We present a heavy traffic analysis of a single-server polling model, with the special features of retrials and glue periods. The combination of these features in a polling model typically occurs in certain optical networking models, and in models where customers have a reservation period just before their service period. Just before the server arrives at a station there is some deterministic glue period. Customers (both new arrivals and retrials) arriving at the station during this glue period will be served during the visit of the server. Customers arriving in any other period leave immediately and will retry after an exponentially distributed time. As this model defies a closed-form expression for the queue length distributions, our main focus is on their heavy-traffic asymptotics, both at embedded time points (beginnings of glue periods, visit periods and switch periods) and at arbitrary time points. We obtain closed-form expressions for the limiting scaled joint queue length distribution in heavy traffic and use these to accurately approximate the mean number of customers in the system under different loads.taking limits in known expressions for the Laplace-Stieltjes transform (LST) of the waiting-time distribution. Alternatively, Olsen and van der Mei [17] provide similar results, by studying the behaviour of the descendant set approach (a numerical computation method, cf. Konheim, Levy and Srinivasan [10]) in the heavy traffic limit. For the derivation of heavy traffic asymptotics for our model, however, we will use results from branching theory, mainly those presented in Quine [18]. Earlier, these results have resulted in heavy traffic asymptotics for conventional polling models, see van der Mei [15]. We will use the same method as presented in that paper, but for a different class of polling system that models the dynamics of optical networks. In addition, for some steps of the analysis, we will present new and straight forward proofs, while other steps require a different approach. Furthermore, we will derive asymptotics for the joint queue length process at arbitrary time points, as opposed to just the marginal processes as derived in [15]. Due to the additional intricacies of the model at hand, we will need to overcome many arising complex difficulties, as will become apparent later.The rest of the paper is organized as follows. In Section 2, we introduce some notation and present a theorem from [18] on multitype branching processes with immigration. In Section 3, we describe in detail the polling model with retrials and glue periods and recall from [2] how the joint queue length process at some embedded time points in this model is related to multitype branching processes with immigration. Next, we will derive heavy traffic results for our model. In Section 4, we consider the joint queue length process at the start of glue periods. In Section 5, we look at the joint queue length process at the start of visit and switch-over periods, while in Section 6, we consider the joint queue length process at ar...