A multimode fiber is a fiber with more than one guided mode at the operating wavelength – sometimes only a few (→ Few-mode fiber), but usually many. The core is usually quite large—not much smaller than the entire fiber (see Figure 1).
Figure 1: Single-mode fiber (left) has a very small core compared to the cladding, while multimode fiber (right) has a large core
At the same time, the numerical aperture tends to be relatively high—for example, 0.3. This combination results in a large V number, which in turn leads to a large number of modes. For a step-index fiber with a large V, it can be estimated using the following equation when calculating the two polarization directions:
Fibers with fewer guided modes, such as those with V-numbers between 3 and 10, are sometimes called few-mode fibers.
If light with poor spatial coherence needs to be transmitted, multimode fiber is required. This is the case, for example, with the output of typical high power laser diodes, such as diode bars. Although only a small fraction of their output power can be launched into single-mode fibers, the launch efficiency is very high for multimode fibers with sufficiently large cores and/or high NA. Another example is the use of light emitting diodes (LEDs) instead of laser diodes as inexpensive signal sources in fiber optic links. Imaging exists for other applications, for example; transmission of image information requires devices with multiple spatial modes.
Multimode Optical Specifications
The basic specifications of multimode fiber include the core diameter and outer diameter of the multimode fiber. Common telecommunication optical fibers (optical fibers for medium-distance optical fiber communications) are 50/125 μm and 62.5/125 μm optical fibers, with a core diameter of 50 μm or 62.5 μm and a cladding diameter of 125 μm. This fiber supports hundreds of guided modes. Large core fibers with even larger core diameters (hundreds of microns) can also be used.
Launch light into multimode fiber
Multimode fiber emits light more easily than singlemode fiber, especially if it supports multiple guided modes. For efficient startup, two conditions must be met:
Both conditions can be satisfied if the M2 factor of the input light is small enough. The maximum M factor for effectively launching a beam with a super-Gaussian profile can be estimated from the following formula:
This is actually an approximate beam quality factor from the fiber if the optical power is well distributed over all modes. (The estimate is only accurate if the fiber has many guided modes.) Of course, efficient launch requires not only a sufficiently low M2 factor, but also a suitable shape of the intensity distribution in real and Fourier space.
For example, consider a fiber with a core radius of 25 μm and a numerical aperture of 0.2. Figure 2 shows the intensity distribution of a monochromatic input beam at 1000 nm, numerically constructed such that it just fills the fiber core, and whose angular distribution reaches the limit set by the fiber’s numerical aperture. The beam profile is basically made starting from a super-Gaussian intensity profile with completely random phase values (resulting in huge divergence), then filtered in the Fourier domain with another super-Gaussian function, and again applying the super-Gaussian filter in space area.
The angular distribution leads to complex intensity variations. For the same beam quality, the intensity distribution of a non-monochromatic beam may be smoother: although each wavelength component has a complex distribution, these fluctuations can be averaged into a smooth overall distribution. (Especially for non-monochromatic beams, a smooth intensity distribution is not indicative of high beam quality.)
Figure 2: Intensity distribution of a multimode beam with approximately the largest possible M2 value that can be efficiently launched into an optical fiber.
Figure 3: Evolution of the intensity distribution in an optical fiber. During the first few millimeters, very little light is lost into the cladding.
Similar simulations exhibit substantial emission losses if the initial beam size or angular range is further expanded. Also, if the beam profile is roughly Gaussian rather than super-Gaussian, slightly lower M2 values (below 10) are required for efficient emission.
If light is emitted into a specific higher-order mode, the M2 value of that light may be about 2 times larger than the above formula.
output beam profile
The output beam profile of a multimode fiber depends on the launch conditions. Furthermore, it is sensitively dependent on the conditions of the entire fiber (bending, temperature, etc.). This is because this effect affects the β values of all modes and thus the interference conditions. Over longer fiber lengths, even small changes in the β value can have a significant effect.
Multimode fibers are sometimes used for beam homogenization, i.e. to obtain a smoother intensity distribution. However, this only works for polychromatic light, where the distribution of the different frequency components is averaged out.
Singlemode Propagation in Multimode Fiber
If light is launched entirely into the fundamental mode of a multimode fiber, the beam profile should in principle remain unchanged during propagation. An output with high beam quality, similar to that of a single-mode fiber, will then be obtained. However, various disturbances can lead to mode coupling: some light may be coupled into higher-order modes, thereby corrupting the beam quality.
Fortunately, this coupling effect is usually not that strong. For example, consider a step-index fiber with a core diameter of 20 μm and an NA of 0.1. This is a few-mode fiber that supports 6 guided modes (when counting all mode directions). We take a 10mm length of fiber and introduce a relatively steep bend where the reverse bend radius rises smoothly to 1/(10mm) in the middle and then returns to zero again. This bending causes a significant shift and deformation of the mode distribution in the middle of the fiber:
Figure 4: The beam profile in the middle of a bent fiber is significantly off center of the core.
However, at the end of the fiber where the bend ends, there is little change in the original beam profile. Almost all power remains in LP 01 mode:
Figure 5: Evolution of the beam profile in a fiber bent only in the middle. (The spatial coordinates do not reflect the bend, which is modeled as a linear addition to the index profile; one only sees a shift in the mode profile as a result of the bend.) The beam profile returns nicely to the original fiber end.
One might wonder why, despite the strong bending effect, essentially no light is coupled into the higher-order modes. For this we need to take into account the phase constant difference between the LP 01 and LP 11 modes, which is up to 4.5 rad/mm, for example. This phase mismatch effectively suppresses the coupling: in different parts of the fiber, the magnitude contributions coupled from the fundamental mode to certain higher-order modes will largely cancel each other out.
For fibers with large mode areas, the β values for different modes are closer. Consequently, the beat length of the two modes is much longer, allowing even relatively slowly varying perturbations to efficiently couple the modes. Therefore, it is more difficult to maintain single-mode propagation in a few-mode fiber with large mode area.
Gradient Index Fiber
For telecom applications, it is sometimes desirable to minimize intermodal dispersion, the width of the group velocity range. This results in time spreading and reduced distortion of telecommunication signals, allowing for higher data rates.
Step index fibers are not good in this respect. It has been found that graded-index fibers with a nearly parabolic index profile are more suitable for such applications. Figure 6 shows such an indexing configuration file.
Figure 6: The refractive index profile of a graded-index fiber, which is parabolic in the core region. The effective indices of the guided modes (shown as gray lines) are equally spaced.
In an intuitive picture, one might expect light oscillating around the fiber axis to have a longer path length than light passing directly through it, but this is compensated by the lower refractive index of the outer regions seen by the oscillating light. However, this vague idea is often very misleading. For example, they might have generated the expectation that higher-order fiber modes with increased transverse wavevector components experience larger phase delays in the fiber, when in fact the opposite is true. Therefore, we recommend using these ideas with caution and skepticism.
Figure 7 shows a simulation where the Gaussian input beam is displaced by some degree relative to the center of the fiber core. In an optical fiber, the intensity distribution oscillates without reaching all the way to the edge of the core region.
Figure 7: Beam propagation in a graded-index fiber with a Gaussian input beam slightly off center of the core. Horizontal gray lines indicate the edges of the core.
For comparison, Figure 8 shows a step-index design with the same core radius and maximum index. The result looks completely different.
Figure 8: Same as Figure 7, but with a stepped index profile.
Figure 9 shows a point for each mode of a graded-index fiber, where the coordinates represent the mode area and group velocity. It can be seen that the group velocities of all modes are almost the same, while the effective mode region spans a large size.
Figure 9: Group velocity versus mode area for graded-index fiber with parabolic index profile. (For simplicity, the refractive index profile ignores material dispersion.) Different colors represent different m values. The group velocity is almost the same for all modes.