Home Forschung Mode Beating Spectroscopy


Mode Beating Spectroscopy

Ralf Eckhardt and Reinhard Ulrich
Technische Universität Hamburg-Harburg, Hamburg, Germany
email: ulrich@tu-harburg.de

Internal perturbations of ideal 'single-mode' telecommunication fibers, such as core ellipticity and internal stress, cause characteristic differences of the propagation constants in nearly degenerated mode groups. We have measured these differences by operating the fibre in the few-mode regime and locally coupling with a magneto-optical modulator, which is scanned along the fibre. Observation of the resulting spatial beatnotes yields the differences of the propagation constants.

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Summary

References

  1. Ralf Eckhardt and Reinhard Ulrich: Mode Beating Spectroscopy in a few-mode optical guide, Appl.Phys.Lett. 63(3), pp.284 ff, 1993
  2. A.W.Snyder and J.D.Love, Optical Waveguide Theory, (Chapman and Hall, NY, 1983)
  3. J.Noda, T.Hosaka, Y.Sasaki and Reinhard Ulrich: Dispersion of verdet constant in stress-birefringent silica fibre, Electronics Letters, 1994, 20, pp.906 ff
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Guided Tour:

This document contains 11 b/w-sketches (total:56k) which are the backbone of this presentation, and about 14k of explaining text. To achieve a reasonable layout of this presentation we recommend to use a full-screen window and landscape orientation at the printer.
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What is mode beating?

Assume two (orthogonal) modes a,b beeing launched into a waveguide forming a linear state of polarization (SOP) Slightly different propagation constants result in a spatial dependence of the phase differences of both waves corresponding to a spatial periodicity of the state of polarization. This periodicity is called the beatlength of these modes. While the propagations constants themselves are somewhat difficult to measure, the difference between them is yielded by measuring the periodicity of the SOP - which is much easier.

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We performed the measurement of the periodicity of the SOP via magnetooptic modulation (Faraday effect). An axial H-field, which is practicallay localized gap (0.3mm) of an AC-driven magnet, 'rotates' the SOP of the wave passing this section. Spoken in other terms, in causes a coupling of both modes, adding a small fraction one mode - say Ev - to the other. Depending on the Phase of Ev relative to Eh the originial amplitude is increased, just phase shifted or decreased, which can be observed by monitoring the Amplitude of Eh at the output end of the guide.

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Experimental Setup

Monochromatic light is launchend into a 3 m long section of single mode telecommunctaion fiber, designed for operation at 1300nm. A soleil babinet compensator provides for effective distribution of power to both mode to be coupled The mode coupling modulator is scanned along the fiber converting spatial phase differences of the modes into variations of the amplitude of each mode. Selecting one mode by a polarization filter and detecting its power finally yields the spatial distribution of the phase difference between both modes.

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What do we get?

In the so-called monomode regime only the two fundamental polarization modes propagates. The plot of the amplitude variation of one mode vs. the coupling position z yields a sine curve containing only one spatial beatfrequency in its spectrum. Now we have obtained the amount of birefringence but no information about whether the birefringence is caused by stress, core ellipticity or other reasons.

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multimode regime

To get more information about the nature of birefringence we looked at the beatfrequencies of high order modes, which each are different influenced by physical parameters of the waveguide. The spectrum of beatfrequencies containing more modes will show enough information for a quantitative analysis of the causes of the birefringence. To enable the next higher modes, i.e. the LP11 mode group, to propagate, we went to shorter wavelength corresponding to higher fiber parameters.

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How will faraday rotation affect high-order modes?

Regarding the fundamental mode again, faraday modulation will generate a small field, orthogonal to the generating one - an image of the other of the two polarization modes. The combination of both is equivalent to a rotation of the field. On high order modes, the faraday effects acts in the same way: The power distribution of the mode field remains, but the orientation of the field vectors is rotates. resuming, faraday rotation of higher (any) modes is equivalent to adding a field to the original mode, which has the same orientation and the same power distribution as another mode or combination of modes of the same group. So faraday rotation will couple pairs of modes. now we have 3 pairs of modes: the fundamental pair and two pairs from the LP11 group.

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Selection of higher modes

The two fundamental polarization modes (LP01) can be easily separated from each other by using a polarizer. The same will work only partially for the LP11 mode group. Though the (ex)-polarization mode is separable from (oy) or (ey) using the polarization of their fields, the (ox) and the (ex) modes cannot be separated in this easy-to-use way.

For this task heterodyne techniques or spatial filters as shown aside are necessary. In combination with a polarizer this allows the isolation of one mode from the set of four.


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Launching the first two modegroups (V=3.6) containing 2 + 4 polarization modes, we obtain 7 spatial beatfrequencies instead of 3, as expected above.

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Fourier spectrum from the above signal. The frequency 1.3/m is covered by the DC-bias, but comes out in a parametric fit.

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We excited the waveguide at various wavelength and obtained slightly different sets of frequency. In the monomode regime at 1300nm however, only one spatial frequency (F0) was visible.

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For each wavelength, this set of 6 spatial frequencies Fij can be self-consestently interpreted as differences of the four polarization modes of the LP11-set. At this level of interpretation, it could also be the equivalent set of hybrid modes HE21, etc. - we will lift this uncertaincy, as well as the uncertaincy of the correct assignent, below.

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Interpretation

Beyond the more formal assignment of beatfrequencies to a set of propagation constants, the assignment and the magnitude of the birefringence between the modes can be explained in physical terms:
  • F0 is assigned to the fundamental mode group and its birefringence should be caused by linear stress.
    1. It's the only modegroup existing below cuf-off
    2. core ellipticity is too small to explain this beatfrequency
    The faster mode is polarized orthogonal to the direction of stress due to the signs of the elasto-optic tensor of silica.
  • Fij is consequently assigned to the next higher modegroup. Without any perturbation these modes are (following non-vectorial theory) degenerate. Degeneracy is lifted due to following:
    1. Ellipticity of the core radius splits modes, whose polarization relative to the scalar field distribution is equal, but whose ortientation of the field distribution relative to the fiber is different. (Splitting F13 and F24) The core diameters should have a relative difference of 0.003 for these splittings.
    2. Tangential stress causes a splitting of equally oriented modes having different polarization (radial vs. tangential) relative to the core-cladding surface - F12 and F34. The observed splitting should be caused by a difference of radial to tangential stress of about ~20MPa.
    3. Finally, following vectorial mode analysis, different polarization relative to the field distribution (F14 and F23) cause an inherent a splitting of the propagation constants - even in an undisturbed fiber.

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Summary

  • usage of LP01- and LP11- mode
  • self consistent set of propagation constants obtained
  • high accuracy measurement of differences of prop.constants
  • determination of stress / ellipticity possible
  • other modulator types will be useful (thermo-optic, stress-optic, electro-optic)
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