nonlinear optics (wise 2017/18) - ufox.cfel.de file1 9 optical parametric amplifiers and oscillators...
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9 Optical Parametric Amplifiers and Oscillators
9.1 Optical parametric generation (OPG)
9.2 Nonlinear optical susceptibilities
9.3 Continuous-wave OPA
9.4 Theory of optical parametric amplification
9.5 Phase matching
9.6 Quasi phase matching (QPM)
9.7 Ultrashort-pulse parametric amplifiers (OPA)
9.8 Optical parametric amplifier designs
9.9 Ultrabroadband optical parametric amplifiers
using noncollinear phase matching
9.10 Optical parametric chirped-pulse amplification (OPCPA)
[5] Largely follows the review paper by G. Cerullo et al., “Ultrafast Optical Parametric Amplifiers,” Rev. Sci. Instrum. 74, 1-17 (2003)
Nonlinear Optics (WiSe 2017/18) Lecture 14: December 5, 2017
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Frequency wp
Spe
ctru
m
0 wi ws
9 Optical Parametric Amplifiers and Oscillators
9.1 Optical Parametric Generation (OPG)
energy conservation:
momentum conservation:
Degeneracy: wi=ws=wp/2
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pump
signal and idler resonant
Optical Parametric Oscillator (OPO)
double resonant:
single resonant: only signal resonant
Advantage: Widely tunable, both signal and idler can be used!
For OPO to operate, less gain is necessary in contrast to an OPA
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Total field: pump, signal and idler:
Nonlinear Optical Susceptibilities
Drives polarization in medium:
Polarization can be expanded in power series of the electric field:
Defines susceptibility tensor:
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Special Cases
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9.2 Continuous-wave OPA
Wave equation :
Include linear and second-order terms:
Changes group and phase velocities of waves
Nonlinear interaction of waves
Wave amplitudes
z-propagation only:
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Slowly varying amplitude approximation:
Separate into three equations for each frequency component:
Introduce phase mismatch:
and effective nonlinearity and coupling coefficients:
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Coupled wave equations:
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Manley-Rowe relations:
Intensity of waves:
X
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9.4 Theory of Optical Parametric Amplification
Undepleted pump approximation:
with:
gain max. gain, when phase matched
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Maximum gain
General solutions:
Here:
For large gain:
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Figure of merit:
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Fig. 9.3 Parametric gain for an OPA at the pump wavelength lp = 0.8 mm and the signal wavelength ls = 1.2 mm, using type-I phase matching in BBO (deff = 2 pm/V).
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Fig. 9.4 Parametric gain for an OPA at the pump wavelength lp = 0.4 mm and the signal wavelength ls = 0.6 mm, using type-I phase matching in BBO (deff = 2 pm/V).
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9.4 Phase Matching
Type I: noncritical
Uniaxial crystal: ne < no
Type I: critical
Fig. 9.6 Type-I critical phase matching by adjusting the angle θ between wave vector of the propagating beam and the optical axis.
Fig. 9.5 Type-I noncritical phase matching.
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9.4 Phase Matching
Critical Phase Matching
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Fig. 9.7 Angle tuning curves for a BBO OPA at the pump wavelength λp=0.8 μm for type-I phase matching (dotted line), type-II (os + ei → ep) phase matching (solid line), and type-II (es + oi → ep) phase matching (dashed line).
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9.4 Phase Matching
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Fig. 9.8 Angle tuning curves for a BBO OPA at the pump wavelength λp=0.4 μm for type-I phase matching (dotted line), type-II (os + ei → ep) phase matching (solid line), and type-II (es + oi → ep) phase matching (dashed line).
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9.5 Quasi Phase Matching
Fig.12.30: Variation of deff in a quasi phase matched material as a function of propagation distance.
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9.6 Ultrashort-Pulse Optical Parametric Amplification
Pulse envelopes
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Temporal walkoff Group Velocity Mismatch (GVM)
Pump pulse width
Fig. 9.9: Pump-signal (δsp) and pump-idler (δip) group velocity mismatch curves for a BBO OPA at the pump wavelength λp=0.8 μm for type-I phase matching (solid line) and type-II (os + ei → ep) phase matching (dashed line).
j=s,i
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Fig. 9.10: Pump-signal (δsp) and pump-idler (δip) group velocity mismatch curves for a BBO OPA at the pump wavelength λp=0.4 μm for type-I phase matching (solid line) and type-II (os + ei → ep) phase matching (dashed line).
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Fig. 9.11: Signal pulse evolution for a BBO type-I OPA with λp = 0.4 μm, λs = 0.7 μm, for different lengths L of the nonlinear crystal. Pump intensity is 20 GW/cm2. Time is normalized to the pump pulse duration and the crystal length to the pump-signal pulse splitting length. [5]
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Figure 9.12: Signal pulse evolution for a BBO type-I OPA with λp = 0.8 μm, λs = 1.5 μm, for different lengths L of the nonlinear crystal. Pump intensity is 20 GW/cm2. Time is normalized to the pump pulse duration and the crystal length to the pump-signal pulse splitting length. [5]
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OPA Bandwidth
Bandwidth limitation due to GVM
For signal-idler group velocity matching:
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Fig. 9.13: Phase matching bandwidth for a BBO OPA at the pump wavelength λp=0.8 μm for type-I phase matching (solid line) and type-II (os + ei → ep) phase matching (dashed line). Crystal length is 4 mm and pump intensity 50 GW/cm2.
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Fig. 9.14: Phase matching bandwidth for a BBO OPA at the pump wavelength λp=0.4 μm for type-I phase matching (solid line) and type-II (os + ei → ep) phase matching (dashed line). Crystal length is 2 mm and pump intensity 100 GW/cm2.
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9.7 Optical Parametric Amplifier Designs
Fig. 9.15: Scheme of an ultrafast optical parametric amplifier. SEED: seed generation stage; DL1, DL2: delay lines; OPA1, OPA2 parametric amplification stages; COMP: compressor.
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Near-IR OPA
Fig. 9.16: Scheme of a near-IR OPA. DL: delay lines; WL: white light generation stage; DF: dichroic filter. [5]
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9.8 Noncollinear Optical Parametric Amplifier (NOPA)
Fig. 9.17: a) Schematic of a noncollinear interaction geometry; b) representation of signal and idler pulses in the case of collinear interaction; and c) same as b) for noncollinear interaction.
Phase-matching condition: vector condition:
p
p
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Variation on phase matching condition by
X
X
and addition
Only possible if:
gs gi Correct index
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Fig. 9.18: Phase-matching curves for a noncollinear type-I BBO OPA pumped at λp=0.4 μm, as function of the pump-signal angle a. [5]
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Fig. 9.19: Scheme of a noncollinear visible OPA. BS: beam splitter; VA: variable attenuator; S: 1-mm-thick sapphire plate; DF: dichroic filter; M1 ,M2 , M3 , spherical mirrors. [5]
NOPA Layout
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Fig. 9.20: a) Solid line: NOPA spectrum under optimum alignment conditions; dashed line: sequence of spectra obtained by increasing the white light chirp; b) points: measured group delay (GD) of the NOPA pulses; dashed line: GD after ten bounces on the ultrabroadband chirped mirrors.
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Fig. 9.21: Reconstructed temporal intensity of the compressed NOPA pulse measured by the SPIDER technique. The inset shows the corresponding pulse spectrum. [5]
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MgO:PPLN 31.0µm
MgO:PPLN 13.1µm
DCM
Nd:YLF regen amp @1047nm
120ps, 1 mJ @1kHz
OPA 1
YDFA
2pJ, 2.0µm, 5.0 ps 100µJ
Si
30 mm
>200 µJ
suprasil
300 mm
10 nJ, 6.7 ps
MgO:PPSLT 31.4µm
OPA 2
3.5mJ
AOPDF
Si
30 mm
BBO
OPA 3
400µJ
2 Nd:YLF-MPS modules 120ps, 6mJ @1kHz
12 ps, 4 mJ 800 nm OPCPA 800 nm OPCPA
YDFA
120ps
Grating Pair Compressor
CFBG stretcher Circulator
Ti:S oscillator
2-µm OPCPA
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9.9 Optical Parametric Chirped-Pulse Amplifier (OPCPA)