis shaping and coding," IEEE J. Quantum Electron. QE-9, 213-218 (1973).
[CrossRef]

Andres, P.

Capmany, J.

J. Capmany and D. Novak, "Microwave photonics combines two worlds," Nature Photon. 1, 319-330 (2007).
[CrossRef]

Desbois, J.

J. Desbois, F. Gires, and P. Tournois, "A new approach to picosecond laser pulse analysis shaping and coding," IEEE J. Quantum Electron. QE-9, 213-218 (1973).
[CrossRef]

Gires, F.

J. Desbois, F. Gires, and P. Tournois, "A new approach to picosecond laser pulse analysis shaping and coding," IEEE J. Quantum Electron. QE-9, 213-218 (1973).
[CrossRef]

Hisatake, S.

Huang, C -B

Z. Jiang,C -B Huang, D. E. Leaird, and A. W. Weiner,"Optical arbitrary waveform processing of more than 100 spectral comb lines," Nature Photon. 1, 463-467 (2007).
[CrossRef]

Jiang, Z.

Z. Jiang,C -B Huang, D. E. Leaird, and A. W. Weiner,"Optical arbitrary waveform processing of more than 100 spectral comb lines," Nature Photon. 1, 463-467 (2007).
[CrossRef]

Kobayashi, T.

Lancis, J.

Leaird, D. E.

Z. Jiang,C -B Huang, D. E. Leaird, and A. W. Weiner,"Optical arbitrary waveform processing of more than 100 spectral comb lines," Nature Photon. 1, 463-467 (2007).
[CrossRef]

Nakase, Y.

Novak, D.

J. Capmany and D. Novak, "Microwave photonics combines two worlds," Nature Photon. 1, 319-330 (2007).
[CrossRef]

Shibuya, K.

Torres-Company, V.

Tournois, P.

J. Desbois, F. Gires, and P. Tournois, "A new approach to picosecond laser pulse analysis shaping and coding," IEEE J. Quantum Electron. QE-9, 213-218 (1973).
[CrossRef]

Weiner, A. M.

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

Weiner, A. W.

Z. Jiang,C -B Huang, D. E. Leaird, and A. W. Weiner,"Optical arbitrary waveform processing of more than 100 spectral comb lines," Nature Photon. 1, 463-467 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

S. Hisatake, K. Shibuya, and T. Kobayashi, "Ultrafast traveling-wave electro-optic deflector using domainengineered LiTaO3 crystal," Appl. Phys. Lett. 87, 081101 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Desbois, F. Gires, and P. Tournois, "A new approach to picosecond laser pulse analysis shaping and coding," IEEE J. Quantum Electron. QE-9, 213-218 (1973).
[CrossRef]

Laser Photon Rev (1)

C -Bin Huang, Z. Jiang, D. E. Leaird, J. Caraquitena, and A. M.Weiner, "Spectral line-by-line shaping for optical and microwave arbitrary waveform generations," Laser Photon Rev 2, 227-248 (2008).
[CrossRef]

Nature Photon. (2)

Z. Jiang,C -B Huang, D. E. Leaird, and A. W. Weiner,"Optical arbitrary waveform processing of more than 100 spectral comb lines," Nature Photon. 1, 463-467 (2007).
[CrossRef]

J. Capmany and D. Novak, "Microwave photonics combines two worlds," Nature Photon. 1, 319-330 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Rev. Sci. Instrum. (1)

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

Other (1)

T. Kobayashi and T. Sueta, "Picosecond electrooptic devices," in. Tech. Dig., Conf. on Lasers and Electro-Opt. Washington, DC: Opt. Soc. Amer., 94- 95 (1984).

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Figures (6)

Fig. 1.
Fig. 1.

Principle of the linear time-to-space mapping. (a) Schematic of the mapping system. The optical wave is sinusoidally deflected by first electrooptic deflector (EOD) to vertical direction (x-axis direction). The vertically deflected beam is then deflected to horizontal direction by second EOD. The temporal position of the input beam is mapped into the spatial position along the circular beam trajectory at the mapping plane (Fourier transform plane of the output facet of second EOD). (b) Beam trajectory at the mapping plane in the case of relative phase of ϕ=π/2 rad. The amplitude of two deflection is assumed to be same.

Fig. 2.
Fig. 2.

Optical beam trajectories at the mapping plane. Input beam is assumed to be CW The optical power is temporally integrated. (a) Δθmx =15 rad, Δθmy =15 rad and ϕ=π/2 rad, (b) Δθmx θmy =15 rad and ϕ=0 rad, (c) Δθmx θmy =15 rad and ϕ=π/4 rad, and (d)Δθmx =15 rad, Δθmy =10 rad, and ϕ=π/2 rad.

Fig. 3.
Fig. 3.

Temporal resolution as a function of the maximum modulation index. The right hand side axis expresses the scale for the deflection period of T=61.5 ps (fm =16.25 GHz), which corresponds to an experimental condition.

Fig. 4.
Fig. 4.

Relation between the normalized actual input pulse width Δτ i and normalized measured pulse width Δτ m .(a) 0<Δτ i <0.4 and (b) 0.4≤Δτ i ≤0.8.

Fig. 5.
Fig. 5.

Experimental setup. AOD:acousto-optic deflector, Att. variable attenuator.

Fig. 6.
Fig. 6.

Optical beam trajectories observed by the CCD camera. The relative phase of the deflection was set to be about (a)0 rad, (b)π/4 rad, (c)π/2 rad, and (d) -π/4 rad, respectively.

Equations (10)

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E 0 (x,y,t)exp( x 2 + y 2 w 2 )exp(j( ω 0 t+Δ θ x (x)cos( ω m t)+Δ θ y (y)cos( ω m t+φ))),
Δ θ x ( x ) = { Δ θ mx d x ( d x d ) 0 ( x < d , x > d )
Δ θ y ( y ) = { Δ θ my d y ( d y d ) 0 ( y < d , y > d )
E 1 ( x 1 , y 1 , t ) exp ( w 2 f 2 λ 2 d 2 ( X ( x 1 , t ) 2 + Y ( y 1 , t ) 2 ) ) exp ( j ω 0 t ) ,
X ( x 1 , t ) = d π x 1 + f λ Δ θ mx 2 cos ( ω m t ) ,
Y ( x 1 , t ) = d π y 1 + f λ Δ θ my 2 cos ( ω m t + ϕ ) ,
Δ τ min T π N = 2 π 1.39 r Δ ν = 2 π 1.39 r 2 Δ θ m f m ,
Δ τ 0 = Δ τ min T = 1.39 π r Δ θ m .
A 0 ( ω mt Δ τ i ) = exp ( 2 log e 2 ω mt 2 Δ τ i 2 ) exp ( j ω 0 t ) ,
Δ τ m ( Δ τ i ) = Δ τ 0 2 + Δ τ i 2 .

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