RP Photonics logo
RP Photonics
Encyclopedia
Technical consulting services on lasers, nonlinear optics, fiber optics etc.
Profit from the knowledge and experience of a top expert!
Powerful simulation and design software.
Make computer models in order to get a comprehensive understanding of your devices!
Success comes from understanding – be it in science or in industrial development.
The famous Encyclopedia of Laser Physics and Technology – available online for free!
The ideal place for finding suppliers for many photonics products.
Advertisers: Make sure to have your products displayed here!
… combined with a great Buyer's Guide!
VLib part of the
Virtual
Library

Mode Coupling

<<<  |  >>>  |  Feedback

Buyer's Guide

Use the RP Photonics Buyer's Guide to find suppliers for photonics products! You will hardly find a more convenient resource.

Ask RP Photonics for advice based on numerical simulations, e.g. of mode coupling phenomena in photonic devices.

Definition: a concept for describing and calculating light propagation in certain situations, e.g. involving nonlinear interactions

German: Modenkopplung, Kopplung zwischen Moden

Categories: fiber optics and waveguides, methods

How to cite the article; suggest additional literature

The concept of mode coupling is very often used e.g. to describe the propagation of light in some waveguides or optical cavities under the influence of additional effects, such as external disturbances or nonlinear interactions. The basic idea of coupled-mode theory is to decompose all propagating light into the known modes of the undisturbed device, and then to calculate how these modes are coupled with each other by some additional influence. This approach is often technically and conceptually much more convenient than, e.g., recalculating the propagation modes for the actual situation in which light propagates in the device.

Some examples of mode coupling are discussed in the following:

Technically, the mode coupling approach is often used in the form of coupled differential equations for the complex excitation amplitudes of all the involved modes. These equations contain coupling coefficients, which are usually calculated from overlap integrals, involving the two mode functions and the disturbance causing the coupling. Typically, the applied procedure is first to calculate the mode amplitudes for the given light input, then to propagate these amplitudes based on the above-mentioned coupled differential equations (e.g. using some Runge–Kutta algorithm), and finally (if required) to recombine the mode fields to obtain the resulting field distribution.

Instead of using coupled-mode theory, which is based on simplifying assumptions (which are not always well fulfilled), one can also study mode coupling phenomena with numerical beam propagation. This method is computationally more intense, but can generate more detailed insight. As an example, Figure 1 shows how the optical powers of several guided modes evolve in a long-period fiber Bragg grating. The field evolution has been calculated with numerical beam propagation, and the local mode powers have been obtained from the results using overlap integrals with the mode functions as obtained from a mode solver applied to the bare fiber.

coupling to a higher-order mode in a fiber Bragg grating

Figure 1: Evolution of mode powers in a long-period fiber Bragg grating, which couples light from the injected fundamental mode radiation into higher-order modes. This diagram has been taken from a case study on beam propagation in fiber devices.

An important physical aspect of such coherent mode coupling phenomena is that the optical power transferred between two modes depends on the amplitudes which are already in both modes. A consequence of that is that the power transfer from a mode A to another mode B can be kept very small simply by strongly attenuating mode B. In this way, mode B is prevented from acquiring sufficient power to extract power from mode A efficiently, so that mode A experiences only little loss, despite the coupling.

Bibliography

[1]A. W. Snyder, “Coupled-mode theory for optical fibers”, J. Opt. Soc. Am. 62 (11), 1267 (1972)
[2]H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers”, J. Appl. Phys. 43 (5), 2327 (1972)
[3]A. Yariv, “Coupled-mode theory for guided-wave optics”, IEEE J. Quantum Electron. 9 (9), 919 (1973)
[4]H. Haus et al., “Coupled-mode theory of optical waveguides”, J. Lightwave Technol. 5 (1), 16 (1987)
[5]W. P. Huang et al., “Optical wavelength filter with tapered couplers”, IEEE Photon. Technol. Lett. 3 (9), 812 (1991)
[6]R. Paschotta et al., “Nonlinear mode coupling in doubly-resonant frequency doublers”, Appl. Phys. B 58, 117 (1994)
[7]W.-P. Huang, “Coupled-mode theory for coupled optical waveguides: an overview”, J. Opt. Soc. Am. A 11 (3), 963 (1994)
[8]N. Matuschek et al., “Exact coupled-mode theories for multilayer interference coatings with arbitrarily strong index modulations”, IEEE J. Quantum Electron. 33 (3), 295 (1997)
[9]R. Paschotta, “Beam quality deterioration of lasers caused by intracavity beam distortions”, Opt. Express 14 (13), 6069 (2006)
[10]M. B. Shemirani et al., “Principle modes in graded-index multimode fiber in presence of spatial- and polarization-mode coupling”, J. Lightwave Technol. 27 (10), 1248 (2009)
[11]A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers”, Opt. Express 19 (11), 10180 (2011)
[12]A. W. Snyder and J. D. Love, Optical Waveguide Theory, Chapman and Hall, London (1983)

(Suggest additional literature!)

See also: modes, fibers, waveguides
and other articles in the categories fiber optics and waveguides, methods

How do you rate this article?

Click here to send us your feedback!

Your general impression: don't know poor satisfactory good excellent
Technical quality: don't know poor satisfactory good excellent
Usefulness: don't know poor satisfactory good excellent
Readability: don't know poor satisfactory good excellent
Comments:

Found any errors? Suggestions for improvements? Do you know a better web page on this topic?

Spam protection: (enter the value of 5 + 8 in this field!)

If you want a response, you may leave your e-mail address in the comments field, or directly send an e-mail.

If you like our website, you may also want to get our newsletters!

If you like this article, share it with your friends and colleagues, e.g. via social media:

arrow

RP Fiber Power – the versatile Fiber Optics Software

An Amazing Tool

RP Fiber Power software

This amazing tool is extremely helpful for the development of passive and active fiber devices.

ASE

Watch our quick video tour!

Single-mode and Multi­mode Fibers

fibers

Calculate mode properties such as

  • amplitude distributions (near field and far field)
  • effective mode area
  • effective index
  • group delay and chromatic dispersion

Also calculate fiber coupling efficiencies; simulate effects of bending, nonlinear self-focusing or gain guiding on beam propagation, higher-order soliton propagation, etc.

Arbitrary Index Profiles

A fiber's index profile may be more complicated than just a circle:

special fibers

Here, we "printed" some letters, translated this into an index profile and initial optical field, propagated the light over some distance and plotted the output field – all automated with a little script code.

Fiber Couplers, Double-clad Fibers, Multicore Fibers, …

fiber devices

Simulate pump absorption in double-clad fibers, study beam propagation in fiber couplers, light propagation in tapered fibers, analyze the impact of bending, cross-saturation effects in amplifiers, leaky modes, etc.

Fiber Amplifiers

fiber amplifier

For example, calculate

  • gain and saturation characteristics (for continuous or pulsed operation)
  • energy transfers in erbium-ytterbium-doped amplifier fibers
  • influence of quenching effects, amplified spontaneous emission etc.

in single amplifier stages or in multi-stage amplifier systems, with double-clad fibers, etc.

Fiber-optic Telecom Systems

eye diagram

For example,

  • analyze dispersive and nonlinear signal distortions
  • investigate the impact of amplifier noise
  • optimize nonlinear management and the placement of amplifiers

Find out in detail what is going on in such a system!

Fiber Lasers

fiber laser

For example, analyze and optimize the

  • power conversion efficiency
  • wavelength tuning range
  • Q switching dynamics
  • femtosecond pulse generation with mode locking

for lasers based on double-clad fiber, with linear or ring resonator, etc.

Ultrafast Fiber Lasers and Amplifiers

fiber laser

For example, study

  • pulse formation mechanisms
  • impact of nonlinearities and chromatic dispersion
  • parabolic pulse amplification
  • feedback sensitivity
  • supercontinuum generation

Apply any sequence of elements to your pulses!

… and even Bulk Devices

regenerative amplifier

For example, study

  • Q switching dynamics
  • mode-locking behavior
  • impact of nonlinearities and chromatic dispersion
  • influence of a saturable absorber
  • chirped-pulse amplification
  • regenerative amplification

RP Fiber Power is an extremely versatile tool!

Mode Solver

fiber modes

For example, calculate

  • amplitude and intensity profiles
  • effective mode areas
  • cut-off wavelengths
  • propagation constants
  • group velocities
  • chromatic dispersion

All this is calculated with high efficiency!

Beam Propagation

beam propagation

Propagate optical field with arbitrary wavefronts through fibers. These may be asymmetric, bent, tapered, exhibit random disturbances, etc.

See our demo video for numerical beam propagation.

Laser-active Ions

level scheme

Work with the standard gain model, or define your own level scheme!

Can include different ions, energy transfers, upconversion and quenching effects, complicated pumping schemes, etc.

Multiple Pump and Signal Waves, ASE

optical channels

Define multiple pump and signal waves and many ASE channels – each one with its own transverse intensity profile, loss coefficient etc.

The power calculations are highly efficient and reliable.

Simple Use and High Flexibility Combined

For simpler tasks, use convenient forms:

signal parameters

Script code is automatically generated and can then be modified by the user. A powerful script language gives you an unparalleled flexibility!

High-quality Documentation and Competent Support

The carefully prepared comprehensive documentation includes a PDF manual and an interactive online help system.

Competent technical support is provided: the developer himself will help you and make sure that any problem is solved!

Our support is like included technical consulting.

Boost your competence, efficiency and creativity!

  • Stop fishing in the dark! Develop a clear quantitative understanding of your devices.
  • Explore the effects of possible design changes on your desk.
  • That way, get most efficient in the lab.
  • Find optimized solutions efficiently, minimizing time to market.
  • Get new ideas by playing with your models.

Efficiency and success of
R & D are not a matter of chance.

See our detailed description with many case studies!

Contact us to get a quotation!

– Show all banners –

– Get your own banner! –