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Development of an Apparatus for Measuring Laser Coherence Length

William Yang

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

The goal of this project was to develop an apparatus to measure the coherence length of the light waves produced by different lasers.The coherence length is the distance over which two interacting waves maintain a constant relative phase.The method selected to achieve the goal of the project was to introduce the laser light into a modified Michelson interferometer arrangement while observing and measuring the resulting interference pattern. This pattern can be interpreted in terms of the properties of the laser light from which the pattern was produced, including, it was predicted, its coherence length. In order to characterize the apparatus and develop a means of interpreting the interference patterns, two different lasers were used: a red diode laser taken from an inexpensive laser pointer, and a red He-Ne laser. As part of this project the quantum eraser phenomenon and bandwidth of the diode and He-Ne lasers were also investigated. The project is continuing an investigation of the utility of the apparatus for coherence length measurements.

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The goal of this project was to develop an apparatus to measure the coherence length of the light waves produced by different lasers.The coherence length is the distance over which two interacting waves maintain a constant relative phase.The method selected to achieve the goal of the project was to introduce the laser light into a modified Michelson interferometer arrangement while observing and measuring the resulting interference pattern. This pattern can be interpreted in terms of the properties of the laser light from which the pattern was produced, including, it was predicted, its coherence length. In order to characterize the apparatus and develop a means of interpreting the interference patterns, two different lasers were used: a red diode laser taken from an inexpensive laser pointer, and a red He-Ne laser. As part of this project the quantum eraser phenomenon and bandwidth of the diode and He-Ne lasers were also investigated. The project is continuing an investigation of the utility of the apparatus for coherence length measurements.
The interference of entangled photon pairs permits the study of the fundamental properties of quantum mechanics. The process is also finding practical applications in optical imaging. The Michelson interferometer provides an elegant means for characterizing the degree of two-photon entanglement, but the technique has not yet been described and analyzed in detail. Here we provide a full description of the interference of collinear down-converted photons in a Michelson interferometer. We explain the basic elements that characterize the interference pattern and complement the theory with experimental measurements. The two-photon Michelson interferometer can be used in quantum optical coherence tomography for dispersion-free imaging and localization.
The superposition principle states that the sum of solutions of the wave equation is also a solution. Linearity forbids scattering of one photon by another and waves with orthogonal polarization will not interfer and if no interference is observed the light is said to be incoherent. There is no record carried by any of the waves to indicate outside of the overlap region that the waves ever commingled. Interference involve dielectric layers can produce antireflection coatings. Michelson interferometer, temporal coherence and its use in spectroscopy. The interferometer coupled with a light source with well defined coherence properties are currently used in optical coherence imaging. With multiple reflections a Fabry Perot interferometer can be created to provide optical feedback in a laser. Young’s two slits interferometer can be used to measure the size of distant stars.
We investigate how the temporal coherence interference properties of light in a Michelson-Morley interferometer (MMI), using only a single-photon detector, can be understood in a quantum-optics framework in a straightforward and pedagogical manner. For this purpose we make use of elementary quantum field theory and Glaubers theory for photon detection in order to calculate the expected interference pattern in the MMI. If a thermal reference source is used in the MMI local oscillator port in combination with a thermal source in the signal port, the interference pattern revealed by such an intensity measurement shows a distinctive dependence on the differences in the temperature of the two sources. The MMI can therefore be used in order to perform temperature measurements. A related method was actually used to carry out high precision measurements of the cosmic micro-wave background radiation on board of the COBE satellite. The theoretical framework allows us to consider any initial quantum state. The interference of single photons as a tool to determine the angular peak-frequency of a one-photon pulse interfering with a single-photon reference pulse is, e.g., considered. A similar consideration for coherent laser pulses leads to a different response in the detector. The MMI experimental setup is therefore in a sense an example of an optical device where one can exhibit the difference between classical and quantum-mechanical light using only intensity measurements.
The temporal coherence interference properties of light as revealed by single detector intensity measurements in a Michelson-Morley interferometer (MMI) is often described in terms of classical optics. We show, in a pedagogical manner, how such features of light also can be understood in terms of a more general quantum-optics framework. If a thermal reference source is used in the MMI local oscillator port in combination with a thermal source in the signal port, the interference pattern revealed by single detector intensity measurements shows a distinctive dependence on the differences in the temperature of the two sources. A related method has actually been used to perform high-precision measurements of the cosmic microwave background radiation. The general quantum-optics framework allows us to consider any initialquantum state. As an example, we consider the interference of single photons as a tool to determine the peak angular-frequency of a single-photon pulse interfering with a single-photon reference pulse. A similar consideration for laser pulses, in terms of coherent states, leads to a different response in the detector. The MMI experimental setup is therefore an example of an optical device where one, in terms of intensity measurements, can exhibit the difference between classical and quantum-mechanical light.
An early criticism of the experimental background of special relativity theory was that the Michelson-Morley experiment was bidirectional in the moving frame. This experiment did not require that the velocity of light is constant in all Galilean frames, but only that the average to-and-fro velocities are constant. These objections were removed with the experimental verification of the time dilation effect predicted by relativity theory. It is coneptually simple to devise a unidirectional ether drift experiment based on a measure of fringe shifts. The experiment could not be performed in Michelson's time because of the large coherence lengths required for the observation of the fringe shifts. For an interference arrangement similar to that used to produce Young's fringes, a coherence length greater than a meter is required in order to observe a displacement of 0.01 fringes. Such coherence lengths are available today from continuous wave lasers.