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Angle Dependency on Second Harmonic Generation of Light
Abstract.
The process of second harmonic generation from a high-power laser beam of light interacting
with a nonlinear crystal was experimented. The high-power laser beam of infrared light of
1064nm wavelength was directed through a nonlinear crystal which doubled the frequency of the
beam, transmitting a green wavelength of light of 532nm. It was determined that there were two
peaks of intensity for the second harmonic generation of light for the angle between the axis of
the nonlinear crystal and the polarization direction of the infrared laser. The intensity peaks were
about 180 degrees apart.
I. Introduction.
Linear optical processes describe systems where an electromagnetic wave comes in contact
with a linear material and will be transmitted or reflected at the same frequency as it started.
Examples of linear materials include simple mirrors, lenses, and diffraction gratings. Linear

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systems also follow the superposition principle which states that when waves in space overlap,
the resulting wave will be the sum of the two original waves. As the study of linear optics
progressed, the discovery of non-linear optics was made.
Nonlinear processes have been observed at low frequencies for the past hundred years,
such as in transformers and solenoids which contain iron [1]. However, it was not until the
1960’s, after the discovery and development of masers, and lasers that nonlinear processes were
proven to exist in optics [1]. The original display was performed by Peter Franken and his
coworkers in the Randall Laboratory at the University of Michigan. They used a quartz crystal
and a ruby laser for second harmonic generation of light following the nonlinear power series
equation describing the induced dipole on light [1]:


 


 


where P is the induced dipole, E is the E-field,

represent first order linear effects,

represents second order effects or second order optical susceptibility, which includes second
harmonic generation, and

represents third order effects, or third order optical susceptibility
[1,2]. The

portion of the formula showed to have an existing tensor element, determining the
results of the Franken and co-workers experiment as a nonlinear process in optics [1]. After the
discovery of non-linear optics, the subject has continued to advance and is now an essential part
to many optical instruments and processes, such as ultra-short pulsed lasers, optical signal
processing, and laser amplifiers [3].
After the discovery of second harmonic generation of light through by a nonlinear
medium lacking inversion symmetry, further studies and experimentation exponentially
expanded the knowledge of nonlinear optics. One particular scientist who greatly contributed to
applications of nonlinear optics using lasers is Nicolaas Bloembergen, who won the Nobel Prize
in Physics in 1981 for his research on the use of nonlinear optics in laser spectroscopy [4].
Bloembergen was able to effectively use the superposition principle of electromagnetic waves
through a nonlinear medium to create laser beams composed of waves with frequencies higher
and lower than those of visible light [4]. The discovery opened a wide range of laser
spectroscopy studies and applications, as lasers were never before able to emit beams in
wavelengths outside of the visible spectrum of light.
Section II of this report reviews the theory behind second harmonic generation, and section
III presents the experimental apparatus used in this experiment. Further, Section IV conveys the
results of the experiment and discusses these results, while section V presents the conclusion of
the experiment.
II. Theory
In traditional linear optics, the polarization in a system is linearly proportional to the
electric field that is placed on the material. However, in nonlinear optics and specifically
second harmonic generation of light, where coherent intensity occurs, the polarization of
light in a material can be expanded based on the electric field being applied to the material in

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Angle Dependency on Second Harmonic Generation of Light Abstract. The process of second harmonic generation from a high-power laser beam of light interacting with a nonlinear crystal was experimented. The high-power laser beam of infrared light of 1064nm wavelength was directed through a nonlinear crystal which doubled the frequency of the beam, transmitting a green wavelength of light of 532nm. It was determined that there were two peaks of intensity for the second harmonic generation of light for the angle between the axis of the nonlinear crystal and the polarization direction of the infrared laser. The intensity peaks were about 180 degrees apart. I. Introduction. Linear optical processes describe systems where an electromagnetic wave comes in contact with a linear material and will be transmitted or reflected at the same frequency as it started. Examples of linear materials include simple mirrors, lenses, and diffraction gratings. Linear systems also follow the superposition principle which states that when waves in space overlap, the resulting wave will be the sum of the two original waves. As the study of linear optics progressed, the discovery of non-linear optics was made. Nonlinear processes have been observed at low frequencies for the past hundred years, such as in transformers and solenoids which contain iron [1]. However, it was not until the 1960’s, after the discovery and development of masers, and lasers that nonlinear processes were proven to exist in ...
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