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The effect of changing the coupling laser transition, and hence the wavelength, on the coherently induced transparency seen by a probe beam in a Doppler-broadened cascade electromagnetically induced transparency ͑EIT͒ configuration is studied experimentally and theoretically. The transparency of the vapor is shown to be an effect not just of EIT, but of the varying Autler-Townes splitting for each velocity group within the vapor. Consequently, the best overall transparency for Rabi splittings less than the Doppler width is not at the position of matched coupling and probe wavelengths, but for coupling wavelengths less than that of the probe.The coherent effect of an electromagnetically induced transparency ͑EIT͒ ͓1͔, and the related one of lasing without inversion ͑LWI͒ ͓2͔ have excited much attention over the last few years. In particular, there has been a great deal of work using rubidium vapor as an interaction medium in which effects can be observed while using cw laser sources ͓3-5͔.In rubidium, the wavelengths involved in the most basic configurations of cascade, and V schemes are in the near infrared, and therefore easily covered by both diode and titanium sapphire laser sources. Also, since the wavelengths of probe and coupling lasers in these configurations are similar, the proper choice of co-or counterpropagating beams can reduce the Doppler-broadened vapor to a virtually Dopplerfree medium. To date, all schemes in rubidium, including that of the first cw inversionless laser ͓6͔, have taken advantage of these Doppler-free schemes. It had been thought that the use of a Doppler-free medium was necessary to reduce the power requirement on the coupling laser before transparency was observable. In this paper we will show both theoretically and experimentally that this is in fact not the case. Instead, for cascade configurations, if the wavelength of the coupling laser is less than that of the probe, there is no disadvantage in using mismatched wavelengths. This point has been previously discussed theoretically in a paper by GeoBanacloche et al. ͓7͔. Within their theoretical analysis the authors show that it is advantageous for the observation of EIT if an atomic system is chosen such that the coupling field is lower in wavelength than that of the probe field. We extend this idea to the experimental regime where the wavelength mismatch between the two optical fields is of the order of hundreds of nanometers. In so doing a physical explanation is obtained and the relative roles of Autler-Townes splitting and EIT are highlighted, in order to emphasize that in a vapor the two cannot be treated separately. The significance of this work lies in the prospect of inducing cw inversionless gain in Doppler-broadened media where the coupling wavelength is not similar to that of the probe, allowing new wavelengths to be accessed. Figure 1͑a͒ shows a typical cascade scheme for observing EIT. In Fig. 1͑b͒ are shown the actual rubidium energy levels used in the experiments described in this paper. In each case the probe wa...

The theoretical basis for electromagnetically-induced focusing ͑EIF͒, which is caused by spatial variations in the coupling laser strength in an electromagnetically-induced transparency ͑EIT͒ experiment, is studied in detail. Using a numerical model it is shown that radial changes in both absorption and refractive index are important in predicting the probe beam's propagation conditions. Detailed calculations of the focusing and defocusing during EIF under various conditions are presented and compared with appropriate experiments. Diffractionlike patterns are predicted for, and observed on, a probe beam after propagation through a smaller EIT aperture.

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