## 1 Introduction  
Recent years have witnessed a dramatic increase in the research on plasmons. From an application point of view, studies that utilize various attractive features of surface plasmons including optical field enhancement [1], surface sensitivity [2], focusing below diffraction limit [3, 4], nonlinear optical effects [5, 6], plasmonic energy conversion [7], etc., are being actively pursued. Further, fundamental research on the properties of plasmons including quantum effects [8] and real space imaging [9] have also attracted attention. However, due to the short lifetime of surface plasmons, the energy distribution of electrons in the momentum space at the time of surface plasmon excitation has not yet been elucidated [10, 11]. The purpose of this research is to obtain information about the electron distribution in the conduction band of metals associated with the surface plasmon excitation.  
To shed light on the energy distribution of electrons in the momentum space in the conduction band of the metal in the presence of surface plasmon excitation, plasmon modulation spectra in the Kretschmann geometry are measured: plasmons are excited with a continuous wave (CW) laser at the surface plasmon resonance, and the interband transition band edge is probed with a CW white light. This is motivated by the expectation that the \(k\)-space distribution dynamics of electrons should be reflected on the spectral change in the interband transition edge (the \(d\) band to the Fermi-surface transition), which is sensitive to the Fermi-surface distribution of electrons. As the signal due to CW laser excitation is unavoidably affected by the temperature increase in the sample, electric current modulation and temperature difference spectra are also measured for independently evaluating the contribution from temperature.  
Further, to probe the plasmon relaxation dynamics before temperature rise (before thermalization with the lattice sub-system), femtosecond pump-probe spectroscopy experiments are performed by pumping plasmons and probing the interband transition. Figure 1 schematically shows the relaxation process of the surface plasmon. Phase relaxation of plasmons takes place within 10-30 fs, as estimated from the surface plasmon polariton (SPP) resonance width. After about 500 fs, the electron system is equilibrated at some electronic temperature, and thereafter, thermal equilibrium with the lattice system is established several ps later. Although fast dynamics of non-equilibrium electrons excited by femtosecond laser pulses has been studied intensively [12; 13; 14; 15], our interest is the dynamics of plasmons before the phase relaxation into individual particles. In order to obtain information before the equilibration of the electron system, the signal on the order of 100 femtoseconds after SPP excitation should be traced. Therefore, pump-probe spectroscopy with a femtosecond pulsed laser is carried out. The spectrum of the probe pulse laser needs to be wide enough to cover the surface plasmon resonance and the interband absorption edge. In view of this requirement, gold is selected as a suitable material to be studied using the femtosecond Ti: sapphire laser. To achieve a longer phase relaxation time, silver is more suitable because the plasmon resonance width is narrower, but the interband transition wavelength is too short (about 325 nm) for the wavelength of the Ti:sapphire laser.