The detailed study of the different stellar populations which can be observed in galaxies is one of the most promising methods to shed light on the evolutionary histories of galaxies. So far, stellar population analysis has been carried out mainly in the optical wavelength range. The infrared spectral range, on the other hand, has been poorly studied so far, although it provides very important insights, particularly into the cooler stellar populations which are present in galaxies. However, in the last years, space telescopes like the Spitzer Space Telescope or the Wide-field Infrared Survey Explorer and instruments like the spectrograph X-Shooter on the Very Large Telescope have collected more and more photometric and spectroscopic data in this wavelength range. In order to analyze these observations, it is necessary to dispose of reliable and accurate stellar population models in the infrared. Only a small number of stellar population models in the infrared exist in the literature. They are mostly based on theoretical stellar libraries and very often cover only the near-infrared wavelength range at a rather low resolution. Hence, we developed new single-burst stellar population models between 8150 and 50000Å which are exclusively based on 180 spectra from the empirical Infrared Telescope Facility stellar library. We computed our single stellar population models for two different sets of isochrones and various types of initial mass functions of different slopes. Since the stars of the Infrared Telescope Facility library present only a limited coverage of the stellar atmospheric parameter space, our models are of sufficient quality only for ages larger than 1 Gyr and metallicities between [Fe/H] = 0.40 and 0.26. By combining our single stellar population models in the infrared with the extended medium-resolution Isaac Newton Telescope library of empirical spectra in the optical spectral range, we created the first single stellar population models covering the whole optical and infrared wavelength range between 3500 and 50000Å which are almost completely based on spectra of
observed stars (apart from two gaps which were fitted with theoretical stellar spectra) .

We analyze the behaviour of the near-infrared (J ¿ K) and the Spitzer ([3.6]¿[4.5]) colour calculated from our models. For ages older than 3 Gyr, both colours depend only slightly on age and metallicity. However, for younger ages, both colours become redder which is caused by the asymptotic giant branch stars contributing significantly to the light in the infrared at ages between 0.1 and 3 Gyr. Furthermore, we find a satisfactory agreement between the optical and near-infrared colours measured from our models and the colours observed from various samples of globular clusters and early-type galaxies. However, our model predictions are only able to reproduce correctly the Spitzer ([3.6]¿[4.5]) colours of older, more massive galaxies that resemble a single-burst population. Younger, less massive and more metal-poor galaxies show redder colours than our models. This mismatch can be explained by a more extended star formation history of these galaxies which includes a metal-poor or/and young population.

The Spitzer ([3.6]¿[4.5]) colours derived from our models also agree very well with those from most other models available in this wavelength range as long as they also correctly take into account a strong CO absorption band situated at 4.5 ¿m. The model predictions for colours in the near-infrared, such as (J ¿ K), differ more between the different sets of models, depending on the underlying prescriptions for the asymptotic giant branch stellar evolutionary
phase. Compared to other authors, we adopt only a moderate contribution of asymptotic giant branch stars to our models.

Our stellar population models allow us also to determine mass-to-light ratios in different infrared bands.Consequently, we can confirm that the mass-to-light ratio determined in the Spitzer [3.6] ¿m band changes much less as a function of both age and metallicity than it does in the optical bands. However, it shows a non-negligible sensitivity to the initial mass function.

Our models are of sufficient resolution to measure line strength indices up to the L-band. Hence, we redefined many indices in the near-infrared and identified new indicators for age, metallicity and the slope of the initial mass function. The equivalent widths of many indices which we computed from our stellar population models cannot be used to trace the large indices measured from observed early-type galaxies. While in the literature, this disagreement between the predicted and the observed line strength indices is usually attributed to a much enhanced contribution of asymptotic giant branch stars, we present a number of evidences which are at odds with such a view. Therefore, we propose an alternative scenario. We argue that a different abundance pattern in the early-type galaxies compared to that of the Milky Way which is characterized by an enhanced [C/Fe] ratio is able to account for this mismatch.The differences in the carbon enhancement between the galaxies can be attributed to the duration of their episodes of star formation which seem to be driven by galactic environment. In denser environments like in galaxy clusters, star formation takes place on a shorter characteristic timescale than in isolated galaxies. Hence, contrary to the situation in clusters, in isolated galaxies, the massive expulsion of carbon into the interstellar medium occurs before star formation has finished. Therefore, in the latter ones carbon is incorporated into the new generation of stars leading to enhanced carbon abundances with respect to cluster galaxies of a similar mass.

We show that if we additionally include the effect of a bottom-heavy initial mass function in the case of the most massive early-type galaxies and assume enhanced abundance ratios for some other elements like sodium, we are able to simultaneously reproduce all of the studied line strength indices. Our analysis also shows that an active galactic nucleus does not seem to have any impact on the line strength indices which we measure for central stellar
populations.