leaky modes (original) (raw)
Author: the photonics expert (RP)
Definition: a concept for quasi-bound waveguide modes with propagation losses due to leakage into the cladding
Category: 
fiber optics and waveguides
Related: modeswaveguidespropagation losses
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DOI: 10.61835/cnf Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn
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Contents
Leaky Modes, an Extension of the Mode Concept
In principle, the light injected into a waveguide can be fully decomposed into a set of modes, which are all either guided modes (bound modes) or radiation modes (unbound modes, cladding modes). This approach, however, often does not fully capture the physics in a satisfactory way, and may also not be mathematically convenient, as a continuum of cladding modes has to be considered. The concept of leaky modes as an extension of the general mode concept may then be useful. While leaky modes are not modes in a strict sense, they conveniently describe certain aspects of light propagation which are of practical interest.
Typical Case: Introducing Another Index Step in the Cladding
This extension is illustrated in a typical example case. First, consider a simple step-index fiber, having a fiber core with a somewhat increased refractive index, surrounded by a cladding with a lower refractive index. Figure 1 shows the index profile and the radial functions of the three guided modes, apart from the effective refractive indices of these modes. (The effective index of the LP21 mode is very close to the cladding index, which indicates that this mode is close to its mode cut-off.)
Figure 1: Refractive index profile of a step-index fiber (bottom), the effective refractive indices of the three guided modes (thin horizontal lines), and the amplitude profiles of the guided modes. Also shown as the gray dotted line is a modification to the index profile which would turn the higher-order modes into leaky modes.
Now consider what changes when the refractive index is somewhat increased for radial positions above 20 μm, as illustrated by the dashed line in the figure:
- The fundamental mode (LP01) would hardly be affected at all; essentially, its intensity would decay more slowly where the index becomes higher, but as the intensity in that region has been low already, this is a minor change.
- However, the higher-order modes (LP11 and LP21) would be strongly affected. It is not only that their amplitude distributions have not decayed as much where the region with the raised refractive index starts: also, the modified refractive index in the outer region is now larger than their original effective mode indices. Therefore, their amplitude distributions should actually grow rather than decay in the cladding. In effect, these modes no longer exist as guided modes in the conventional sense; they would thus not be computed by a normal mode solver algorithm.
However, by simply regarding that modified fiber as a single-mode fiber, an important physical aspect of the waveguide properties would not be recognized. If an amplitude distribution is injected into the fiber which resembles the shape of the original LP11 mode, for example, that light will propagate over some distance in a similar fashion as that LP11 mode of the original fiber, since only a tiny fraction of its optical power probes the region with raised refractive index. One can imagine that this part of the intensity distribution will be shed away from the fiber core and eventually lost (typically, at the outer boundary of the fiber cladding). Therefore, we essentially have the behavior of a guided mode, except that it continuously loses some tiny fraction of its power due to radiation into the fiber cladding. Exactly this aspect (which can also be investigated with numerical beam propagation) is behind the concept of leaky modes: One considers the LP11 and LP21 modes to still exist for the fiber with modified index profile, but now as leaky modes and no longer as true guided modes. In the considered example, the LP21 mode would have substantially higher propagation losses than the LP11 mode. Its amplitude profile approximately agrees with the LP21 mode of the original fiber profile (without the outer index step) in the inner region.
Unfortunately, the concept of leaky modes involves a number of mathematical subtleties, the understanding of which requires a detailed and careful study. For example, the leaky modes are not part of a complete orthogonal system of modes.
Examples of Applications
The concept of leaky modes can be quite useful both for qualitatively understanding the characteristics of certain waveguides and for doing certain simulations of light propagation in a fiber. In the following, we discuss some applications.
Large Mode Area Fibers
Large mode area fibers are an important kind of fibers, often used for mitigating nonlinear optical effects and/or for obtaining a sufficiently high saturation energy in an active fiber. There are different ways of achieving a large effective mode area; for particularly large areas, one often uses a design which is no longer strictly single-mode, but where the higher-order modes have relatively high propagation losses by being leaky modes. The higher those losses can be made (without affecting the fundamental mode), the easier it generally is to operate the fiber effectively like a single-mode fiber, resulting in a well-defined and stable output mode profile. In particular, such designs can be realized for photonic crystal fibers.
It is also possible to use fibers with leaky modes only (and no true guided modes at all), where however the lowest-order mode has very small propagation losses.
Fiber Polarizers
The operation principle of some fiber polarizers is that the fundamental mode is substantially leaky for one polarization direction but not for the other. This can be realized, for example, by using a strongly birefringent fiber core (as in polarization-maintaining fibers) in conjunction with a suitable fiber cladding structure.
Optical Sensors
Some sensors leverage leaky modes for probing the refractive index of a medium close to a waveguide core. The operation principle can be that the resulting degree of attenuation sensitively depends on the refractive index of the test medium. Tapered fibers can be made for that purpose, but also other types of waveguides.
Frequently Asked Questions
This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).
What is a leaky mode in a waveguide?
A leaky mode describes a pattern of light propagation that is similar to a guided mode but continuously loses a small fraction of its optical power. This power radiates away from the waveguide core into the cladding.
Under what conditions does a guided mode become a leaky mode?
A guided mode can become a leaky mode if the refractive index in an outer part of the waveguide structure becomes higher than the mode's effective refractive index. This prevents the mode from being fully confined.
Are leaky modes considered true modes of a waveguide?
No, in a strict mathematical sense, leaky modes are not true modes. For instance, they are not part of a complete orthogonal system of modes, which distinguishes them from guided and radiation modes.
How are leaky modes utilized in large mode area fibers?
In large mode area fibers, higher-order modes can be intentionally designed to be leaky, giving them high propagation losses. This effectively suppresses them, allowing the fiber to operate like a single-mode fiber while supporting a large fundamental mode.
What are some practical applications of leaky modes?
Leaky modes are used to create large mode area fibers, fiber polarizers that attenuate one polarization, and optical sensors that probe the refractive index of a nearby medium through changes in attenuation.
Can a fiber guide light if it only has leaky modes?
Yes, it is possible to design fibers with no true guided modes at all. In such cases, the lowest-order mode is a leaky mode engineered to have very small propagation losses, allowing it to travel over significant distances.
Bibliography
| [1] | A. K. Ghatak, “Leaky modes in optical waveguides”, Opt. Quantum Electron. 17 (5), 311 (1985); doi:10.1007/BF00620394 |
|---|---|
| [2] | J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited”, Adv. Opt. Photon. 1, 58 (2009); doi:10.1364/AOP.1.000058 |
| [3] | A. W. Snyder and J. D. Love, Optical Waveguide Theory, Chapman and Hall, London (1983) |
(Suggest additional literature!)
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