on technological progress and growth

Prof. Love said I have comparative advantage in trade, analyzing things with heterogeneity. Ok, let me do this.
In growth theory, so many models (Ramsey, Solow, Cass-Koopman) has used a single commodity model. I think this simplification could be modified. I would divide the economy into two industries--technology-intensive and labor-intensive (euphemism for technology-nonintensive). If Country A is a leading country in technological innovation, while country B is only catching up by borrowing the innovation from Country A. However, there is a time lag because of the patent law. Also, Country B also has to incur some cost in using the technology developed by Country A to adapt it to its own country. With this setting, I wish to show that country A will always have a comparative advantage in the technology-intensive industry, and thus specializing in it, while country B, never specializing in industry B. Thus, even with the possibility of technology leak, the technological progress made by country A will not be shared by country B, because country B does not have the industry with the innovation.
There are two extensions to this model.
Extension 1:
Consider countries specializing in many different industries (exogenously determined). Progress made in basic R&D may benefit one industry exclusively (or a weaker version, disproportionately)--leading to rapid technological innovation in that industry. Thus, countries where that sector is bigger will benefit more, leading to higher growth rate. This might be a case for industrial strategic planning as done by Japan.
This line of thought has implication for interpreting data on growth. When we look for evidence of divergence or convergence based on a couple of decades' data, what we see might be distorted--countries may concentrate in different industries depending on their wealth. For example, what we see as evidence for divergence might merely be result of the industry that rich countries (like banking) focused on had a boom in that time period. A boom in an industry can last for some extended period of time, thus 20 year period data should be interpreted carefully.
Extension 2:
This is complicated and I have not yet thought it out. I might want to add heterogeneity in the quality of final products making it more compatible with new trade theory.