Related Experiment Video
Updated: Feb 12, 2026

17:14
Compact Quantum Dots for Single-molecule Imaging
Published on: October 9, 2012
18.7K
Size and edge dependence of two-photon absorption in rectangular graphene quantum dots
Optics Express
|April 4, 2018
Summary
This study explores two-photon absorption in graphene quantum dots (GQDs). GQD properties, like semiconductor or metallic behavior, depend on edge size, influencing TPA tuning.
Area of Science:
- Condensed Matter Physics
- Materials Science
- Quantum Optics
Background:
- Graphene quantum dots (GQDs) exhibit unique electronic and optical properties.
- Two-photon absorption (TPA) is a crucial nonlinear optical phenomenon with applications in various fields.
- Understanding TPA in GQDs requires theoretical investigation of size and edge effects.
Purpose of the Study:
- To theoretically investigate the size and edge-dependence of TPA in rectangular GQDs.
- To derive the TPA cross-section and transition selection rules around the K point.
- To analyze the impact of zigzag and armchair edge dimensions on TPA.
Main Methods:
- Theoretical investigation using the Dirac equation under hard wall boundary conditions.
- Derivation of the TPA cross-section for interband transitions.
- Analysis of transition selection rules based on GQD dimensions.
Main Results:
- Rectangular GQDs behave as semiconductors for zigzag-edge sizes M = 3M0 ± 1 and metallic for M = 3M0.
- For semiconducting GQDs, TPA is tunable by both edge sizes, with armchair-edge contributing more.
- For metallic GQDs, armchair-edge size dictates absorption peak position and TPA coefficient magnitude, with resonant enhancement.
Conclusions:
- Graphene quantum dot electronic and optical properties are highly sensitive to edge structure and dimensions.
- Tailoring GQD dimensions allows for controlled tuning of two-photon absorption characteristics.
- The findings provide insights for designing GQD-based optical devices.
Related Concept Videos
Quantum Numbers
52.3K
It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
52.3K
The Quantum-Mechanical Model of an Atom
59.7K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
59.7K
Curvilinear Motion: Rectangular Components
1.3K
Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the...
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the...
1.3K
Rectangular and Triangular Pulse Function
2.0K
The unit rectangular pulse function is mathematically represented by a rectangular function centered at the origin with a height of one unit. This function is defined by two parameters: T, which specifies the center location of the pulse along the time axis, and τ, which determines the pulse duration.
For example, consider a rectangular pulse with a 5V amplitude, a 3-second duration, and centered at t=2 seconds. This pulse can be expressed using the rectangular function, written as,
For example, consider a rectangular pulse with a 5V amplitude, a 3-second duration, and centered at t=2 seconds. This pulse can be expressed using the rectangular function, written as,
2.0K
The Dot Product
266
Measuring how one directional quantity affects another along a specific path involves comparing their orientation and strength. When two such quantities are represented using direction and amount, a numerical result is computed to show how much one acts along the path of the other. This result comes from a rule combining both inputs' horizontal and vertical parts and adding the results.This calculation gives a single value that grows larger when both inputs point in similar directions and...
266
Dot Product
1.0K
The dot product is an essential concept in mathematics and physics.
In engineering, the dot product of any two vectors is the product of the magnitudes of the vectors and the cosine of the angle between them. It is denoted by a dot symbol between the two vectors.
Consider a vehicle pulling an object along the ground using a rope. If the rope makes an angle with the horizontal axis, the work done can be calculated using the dot product of the force applied and the object's displacement.
The dot...
In engineering, the dot product of any two vectors is the product of the magnitudes of the vectors and the cosine of the angle between them. It is denoted by a dot symbol between the two vectors.
Consider a vehicle pulling an object along the ground using a rope. If the rope makes an angle with the horizontal axis, the work done can be calculated using the dot product of the force applied and the object's displacement.
The dot...
1.0K

