Optical fields that are periodic in the transverse plane self-image periodically as they propagate along the optical axis: a
phenomenon known as the Talbot effect. A transfer matrix may be defined that relates the amplitude and phase of point
sources placed on a particular grid at the input to their respective multiple images at an image plane. The free-space
Talbot effect may be mapped to the waveguide Talbot effect. Applying this mapping to the transfer matrix enables the
prediction of the phase and amplitude relations between the ports of a Multimode Interference (MMI) coupler– a planar
waveguide device. The transfer matrix approach has not previously been applied to the free-space case and its mapping
to the waveguide case provides greater clarity and physical insight into the phase relationships than previous treatments.
The paper first introduces the underlying physics of the Talbot effect in free space with emphasis on the positions along
the optical axis at which images occur; their multiplicity; and their relative phase relations determined by the Gauss
Quadratic Sum of number theory. The analysis is then adapted to predict the phase relationships between the ports of an
MMI. These phase relationships are critical to planar light circuit (PLC) applications such as 90° optical hybrids for
coherent optical receiver front-ends, external optical I-Q modulators for coherent optical transmitters; and optical phased
array switches. These applications are illustrated by results obtained from devices that have been fabricated and tested by
the PTLab in Si micro-photonic integration platforms.
Silicon-on-insulator (SOI) photonic integrated circuits have recently become a research topic of great interest due to their
compact confinements and compatibility with the modern micro-electronics. As the dominant issues of the integration
density of planar lightwave circuits on a single SOI chip, low-loss SOI curved waveguides and corner turning mirror
(CTM) structures are attracting attention. This work aims at the performance comparison between the SOI curved
waveguides and CTM structures. For this goal we have designed both SOI curved waveguides and SOI CTM structures
and then fabricated them. The performance of these two devices, such as the propagation loss and polarization dependent
loss, is measured and compared.
For the SOI-waveguide directional coupler (WDC), optical access loss (OAL) and polarization dependence (PD) are two
critical performance specifications which seriously affect the adoptability and deployment of a device, including optical
on-chip loss (OCL), polarization dependent loss (PDL) and extinction ratio of a 3dB-coupler based device. In this work,
using a commercial software tool - FIMMPROP, the performance of an SOI-WDC is simulated. Simulations find that the
curved waveguides for the turning sections of a 3dB WDC not only enlarge the footprint size, but also seriously
deteriorate the device performance. For instance, the two curved waveguide sections of a WDC induce an unpredictably
large change in the 3dB-coupling length, increase an OAL of 0.4-0.9dB, and seriously deteriorate the PD, and these
performance changes radically depend on rib size. After a corner-turning mirror (CTM) structure is introduced to a 3dB
SOI-WDC, the experiments show both the footprint length and 3dB-coupling length are unchanged, the OAL of the 3dB
coupler is only 0.5dB which is close to the simulation value. Therefore, for a 3dB-coupler based Mach-Zehnder
interference (MZI) structure, the OCL will be controlled to be <1.0dB in device design and will not depend on rib size.