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Dimensions for Mounted Stainless Steel Slits in Ø1" Housings

Features

• Precision Double Slits in Stainless Steel Foils Mounted in Ø1" Aluminum Housings
• Black-Anodized Aluminum Housing:
  • 1" Outer Diameter, 0.10" Thick
  • Includes Engraved Horizontal Lines on the Front Face to Facilitate Slit Alignment
• Slit Widths: 40, 50, or 100 µm
• Slit Spacing: 3X or 6X Slit Width
• Slit Length: 3 mm
• Contact Tech Support to Discuss Custom Options

Thorlabs' Optical Double Slits in blackened stainless steel foils have 3 mm long slits with widths of 40 µm, 50 µm, or 100 µm and are available with a spacing of 3X or 6X the slit width. For example, SD40K3 is a double slit with 40 µm slit width and 120 µm spacing, while SD40K6 is a double slit with 40 µm slit width and 240 µm spacing. To avoid creating interference and diffraction patterns in multiple directions, ensure that the size of the incident beam is smaller than the length (3 mm) of the slit. Foils are mounted in Ø1" aluminum housings.

If you do not see what you need in our stocked offerings below, it is possible to special order slits that are fabricated from different substrate materials, have different slit sizes, incorporate multiple slits in one foil, or provide different slit configurations. Low-power applications may benefit more from the absorbance of blackened stainless steel foils. High-power applications may need the high damage threshold and reflectance of gold-plated copper foils, the high melting point and lower reflectance of our tungsten foils, or the high melting point of our molybdenum foils paired with the low reflectance (4% @ 800 nm) of their black-coated front side. Please see the Foil Comparison and Graph tabs for more information. Customized housings are also available. Please contact Tech Support to discuss your specific needs.

Reflectance Graph

Below is presented a reflectance graph for the blackened stainless steel on the mounted optical slits. The raw reflectance data can be found here.

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Figure 2: Two identical sine waves are shown out-of-phase.
The top two curves are added together in order to get the
resultant in the bottom row. When both waves are
out-of-phase, they interfere destructively.

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Figure 1: Two identical sine waves are shown in-phase. The top two curves are added together in order to get the resultant in the bottom row. When both waves are in-phase, they interfere constructively.

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Figure 3: A plane wave is incident on a pair of slits such that each slit acts like a point source that radiates toward a detection screen. The intensity observed on the screen will be an alternating bright and dark pattern due to interference between light from the two slits.

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Figure 4: Two slits are shown separated by a distance d, positioned a distance L from a detection screen. The difference in path length, Δx, from each slit to a particular point y on the screen results in varying levels of constructive and destructive interference.

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Figure 5: The intensity of light of wavelength λ is plotted at points along a screen which
is a distance L away from a pair of optically small slits that are separated by a distance d.

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Figure 6: Light of wavelength λ is shown passing through a slit of width a at three
different angles. Case (a) is at an angle of 0°, while cases (b) and (c) are at angles
that result in the first dark fringe and the first non-central maximum, respectively.

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Figure 8: The intensity of light of wavelength λ passing through a pair of slits of width a
which are separated by a distance d=3a is plotted at points along a detection screen at
angles θ away from the horizontal.

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Figure 7: The intensity of light of wavelength λ passing through a slit of width a 
is plotted at points along a detection screen at angles θ away from the horizontal.

Double Slit Interference and Diffraction

Constructive and Destructive Interference

Light can be accurately described as both a wave and a particle. The wave-like properties of light determine in what ways light can be manipulated and the phenomena that we can observe. A fundamental property of waves is the principle of superposition, which states that for any number of waves existing in the same space, the observed amplitude at a particular point will be the vector sum of each wave at that position. This phenomenon is easily observed through the concepts of constructive and destructive interference. Consider the two identical sine waves pictured in Figures 1 and 2. To determine how these will interfere, we take the amplitude of each wave at a particular point and add these together. In Figure 1, the two waves are perfectly in phase, so their peaks will be in the same positions. When these identical waves are added together, the result is a wave with the same wavelength, but twice the amplitude; this is known as constructive interference. In Figure 2, the two waves are 180° out of phase with one another; where one wave has a peak, the other will have a trough. Thus, when added together, these waves will effectively cancel out, giving 0 amplitude at every point; this is known as destructive interference.

Young's double slit experiment demonstrates the phenomenon of interference between two light sources and allows us to explore the wave-particle duality of light. To develop the theory behind double slit interference, we will consider two parallel apertures that are significantly smaller than the space between them, d. When a plane wave is incident on a double slit such that the light at each slit is in phase, the light passing through each respective aperture will act as a spherical point source according to Huygens' principle. When observing the light on a screen at a perpendicular distance L away from the double slit plane, we will select a few points of interest to consider. At the point y₀ on the screen equidistant between the two slits, since the path length from each source is the same, the light will be in-phase, resulting in constructive interference and a bright spot on the screen. Moving symmetrically up or down from this position, the interfering light will move out of phase as the path lengths begin to differ. Eventually, once the path length difference Δx becomes equal to half of the source wavelength, the light will from each slit will be 180° out of phase, resulting in perfect destructive interference and a dark fringe on the screen. Moving further from the center, we will reach a point where the path lengths differ by another half wavelength, making the light from each source in-phase again. This will then result in constructive interference and another intensity maximum on the screen. These alternating bright and dark fringes make up what is known as a double slit interference pattern, which is shown in Figure 3.

Considering the diagram in Figure 4, we can determine the position y of each bright and dark fringe relative to the center point y₀. The relationship between path length difference Δx, slit spacing d, and angle to detection screen θ can be represented trigonometrically as:

Now, the detection angle at which the first intensity minimum (dark fringe) can be found will occur when the path difference is equal to one half of the incident wavelength λ. This angle can also be represented in terms of the perpendicular distance to the screen, L, and the position of the first dark fringe, y, as:

If we now apply the condition that the path length difference will be λ/2 for the first dark fringe, and take advantage of the small angle approximation (for sufficiently small angles, sin(θ) ≅ tan(θ)) we arrive at the result:

Now, to determine subsequent minimum and maximum positions, we can use the same principle; the first non-central bright fringe will occur when the path lengths differ by one full wavelength, λ, and the next dark fringe will occur at the next half-wavelength distance, 3λ/2, etc. Generalizing in terms of an integer m, bright fringes will occur at:

and dark fringes will occur at:

where m is any integer. When m=0, the 0^th order maximum will be a distance y=0 away from the central point y₀, and the first minimum we found above is known as the 0^th order minimum. For a generic case with light of wavelength λ, slit spacing d, and distance L to the screen, this intensity pattern is plotted in Figure 5.

Now, the formulation above assumes that the two slits are infinitesimally small. In reality, the finite size of the slits plays an important role in the resulting intensity pattern. Figure 6 shows a single, finite sized slit of width a with a plane wave incident from a few different angles. By the same principle as the interference discussed above, the range of source positions within the slit will have different path lengths to a detection screen. This leads to a phenomenon known as single slit diffraction. When light passes straight through the slit at θ=0, as in case (a) in Figure 6, each point some distance away from the center of the slit will have an in-phase pair on the opposite side of the slit with which it will interfere constructively at the screen, resulting in a strong central maximum.

In case (b) where sin(θ)=λ/a, the rays originating at each point in the slit will have a different path length to the same spot; the difference in path length between the top and the bottom of the slit is one full wavelength, while the central point will be out of phase with both by half of a wavelength. We can then consider a point just above the bottom of the slit; similarly to above, there will be a corresponding point that is a/2 above it that will arrive 180° out of phase. In fact, each point in this case will have another with which it interferes destructively, resulting in our first single-slit dark fringe. Similarly to the double slit pattern, for an integer m, the m^th order destructive minimum will be found at angles that satisfy the following equation:

Next, considering case (c) where sin(θ)=3λ/2a, the path length for light at the top of the slit will differ from that of the bottom of the slit by 3λ/2. Two thirds of the way down the slit, light will arrive shifted by exactly one wavelength relative to the top of the slit, resulting in constructive interference. Selecting two points slightly below these two will show the same relative phase, such that most rays from this slit will find another with which they interfere constructively, resulting in an intensity maximum. However, unlike the central maximum case, not all rays here will interfere constructively. This results in weaker local maxima on either side of the central bright fringe. Thus, it can be shown that the intensity pattern for light of wavelength λ passing through a single slit of width a will have the following form:

where

which is plotted in Figure 7.

In reality, our double slit is a pair of two finite slits which will both individually undergo diffraction before interfering with each other. Considering cases where the slit spacing d is greater than the slit width a, the positions of the maxima will still be the same as they were for the point-source approximation, y_m = mλL/d, but the intensities of each peak are now reduced due to diffraction. To generate the finite-double-slit diffraction pattern, we can just take the product of the theoretical double slit interference pattern and the single slit diffraction pattern. This result for a case where the slit spacing is three times the slit width (as are our double slits with the suffix "K3") is plotted in Figure 8. Generally, the "ideal" double slit intensity pattern will be seen within the diffraction wave packet defined by their individual slit widths.