Since the first observation of accumulated photon echoes by Hesslink and Wiersna [1], nearly transform-limited mode-locked pulse trains have been used as the excitation source, and the resolution times have been limited by the widths of the pulses. In this paper we show theoretically and experimentally that the time resolution of the accumulated photon echoes is determine not by the pulse width but by the correlation time of the excitation field [2]. This indicates that it is possible to obtain a sub-picosecond resolution in accumulated photon echoes Sven by using a cw laser (non-mode-locked), if the laser output has a sufficiently broad and smooth spectrum.
It has been recently pointed out that incoherent light can be used to generate coherent optical transients and that there are decided advantages in using such broad-band non-laser source to achieve very high time resolution {1,2}. When a light pulse and its time-delayed replica interact with a sample to produce the non-linear optical response, the ultimate time resolution should identify with the correlation time τC of the light field rather than with the pulse duration τL. The situation where τC ≪ τL is easily obtained with broad-band incoherent light sources. Time resolution in the femtosecond range is then attainable using nanosecond light pulses. This has been recently demonstrated through the observation of the relaxation of photon echoes in Nd3+-doped silicate glass {1,2}. In these cases, attention is focused on the measurement of fast homogeneous decay rates and the inhomogeneous broadening ΩD is assumed to be much larger than the spectral width of the excitation light.
Accumulated photon echoes were observed in
Nd3+-doped silicate glass by using coherent and incoherent light, and it was theoretically and experimentally verified that the time resolution is determined not by the pulse width but by the correlation time of the excitation field. Even by using a cw laser, instead of a mode-locked laser, a subpicosecond time resolution was obtained when it was operated with a broad and smooth spectrum. The broadest output spectrum, and hence the highest time resolution, was attained when the dye laser was pumped by a mode-locked
Ar+ laser, and their cavity lengths were mismatched by a few \ensuremath{\mu}m. In an experiment with a resolution time of 220 fsec, a new very fast decay was observed in the echo decay curve besides a slower decay already reported.
An analytic theory and experimental studies of the accumulated photon echo is presented. We define a temporal correlation function
G~ of the excitation field E ( t ) as
G~(τ,t)=(1/T1)∫0∞dt′E(t−t′)E(t−t′−τ)⋅exp(−t′/T1), where T 1 is the population relaxation time of the sample, and call the width of
G~ with respect to τ a temporal correlation time
τ~c(t). It is proved that the echo intensity is written by the temporal correlation functions when (1) T 1 and the duration of the excitation light τ p are much longer than
τ~c(t) in order to make the function
G~((τ,t) well-defined, (2) T 1 and τ p are much longer than the homogeneous dephasing time T 2 , and (3) one can find a time interval Δ t such that
G~(τ,t) does not change much between t and t + Δ t , where
Δt≫τ~c. Then we can show that the time resolution of the accumulated photon echo is determined by the averaged
τ~c(t) over an interval of the integration of the echo signal. This discussion is valid for any excitation source if the above conditions are satisfied, and applies to almost all cases of the practical accumulated photon echo experiment. A discussion is also made on the spurious spike on the echo decay curve near zero delay time that appeared in an experiment with a high time resolution in Nd 3+ -doped silicate glass. It is shown that the most probable cause for this spike is uncorrelated inhomogeneous broadenings of the resonant lines of neodymium ions.
Using a superluminescent diode, we observed femtosecond accumulated photon echoes in 1, 1′-diethyl-4, 4′-quinodicarbocyanine iodide embedded in polyvinyl acetate. The output of the superluminescent diode directly excited the sample to produce photon echoes. By using a simple experimental system we obtained a temporal resolution as high as 100 fsec. This resolution is determined by the spectral width of the superluminescent diode and the noncollinear excitation beam configuration of the system.
We demonstrate that accumulated photon echoes can be generated by synchrotron radiation. This is an experiment of a nonlinear optical effect carried out by using the radiation from an electron storage ring. A dye-doped polymer film was excited by the visible light from the storage ring, and the accumulated photon echoes from the sample were observed by employing a phase-modulation technique. The use of synchrotron radiation facilitates the extension of the spectral range where we can observe photon echoes with ultrahigh time resolution.