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Production sequence of Si-spheres and interferometrical determination of the sphere volume

Fibre-based spatial superposition of spectrally vastly separated beams


Beams of different optical wavelengths must be superimposed as perfectly as possible in space in many optical sensors. The wavelengths of the individual beams can be spectrally far apart, e.g. when combining frequency-doubled beams with their fundamental. The quality of the agreement of the beam propagation directions, however, is often a decisive contribution to the practically achievable measurement uncertainty. This applies e.g., to sensors that are based on so-called multi-wavelength interferometry. By this interferometry technique, the non-ambiguity range of an interferential measurement can be increased or the influence of the refractive index of the air can be compensated. It can ensure direct traceability of a macroscopic measurement to the SI definition of the meter. Therefore, it plays an important role in many modern primary optical standards.

Many applications in interferometry require a well-defined polarization, as well as a Gaussian wavefront that is as ideal as possible, and a high degree of spatial coherence. For this reason, wavelengths that are spectrally far apart are today usually superimposed in free-space configuration. This is a very complex and error-prone procedure whose long-term stability is also limited by the stability of the optomechanical components.

Modern fiber components such as wavelength division multiplexers (WDM) or photonic crystal fibers promise a wide bandwidth in the transmission of radiation of different wavelengths. An almost perfect superposition of the beams is ensured by superimposing the beam modes in the waveguide. This reduces the alignment to the standard procedure of coupling light into an optical fiber as efficiently as possible. Since none of the available commercial waveguide architectures offers a perfect solution, three different modern fiber optic architectures were investigated and compared in a systematic study. In particular, polarization preservation and spatial coherence, which are of particular importance for interferometry, were taken as criteria [1].

When combining two laser beams at 532 nm and 1064 nm using multi-mode wavelength division multiplexers (multi-mode MM-WDM), maximum power transmission is achieved because of the large fiber core. But the multimode transmission reduces spatial coherence. In single-mode multiplexing (single-mode wavelength division multiplexer, SM-WDM), the two beams can be superimposed with high spatial coherence. However, external disturbances such as temperature changes or mechanical disturbances cause changes in the polarization directions and decrease the degree of polarization. Polarization-maintaining photonic crystal fibers (PM-PCF) ensure single-mode polarization-maintaining transmission of both beams with their patterned waveguide. Spatial coherence is also maintained to a high degree. A disadvantage, however, is the strongly wavelength-dependent intensity profile of the emitted beams, as exemplified in Fig. 1 for three investigated waveguides.

The results of the study provide the developer of an optical system with criteria according to which a solution for fiber-based beam merging can be found, optimized for the specific problem. With such approaches, improved uncertainties for standards in length metrology based on multi-wavelength interferometry, among other things, can be expected in the future.

This work was partially performed within the EMPIR project 18SIB01 GeoMetre. This project has received funding from the EMPIR programme co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme.

Comparison of the full beam profiles and the equatorial line scans of the wavefronts transmitted through the three different fiber combiners. A high noise component is noticeable for the multi-mode fiber. The single-mode fiber achieves comparable distributions for both colors. For the polarization-maintaining photonic crystal fiber, the emitted beam radii are strongly wavelength-dependent.

Figure 1. Full beam profile investigation with zoom of the equatorial line of transmitted beams using a camera-based beam profile sensor. (a) Experimental setup, (b) and (c) results for the multi-mode multiplexer (MM-WDM), (d) and (e) for the single-mode multiplexer (SM-WDM), and (f) and (g) for the polarization-maintaining photonic crystal fiber (PM-PCF). Figure modified from [1].

 [1] Y. Liu, A. Röse, G. Prellinger, P. Köchert, J. Zhu, F. Pollinger 2020 J. Lightwave Technology 38 1945 (2020)



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