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The analysis of wave patterns in a structure which possesses periodicity in the spatial and temporal dimensions is presented. The topic of imperfect chiral interfaces is also considered. Although causality is fundamental for physical processes, natural wave phenomena can be observed when a wave is split at a temporal interface. A wave split at a spatial interface is a more common occurrence; however, when the coefficients of the governing equations are time-dependent, the temporal interface becomes important. Here, the associated frontal waves are studied, and regimes are analysed where the growth of the solution in time is found. Imperfect interfaces, across which the displacements are discontinuous, are also considered in the vector case of chiral elastic systems. Analytical study and asymptotic approximations are supplied with illustrative numerical examples. This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)’. 

The BICEP/Keck (BK) series of cosmic microwave background (CMB) polarization experiments has, over the past decade and a half, produced a series of field-leading constraints on cosmic inflation via measurements of the “B-mode” polarization of the CMB. Primordial B modes are directly tied to the amplitude of primordial gravitational waves (PGW), their strength parameterized by the tensor-to-scalar ratio, r, and thus the energy scale of inflation. Having set the most sensitive constraints to-date on r, σ(r) = 0.009 (r0.05 < 0.036, 95% C.L.) using data through the 2018 observing season (“BK18”), the BICEP/Keck program has continued to improve its dataset in the years since. We give a brief overview of the BK program and the “BK18” result before discussing the program’s ongoing efforts, including the deployment and performance of the Keck Array’s successor instrument, BICEP Array, improvements to data processing and internal consistency testing, new techniques such as delensing, and how those will ultimately serve to allow BK reach σ(r) ≲ 0.003 using data through the 2027 observing season.