Abstract

The photon echo is often the best technique for measuring ultra narrow homogeneous linewidths of an inhomogeneously broadened optical transition for which a higher spectral resolution than the laser bandwidth is required. Homogenous linewidths on the order of one kHz have been measured for Eu³⁺ and Pr³⁺ in different host materials at liquid helium temperature from the echo intensity as a function of the delay between the two excitation pulses. These linewidths arc three orders of magnitude narrower than the long term jitter bandwidth of the laser which was used for excitation.¹ Here we present a novel spectroscopic method based on the modulation of a 2-pulsc photon echo or a stimulated echo by an externally applied field, for the accurate measurement of frequency shifting perturbations with sub-homogeneous linewidth resolution. This is illustrated by the Stark effect on the ⁷F₀→⁵D₀ transition of Eu³⁺:YAIO₃. The basic idea is that two coherent preparation pulses create an excited state population grating in the frequency domain of an inhomogeneously broadened line, which then gives rise to the echo in the course of the free induction decay of the coherently prepared ions. Since the photon echo can be observed for pulse separations much larger than T₂, it is possible to generate frequency gratings which have a periodic spacing smaller than the homogeneous linewidth.² In the case of a centrosymmetric crystal there are two groups of ions with equal and opposite dipole moments. An applied electric field E_s shifts the ground and excited state energy levels through interaction with the electric dipole moments of these states and hence leads to a linear frequency shift, $\Omega =\delta \stackrel{\rightharpoonup }{\mu }\cdot {\stackrel{\rightharpoonup }{\text{E}}}_{\text{s}}/\hslash$, for the two sets of ions in opposite directions, where $\delta \stackrel{\rightharpoonup }{\mu }$ is the difference between the ground and excited state dipole moments. If the electric field is applied after the first pulse, the two sets of ions accumulate equal and opposite phase shifts Φ = ± Ωt during the time interval, t. The result of the second pulse is that an excited state population grating is created in the frequency domain with a period (t + τ)^-1 where t is the time interval between the pulses and τ is the duration of one pulse. Since there arc two sets of ions with opposite phase shifts, we formally get two population gratings, one with the phase Φ = + Ωt and one with the phase Φ = − Ωt. with respect to the population grating that is caused without an applied field.

© 1992 Optical Society of America