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Related Concept Videos

Quadratic Equations01:29

Quadratic Equations

A quadratic equation is an algebraic expression where a variable is raised to the second power and combined with its first power and a constant; all equated to zero. These equations are frequently used to model relationships involving area, motion, and optimization. The general representation of a quadratic equation iswhere a, b, and c are real values, and a is nonzero to ensure the presence of the squared term.One method for solving a quadratic equation involves rewriting it as a product of...
Quadratic Equations in the Complex Number System01:29

Quadratic Equations in the Complex Number System

A quadratic equation in the form ax2+bx+c=0 can have solutions that vary in nature depending on the value of the discriminant, b2−4ac. In this expression, a is the coefficient of the quadratic term x2, b is the coefficient of the linear term x, and c is the constant term. When the discriminant is negative, the equation has no real number solutions. However, by introducing complex numbers through the imaginary unit i, defined by i=-1, these equations can still be solved.The square root of a...
Bessel Function of Order Zero01:20

Bessel Function of Order Zero

A common physical example of wave propagation with radial symmetry is the ripple formed when a stone is dropped into a still pond. The disturbance originates at a central point and travels outward as a circular wave. As the radius of the wavefront increases, the same initial energy is distributed along a progressively larger circumference. Consequently, the amplitude, or height, of the wave decreases with distance from the center. This decay behavior cannot be captured by simple sine or cosine...
Standing Waves01:17

Standing Waves

Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a refrigerator, which is one example of standing waves. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed or created by the superposition of two or more identical moving waves in opposite directions. The waves move through each other, with their...
Quadratic Models01:23

Quadratic Models

Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...
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:

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Related Experiment Video

Updated: Jul 9, 2026

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
07:42

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Published on: December 15, 2021

One-dimensional quadratic walking solitons.

R Schiek, Y Baek, G I Stegeman

    Optics Letters
    |December 12, 2007
    PubMed
    Summary

    One-dimensional quadratic walking solitons were studied in lithium niobate waveguides. Researchers explored wave propagation under various phase-matching and power conditions to understand soliton behavior.

    Area of Science:

    • Nonlinear optics
    • Integrated photonics
    • Materials science

    Background:

    • Quadratic solitons are nonlinear optical phenomena crucial for all-optical signal processing.
    • Lithium niobate (LiNbO3) is a key material for nonlinear optical devices due to its strong second-order nonlinearity.
    • Understanding soliton propagation in engineered waveguides is essential for device development.

    Purpose of the Study:

    • To investigate the properties of one-dimensional quadratic walking solitons.
    • To analyze soliton behavior in planar lithium niobate waveguides.
    • To explore the influence of phase-matching conditions, walk-off angle, and power on soliton propagation.

    Main Methods:

    • Experimental investigation of wave propagation in lithium niobate waveguides.

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  • Utilizing the type I phase-matching condition for second-harmonic generation.
  • Varying parameters such as phase matching, walk-off angle, and incident fundamental power.
  • Main Results:

    • Characterization of one-dimensional quadratic walking soliton properties.
    • Observation of wave propagation dynamics under controlled experimental conditions.
    • Demonstration of the impact of key parameters on soliton behavior.

    Conclusions:

    • The study provides insights into the fundamental properties of quadratic walking solitons in lithium niobate.
    • Findings contribute to the understanding of nonlinear light propagation in integrated photonic devices.
    • Results can inform the design and optimization of devices utilizing second-harmonic generation.