## Chipscale, single-shot gated ultrafast optical recorder |

Optics Express, Vol. 20, Issue 1, pp. 414-425 (2012)

http://dx.doi.org/10.1364/OE.20.000414

Acrobat PDF (1293 KB)

### 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.

© 2011 OSA

## 1. Introduction to device concept

1. C. A. Haynam, P. J. Wegner, J. M. Auerbach, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, E. Moses, J. R. Murray, M. C. Nostrand, C. D. Orth, R. Patterson, R. A. Sacks, M. J. Shaw, M. Spaeth, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. Van Wonterghem, “National Ignition Facility laser performance status,” Appl. Opt. **46**(16), 3276–3303 (2007). [CrossRef] [PubMed]

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

3. 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]

7. 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]

8. 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**(26), 12704–12711 (2006). [CrossRef] [PubMed]

9. C. H. Sarantos and J. E. Heebner, “Solid-state ultrafast all-optical streak camera enabling high-dynamic-range picosecond recording,” Opt. Lett. **35**(9), 1389–1391 (2010). [CrossRef] [PubMed]

^{2}sampling gate. By diagonally orienting the pump stripe at an angle

*θ*to the axis of propagation, the window is linearly shifted in time as a function of lateral position across the waveguide. Much like a tilted-pulse front cross-correlator [6], the serial, temporal waveform is thus encoded spatially along the lateral dimension of the planar waveguide for recording in parallel on a camera.

## 2. Gate response and device resolution limits

*∆φ*= -π, the MZI response reaches its maximum (recall that the arms are originally π-phase shifted). When

_{12}*∆φ*= π

_{12}_{±}π/2, the result is ½ of the peak intensity. Because the mapping is linear, each of the diffraction-limited spots shown is equivalent to the impulse response of the device’s time to space mapping. Here, for simplicity, we treat the pump fluence profile as uniform. That is,where

*P*is the area occupied by the pump beam. We will further assume that the pump temporal profile is a delta-impulse,

*w*= 0. That is,

_{t}*∆n*, where

^{eff}_{12}(t) = ∆n^{eff}_{12}u(t)*u(t)*is the Heaviside step function.

*∆φ*−2π, so that the impulse response is localized between points A and E. This constrains the pump’s spatial beam width along the

_{12}=*z*axis to be

*θ*, the spatial

*1/e*half width of the pump stripe can be determined from

^{2}*w*, as depicted in Fig. 2. The points between positions A and E experience

_{z}*∆φ*[0,-2

_{12∈}*π*];

*∆φ*decreases monotonically with increasing

_{12}*x*, a property that results in a smooth, single-peaked impulse response. The position where

*∆φ*-

_{12}=*π*is denoted by C. The position B experiences

*∆φ*= -π/2, after propagating through a distance of

_{12}*w*through the pumped region. The position D experiences

_{1}*∆φ*= −3π/2, after propagating through a distance of

_{12}*w*through the pumped region.

_{2}*δx*of the device is defined to be consistent with the Rayleigh criterion for resolvability, which states that two spots are “just resolvable” if they are separated by their 3dB full width at half maximum (FWHM). Positions B and D correspond to the 3dB-points of the impulse response. Thus, the spatial resolution of the device is given by

*δt*is linearly mapped from

*δx*by the orientation angle

*θ*of the pump.

*δt*. As a result, the time-to-space mapping of Impulse 2 places its corresponding diffraction-limited spot one resolvable unit

*δx*away from the diffraction-limited spot corresponding to Impulse 1.

*δt*to be 1.1 ps. In general, a larger spatial resolution

*δx*is desirable to mitigate diffraction effects and to reduce imaging requirements. The trade-off here is between

*δx*and the record length, which is also a function of

*θ*. Note that to first order, the time resolution

*δt*is not a function of the pump stripe orientation,

*θ*.

## 3. Required pump-induced differential phase shift (nonlinear index change)

*∆n*, and a change in the local refractive index,

^{eff}_{i}(x,z,t)*∆n*. The local refractive index change has a

_{i}(x,y,z,t)*y*dependence. The effective index change can be calculated from the local index change by applying first-order perturbation theory to the Helmholtz equation.where

*U*is the unperturbed transverse mode profile,

_{i}(y)*n*is the unperturbed effective index, and

^{eff}_{i}*∆ε*. Here,

_{i}(x,y,z,t) = 2n_{core}∆n_{i}(x,y,z,t) + ∆n_{i}^{2}(x,y,z,t)*n*is the unperturbed waveguide core index. The waveguides are designed so that the pump photon energy is larger than the bandgap of the core but smaller than the bandgap of the cladding. Thus,

_{core}*∆n*is negligible in the waveguide cladding. The photon energy of the signal is smaller than the bandgap of the waveguide cladding and core materials.

_{i}(y,t)_{⊗}is the convolution,

*I*is the instantaneous intensity, and

*F*is the pump fluence. Or, at a certain position of interest

_{o}*(x,z)*

_{∈}*P*,

*h(y,t)*is the impulse response of the refractive index change. The term

*n*is the group index of the pump pulse propagating in the planar waveguide. The temporal 1/e

_{g}^{2}half width,

*w*, is generally a few hundred femtoseconds. The time dependence of

_{t}*h(y,t)*is a complicated expression that depends on the contributions from spectral hole burning (SHB), carrier heating, the increase in carrier density, and mechanisms much faster than the pump width, such as two photon absorption (TPA) and the optical Stark effect (OSE) [10].

*n*is the value of the index change associated with the change in carrier concentration ∆

_{ρ}(y)*ρ(y)*. Substituting in the simplified

*h(y,t)*, Eq. (10) can be written

*n*and ignoring the faster dynamics, our closed-form description of the refractive index change is conservative, in the sense that it underestimates the magnitude of

_{ρ}(y)*∆n*. Carrier heating and SHB generally decrease the refractive index for photon energies below the bandgap. Two-photon absorption and OSE provide negative and positive contributions to the refractive index change, respectively. In actuality, the transient is not monotonic as described by Eq. (13); rather it overshoots and then quickly converges [10]. However, simulations suggest that this transient has only a small impact on the resolution of the device.

_{i}(y,t)*ρ(y)*, which is approximately the carrier concentration induced by the pump

*ρ(y)*, since intrinsic GaAs has a relatively small number of free carriers in steady state.

*β*is the TPA coefficient and α is the single photon absorption (SPA) coefficient. Notice that we cannot ignore TPA and SHB here since the relevant timescales for pump absorption is much shorter than that of signal propagation. The pump is absorbed in waveguides that are 0.6 μm thick, while the signal experiences the index change over a distance that is 50 to 100 times longer. Over these timescales, spectral hole burning bleaches the absorption at the pump photon energy. To first order, the SPA coefficient

*α*at the pump wavelength is proportional to the density of available states,

*ρ*-

_{max}*ρ*, where

*ρ*is the population inversion carrier density threshold and

_{max}*ρ*is the carrier density due to SPAwhere α

_{o}is the non-saturated absorption coefficient. Neglecting the possible reshaping of

*I(y,t)*due to nonlinearities, Eq. (15) and 16 can be solved simultaneously for the free carrier distribution [12

12. 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]

*r*is a pulse-shape-dependent numerical constant (

*r*= 1 for a rectangular pulse,

*r*= 0.67 for a Gaussian pulse) [12

12. 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]

*F*is the saturation fluence

_{s}*F(y)*is the pump fluence that passes through a thin layer of semiconductor at depth

*y*

*n*can be attributed to three main carrier density dependent effects: bandfilling, bandgap shrinkage, and the plasma loading effect, also known as free carrier absorption. Bandfilling describes the decrease in absorption due to the population of conduction states and depopulation of valence states, and through the Kramers-Kronig integral, results in a decrease in refractive index for photon energies slightly below the bandgap [13]. Bandgap shrinkage shifts the absorption edge to lower energies, thus increasing absorption below the bandgap, resulting in a positive change in refractive index proportional to

_{ρ}*ρ*[14

^{1/3}14. P. Wolff, “Theory of the band structure of very degenerate semiconductors,” Phys. Rev. **126**(2), 405–412 (1962). [CrossRef]

*ρ*[15

15. 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]

*n*is dominated by the effects of bandfilling. We numerically calculate ∆

_{ρ}*n*as a function of wavelength and carrier density and use Eq. (8) to determine

_{ρ}(y)*∆n*and

^{eff}_{1}*∆n*, which are shown in Fig. 3(b) along with

^{eff}_{2}*∆n*as a function of the pump fluence [16

^{eff}_{12}16. 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]

*∆n*0.005 is achieved for a pump fluence of 60 μJ/cm

^{eff}_{12}=^{2}, limited ultimately by absorption saturation. The optimal temporal resolution is correspondingly calculated to be 1.1 ps. Using Eq. (13), the transient can be obtained by taking

*I(t)*to be of the form described in Eq. (11).where by nature of the construction

*t = 0*is when the pump has maximum intensity. We can assume that the impact of the pump pulse width on the temporal resolution is negligible when

*w*. Temporal resolution is not very sensitive to the pump pulse width: for example, a pump pulse width of 1 ps will degrade the resolution by 0.3% compared to a pulse width of zero.

_{t}« w_{1}/v_{g}*t*is less than the free carrier lifetime. For the purposes of this analysis, free carrier diffusion will be neglected. However, for completeness, if the carrier distribution is uniform within the waveguides, due to diffusion, Eq. (8) can be simplified towhere

*∆n*is the index change associated with the uniform carrier density. At room temperature, for undoped GaAs, the diffusion coefficient is approximately

^{unif}_{i}*D*= 200 cm

^{2}/s and the diffusion length is approximately 4 μm in 200 ps [17]. In Fig. 3(b), the dotted blue curve represents

*∆n*for a uniform carrier distribution. As carriers diffuse within the waveguide core, dotted red curve of Fig. 3(b) will evolve into the dotted blue curve.

^{eff}_{12}## 4. Record length limitations: illumination length and diffraction

_{12}due to the pump stripe causes the signal waveform to be gated out, effectively mapping time to space. In the previous section, the form of

*∆n*was derived. With

^{eff}_{12}*∆n*, the spatial resolution and temporal resolution can be found via Eqs. (6) and (7). Another parameter of interest is the record length of the device, measured in time. Neglecting diffraction, the record length is limited by the orientation of the pump stripe and the geometry of the chip. Figure 4 depicts the spatial resolution (green solid curve) and the record length (blue dotted curve) as a function of θ, for the maximum value of

^{eff}_{12}*∆n*from Fig. 3(b).

^{eff}_{12}*δx*, while for large

*δx*the record length is limited by the device dimensions.

## 5. Experimental

_{0.24}Ga

_{0.76}As cladding layers, the details of which are depicted in Fig. 6 . The structure was built without splitting and combining couplers, which greatly simplifies the fabrication process: after cleaving the wafers to the operating size of 5 cm (

*z*) by 1 cm (

*x*) with optical quality input/output facets, no further processing was necessary. Eliminating the integrated couplers decreases the throughput efficiency but does not otherwise detract from device performance. The signal is end-fire coupled 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 rows. The signal was coupled into and out of the two waveguides with the help of fast-axis collimating microlenses. The interference pattern at the waveguide output was captured on a CCD camera. To obtain the signal trace, a lineout was taken in

*x*along the first (zero-order) null of the interferogram integrated on the camera. Note that operating on this zero-order null yields an octave-spanning spectral bandwidth over which fringe smearing is negligible—much larger than the 8 nm bandwidth of the signal.

*θ*with respect to the z axis. A test signal was generated by diverting part of the pump energy to drive an optical parametric amplifier that produced an idler beam at 1.9 μm, which was subsequently frequency-doubled to 950 nm, which is just below the bandgap of the waveguide cores so that it experiences a strong carrier-induced index change. The lateral width of the signal beam was 10 mm. A silicon CCD camera captured the output fringe pattern. A test signal at 950 nm was generated by a Michelson interferometer, yielding two 170 fs (FWHM) impulses separated by 124 ps. The experimental setup is illustrated in Fig 7(a) .

*θ*is set to 12°, corresponding to the edge of the roll-off in the record length when no diffraction is assumed, from Fig. 4. This is achieved by formatting the pump beam into an approximately 60 μm (full width

*1/e*) diagonal Gaussian stripe providing a peak fluence of 275 μJ/cm

^{2}^{2}. For a Gaussian pump beam, the fluence is not uniform in

*z*, which means

*∆n*is not constant with

^{eff}_{12}*z*, nor is it a nice single-peaked function of

*z*, in general. The Gaussian beam does not degrade the resolution with respect to a square uniform beam if we operate at the regime near the optimal temporal resolution.

## 6. Conclusion

## Acknowledgments

## References and links

1. | C. A. Haynam, P. J. Wegner, J. M. Auerbach, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, E. Moses, J. R. Murray, M. C. Nostrand, C. D. Orth, R. Patterson, R. A. Sacks, M. J. Shaw, M. Spaeth, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. Van Wonterghem, “National Ignition Facility laser performance status,” Appl. Opt. |

2. | R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm. |

3. | D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using Frequency-Resolved Optical Gating,” IEEE J. Quantum Electron. |

4. | 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). |

5. | 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 |

6. | 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). |

7. | C. Dorrer, J. Bromage, and J. D. Zuegel, “High-dynamic-range single-shot cross-correlator based on an optical pulse replicator,” Opt. Express |

8. | 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 |

9. | C. H. Sarantos and J. E. Heebner, “Solid-state ultrafast all-optical streak camera enabling high-dynamic-range picosecond recording,” Opt. Lett. |

10. | K. Hall, E. Thoen, and E. Ippen, |

11. | W. Lin, L. Fujimoto, and E. Ippen, “Femtosecond carrier dynamics in GaAs,” Appl. Phys. Lett. |

12. | F. Kadlec, H. Němec, and P. Kužel, “Optical two-photon absorption in GaAs measured by optical-pump terhertz-probe spectroscopy,” Phys. Rev. B |

13. | T. Moss, G. Bureell, and B. Ellis, |

14. | P. Wolff, “Theory of the band structure of very degenerate semiconductors,” Phys. Rev. |

15. | 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. |

16. | 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. |

17. | B. L. Anderson and R. L. Anderson, |

18. | J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. |

**OCIS Codes**

(160.6000) Materials : Semiconductor materials

(320.7080) Ultrafast optics : Ultrafast devices

(320.7100) Ultrafast optics : Ultrafast measurements

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: August 31, 2011

Revised Manuscript: November 12, 2011

Manuscript Accepted: November 21, 2011

Published: December 21, 2011

**Citation**

Ta-Ming Shih, Chris H. Sarantos, Susan M. Haynes, and John E. Heebner, "Chipscale, single-shot gated ultrafast optical recorder," Opt. Express **20**, 414-425 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-414

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### References

- C. A. Haynam, P. J. Wegner, J. M. Auerbach, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, E. Moses, J. R. Murray, M. C. Nostrand, C. D. Orth, R. Patterson, R. A. Sacks, M. J. Shaw, M. Spaeth, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. Van Wonterghem, “National Ignition Facility laser performance status,” Appl. Opt.46(16), 3276–3303 (2007). [CrossRef] [PubMed]
- R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm.17(4), 539–550 (1999). [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]
- 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).
- M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature456(7218), 81–84 (2008). [CrossRef] [PubMed]
- 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. Dorrer, J. Bromage, and J. D. Zuegel, “High-dynamic-range single-shot cross-correlator based on an optical pulse replicator,” Opt. Express16(18), 13534–13544 (2008). [CrossRef] [PubMed]
- 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. Express14(26), 12704–12711 (2006). [CrossRef] [PubMed]
- C. H. Sarantos and J. E. Heebner, “Solid-state ultrafast all-optical streak camera enabling high-dynamic-range picosecond recording,” Opt. Lett.35(9), 1389–1391 (2010). [CrossRef] [PubMed]
- K. Hall, E. Thoen, and E. Ippen, Nonlinear optics in semiconductors II (Academic Press, 1999), Chap. 2.
- W. Lin, L. Fujimoto, and E. Ippen, “Femtosecond carrier dynamics in GaAs,” Appl. Phys. Lett.50(3), 124–126 (1987).
- F. Kadlec, H. Němec, and P. Kužel, “Optical two-photon absorption in GaAs measured by optical-pump terhertz-probe spectroscopy,” Phys. Rev. B70(12), 125205 (2004). [CrossRef]
- T. Moss, G. Bureell, and B. Ellis, Semiconductor opto-electronics (Wiley, 1973).
- P. Wolff, “Theory of the band structure of very degenerate semiconductors,” Phys. Rev.126(2), 405–412 (1962). [CrossRef]
- 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]
- 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]
- B. L. Anderson and R. L. Anderson, Fundamentals of semiconductor devices (McGraw-Hill, 2005).
- J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron.28(12), 1759–1763 (1996). [CrossRef]

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