View the related article [J. Phys. Soc. Jpn. 77 (2008) 044701]

Drastic Nonlinear Optical Response beyond Long-Wavelength Approximation Regime [April 10, 2008]
Hajime Ishihara
(Department of Physics and Electronics, Osaka Prefecture University)

  The design and control of light-matter interaction has been a central subject in a variety of research fields. For the control of the light-matter interaction, two main types of strategies have been considered. One is the manipulation of electronic states (elementary excitations) using confinement by nanostructures, and the other is the manipulation of photon modes by using microstructures such as microcavities, photonic crystals, metamaterials, etc. Considering these two types of approaches, we observe that conventionally, a type of hierarchical approach has been employed according to the standard description of light-matter coupling. When the dielectric function is discussed from the microscopic viewpoint, the coherent length of the relevant electronic states (elementary excitations) is considered to be much shorter than the wavelength of light and thus the spatial variation of the latter is neglected; this is called long-wavelength approximation (LWA). On the other hand, the motion of a light wave is usually studied with a given dielectric function. Even when electronic resonance is considered, the microscopic spatial structure of the electronic system is not explicitly treated in this case.

  A recent paper by Kojima et al. [1] reports a peculiar nonlinear response in GaAs thin layers that strongly violates the LWA. They found a beating behavior between the nondipole-type polarization waves that leads to an ultrafast optical response that is much faster than the dephasing of the induced polarization. In the observed effect, the spatial interplay between the elementary excitation and the internal light field plays an essential role, which is in striking contrast to the above-mentioned hierarchical description of the light-matter interaction. By going into the non-LWA regime, this study reveals the potential of a missing size regime of materials for a new search space of photonic functions.

   If the sample is much larger than the excitonic Bohr radius, the excitonic center-of-mass (c. m.) motion conveys the excitation energy as a polarization wave in a crystal and characterizes the optical properties of the sample. In nanostructures, the polarization wave is confined, and characteristic effects such as the size-dependent quantized spectrum [2] and the size-linear increase in the radiative decay rate [3-5] are known to appear. These effects have been suitably explained based on the LWA framework. On the other hand, the light-exciton interaction in a bulk sample has been explained in terms of the polariton concept; this is a superposed state comprising an exciton and a light wave. However, in the intermediate size regime between the nanoscale and bulk regimes, the light-exciton coupling scheme and its potential have not been sufficiently understood until recently, although some studies on polariton interference in thin films have been conducted [6]. (See Fig. 1)



Fig. 1: Left-hand side: Schematic diagram of confined excitonic c. m. states and light in the LWA size regime. The typical reflectance is shown, where the odd parity selection rule holds and the lowest state mainly contributes to the response. Right-hand side: Schematic diagram of the polariton dispersion and the typical reflectance in a bulk.


  For the intermediate size regime, a peculiar size dependence of the nonlinear response was theoretically proposed for the excitonic c. m. confinement regime; wherein the internal field with a nanoscale spatial pattern is size-resonantly enhanced [7]. This effect was also experimentally demonstrated later by using GaAs thin layers [8,9], where a degenerate four-wave-mixing signal from the second level of a confined exciton (n = 2 exciton; see Fig. 1) becomes 25 times larger than that in the bulk regime for a particular thickness. Moreover, this nondipole-type state, which is optically forbidden in the LWA, exhibited a fast radiative decay of less than a few picoseconds [10].

  After the above studies, the authors of ref. 1 have been aiming to demonstrate high-level compatibility between the large nonlinearity and the ultrafast response by making the best use of the characteristic optical response in the non-LWA regime. This appears to be challenging because the resonant excitation generally requires a long time to decay. For the investigation of the mechanism that balances the large nonlinearity and fast response in the non-LWA regime, these authors have studied the systematic dependence of the nonlinear response on the incident pulse width. In a previous study [10], the n = 2 exciton in a GaAs thin layer excited by a picosecond pulse exhibited a radiative decay time of the order of picoseconds. However, for the further study of faster responses, an incident pulse should be spectrally broader, while the contributions of multiple confined c. m. levels make it difficult to observe the decay rate of an isolated single level. One of the possible scenarios was that the decay time of the n = 2 exciton was clearly observed even for the spectrally broader incident pulse if the nonlinear signal was dominated by this state due to the size-resonant enhancement of the signal from this state alone. However, the result obtained in ref. 1 appears to be quite different from such an expected scenario.

  First, the apparent response time of the observed signal is much faster than the expected radiative decay time when the spectrally broader pulse is applied: When an incident pulse with a duration of approximately 100 fs is irradiated, the observed response time is almost the same as this duration. Second, with the increase in the pulse width, a peculiar oscillating behavior appears in the tail of the signal. In order to further elucidate these observations, they have performed careful examinations of the beating periods by changing the width and center frequency of the incident pulse. As a result, they have identified all the observed periods to be those caused by beatings due to particular combinations of c. m. levels. In the case of a spectrally broader pulse excitation, many excitonic states in a wider frequency range participate in the beating, and the superposition of these beatings with different oscillations rapidly eliminates the signal, as observed in the experiment shown in Fig. 2.



Fig. 2: (a) Configuration of the degenerate four-wave-mixing (DFWM). (b) Schematic diagram of confined excitonic c. m. states and light beyond the LWA size regime. In the case of this figure, an even parity selection rule holds and the signal from the second exciton (n = 2) state is the largest due to a spatial variation of the internal field. (c) Delay time (between pulses 1 and 2) dependence of the DFWM signal for various widths of the incident pulse (Figure is taken from ref. 1). For a wider incidence pulse, multiple even-parity states contribute to the beating and their interference rapidly eliminates the signal.
  From the viewpoint of applications, this report is interesting in that it reveals a novel mechanism of fast responses that is not limited by either the dephasing or the population decay of excitation. From a fundamental viewpoint, it is significant that this study has demonstrated an interesting effect as one among a variety of potential phenomena in the non-LWA size regime. The demonstrated compatibility of the large nonlinearity and fast response is due to a size-resonant enhancement of the response of the nondipole-type excitonic state and the beatings by multiple c. m. confined levels. Both of these effects are characteristic of the non-LWA regime. We hope that this study will lead to further studies exploring the potential of optical responses in the non-LWA size regime for photomaterials science and engineering.

References
[1] O. Kojima et al.: J. Phys. Soc. Jpn. 77 (2008) 044701.
[2] Z. K. Tang et al.: Phys. Rev. Lett. 71 (1993) 1431.
[3] E. Hanamura: Phys. Rev. B 37 (1988) 1273.
[4] A. Nakamura et al.: Phys. Rev. B 40 (1989) 8585.
[5] T. Itoh et al.: Solid State Commun. 73 (1990) 271.
[6] K. Cho et al.: J. Phys. Soc. Jpn. 59 (1990) 1853.
[7] H. Ishihara and K. Cho: Phys. Rev. B 53 (1996) 15823.
[8] K. Akiyama et al.: Appl. Phys. Lett. 75 (1999) 475.
[9] H. Ishihara et al.: Phys. Rev. Lett. 89 (2002) 17402.
[10] T. Isu et al.: Proc. SPIE 4992 (2003) 165.


The above article should be referred as “H. Ishihara: JPSJ Online-News and Comments [Apr. 10, 2008]” when citing.

Copyright © the Physical Society of Japan.