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Standing Electromagnetic Waves

Standing Electromagnetic Waves

Electromagnetic waves can be reflected; the surface of a conductor or a dielectric can act as a reflector. As electric and magnetic fields obey the superposition principle, so do electromagnetic waves. The superposition of an incident wave and a reflected electromagnetic wave produces a standing wave analogous to the standing waves created on a stretched string.
Suppose a sheet of a perfect conductor is placed in the yz-plane, and a linearly polarized electromagnetic wave traveling in the...

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Eccentric Axial Loading in a Plane of Symmetry

Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.

Modes of Standing Waves: II

Modes of Standing Waves: II

The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
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Standing Waves

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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...

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Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
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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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Updated: Jun 22, 2026

Stretching Short Sequences of DNA with Constant Force Axial Optical Tweezers

Stretching Short Sequences of DNA with Constant Force Axial Optical Tweezers

Published on: October 13, 2011

Extreme axial optical force in a standing wave achieved by optimized object shape.

J Trojek¹, V Karásek, P Zemánek

¹Institute of Scientific Instruments of the ASCR, Brno, Czech Republic.

|June 25, 2009

Summary

Optimized prolate objects in standing wave optical traps show a tenfold increase in axial optical force compared to unmodulated shapes. This advancement benefits the manipulation of submicrometer particles, particularly those with higher refractive indices.

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Last Updated: Jun 22, 2026

Stretching Short Sequences of DNA with Constant Force Axial Optical Tweezers

Stretching Short Sequences of DNA with Constant Force Axial Optical Tweezers

Published on: October 13, 2011

Area of Science:

Optics
Nanotechnology
Soft Matter Physics

Background:

Standing wave optical trapping offers advantages over single beam trapping for submicrometer particles.
Existing research primarily focuses on spherical particles, limiting the scope of theoretical and experimental studies.
Key benefits of standing wave traps include stronger axial forces, higher trap stiffness, and improved confinement for high refractive index particles.

Purpose of the Study:

To theoretically investigate the optical forces acting on prolate objects with periodically modulated radii in standing wave optical traps.
To optimize object shapes for enhanced axial optical force compared to unmodulated shapes.
To develop analytical formulas for low refractive index objects and validate findings with numerical simulations for higher refractive index objects.

Main Methods:

Theoretical analysis using analytical formulas for axial optical force on low refractive index objects.
Numerical simulations employing the coupled dipole method for objects with higher refractive indices.
Shape optimization of prolate objects with periodically modulated cylindrical symmetry.

Main Results:

Achieved up to a tenfold enhancement in axial optical force by optimizing object shapes.
Derived analytical expressions for axial optical force applicable to negligible light scattering scenarios.
Numerical results confirmed the enhanced force and supported the analytical conclusions for higher refractive index objects.

Conclusions:

Optimized prolate object shapes in standing wave optical traps significantly enhance axial optical force.
The study provides a theoretical framework and numerical validation for improved optical manipulation of non-spherical particles.
Findings pave the way for more efficient and precise manipulation of micro- and nanoparticles using tailored optical trap geometries.