This experiment demonstrates the splitting and recombination of light beams using a beam splitter to observe interference patterns and analyze beam focusing properties.

Objective

The primary objective of the experiment is to investigate the behavior of light when split by a beam splitter, observe interference patterns, and analyze the focusing characteristics of the resulting beams. This includes measuring optical path differences, understanding phase shifts, and evaluating the performance of optical waveguides or splitters in guiding light .

Experimental Setup

The experiment typically uses a Michelson interferometer configuration or a femtosecond laser-fabricated waveguide splitter:

• Light Source: A coherent laser, often at 632.8 nm, provides a monochromatic beam .
• Beam Splitter: A 50/50 non-polarizing beam splitter divides the incident beam into two paths. One beam is reflected toward mirror M1, and the other is transmitted toward mirror M2 .
• Mirrors: M1 and M2 reflect the beams back to the beam splitter, where they recombine and interfere on a viewing screen or photodetector .
• Focusing Elements: Lenses or microscope objectives may be used to focus the beams into waveguides or onto the detector for precise measurement .
• Waveguides (Optional): In advanced setups, femtosecond laser direct writing (FLDW) can create single-line waveguides and 1×3 beam splitters in YAG crystals, allowing controlled propagation and splitting of light with minimal loss .

Procedure

1. Align the laser to the beam splitter at a 45° angle of incidence.
2. Adjust mirrors M1 and M2 to ensure the reflected beams recombine at the same spot on the screen.
3. Observe the interference pattern, noting bright and dark fringes corresponding to constructive and destructive interference .
4. For waveguide experiments, focus the laser into the crystal using a microscope objective and translate the sample using a computer-controlled XYZ stage to fabricate the splitter .
5. Measure the intensity distribution and mode profiles of the output beams to analyze focusing and guiding efficiency.

Observations

• Interference Patterns: Alternating bright and dark fringes appear on the screen, indicating the relative phase difference between the two beams .
• Beam Splitting: The beam splitter divides the incident light into reflected and transmitted components, each carrying approximately 50% of the optical power in non-polarizing setups .
• Waveguide Propagation: In FLDW-fabricated splitters, the beams propagate through the crystal with low loss (~1.9 dB/cm) and support fundamental-mode laser propagation at 632.8 nm .

Analysis

• The intensity at any point on the screen is given by $I=I_1+I_2+2\sqrt{I_1{I}_2}\cos ({\varphi }_1-{\varphi }_2)$, where ${\varphi }_1$ and ${\varphi }_2$ are the phases of the two beams .
• Phase shifts occur due to reflection and transmission at the beam splitter, which must be accounted for in precise measurements.
• Focusing efficiency is evaluated by measuring the mode profile and propagation loss in waveguides, ensuring minimal distortion and polarization-insensitive behavior .

Conclusion

The optics splitter focusing experiment demonstrates the fundamental principles of beam splitting, interference, and focusing. Using a beam splitter, light can be divided and recombined to produce interference patterns, which provide insights into optical path differences and phase relationships. Advanced techniques, such as femtosecond laser direct writing, allow the fabrication of integrated optical splitters with precise guiding and low-loss propagation, offering applications in photonics and optical communication .