Physical optics propagation (POP) is used in Zemax to model the propagation of optical fields in systems where diffraction, interference, and wavefront effects are significant. Unlike geometric ray tracing, which simplifies light as rays, POP considers the full wave nature of light. This is crucial for modeling applications such as laser beam propagation, fiber coupling, and diffractive optics. Figure below shows a typical POP scheme that reveals Gaussian beam wave layout at different locations of laser propagation.
Using POP for fiber coupling in Zemax involves modeling how a laser beam propagates through free space and optical elements, such as lenses or collimators, and then couples into an optical fiber. The figure below shows how physical optics conduct laser mode in fiber coupling procedure. Figure below shows a schematic of coupling of light into a multimode or single-mode optical fiber (left). Launching conditions in a multimode optical fiber resulting in an overfilled (upper right) and underfilled (lower right) fiber.
For optimal coupling efficiency, the characteristics of the focused beam (typically a laser) must align with the fiber's parameters. The general rules are:
- The focused spot size should be comparable to the fiber's core diameter.
- The focused beam should be precisely centered on the fiber core.
- The incident beam's cone angle should not exceed the fiber's numerical aperture (NA).
Conditions (1) and (2) are shown on the left side of Figure 1, while condition (3) is depicted on the right side. Multimode fibers, with their large core diameters, make it easier to satisfy the first two conditions, allowing for good coupling efficiency by matching the coupling lens to the fiber's NA. However, coupling into single-mode fibers is significantly more challenging due to their small core diameters. Achieving efficient coupling in single-mode fibers requires additional opto-mechanical components for sub-micron positioning of the focused beam. Additionally, the incident laser beam’s mode must match the fiber's mode, meaning the coupling efficiency is determined by the overlap integral between the Gaussian mode of the input laser and the fiber’s nearly Gaussian fundamental mode.
The example below demonstrates the analysis steps of using POP to optimize fiber coupling. The layout of output and input fiber tips are shown below.
From the POP setup, the waist sizes in both X and Y before the entrance face are set as 0.0046 mm below. X and Y sampling are set as 256. When clicking Automatic, the X- and Y width are calculated, as 0.13 mm below.
The Display tab requested the Cross-X section view of phase distribution at the image plane. The column displays the center of the overall image.
The Fiber Data set the propagation from the waist X and Y at surface 1. The POP window displays fiber coupling results, as shown in the screenshot. In Merit Function, the POPD operand provides all the Physical Optics data within the Merit Function Editor, making it a more useful reference in many cases.
In the Merit Function Editor (MFE), the first three POPD operands yield coupling efficiency (data=0), system efficiency (data=1) and receiver efficiency (data=2) respectively. The next four POPD operands output the beam waist size (data=10), beam radius size (data=23) and M2 value (data=26). Other than the first, the other 5 POPD command weight are set as 0.
Here we optimize the system to get the best coupling efficiency in command 2. From the POP window, the best coupling can also be read as 0.993780. From the phase shift plot below and it numbers in text, the maximum phase shift is 1.2352E-1 rad.
A universal plot can be launched to plot the relation of distance of the fiber tips to the coupling efficiency (Data=0 @ POPD). From the curve, the peak is at thickness of surface 3 equals to 2 mm.
