### Higher Education

 Diffraction, Interference and Young's Double Slit Experiment
Written by Boyang Liu, Seng-Tiong Ho
Tuesday, 02 May 2006 15:56

### DESCRIPTION:

Interference and Diffraction are important characteristics of light waves. They can be illustrated using the classic single and double slit experiments. This simple educational tool simulates these two experiments for a variety of user chosen parameters such as different slit sizes, different distances between silts and the incident light wavelength. The simulation is in both micro- and nano-scale: slit size and slit distance are comparable to the wavelength of incident light (hundreds of nanometers for visible light) and the total simulation area is 20 micrometers by 20 micrometers.

The simulation was created using the Finite Difference Time Domain (FDTD) electromagnetic modeling technique. In this method, the whole pictured area of the simulation is divided into small grids (each with a size of tens of nanometers), and then the electric field of the light within each grid box is calculated to high precision.

The sample 2-D visualization below depicts light propagation through a double slit. Each row shows the same light incident on slits with different widths (given as multiples of the wavelength of the incident light). The columns show the evolving patterns of diffraction and interference of the light emerging from the slits as a function of time (in femtoseconds). The color scale represents the varying electric field intensity of the light (the higher the intensity, the darker the color).

### FOR CLASSROOM:

This simulation is appropriate for high school or college level courses. By manipulation of the various parameters students can develop an intuitive understanding of the diffraction and interference of light waves. This simulation could be incorporated into a general physics course to illustrate the concepts of interference and diffraction of light waves. The "Manipulation of Light at the Nanoscale" module incorporates these simulations.

### CONNECTION TO NANOSCIENCE:

This simulation begins at the more familiar microscale and spans the transition to the nanoscale. As the parameters such as slit size and slit separation approach the nanoscale, the expected interference and diffraction effects change. Additionally, the total area of these simulations is much smaller than the meter or so distance typically used in demonstrating diffraction. Here, it is the near-field (Fresnel) diffraction that is being simulated rather than the usual far-field (Fraunhofer) diffraction. The simulations can also be used in conjunction with the photonic band gap and metal single and double slit simulations, which demonstrate other interesting nanoscale light-matter interactions.

» USER MANUAL

### EXAMPLE:

Diffraction of Light:

Diffraction, the bending of light as it passes the edge of an object, is one of the essential characteristic s of light. The most conceptually simple example of diffraction is the single-slit experiment. In this experiment, the slit is very narrow, that is, around the same size as the wavelength of the light. After the light wave passes through the slit, a pattern of semicircular ripples is formed, as if there were a single light wave source at the position of the slit. This semicircular light wave is called a diffraction pattern.

There are two simulation examples shown below for the diffraction of light. The single-slit width is different: one is λ/2 and the other is 2λ, where λ is the wavelength of the incidentlight. Comparing the two results, we can see that the narrower the slit width, the larger the diffraction angle.

Visualization of simulation results for the diffraction of a light wave:

» Open Single Slit Simulation

 Slit Width= λ/2 Slit Width= 2λ

Interference of Light:

One of the most important experiments of light wave theory is that of Young's double slits. When light passes through two close slits, the resulting two light beams interact with one another. This interference of the two light waves can be constructive or destructive.

Because the simulation is at the nanometer scale, i.e. slit size and slit distance are comparable to the wavelength of incident light (which is hundreds of nanometers) and the whole simulation area is only around tens of micrometers square, it enables users to see what "really" happens at nanoscale when light passes through a slit. For comparison, in order to achieve the same results as the classical Young's double slit experiment, the experimenter would have to move the projection screen far enough from the slit screen to amplify the interference so that it could be seen by naked eyes - a few meters (1 meter=109nm)!

The following example shows the time evolution of the incident light when it passes through a screen with a double slit for a specific slit sizes. Parameters of the three simulations are as follows: the wavelength (λ) of the incident light is 300nm, the distance between the two slits is 1500nm, and the size of each slit is 150nm (0.5λ), 300nm (1λ), and 1500nm (5λ), respectively. Note that the smaller the size of the slit, the more obvious the interference.

Visualization of simulation results for the Interference of a light wave:

» Open Double Slit Simulation

 Slit Width = λ/2 Slit Width = λ Slit Width = 5λ

Authors:
Boyang Liu,
Prof. Seng-Tiong Ho

Institution:
Northwestern University
Evanston, IL USA

Level: