Time
www.edmundoptics.eu/LO 41
GVD is highly wavelength dependent and has typical units of fs2/mm.
For example, the GVD of fused silica is +57 fs2/mm at 589,3 nm and
-26 fs2/mm at 1500 nm. Somewhere between those wavelengths (at
about 1,3 m), there is a zero-dispersion wavelength where GVD is zero.
Figure 13.3 shows the signi cant amount of variation of the GVD of
fused silica vs. wavelength. For optical ber communications, the GVD
is typically de ned as the derivative with respect to wavelength instead
of frequency and is usually speci ed with units of ps/(nm km).
Section 13.2: Ultrafast Lasers
Ultrafast lasers are highly advantageous because of their short pulse durations
and high peak powers for a variety of applications including precise
biomedical applications, materials processing, micromachining, nonlinear
microscopy and imaging, and communications. Ultrafast lasers lead to
better dimensional tolerances in materials processing and micromachining
while eliminating typical post-processing steps and minimizing damage
to surrounding areas,2 Similarly, ultrafast lasers result in less trauma in
laser surgery and other medical applications, while also lessening the need
for anesthetics and sterilization,3 Ultrashort laser pulses are created when
light waves containing a large quantity of modes, or integer multiples of
half of the wavelength of the light, are emitted coherently through their
in-phase superposition (Figure 13.4). This is also known as mode-locking.
For a transform-limited Gaussian pulse, the spectral width is given by:
where λc is the central wavelength, λ is the pulse duration, and c is the
speed of light.
The dependence of GVD on wavelength signi cantly a ects ultrafast
pulses due to their broad bandwidth, stretching out the pulse duration
of ultrafast pulses as they travel through an optical system (Figure 13.5).
The amount of pulse broadening from the incident pulse duration (τIn) to
the output pulse duration (τOut) is related to the GDD (Figure 13.6):
Most optical media exhibit positive dispersion, so long wavelengths
transmitting through them will have a higher phase velocity than that
of shorter wavelengths, elongating the pulse duration (Figure 13.5). This
is known as positive chirp. Ultrafast lasers are a ected by dispersion
signi cantly more than other laser types due to their broad bandwidth.
White light interferometry is the most common metrology used for measuring
group delay and GVD for ultrafast optical components. More information
can be found in Section 16: Metrology from pages 52-57.
In addition to pulse broadening, chromatic dispersion may also make refraction
angles at optical surfaces frequency-dependent, causing angular
dispersion and frequency-dependent path lengths. Methods for dispersion
compensation to improve the performance of ultrafast laser systems
can be found in Section 14: Highly-Dispersive Mirrors from pages 42-43.
References:
1. Ghatak, Ajoy, and K. Thyagarajan. “Optical Waveguides and Fibers.”
University of Connecticut, 2000.
2. Mielke, Michael. “Ultrafast Lasers: Ultrashort Pulse Lasers Bring Cost-
E cient Precision to Micromanufacturing.” Laser Focus World, 8 Apr. 2015.
3. “The Bene ts of Femtosecond Lasers and Why We Use Them.” Spindel Eye
Associates, 16 May 2017, www.spindeleye.com/blog/2017/05/the-
bene ts-of-femtosecond-lasers-and-why-we-use-them/.
λ t
Figure 13.4: Interference of coherent waves with many modes during
mode-locking generates pulses with an ultrashort temporal width but
broad wavelength bandwidth
10ns
10fs 100fs 1ps 10ps 100ps
τOut
1ns
100ps
10ps
1ps
100fs
10fs
1fs
1ns τIn
GDD = 106 fs2
GDD = 105 fs2
GDD = 104 fs2
GDD = 103 fs2
GDD = 102 fs2
Figure 13.6: Depiction of temporal broadening, or increasing pulse
duration, of a femtosecond ultrafast pulse after traveling through di erent
optical media.
13.5
Ultrafast Laser
Optical Medium
(Objective, AOM, Window, Lens, etc.)
Irradiance
Time
Irradiance
Figure 13.5: Dispersion leads to the broadening of ultrafast laser
pulses. AOM stands for acousto-optic modulator, which is a component
that allows lasers to emit a pulsed output
13.4
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