^{1,a)}, Philip J. Harding

^{1}, Yoanna-Reine Nowicki-Bringuier

^{2}, Jean-Michel Gérard

^{2}and Willem L. Vos

^{1,3}

### Abstract

We performed nondegenerate pump-probe experiments on a GaAs/AlAs photoniccavity structure. We switched the photonic properties using the optical Kerr effect and free carriers excited by three photon absorption. The structure was probed at 1150–1640 nm, in the telecom spectral range below the stop gap. In the measurements we observe surprisingly large nondegenerate electronic Kerr coefficients over a broad wavelength range. We also extracted the three photon absorption coefficient for GaAs at three wavelengths in the near infrared. We conclude that the electronic Kerr effect is so large that the resonance of a moderate photoniccavity could be successfully switched instantaneous.

We want to thank Allard Mosk and Patrick Johnson for stimulating discussion. This research was supported by NanoNed, a nanotechnology program of the Dutch Ministry of Economic Affairs, and by a VICI fellowship from the “Nederlandse Organisatie voor Wetenschappelijk Onderzoek” (NWO) to WLV. This work is also part of the research program of the “Stichting voor Fundamenteel Onderzoek der Materie” (FOM), which is financially supported by the NWO.

I. INTRODUCTION

II. EXPERIMENTAL

A. Sample

B. Optical measurements

III. RESULTS

A. Linear reflectivity

B. Ultrafast switched reflectivity

C. Interpretation of time-resolved reflectivity

D. Nonlinear coefficients GaAs

1. Kerr coefficient for GaAs

2. Three photon absorption coefficient for GaAs

IV. CONCLUSION

### Key Topics

- Kerr effects
- 32.0
- Reflectivity
- 30.0
- Refractive index
- 21.0
- III-V semiconductors
- 11.0
- Photon absorption
- 11.0

## Figures

[(a) and (b)] Energy schematics of GaAs. is the electronic bandgap of GaAs, is the probe wavelength and is the pump wavelength. (a) In the dispersive spectral region the summed energy of a pump and a probe photon is smaller than the bandgap, while (b) the summed energy is larger in the absorptive spectral region. The edge between diagrams (a) and (b) is at probe wavelengths of 1510 and 1340 at pump wavelengths of 2000 and 2400 nm, respectively. We present measurements in the spectral region indicated with a square, to obtain a change in the real part of the refractive index. (c) Linear reflectivity spectrum and TM calculation of the GaAs/AlAs structure. The trough at 980 nm is due to the cavity resonance of the lambda thick GaAs layer. The hatched regions are based on a pump wavelength of 2400 nm. The slight difference in amplitude of the measured and calculated reflectivity on the red side of the stop band is caused by a small error in the normalization measurement.

[(a) and (b)] Energy schematics of GaAs. is the electronic bandgap of GaAs, is the probe wavelength and is the pump wavelength. (a) In the dispersive spectral region the summed energy of a pump and a probe photon is smaller than the bandgap, while (b) the summed energy is larger in the absorptive spectral region. The edge between diagrams (a) and (b) is at probe wavelengths of 1510 and 1340 at pump wavelengths of 2000 and 2400 nm, respectively. We present measurements in the spectral region indicated with a square, to obtain a change in the real part of the refractive index. (c) Linear reflectivity spectrum and TM calculation of the GaAs/AlAs structure. The trough at 980 nm is due to the cavity resonance of the lambda thick GaAs layer. The hatched regions are based on a pump wavelength of 2400 nm. The slight difference in amplitude of the measured and calculated reflectivity on the red side of the stop band is caused by a small error in the normalization measurement.

Differential reflectivity per wavelength as a function of delay between pump and probe pulse. At negative delays the pump hits the sample before the probe. The scans were measured at different pump wavelengths. (a) , , (c) , . Cross cuts indicated by dashed lines in (a) and (c) are shown in (b) and (d), respectively. (a) and (c) show a fringe pattern indicating a shift of the Fabry–Pérot fringes. Cross sections (b) and (d) show that the sign of the differential reflectivity at coincidence is different from the sign at positive delay.

Differential reflectivity per wavelength as a function of delay between pump and probe pulse. At negative delays the pump hits the sample before the probe. The scans were measured at different pump wavelengths. (a) , , (c) , . Cross cuts indicated by dashed lines in (a) and (c) are shown in (b) and (d), respectively. (a) and (c) show a fringe pattern indicating a shift of the Fabry–Pérot fringes. Cross sections (b) and (d) show that the sign of the differential reflectivity at coincidence is different from the sign at positive delay.

Differential reflectivity at positive delay measured at different probe wavelengths at a pump wavelength of 2000 nm. The differential reflectivity is plotted as a function of pump power cubed. The relation between the differential reflectivity at positive delay and the power cubed is linear. We conclude that the carriers are solely generated through a three photon process.

Differential reflectivity at positive delay measured at different probe wavelengths at a pump wavelength of 2000 nm. The differential reflectivity is plotted as a function of pump power cubed. The relation between the differential reflectivity at positive delay and the power cubed is linear. We conclude that the carriers are solely generated through a three photon process.

Calculated switched and unswitched reflectivity for a change in the (a) and a change in (b). The calculation was done with a TM model using parameters relevant to our structure. (a) shows that the introduction of absorption mainly affects the modulation depth of the fringes. A change in causes a shift of the fringe pattern (b). The differential reflectivity has maxima at different spectral positions, which makes it possible to distinguish between a purely dispersive and a purely absorptive regime.

Calculated switched and unswitched reflectivity for a change in the (a) and a change in (b). The calculation was done with a TM model using parameters relevant to our structure. (a) shows that the introduction of absorption mainly affects the modulation depth of the fringes. A change in causes a shift of the fringe pattern (b). The differential reflectivity has maxima at different spectral positions, which makes it possible to distinguish between a purely dispersive and a purely absorptive regime.

Cross section of Fig. 2 (black solid circles) showing the differential reflectivity as a function of probe wavelength at pump-probe coincidence . The structure was pumped at 2000 nm (a) and 2400 nm (b). The solid and dashed lines are results from TM calculations. In (a) the dashed line represents a change in the real part of the refractive index while the solid line represents a change in the imaginary part of the refractive index. This is the other way around in (b): dashed represents a change in imaginary part, while solid represents a change in the real part of refractive index. As expected we see mainly a change in the imaginary part of the refractive index at 2000 nm pump and a change in at 2400 nm. Furthermore our model slightly deviates near the blue side of the spectrum.

Cross section of Fig. 2 (black solid circles) showing the differential reflectivity as a function of probe wavelength at pump-probe coincidence . The structure was pumped at 2000 nm (a) and 2400 nm (b). The solid and dashed lines are results from TM calculations. In (a) the dashed line represents a change in the real part of the refractive index while the solid line represents a change in the imaginary part of the refractive index. This is the other way around in (b): dashed represents a change in imaginary part, while solid represents a change in the real part of refractive index. As expected we see mainly a change in the imaginary part of the refractive index at 2000 nm pump and a change in at 2400 nm. Furthermore our model slightly deviates near the blue side of the spectrum.

Relative change of refractive index due to a 2400 nm pump as a function of probe wavelength at a delay of (a) , (b) 0 ps, and (c) 0.5 ps. The dashed line in all three cases represent no change in refractive index. The solid line in (b) represents the dispersion of the change in refractive index from Ref. 26. The solid line in (c) is calculated with the Drude model for free carriers (Ref. 19). Points obtained from spectral regions close to extreme of the fringes were removed because of their poor precision.

Relative change of refractive index due to a 2400 nm pump as a function of probe wavelength at a delay of (a) , (b) 0 ps, and (c) 0.5 ps. The dashed line in all three cases represent no change in refractive index. The solid line in (b) represents the dispersion of the change in refractive index from Ref. 26. The solid line in (c) is calculated with the Drude model for free carriers (Ref. 19). Points obtained from spectral regions close to extreme of the fringes were removed because of their poor precision.

Measured nondegenerate Kerr coefficient as a function of probe wavelength (open circles). We averaged the data over the period of one fringe since the coefficients are correlated within this fringe period (solid squares). We observe dispersion in toward the blue side of the spectrum as expected from Fig. 5.

Measured nondegenerate Kerr coefficient as a function of probe wavelength (open circles). We averaged the data over the period of one fringe since the coefficients are correlated within this fringe period (solid squares). We observe dispersion in toward the blue side of the spectrum as expected from Fig. 5.

Three photon absorption coefficient as a function of wavelength extracted from the differential reflectivity data. The relative error of 30% is indicated.

Three photon absorption coefficient as a function of wavelength extracted from the differential reflectivity data. The relative error of 30% is indicated.

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