Increasing Efficiency of Second Harmonic Generation
A. Lytle and A. Penfield Franklin and Marshall College, Lancaster, PA Mo#va#on Frequency doubling, or the conversion of light from one
frequency to double its frequency, is a common technique for
creating laser systems for a wide range of wavelengths.
Frequency doubling and other related frequency conversion
processes are generally inefficient due to dispersion, the
property that light of different wavelengths see different indices
of refraction in transparent media. We hope to show that that the
second harmonic emission can be manipulated by counterpropagating light and eventually boost the conversion efficiency
with carefully designed counter-propagating light pulses. Phase Matching with a Counter-­‐Propaga#ng Pulse This experiment attempts to show that the second harmonic
generation, naturally created when intense light interacts with a
birefringent crystal, can be suppressed or enhanced using a
counter-propagating pulse. Instead of perfect phase
matching this process uses
the counter-propagating
pulse to periodically
modulate the forward pulse
inside the crystal.
Frequency Doubling Frequency doubling, also
known as second harmonic
generation, is a process where
two photons of the same
frequency combine to create
one photon of double the
frequency. Experimental Setup As the crystal is rotated, the path
length, LP, and the coherence
length, LC, change.
In order to find the angles
for different coherence
lengths, we measured the
second harmonic intensity
as a function of incidence
angle. This allowed a
precise measurement of the
length of our beta-Barium
Borate crystal.
Relative Intensity =
Sinc(
πLP
)
2LC
LP = LSec(Sin −1 (Sin(θ ) /n o )))
€
While the relationship between the electric field and the
polarization is usually assumed to be linear, in nonlinear optics
the relationship can not be treated as such. Instead the
relationship between electric field and polarization is described
by a power series.
Phase Mismatch €
After photons become out of
phase by pi they destructively
interfere, causing a decay in the
second harmonic build up. This
means that the second harmonic
signal can only build up over the
final coherence length.
Δk = 2kω − k 2ω
LC =
€
π
Δk
Fitting to the measured
€ data, the theory predicts
a 112.5 ± 0.5 μm crystal. P(t) = E 0 χ (1) (e−iωt + e iωt ) + 2E 02 χ (2) (1+ e−i2ωt ) + 2E 03 χ (3) (2e−iωt + e iωt + e−i3ωt ) + ...
Dispersion causes a phase
mismatch between the
fundamental and harmonic
light over a distance LC. Phase Matching Characteriza#on of BBO Conclusions/ Future Work A birefringent crystal, such as our
beta-Barium Borate (BBO) crystal,
causes light of different
polarizations to see different
indices of refraction. We utilized
type I birefringent phase matching,
where the 800 nm light has the
same polarization and the 400 nm
light has a polarization that is
orthogonal to the 800 nm light. The birefringence of the crystal allows us to continuously
control the phase matching condition, giving us a known system
we can probe with counter-propagating pulses. Using our theoretical plot in comparison to our data, we were
able to accurately determine the length of our BBO crystal.
This enables us to find the coherence length at a given angle,
which is essential to moving forward with the experiment. The information that was collected about the BBO crystal will
be used to accurately match the pulse duration to coherence
length, which will hopefully allow the counter-propagating
pulse to affect the forward pulse. Acknowledgments Thanks to the Hackman Scholars Program, the Howard Hughes
Medical Institute Undergraduate Science Education Program,
and the Andrew W. Mellon Foundation.