Design and characterization of diffractive lenses based on the aperiodic paperfolding sequence

In this work, we present the design of a new family of diffractive lenses based on the aperiodic Paperfolding sequence, with two different phase configurations, the binary phase lens and the kinoform profile. This family of functions exhibits a distinctive feature, while the binary phase lens displays an aperiodic phase distribution, consistent with the generating sequence, the kinoform lens shows a periodic phase profile with a period of 8, which is a consequence of the partially repetitive nature of the sequence. A comparison of the irradiance distributions of both phase profiles reveals a significant increase in intensity for the kinoform lens over the binary lens, approximately 70%. The corresponding irradiance distribution exhibits four intensity planes to consider. For the binary-phase lens, the outer planes present significantly higher intensity than the inner planes, while for the kinoform profile, these relationships are inverted, in this configuration, the outer planes are apodized. As a result, both lenses are considered bifocal, with the focal relationship varying depending on the phase profile, a feature that opens possibilities for advanced technological applications, such as multifocal optical imaging systems and optical tweezers arrangements.