Related Experiment Video
Updated: Jun 22, 2026

08:39
Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
Published on: January 28, 2019
Stationary optical wave fields with arbitrary longitudinal shape by superposing equal frequency Bessel beams: Frozen
Optics Express
|June 2, 2009
Summary
Researchers created "Frozen Waves," a stationary localized wave field using Bessel beams. This breakthrough allows for customizable longitudinal intensity patterns, enabling novel applications in optics and medicine.
Area of Science:
- Physics
- Optics
- Wave Phenomena
Background:
- Localized wave phenomena are crucial for various scientific and technological applications.
- Controlling the longitudinal intensity distribution of wave fields has been a significant challenge.
Purpose of the Study:
- To demonstrate a method for generating stationary localized wave fields using Bessel beams.
- To achieve arbitrary longitudinal intensity patterns for these wave fields.
- To introduce the concept and nomenclature of "Frozen Waves".
Main Methods:
- Utilizing Bessel beams to construct wave solutions.
- Engineering the wave field's longitudinal intensity profile.
- Demonstrating the static nature (zero velocity) of the intensity envelope.
Main Results:
- Successfully generated stationary localized wave fields with high transverse localization.
- Developed solutions to wave equations, including Maxwell's equations, termed "Frozen Waves".
- Showcased the ability to shape the longitudinal intensity pattern arbitrarily within a defined propagation interval.
Conclusions:
- Bessel beams provide a powerful tool for creating "Frozen Waves" with controllable intensity profiles.
- "Frozen Waves" offer a static, localized wave field with significant potential for diverse applications.
- The demonstrated technique opens new avenues for advancements in optical tweezers, atom guides, medical technologies, and more.
Related Concept Videos
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...
Suppose a sheet of a perfect conductor is placed in the yz-plane, and a linearly polarized electromagnetic wave traveling in the...
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...
Plane Electromagnetic Waves I
The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
The EM field is assumed to be a...
The EM field is assumed to be a...
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...
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:
Propagation of Waves
When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...

