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Related Concept Videos

Magnetic Vector Potential01:15

Magnetic Vector Potential

In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the magnetic field ensures that the magnetic field can be expressed as the curl of a vector potential. This potential is known as the magnetic vector potential.
Consider an ideal solenoid with n turns per unit length and radius R. If I is the current through the solenoid, the magnetic field inside the solenoid is expressed as the product of vacuum...
Boundary Conditions: Lossless Lines01:21

Boundary Conditions: Lossless Lines

Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
Standing Waves in a Cavity01:28

Standing Waves in a Cavity

A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
Equipotential Surfaces and Field Lines01:29

Equipotential Surfaces and Field Lines

Electric potential can be pictorially represented as a three-dimensional surface. On such a surface, the electric potential is constant everywhere. The equipotential surface is always perpendicular to the electric field lines, and while it is three-dimensional, it can be treated as an equipotential line in a two-dimensional case. These equipotential lines are also always perpendicular to electric field lines. The term equipotential is often used as a noun, referring to an equipotential line or...
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...

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Updated: Jun 22, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Surface multi-gap vector solitons.

Ivan Garanovich, Andrey A Sukhorukov, Yuri S Kivshar

    Optics Express
    |June 12, 2009
    PubMed
    Summary
    This summary is machine-generated.

    Researchers discovered multi-gap surface solitons, a new type of mutually trapped state in periodic systems. These solitons exist in different spectral gaps, enabling novel nonlinear collective effects near surfaces.

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    Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
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    Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

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    Area of Science:

    • Nonlinear optics
    • Condensed matter physics
    • Waveguide optics

    Background:

    • Periodic systems exhibit complex transmission spectra with multiple gaps.
    • Surface states in such systems are crucial for understanding boundary phenomena.
    • Nonlinear effects can lead to the formation of localized wave structures.

    Purpose of the Study:

    • To introduce and analyze the concept of multi-gap surface solitons.
    • To investigate nonlinear collective effects at the surfaces of semi-infinite periodic systems.
    • To explore the formation and properties of mutually trapped surface states within different spectral gaps.

    Main Methods:

    • Numerical analysis of nonlinear collective effects.
    • Modeling of semi-infinite periodic systems, specifically binary waveguide arrays.
    • Identification and characterization of discrete surface modes and multi-gap states.

    Main Results:

    • Demonstrated the existence of discrete surface modes in binary waveguide arrays.
    • Confirmed the simultaneous support of two types of discrete solitons.
    • Identified multi-gap states, including soliton-induced waveguides and composite vector solitons.

    Conclusions:

    • Multi-gap surface solitons represent a novel class of mutually trapped surface states.
    • These solitons leverage different spectral gaps for their formation and stability.
    • The findings open new avenues for controlling light in periodic optical structures.