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Unformatted text preview: ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers Laser Dynamics and Pulsed Lasers Pulsed Laser
Characterization ECE 455 Optical Electronics Pulsing
Methods
QSwitching
Mode Locking Tom Galvin
Gary Eden
ECE Illinois Introduction
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods In this section, the following subjects will be covered:
Nonsteady state behavior of lasers
Motivations for pulsing lasers QSwitching
Mode Locking Methods for pulsing lasers Starting a Laser I
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization High
Reflector PUMP Pulsing
Methods
QSwitching
Mode Locking Gain Medium Output
Coupler Starting a Laser II
ECE 455
Lecture 5
1 Before the cavity has begun lasing, the cavity has deﬁned
discrete opitcal modes which may oscillate. 2 When the laser is started these modes are seeded by
photons emitted via spontaneous emission. 3 All modes which are above threshold when the gain is γ0
grow exponentially, but the mode with the highest net
gain will grow more rapidly than all others. 4 The mode with the highest gain will reach a level where it
saturates the medium before the other modes. The gain
for all modes falls until only one is above threshold. 5 The other modes decay away and a single mode is left
lasing. Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Starting a Laser Level Diagram
ECE 455
Lecture 5 τ32 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods R3 N3
N2
τ21 Laser QSwitching
Mode Locking τ10 N1
N0 Throughout the analysis that follows, we’ll analyze a fourlevel
system as shown above Starting a Laser III Seeding Rate
ECE 455
Lecture 5 Laser Dyamics The ﬁrst question to answer is how long will it take for a cavity
mode above thresold to become seeded? The density of states
for photons per unit volume and frequency is: Pulsed Lasers ρ(ν )d ν = Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking 8π n3 ν 2
dν
c3 (1) Spontaneous emission can emit into any of these modes. But
only one of these modes is the mode with the highest gain
dφ
dt 1
N2 Vc
g (ν21 )∆ν21
τ21
Vc ρ(ν )∆ν21
N2
1
g (ν21 )
=
τ21
ρ(ν )
N2
= ηseed
τ21
= (2)
(3)
(4) Starting a Laser IV Buildup Time
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods How long will it take for a single photon to stabilize into laser
output? The small signal gain form of the gain equation may
be used because saturation eﬀects can be ignored before laser
oscillation has begun.
Isat = QSwitching
Mode Locking hν (γ0 −γth )ct /n
e
Aτ21 (5) Therefore the buildup time is
τbuildup = n
ln
(γ0 − γth )c Isat Aτ21
hν (6) Starting a LaserV Buildup Time II
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking There are many ways to estimate the buildup time. The net
gain per round trip is
GRT = R1 R2 exp [2γ0 Lg ] (7) The number or round trips necessary to reach a total gain of G
is
logG
N=
(8)
logGRT
The round trip time
tRT = 2nLg + 2(L − Lg )
c (9) Therefore the buildup time is
τbuildup = 2nLg + 2(L − Lg ) logG
c
logGRT (10) Example: Laser Buildup Time
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization Problem: Estimate the buildup time of a Pulsing
Methods
QSwitching
Mode Locking Solution: Starting a Laser: Alternative View
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Laser dyanamics can be approximated with the following model
d ∆N
g2
=− 1+
dt
g1 Lg c φ
N2 g2 N1
σse ∆N − +
+R3 (t ) (11)
L nV
τ2 g1 τ1 Lg c
dφ
φ
N2
=
φσse ∆N −
+ ηseed
dt
Ln
τc
τ21 (12) There is no simple analytic solution to this non linear system of
equations; they must be solved numerically. Laser Spiking
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Relaxation Oscillations
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers Relaxation oscillations occur in lasers where τ21 Pulsed Laser
Characterization φ = φss + φ(t ) QSwitching φ(t ) ≈ exp − (13) ∆N = ∆Nss + ∆N (t ) Pulsing
Methods Mode Locking τc (14) σse c φss
t sin σse c (φss ∆Nss )1/2 t
2 (15) Why Pulse a Laser?
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Physical parameters of gain medium
Increase peak output power
Nonlinear optical processes scale as I n , where n is the order
of the nonlinearity and I is the intensity of the optical ﬁeld. Extreme pumping requirements for threshold gain
Increase laser bandwidth
Time resolved spectroscopy Example: Pumping Requirements of an Excimer
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods Problem: Predict the threshold pumping rate for a KrF laser.
The laser has the following properties: R1 = 0.99, R2 = 0.04,
L = 1 m, Amode = 5.25 cm2 , λ = 248 nm, τ2 = 5 ns and σse
= 2.6 ˚2 . Only 15% of pump energy will go into upper state
A
formation.
Solution: The ﬁrst step is to calculate the threshold gain: QSwitching
Mode Locking γth = − 1
ln(R1 R2 ) = 0.016 cm−1
2L This requires:
∆Nth = γth
= 6.21 × 1013 cm−3
σse Example: Pumping Requirements of an Excimer
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching The required volumetric pumping rate at threshold is:
R= 1 hc ∆Nth
= 66.3 kWcm−3
η λ τ2 which means the total pump power must be: Mode Locking P = RV = (66.3 kWcm−3 ) · (100 cm) · (5.25 cm2 ) = 34.8 MW Characterizing Pulsed Lasers
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Two parameters are commonly used to characterize pulsed
lasers. The ﬁrst is the average output power:
Pave = Epulse frep (16) The second is the peak power, which may be approximated as
follows:
Epulse
(17)
Ppeak =
∆t
Where Epulse is the energy per pulse and ∆t is the FWHM of
the pulse. Pulse Laser Characterization Example
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching Problem: LOPE’s femtosecond laser produces 40 fs pulses
containing up to 4.5 mJ of energy at a repetition rate of 1 kHz.
Find the peak and average power of the laser.
Solution:
Pave = (4.5 mJ) · (1 kHz) = 4.5 W (18) Mode Locking 4.5 mJ
= 112.5 GW !!!
40 fs
For comparison, summer electricity demand in the US is
783 GW.
Ppeak ≈ (19) The Idea
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization In steady state the round trip gain must be equal to one
for a laser. Pulsing
Methods Therefore in steady state ∆N is locked to ∆Nth QSwitching This limits the rate at which energy can be extracted Mode Locking Nothing prevents ∆N ∆Nth on a transient basis. QSpoiling (Pump and Dump)
ECE 455
Lecture 5 The process:
1 Create an extremely high Q cavity and pump continuously Pulsed Lasers 2 Allow the CW intensity to build up inside the cavity Pulsed Laser
Characterization 3 Suddenly lower the cavity Q by increasing the strength of
the output coupling. Laser Dyamics Pulsing
Methods
QSwitching
Mode Locking Discussion:
Intracavity intensity is much greater than outputcoupled
light
Minimum pulse duration limited by round trip time of
cavity
Maximum intensity limited by cavity losses
Don’t try this on Wall St. Pulse the Pump
ECE 455
Lecture 5 Laser Dyamics The process: Pulsed Lasers
1
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Rapidly switch on a highpowered pumping mechanism 2 Wait for a pulse to come out
Minimum pulse duration is limited by cavity build up time
or speed of pump
This approach requires fast, high power electronics.
This is the most primitive method. It is commonly used in
conjuction with QSwitching. QSwitching
ECE 455
Lecture 5 Laser Dyamics The process:
1 Pump at low rate with cavity Q spoiled to prevent
oscillation 2 Generate a large population inversion ∆N > ∆Nth 3 Quickly restore Q to a high value to allow laser oscillation 4 Laser pulse extracts energy from inversion, driving
∆N < ∆Nth (absorption) 5 Laser pulse terminates 6 Turn oﬀ Q Switch and repeat Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Two types of QSwitches are:
Rotating mirror
Pockells cell QSwitching Methods: Rotating Mirror
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods Gain
Medium QSwitching
Mode Locking Rotating
Mirror QSwitching Methods: AcoustoOptic Modulator
(AOM)
ECE 455
Lecture 5 Scattering
loss Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods Light QSwitching
Mode Locking Acoustic
density
waves QSwitching Methods: Pockels Cell
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods M1 Gain PBS QWP PC M2 PC Off QSwitching
Mode Locking PC On PBS = Polarizing Beam Splitter; QWP = Quarter Wave Plate;
PC = Pockels Cell QSwitching Methods: Saturable Absorber
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking QSwitch: Energy Storage
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods The length of time that energy can be stored is limited by
the lifetime of the of upper state. The lifetime sets an
upper limit on the maximum useful pump duration.
Energy storage in an ampliﬁer or laser is limited by the
onset of parasitic oscillations QSwitching
Mode Locking Small stimulated emission cross sections keep the and
allow a large population in the upper state
An ideal ampliﬁer material has a high ﬂuoresence lifetime
and a small stimulated emission cross section Energy Storage Example
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Problem: Nd:YAG and Nd:YLF both lase at similar
wavelengths (1064 nm and 1053 nm respectively). Calculate
the maximum amount of energy that can be stored in both a
Nd:YAG and Nd:YLF ampliﬁer before parasitic oscillations
begin. Assume the ampliﬁer crystal is 8 cm long and that 1%
of radiation is scattered back at each interface.
For Nd:YAG
σse = 2.8 × 10−19 cm2
For Nd:YLF
σse = 1.8 × 10−19 cm2
Solution: The ﬁrst step is to calculate the threshold gain:
γth = − 1
1
ln(R1 R2 ) = −
ln(.01 · 0.1) = 0.576 cm−1
2L
2 · 8cm Energy Storage Example Continued
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization From the threshold gain, we can calculate the threshold
inversions of both of these lasers. From the inversion density,
we can easily calculate the energy storage desnity.
∆Nth (YAG ) = Pulsing
Methods
QSwitching γ0
0.576cm−1
=
= 2.06 × 1018 cm−3
σse
2.8 × 10−19 cm2 ρ(YAG ) = Mode Locking ∆Nth (YLF ) = hc ∆Nth
= 0.384J · cm−3
λ γ0
0.576cm−1
=
= 3.20 × 1018 cm−3
σse
1.8 × 10−19 cm2 hc ∆Nth
= 0.597 Jcm−3
λ
This analysis is of course approximate.
ρ(YLF ) = QSwitch Discussion
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Minimum pulse duration limited by cavity build up time
Maximum energy of pulse is limited by energy storage
density inside medium and how eﬃciently it can be
extracted Pulsing Methods: Medium Behavior Outside Cavity
ECE 455
Lecture 5 Pump
Pulse Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Exponential
Decay Linear
Rise
Nth t Pulsing Methods: Pulsing the Pump
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers Pump
Pulse Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Gain Below
Threshold Laser
Pulse Nth t Pulsing Methods: QSwitch
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers Pump
Pulse QSwitch
Activated Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Laser
Pulse
Nth t Pulsing Methods: Poorly Timed QSwitch
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers Pump
Pulse QSwitch
Activated Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Laser
Pulse Nth t Keep Track of Assumptions
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Pump pulse much faster than relaxation time
Pumping rate will not have a nice ﬂattop
Saturation of the pumping process has been ignored
Spatial eﬀects (transverse and logitudinal) have been
ignored Fourier Series
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization Recall that any periodic function may be represented as a
weighted sum of complex exponentials
∞ cn · exp ın a (t ) = Pulsing
Methods n=−∞ 2π
t
T (20) 2π
t dt
T (21) QSwitching
Mode Locking where
cn = 1
2T T a(t )exp −ın
0 Properties of Fourier Series
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking The fundamental frequency of a(t ) is f0 = 1
T The fourier spectrum of a(t ) comprises delta functions
separated by f0
The more rapid the variations in a(t ), the more terms will
be needed in the fourier series to approximate a(t ) Optical Fourier Series
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods Recall that the frequencies of the longitudinal modes of a
cavity are
c
(22)
νq = q
2Lopt
If several of these modes are oscillating simultaneously, the
electric ﬁeld may be written QSwitching
Mode Locking Eq exp [ıφq ] · exp [ıq 2πνq t ] E (t ) = (23) q Eq exp [ıφq ] · exp ıq 2πνq t (24) = exp [ı2πν0 t ]
q where νq ≡ νq − ν0 Properties of Optical Fourier Series
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Relatively low frequency envelope modulated by optical
carrier frequency ν0
The fundamental frequency of the envelope is f0 = c
2Lopt The fourier spectrum E (t ) comprises delta functions
separated by f0 and oﬀset from the axes by ν0
The more rapid the variations in the envelope, the more
terms will be needed in the fourier series to approximate
the pulse Mode Locking I
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking In our discussion of homogenously broadened media, the mode
with the highest net gain would oscillate to the exclusion of
other modes. What if a coherent superposition of cavity modes
could have lower loss (and thus higher net gain) than any
individual longitudinal mode? This is the idea behind the
technique known as modelocking. Mode Locking II
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking The cavity dispersion must go to zero.
There must be a mechanism to lock the phases of the
various longitudinal modes.
The shortest pulse possible is limited by one of four
factors:
The
The
The
The recovery time of the mode locking mechanism
bandwidth of the lasing transition
reﬂectivity and dispersion of the cavity optics
frequency of the optical carrier wave Pulse Propagation in a Material Medium
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods The actual condition for resonance of the qth longitudinal
cavity resonance is
φRT = q · 2π
(25)
The phase shift from propogating through the gain medium
once is QSwitching
Mode Locking φ(ω ) =
= 2π
Lg n(ω )
(26)
λ
2π
∂n
1 ∂2n
Lg n(ω0 ) +
(ω − ω0 ) +
(ω − ω0 )2 + . . .
λ
∂ω
2 ∂ω 2 Which terms are important? Pulse Propagation in a Material Medium
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods The fourier transform
E (ω ) = A(ω )e ıω0 t (27) where A(ω ) is the fourier transform of the envelope and e ıω0 t is
the optical carrier frequency. QSwitching
Mode Locking The fourier transform of the pulse after is has propagated
through a material medium is
E (ω ) = A(ω )e ıω0 t e ıφ(ω) (28) Propagation Through Sapphire 120 fs Pulse
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Propagation Through Sapphire 40 fs Pulse
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Propagation Through Sapphire 10 fs Pulse
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Lessons
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Pulse dispersion is more sevfere for shorter pulses
We need a mechanism to counteract the dispersion
present in the cavity
Prisms
Chirped mirrors
Photonic Crystals Propagation through materials is bad. Use reﬂective
optics. Multiple Longitudinal Modes: Random Phase
N = 30
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Multiple Longitudinal Modes: Zero Phase N = 30
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Multiple Longitudinal Modes: Zero Phase N = 90
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Active Mode Locking: AcoustoOptic Modulator
ECE 455
Lecture 5 Laser Dyamics An acoustic transducer is
coupled to a crystal Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking The acoustic waves forms
a standing wave pattern
The periodic variation in
density forms a grating,
which scatters the laser
beam
This can be modulated
rapidly. The modulation
must be synchronized with
the cavity round trip time. PICTURE OF AOM Modelocking Shutter Picture
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Shutter
Pulse t Passive Mode Locking: Saturable Absorber
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching An absorber is placed inside the laser cavity
Low intensity light, such as noise is absorbed by the
aborber
High intensity ’bleaches’ the medium, making it
transparent. Mode Locking It only works if the recovery time of the medium is much
less than the round trip time. Passive Mode Locking: Kerr Lens
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Relies on a third order nonlinearity known as self focusing
n = n1 + n2 I The higher peak intensity (pulsed) mode suﬀers lower
diﬀraction losses than any individual longitudinal mode.
Kerr lensing is a nonlinear optical process. Hence it is
(approximately) instantaneous
Discovered by graduate students who forgot to turn the
AOM on A ModeLocked Oscillator
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking D. E. Spence et al. Optics Letters 16, 42 (1991) CW and Modelocked Operation
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Figure: A Ti:Sapphire laser
operating CW. Figure: The same laser
modelocked. One More Option
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Figure: A Ti:Sapphire laser in modelocked operation with continuous
wave breakthrough Example: Shortest Possible Pulses
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching Mode locking produces the shortest pulses. As a ﬁrst estimate,
the shortest possible pulse possible is:
∆t ≈ 1
∆f Mode Locking where ∆f is the bandwidth FWHM. (29) Example Shortest Pulse
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods Problem: As a gain medium, Ti:Sapphire exhibits gain from
roughly 650 nm to 1100 nm. What is the short possible pulse
which a Ti:Sapphire laser can generate?
Solution:
∆f = c
c
−
= 1.89 × 1014 Hz
650 nm 1100 nm Therefore, an estimate for the shortest pulses possible is: QSwitching
Mode Locking ∆t ≈ 1
= 5.29 fs
∆f For comparison, a single optical cycle at 800 nm (the peak of
Ti:Sapphire gain spectrum) is
T= 800 nm
= 2.67 fs
c Example: Finding Number of Modes Locked
Together
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Problem: A modelocked Ti:Sapphire oscillator has mirrors
which are 1.8 m apart. Consider the spectrum in Figure 2, how
many longitudinal modes are oscillating simultaneously?
Solution: The separation between longitudinal modes is simply
the free spectral range of the cavity.
c
FSR =
= 83.3 MHz
2nL
To determine the number of modes oscillating simulatenously,
we take the entire spectrum bandwidth, not the FWHM. This
bandwidth is:
c
c
∆f =
−
= 6 × 1013 Hz
730 nm 855 nm
The number of modes oscillating simultaneously is therefore:
∆f
= 721000
FSR Regenerative Ampliﬁcation I
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization The pulse energy possible with mode locking is limited because
the high repition rate of oscillators would require a very high
power pump laser. In order to generate high powered short
pulses, a technique known as regnerative amplication is used.
The strategy is as follows:
1 Create lowenergy highrepetition rate pulses from an
oscillator 2 Use an optical switch to lower the repetition rate 3 Temporally stretch pulses by using diﬀraction gratings to
’chirp’ the pulses 4 Amplify the pulse by passing it through another crystal
multiple times. 5 Use another diﬀraction grating to remove the chirp
introduced by the stretcher and cavity dispersion Pulsing
Methods
QSwitching
Mode Locking A Regnerative Ampliﬁer
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking A02/G  Pump Laser; FI  Faraday Isolator; PC  Pockells Cell;
TFP  Thin Film Polarizer
I. Matsushima et al. Optics Letters 31, 2066 (2006) ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization From the examples given, you may get the impression that
Ti:Sapphire is the only medium for mode locking, not so!
Dye Lasers Pulsing
Methods Nd:YAG QSwitching Cr:LiCAF and Cr:LiSAF Mode Locking Er and Yb doped ﬁber
Semiconductor Lasers Summary
ECE 455
Lecture 5 Laser Dyamics
Pulsed Lasers
Pulsed Laser
Characterization
Pulsing
Methods
QSwitching
Mode Locking Lasers are ’seeded’ from spontaneous emission
Full models of laser dynamics are quite complicated
Pulsing lasers can result in a dramatic increase in peak
intensity
Modelocking produces the shortest laser pulses, but due
to the high rep rate, the energy per pulse is low ...
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This note was uploaded on 02/28/2012 for the course ECE 455 taught by Professor Eden,j during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Eden,J

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