Abstract

We introduce a novel, chipscale device capable of single-shot ultrafast recording with picosecond-scale resolution over hundreds of picoseconds of record length. The device consists of two vertically-stacked III-V planar waveguides forming a Mach-Zehnder interferometer, and makes use of a transient, optically-induced phase difference to sample a temporal waveform injected into the waveguides. The pump beam is incident on the chip from above in the form of a diagonally-oriented stripe focused by a cylindrical lens. Due to time-of-flight, this diagonal orientation enables the sampling window to be shifted linearly in time as a function of position across the lateral axis of the waveguides. This time-to-space mapping allows an ordinary camera to record the ultrafast waveform with high fidelity. We investigate the theoretical limits of this technique, present a simulation of device operation, and report a proof-of-concept experiment in GaAs, demonstrating picosecond-scale resolution over 140 ps of record length.

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010

2008

C. Dorrer, J. Bromage, and J. D. Zuegel, “High-dynamic-range single-shot cross-correlator based on an optical pulse replicator,” Opt. Express 16(18), 13534–13544 (2008).
[CrossRef] [PubMed]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[CrossRef] [PubMed]

2007

2006

2004

F. Kadlec, H. Němec, and P. Kužel, “Optical two-photon absorption in GaAs measured by optical-pump terhertz-probe spectroscopy,” Phys. Rev. B 70(12), 125205 (2004).
[CrossRef]

1999

R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm. 17(4), 539–550 (1999).
[CrossRef]

1996

J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28(12), 1759–1763 (1996).
[CrossRef]

1993

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using Frequency-Resolved Optical Gating,” IEEE J. Quantum Electron. 29(2), 571–579 (1993).
[CrossRef]

1990

B. R. Bennett, R. A. Soref, and J. A. del Alamo, “Carrier-induced change in refractive index of InP, GaAs, and InGaAsP,” IEEE J. Quantum Electron. 26(1), 113–122 (1990).
[CrossRef]

1987

W. Lin, L. Fujimoto, and E. Ippen, “Femtosecond carrier dynamics in GaAs,” Appl. Phys. Lett. 50(3), 124–126 (1987).

1981

C. Henry, R. Logan, and K. Bertness, “Spectral dependence of the change in refractive index due to carrier injection in GaAs lasers,” J. Appl. Phys. 52(7), 4457–4461 (1981).
[CrossRef]

1962

P. Wolff, “Theory of the band structure of very degenerate semiconductors,” Phys. Rev. 126(2), 405–412 (1962).
[CrossRef]

Auerbach, J. M.

Bennett, B. R.

B. R. Bennett, R. A. Soref, and J. A. del Alamo, “Carrier-induced change in refractive index of InP, GaAs, and InGaAsP,” IEEE J. Quantum Electron. 26(1), 113–122 (1990).
[CrossRef]

Bertness, K.

C. Henry, R. Logan, and K. Bertness, “Spectral dependence of the change in refractive index due to carrier injection in GaAs lasers,” J. Appl. Phys. 52(7), 4457–4461 (1981).
[CrossRef]

Bowers, M. W.

Bromage, J.

del Alamo, J. A.

B. R. Bennett, R. A. Soref, and J. A. del Alamo, “Carrier-induced change in refractive index of InP, GaAs, and InGaAsP,” IEEE J. Quantum Electron. 26(1), 113–122 (1990).
[CrossRef]

Dixit, S. N.

Dorrer, C.

Erbert, G. V.

Foster, M. A.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[CrossRef] [PubMed]

Fujimoto, L.

W. Lin, L. Fujimoto, and E. Ippen, “Femtosecond carrier dynamics in GaAs,” Appl. Phys. Lett. 50(3), 124–126 (1987).

Gaeta, A. L.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[CrossRef] [PubMed]

Geraghty, D. F.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[CrossRef] [PubMed]

Haynam, C. A.

Hebling, J.

J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28(12), 1759–1763 (1996).
[CrossRef]

Heebner, J. E.

Heestand, G. M.

Henesian, M. A.

Henry, C.

C. Henry, R. Logan, and K. Bertness, “Spectral dependence of the change in refractive index due to carrier injection in GaAs lasers,” J. Appl. Phys. 52(7), 4457–4461 (1981).
[CrossRef]

Hermann, M. R.

Hisatake, S.

Ippen, E.

W. Lin, L. Fujimoto, and E. Ippen, “Femtosecond carrier dynamics in GaAs,” Appl. Phys. Lett. 50(3), 124–126 (1987).

Jancaitis, K. S.

Kadlec, F.

F. Kadlec, H. Němec, and P. Kužel, “Optical two-photon absorption in GaAs measured by optical-pump terhertz-probe spectroscopy,” Phys. Rev. B 70(12), 125205 (2004).
[CrossRef]

Kane, D. J.

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using Frequency-Resolved Optical Gating,” IEEE J. Quantum Electron. 29(2), 571–579 (1993).
[CrossRef]

Kobayashi, T.

Kužel, P.

F. Kadlec, H. Němec, and P. Kužel, “Optical two-photon absorption in GaAs measured by optical-pump terhertz-probe spectroscopy,” Phys. Rev. B 70(12), 125205 (2004).
[CrossRef]

Lin, W.

W. Lin, L. Fujimoto, and E. Ippen, “Femtosecond carrier dynamics in GaAs,” Appl. Phys. Lett. 50(3), 124–126 (1987).

Lipson, M.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[CrossRef] [PubMed]

Logan, R.

C. Henry, R. Logan, and K. Bertness, “Spectral dependence of the change in refractive index due to carrier injection in GaAs lasers,” J. Appl. Phys. 52(7), 4457–4461 (1981).
[CrossRef]

Manes, K. R.

Marshall, C. D.

Mehta, N. C.

Menapace, J.

Moses, E.

Murray, J. R.

Nemec, H.

F. Kadlec, H. Němec, and P. Kužel, “Optical two-photon absorption in GaAs measured by optical-pump terhertz-probe spectroscopy,” Phys. Rev. B 70(12), 125205 (2004).
[CrossRef]

Nostrand, M. C.

Orth, C. D.

Patterson, R.

Sacks, R. A.

Salem, R.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[CrossRef] [PubMed]

Sarantos, C. H.

Shaw, M. J.

Soref, R. A.

B. R. Bennett, R. A. Soref, and J. A. del Alamo, “Carrier-induced change in refractive index of InP, GaAs, and InGaAsP,” IEEE J. Quantum Electron. 26(1), 113–122 (1990).
[CrossRef]

Spaeth, M.

Sutton, S. B.

Trebino, R.

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using Frequency-Resolved Optical Gating,” IEEE J. Quantum Electron. 29(2), 571–579 (1993).
[CrossRef]

Turner-Foster, A. C.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[CrossRef] [PubMed]

Van Wonterghem, B. M.

Walden, R. H.

R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm. 17(4), 539–550 (1999).
[CrossRef]

Wegner, P. J.

White, R. K.

Widmayer, C. C.

Williams, W. H.

Wolff, P.

P. Wolff, “Theory of the band structure of very degenerate semiconductors,” Phys. Rev. 126(2), 405–412 (1962).
[CrossRef]

Yang, S. T.

Zuegel, J. D.

Appl. Opt.

Appl. Phys. Lett.

W. Lin, L. Fujimoto, and E. Ippen, “Femtosecond carrier dynamics in GaAs,” Appl. Phys. Lett. 50(3), 124–126 (1987).

IEEE J. Quantum Electron.

B. R. Bennett, R. A. Soref, and J. A. del Alamo, “Carrier-induced change in refractive index of InP, GaAs, and InGaAsP,” IEEE J. Quantum Electron. 26(1), 113–122 (1990).
[CrossRef]

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using Frequency-Resolved Optical Gating,” IEEE J. Quantum Electron. 29(2), 571–579 (1993).
[CrossRef]

IEEE J. Sel. Areas Comm.

R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm. 17(4), 539–550 (1999).
[CrossRef]

J. Appl. Phys.

C. Henry, R. Logan, and K. Bertness, “Spectral dependence of the change in refractive index due to carrier injection in GaAs lasers,” J. Appl. Phys. 52(7), 4457–4461 (1981).
[CrossRef]

Nature

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28(12), 1759–1763 (1996).
[CrossRef]

Phys. Rev.

P. Wolff, “Theory of the band structure of very degenerate semiconductors,” Phys. Rev. 126(2), 405–412 (1962).
[CrossRef]

Phys. Rev. B

F. Kadlec, H. Němec, and P. Kužel, “Optical two-photon absorption in GaAs measured by optical-pump terhertz-probe spectroscopy,” Phys. Rev. B 70(12), 125205 (2004).
[CrossRef]

Other

T. Moss, G. Bureell, and B. Ellis, Semiconductor opto-electronics (Wiley, 1973).

K. Hall, E. Thoen, and E. Ippen, Nonlinear optics in semiconductors II (Academic Press, 1999), Chap. 2.

B. L. Anderson and R. L. Anderson, Fundamentals of semiconductor devices (McGraw-Hill, 2005).

I. Jovanovic, C. Brown, C. Haefner, M. Shverdin, M. Taranowski, and C. P. J. Barty, “High-dynamic-range, 200-ps window, single-shot cross-correlator for ultrahigh intensity laser characterization,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2007).

C. V. Bennett, B. D. Moran, C. Langrock, M. M. Fejer, and M. Ibsen, “640 GHz real-time recording using temporal imaging,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2008).

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Figures (7)

Fig. 1
Fig. 1

The signal is coupled into the MZI of the SCALPEL chip uniformly along the lateral x-axis. The arms of the MZI are biased with a π-phase shift, so that no signal appears at the output in the passive state. When a pump stripe is introduced, a phase shift difference of 2π is induced, temporarily opening a short window via constructive interference and then closing it again via destructive interference. Because the pump stripe is oriented diagonally and time-of-flight dictates the z-position of a given slice in time, the signal sampling window is linearly shifted, translating across the lateral axis. This creates a time-to-space mapping that allows a conventional, high fidelity camera to record the ultrafast waveform.

Fig. 2
Fig. 2

Schematic of the geometry of the diagonal pump beam and test signal of two impulses. The pump pulse (diagonal stripe) and two impulses (with no structure in the x direction) are shown from a top view propagating in the z direction. The impulse response is shown on the right side, separated by the temporal resolution δx.

Fig. 3
Fig. 3

(a) The carrier distribution ρ(y) is solved numerically for different pump fluences. The waveguide cores are outlined in black. Absorption in the cladding layers is assumed to be negligible. The effect of absorption saturation can be observed as the flattening of the carrier density profile for higher fluences. (b) The effective index change as a function of pump fluence (solid curves) for the upper (blue) and lower (green) waveguides. The dotted red curve is the difference between the blue and green curves. The dotted light blue curve is the difference in effective index change assuming a uniform carrier distribution due to carrier diffusion.

Fig. 4
Fig. 4

The record length assuming no diffraction (dashed blue curve) and the spatial resolution (solid green curve) as a function of θ, for a rectangular pump stripe at the optimal temporal resolution. The device dimensions are assumed to be 5cm (z) by 1cm (x). The record length limited by diffraction is plotted as squares.

Fig. 5
Fig. 5

(a) The phase of the wavefront ramps from 0 to −2π, which can be qualitatively described as localized off-axis beam propagation, resulting in a localized lateral deflection. (b) Simulation of the localized lateral deflection. The pump shape g(z) is rectangular, wt = 1ps, θ = 12°, and the fluence is 58μJ/cm2, which corresponds to ∆neff12 = 0.005. The power shifts towards the end of the record. (c) Simulated recording—same pump parameters as (b)—of a series of impulses separated by the temporal resolution of the device. Toward the end of the record the impulse response is distorted due to the localized lateral deflection.

Fig. 6
Fig. 6

The heterostructure of the experimental SCALPEL device, which was fabricated without input/output couplers. The signal is end-fire coupled in with a line focus that overlaps both cores, exciting them with equal intensities. The outputs of both waveguides diffract and interfere, creating a fringe pattern of bright and dark spots. Biasing for destructive interference can be achieved by sampling the spatially recorded signal along a null of the vertical fringe pattern recorded on the camera.

Fig. 7
Fig. 7

(a) Experimental setup. The pump is timed to arrive when the signal has filled the length of the chip. The interference fringe pattern is analyzed to obtain the desired recording. (b) Lineout of the recorded far-field interference pattern demonstrating the single-shot recording of two 169 fs (FWHM) impulses separated by 124 ps created by a Michelson interferometer. The observed resolution is 7.5 ps. We believe that due to the excess bandwidth of the test signal, group velocity dispersion in the waveguides degraded the resolution from its theoretical value of 1.1 ps.

Equations (22)

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Δ φ 12 (x)=Δ φ 1 (x)Δ φ 2 (x)
Δ φ 12 (x)= 2π λ z o Δ n eff 12 ( x,z, z z o v g ) dz
Δ n eff 12 (x,z,t)={ Δ n eff 12 (t) if (x,z)P 0 otherwise
w z = λ 2Δ n eff 12
w 1 = λ 4Δ n eff 12 w 2 = 3λ 4Δ n eff 12
δx=( w 2 w 1 )tanθ= λ 2Δ n eff 12 tanθ
δt= δx tanθ ( n g c )= λ 2Δ n eff 12 ( n g c )
Δ n eff i (x,z,t)= Δ ε i (x,y,z,t)| U i (y) | 2 dy | U i (y) | 2 dy + ( n eff i ) 2 n eff i
Δ n i (x,y,z,t)= I i (x,y,z,t) F o (x,z) h(x,y,z,t)
Δ n i (y,t)= I i (y,t) F o h(y,t)
I(y,t)= F o 2 π w t exp( 2 ( t n g c y ) 2 ( w t ) 2 )
h(y,t)Δ n ρ (y)u(t)
Δ n i (y,t)= I i (y,t) F o Δ n ρ (y)u(t)
Δρ(y)ρ(y)
I(y,t) y =α(ρ(y,t))I(y,t)β I 2 (y,t) n g c I(y,t) t
ρ(y,t) t = α(ρ(y,t)) ω I(y,t)
α(ρ)= α o ( ρ max ρ ρ max )
ρ(y,t)= ρ max [ 1exp( F(y) F s ) ]+ βr 2ω w t F 2 (y)
F s ω ρ max α o
F(y)= I (y,t)dt
Δ n eff 12 (t)=Δ n eff 12 [ 1 2 + 1 2 erf( t w t /2 2 ) ]
Δ n eff i (x,z,t)= 2 n core Δ n unif i (x,z,t)+Δ n unif i (x,z,t) 2 + ( n eff i ) 2 n eff i

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