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Effective dispersion model in multimode fiber


Recently, the team of Martin Villiger of Wilman Optoelectronic Medical Center at Harvard Medical School and Massachusetts General Hospital reported an effective parameter dispersion model, verified the effectiveness of the model in various multimode fibers, and demonstrated the accurate estimation of the complete transmission matrix within the wide spectral bandwidth, and the results can approach the bandwidth of the best performance main mode and exceed the original spectral correlation width by more than two orders of magnitude. This model makes it easy to study the spectral behavior of the main mode without the need for intensive spectral measurements, enabling efficient reconstruction of multimode fiber transmission matrices.

Managing and controlling light scattering in complex or disordered media opens up new possibilities for imaging, sensing, and manipulation in optical engineering and physics. Dispersion creates additional spectral perturbations due to geometric effects and material properties, which until now remain a significant technical hurdle prevalent in multicolor or broadband applications in complex media. The transmission of light in complex media produces independent intensity distributions outside the narrow spectrum correlation range, which facilitates spectral analysis, but requires independent calibration at many frequencies for precise multispectral wave control. However, this results in heavy measurement time and data storage, which is linearly proportional to the sampling rate determined by spectral bandwidth and resolution.

Due to its advantages of high throughput, low loss, determination of degrees of freedom, small external size, controllable geometry and significant dispersion, optical multimode fiber has become an ideal tool for studying complex media transmission. The principal mode, the eigenmode of the group delay operator, defines a pair of specific input and output modes that are not affected by wavelength variations. However, master-mode superposition generalized to arbitrary input modes results in a chaotic output that is very sensitive to wavelength changes. Chromatographic axial memory effects have been shown to correlate with the spectral shift of the input illumination and the axial isotope expansion of the output speckle pattern. Whether this effect applies to all available spatial channels is studied, but it proves that multimode fiber transmission matrices are highly deterministic wavelength dependent.

Here, the researchers modeled the difference between the transmission matrices of the two frequencies into an exponential map, thus establishing a parametric dispersion model of transmission through multimode fiber.

In single-mode fibers, polarization-dependent dispersion is modeled with a Jones matrix, described by an exponential mapping of a special unitary group SU(2), and used to analyze the main states of polarization mode dispersion. As shown in Figure 1, the researchers extended this concept to the higher dimensions of the transmission matrix. Due to the limited parameter space of this model, it can be fitted to experimental transmission matrix measurements of a few discrete frequencies and predict the transmission matrix over a wide range of frequencies.

The researchers verified the performance of the model in different types of multimode fibers by comparing the predicted transmission matrix with the independently measured transmission matrix, as shown in Figure 2. To illustrate, the researchers used the predicted transport matrix to calculate focus through independent measurements, and used a higher-order model to study the frequency dependence of its principal mode, as shown in Figure 3.

In addition, the researchers discussed the spectral sampling conditions for discrete frequency measurements and studied the relationship between the number of measurements and the fidelity of the transmission matrix; and the trade-off between closed-form reconstruction of linear models and optimization-based fitting of higher-order models.

Figure 1: Concept of parametric dispersion model. (a) For the propagation of waves in isotropic media such as glass, by the frequency difference? The dispersion caused by ω is equivalent to a scalar phase term ψ. In single-mode fibers, the polarization dependence of the remaining waveguide anisotropy results in wavelength-dependent polarization states and polarization mode dispersion. In multimode fibers, changes in wavelength have an effect on both polarization and spatial patterns. (b) Can all of these dispersion representations be represented with frequency differences? The polynomial exponent of ω to simulate. Specifically, a multimode fiber transmission matrix was measured at several discrete optical frequencies and these measurements were fitted to a dispersion model corresponding to the matrix. The transport matrix is then reconstructed at continuous frequencies to predict the transport matrix of the complete spatial spectrum.

Figure 2: Principal mode characteristics of spectral variation. (a) Normalized commutativity of m(ω). (b) Persistence of ordered 200 output master modes calculated by averaging spectral correlations across the source spectrum. (c) H and V polarization mode distribution of output master modes at different wavelengths and corresponding persistence for the 25th, 98th, 127th, and 200th output modes. Scale bar is 20 μm. (d) Left: Frequency dependence of the delay of a single principal group in a higher-order dispersion model; Right: Enlarged illustration highlights the group delay evolution of the example main mode (black arrow) and the degenerate effect.

Figure 3: Efficient calculation of second-order dispersion. (a) Measuring the spectral correlation of multimode fiber transmission and focusing over multimode fiber using a transmission matrix. (b) Focus contrast for each spatial channel at different wavelengths at h = 13.

The article was recently published in the top international academic journal Light: Science & Applications, entitled “Efficient dispersion modeling in optical multimode fiber”, with Szu-Yu Lee as the first author and Professor Martin Villiger as the corresponding author of the paper. (Source: LightScience Applications WeChat public account)

Related paper information:https://www.nature.com/articles/s41377‍-022-0‍1061-7

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