Back in 1993 this diagram was published, but the paper I am looking at was published in 1998 by Llinas and others (citation below); it contains the same diagram.
Here is the abstract:
Attempting to understand how the brain, as a whole, might be organized seems, for the first time, to be a serious topic of inquiry. One aspect of its neuronal organization that seems particularly central to global function is the rich thalamocortical interconnectivity, and most particularly the reciprocal nature of the thalamocortical neuronal loop function. Moreover, the interaction between the specific and non-specific thalamic loops suggests that rather than a gate into the brain, the thalamus represents a hub from which any site in the cortex can communicate with any other such site or sites. The goal of this paper is to explore the basic assumption that large-scale, temporal coincidence of specific and non-specific thalamic activity generates the functional states that characterize human cognition.
And here is the diagram:
And here is the explanation of the diagram:
Figure 6. Thalamocortical circuits proposed to subserve temporal binding. Diagram of two thalamocortical systems. (a) Specific sensory or motor nuclei project to layer IV of the cortex, producing cortical oscillation by direct activation and feedforward inhibition via 40 Hz inhibitory interneurons. Collaterals of these projections produce thalamic feedback inhibition via the reticular nucleus. The return pathway (circular arrow on the right) re-enters this oscillation to specific- and reticularis-thalamic nuclei via pyramidal cells in layer VI. (b) Second loop shows non-specific intralaminary nuclei projecting to the most superficial layer of the cortex and giving collaterals to the reticular nucleus. Pyramidal cells in layer V return the oscillation to the reticular and the non-specific thalamic nuclei, establishing a second resonant loop. The conjunction of the specific and non-specific loops is proposed to generate temporal binding. (Modified from Llinas & Ribary (1993).)
So in more less detailed language, the Llinas theory has the sensory input coming into the cortex via the specific neurons (like lateral geniculate nucleus of the thalamus to the visual cortex). This starts a gamma band oscillation. The non-specific neurons do not input sensory data but signals from places like the brain stem or the frontal lobe. This also starts a gamma oscillation. It is the coincidence of these two oscillating loops that produces a binding.
This paper also has interesting things to say about the formation of cortical columns and the formation of gamma rhythms.
Llinas, R., Ribary, U., Contreras, D., & Pedroarena, C. (1998). The neuronal basis for consciousness Philosophical Transactions of the Royal Society B: Biological Sciences, 353 (1377), 1841-1849 DOI: 10.1098/rstb.1998.0336