Theoretical investigations of the high resolution optical heterodyne spectroscopy with a phase-modulated pump field and experimental realization of an optical frequency standard at 532 nm by using a diode-pumped frequency-doubled Nd:YAG laser of which frequency is stabilized to the hyperfine component of the Iodine molecule are discussed. The 532 nm OFS is applied to measure the absolute spacing of the diffraction grating which can transfer the traceability of the standard of length down to the nanometer range.
The theory of the modulation transfer spectroscopy employing a phase-modulated pump field is generalized to include the parametric interactions associated with an arbitrarily intense probe field. General solutions, and analytical solutions at some special cases, of the density matrix equations describing the interactions between a homogeneous two-level atomic system and the external driving field which consists of an equidistant trichromatic pump with frequency difference Ω and an arbitrarily intense probe field with frequency detuning δ from the average frequency of the pump field are obtained. In order to solve the optical Bloch equations a two dimensional harmonic expansion method in terms of two frequencies of Ω and δ is introduced. From the general solutions the polarization spectrum of the probe field induced in the atomic medium, which immediately gives the dimensionless probe absorption and dispersion spectrum, is obtained. The physical nature of the discrete polarization components at δ = -nΩ/(m+1), n ≠ 0, m ≠ -1, where n,m are integers, on the continuous polarization spectrum as well as the generalized Rabi resonances observed on the continuous probe absorption and dispersion spectrum are extensively discussed. The quasienergies and eigenstates of the two-level atom dressed by the trichromatic pump field are obtained and the observed structures of the generalized Rabi resonances are successfully explained on the basis of the obtained quasienergy level structure. Futhermore, the physical nature of the discrete elastic peaks on the continuous polarization spectrum has been explained using the theory of parametric four-wave interactions between the polychromatic pump field and the two-level atom. In addition, for the case of the bichromatic pump field the amplification of the probe field without population inversion at the line center is observed for the first time, which originates from the stimulated two-photon emission of the probe field through the heterodyne parametric four-wave interactions including the probe field.
A modulation transfer spectrometer is constructed by using a diode-pumped frequency-doubled 532 nm Nd:YAG laser. The Doppler-free dispersion spectrum belonging to the R(58)32-0 rotational-vibrational transition of the hyperfine component of the $^{127}I_2$ molecule is measured by using the constructed modulation transfer spectrometer. The dispersion spectrum of the $α_1$ component of the R(58)32-0 transition line is used to stabilize the frequency of the 532 nm Nd:YAG laser for the optical frequency standard at 532 nm. We propose two methods to measure the absolute spacing of the diffraction grating, which can transfer the traceability of the standard of length down to the nanometer range. As a first application the constructed optical frequency standard at 532 nm is applied to measure the absolute spacing of the commercial plane grating in order to demonstrate the proposed one wavelength method.