Haseet al.Reply:

Abstract

Hase et al. Reply: The Comment from Fahy and Reis [1] presents calculations of the time-dependent A 1g phonon frequency in photoexcited Bi using the simple model of electronic softening [2], including carrier recombination and carrier diffusion effects but without anharmonicity. The calculated variation in the A 1g frequency looks similar to that observed in Fig. 4 in our Letter [3], regarding to the amplitude in arbitrary units for the 7:6 mJ=cm 2 pulse fluence. They claimed that recombination and diffusion of the electron-hole (e-h) plasma is rather more important than anharmonicity of the phonon.First of all, we have recently observed, using highdensity photoexcitation, the 2nd order and the higher harmonics of the coherent A 1g phonon in Bi at 7 K [4]. Formation of such higher harmonics of the fundamental phonon mode provides evidence of lattice anharmonicity as confirmed in ferroelectric materials [5]. Thus our data clearly show that the coherent A 1g phonon in Bi under high-density photoexcitation that we observe is really anharmonic oscillation.There are some points they could consider in addition, when comparing with the experimental data. Our observation of the time-dependent frequency of the coherent A 1g phonon in Bi includes the contribution from the electronic softening due to photoexcited e-h plasma, in addition to the anharmonicity, as discussed in our Letter [3], and the calculation by Fahy and Reis for that in photoexcited Bi using the electronic softening model is important. However, the calculation seems to be not sufficient for complete discussion on the anharmonic phonon dynamics.They use the slow e-h recombination time of 5 ps to evaluate the variation of the frequency of the coherent A 1g phonon versus the square of the oscillation amplitude. However, the e-h recombination time is much less under the high-density excitation (10 21 cm ÿ3 ). Actually it was obtained from the pump and probe measurement to be only 1 ps for Bi at 300 K. Therefore, the carrier density in the conduction bands decays within the first few cycles of the coherent phonon oscillation, which is much faster than they expect.The ambipolar diffusion constant D 5 cm 2 =s should also be corrected for the optically excited carriers in Bi. The carrier diffusion constant depends on the carrier density [6], particularly for the case of high-density excitation. They estimated D 10 cm 2 =s by considering this effect for photoexcited Te, which was significantly smaller than its equilibrium value D 40 cm 2 =s [2], but do not consider this effect for Bi in the Comment. The value of D in photoexcited Bi becomes 1:25 cm 2 =s if taking the same ratio of D excited =D equilibrium 0:25 as in Te. In this case, the e-h plasma density at the surface falls to 0.434 (1=e) of its initial value in a time l 2 =D 2:3 ps, indicating the carrier diffusion is less efficient than they expected (l 2 =D 0:6 ps), where l 17 nm is the optical penetration depth for the pump light with 800 nm.In addition to the arguments for the e-h recombination time and the...

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