On the optimal design of 2 nonlinear laser sources

1
On the optimal design of ? (2) nonlinear laser
sources

• Lecture by
• Jean-Jacques Zondy
• BNM-SYRTE, Observatoire de Paris
• www.obspm.fr

European Graduate College Workshop, Harz, Germany
(21-23 June 2004)
2
Introduction

• Imperfect spectral coverage by available primary
  lasers

?
Mid-IR
VIS
NIR
UV-Blue
(um)
0.2
0.5
0.7
2
10
1
5
gas
Dye lasers
SSL
TiSa
(tunable)
RE, TM
semi-conductors
CrZnSe
NdYAG
Many gaps
Parametric generation in NLO crystals

• UV-Blue upconversion (SHG, SFG) of SSL or
  diode
• MIR downconversion (DFG, OPA, OPO)

Applications laser cooling, spectroscopy,
printing, RGB color display
3
?(2) frequency conversion processes in
non-centrosymmetric media (3-wave mixing)
SHG / SFG
???
Pump laser ?
OPG, DFG, OPO
?s
Pump laser ?p
?s
Signal wave
?i
?(2)
Idler wave
?i

• Energy / momentum conservation ?p ???s ?i
  kp ks ki
• Single-pass conversion efficiency very low,
  especially for downconversion processes amplific
  ation

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Case of upconversion (SHG, SFG)

• For VIS-UV generation, cw regime
• singly-resonant (pump-enhanced) or doubly
  resonant

Performance in terms of conversion efficiency
depends on
a) NLO crystals properties (nonlinearity, loss,
phase-matching properties) b) Resonator parameters
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Outline of the lecture

• Choice of the ? (2) optical material
• ( from UV to mid-IR )
• Phase-matching considerations
• ( birefringence PM, QPM, Poynting walkoff )
• Single-pass conversion efficiency
• ( focusing or aperture functions h )
• Enhancement resonator optimization
• ( mode impedance matching, thermal effects )
  
• Resonator design ( linear or ring cavity ? )
• Cavity length servo ( SL, HC, PDH, FM-AM )

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I. Choice of the nonlinear optical materials

• Available NLO materials versus wavelength

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VIS-UV generation using birefringence
phase-matching
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VIS-UV generation using quasi phase-matching
(periodic reversal of ?(2) sign)

• oxide ferroelectrics can be polarization
  domain-inverted

Possibility to tailor any phase-matching

• PPLN, PPKTP, PPRTA commercially available
• pp-LiTaO3, pp-KNbO3 more restricted

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b) Is the nonlinear coefficient a determining
criterion for conversion efficiency?

• YES for single-pass frequency mixing
• typically for 1W laser power nW to mW SH
• NO for cavity-enhanced frequency mixing
• small nonlinearity can be compensated for by
  the build-up Q-factor of the resonant waves

However, the larger ? (2) the better when
nonlinear loss exceeds passive cavity loss, the
intra-cavity FF power is lower ( less thermal
effects )
c) Absorption loss determines the Q factor of
the resonant wave(s)
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Material criteria

• choosing a material which
• satisfies phase-matching for the 3 waves with
  lowest walkoff
• has the lowest possible loss at the resonant
  wave(s)
• has the lowest thermal figure-of-merit ?
  (dn/dT)/Kc (thermal lensing) and highest cw
  damage threshold ( MW/cm2)
• has the largest effective nonlinearity

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Reference textbook for NLO materials

• V.G. Dmitriev, G.G. Gurzadyan, D.N. Nikogosyan,
  Handbook of Nonlinear Optical Crystals,
  Springer-Verlag

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• Birefringence phase-matching
• Quasi phase-matching

Objective increase interaction length in the
medium by adjusting the proper phase relationship
among the waves
Phase-matched case (?k0) constructive
interference between polarization wave and SH
Non phase-matched case Back-and-forth conversion
every coherence length
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Type-II SHG
Normalized propagation distance
Phase-mismatch parameter
Internal wavevectors
Plane-wave, undepleted pump
The generated wave (SH) growths up efficiently
along z only if ?k ? 0
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A. Birefrigence phase-matching

• The PM condition ?k0 can be realized for (?3
  ?1 ?2) taking profit of the two sheets of index
  surfaces (o and e) in birefringent media

Phase-matching matching the phase velocities of
the 3 waves
NB in pulsed regime, group velocity matching
also is required
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Light Wave Propogation in Anisotropic
(Birefringent) media

• Birefringent medium
• 1 optical axis (uniaxial)
• 2 optical axes (biaxial)

Fresnel equation

• 2 orthogonally-polarized modes of propagation
• n-(???) slow index n(???) fast index

ordinary
Principal dielectric frame
? 0 non-critical PM (?90) (NCPM)
extraordinary
Walkoff impedes overlap of the 3 waves
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• Phase-matching condition
• possible for a suitable choice of polarization
  for each of the waves
• (ordinary o or extraordinary e n?(???)
  in biaxial crystals)

• In biaxial crystal, extended phase-matching
  capabilities (in-and-out principal planes)

?1 gt ?2 gt ?3

• Convention

Type-I o1o2 gt e3 e1e2
gt o3
Type-II o1 e2 gt o3
e1 o2 gt o3 e1 o2 gt
e3
Walkoff angle in uniaxial or principal plane of
biaxial crystals
sin 2?
Effect of walkoff on efficiency more critical in
type-II coupling
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Angular acceptance bandwidth tolerance on ?k0
around PM direction
Critical phase-matching
Angular bandwidths in LiInS2 (type-II SHG _at_
?2.6?m)
Ex UV generation in 7mm BBO (n1.65) ???lt 0.1
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B. Quasi phase-matching

• More flexible than accidental birefringence PM,
  no walkoff
• QPM only possible in ferro-electric materials
  (KTP, LN, KN, LT)
• Spatial periodic reversal of the sign of ?(2)
  (polarization grating) results (in Fourier
  K-space) in a discrete wavevector harmonics ?k
  ???c

(c)

• ? 0 ( eee )
• PM tailoring

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III. Single-pass SHG nonlinear conversion
( in unit of W-1 or W/W2 )

• Useful parameter for cavity enhanced optimization
  because determines the nonlinear loss on the FF
  resonating field.

b) walkoff-compensation schemes UV generation
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Focusing functions h for SHG

• In cw undepleted pump regime P?(LC) ? P?(0)

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• for type-II, additional attenuation term ?2
  (worse overlap of o and e FF waves)

For NCPM or QPM ( ? 0 ) , waist location at
center ( f L / 2 )
When linear FF and SH absorption is accounted a
(?? ????/ 2 ?zR
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Optimized focusing/walkoff function h(B,L)(over
?k, fC)
Walkoff is more critical for type-II in terms of
efficiency!!
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Geometric effect of walkoff vs interaction type
Walkoff compensation techniques can be used to
improve wave overlap at identical interaction
length (e-wave guiding by birefringence)
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• Case of optically-contacted 2N-OCWOC periodic
  structures
• Zondy et al, Proc. SPIE 2700 (1996)
• French Patent N 96 01 197 J.-J.
  Zondy / Cristal Laser SA (1997)

(a)
(a) Sketch of the fabrication of 2N-OCWOC
structures, showing the geometrical walkoff
compensation effect on an e-ray path (N3 unit
cells). (b) photograph of the 10-OCWOC structure
(left) and the withness bulk crystal (right).
The (X) principal axis of KTP points in the
vertical direction from Zondy et al, J. Opt.
Soc. Am. B 20, 1695 (2003)
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3. Theory of SHG with 2N-OCWOC structures Zondy
et al, J. Opt. Soc. Am. B 20, Part I II (2003)

• No Fresnel loss at interfacets
• WOC ?k, -?k, ?k,
• Unavoidable small Dk orientation
• mismatches from plate to plate (? ?i)
• in practical structures
• Ideal structures (no orientation mismatches)

M
M
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N 5
hnum
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Experimental check with type-II (oee) KTP cw SHG
(10-OCWOC structure)
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Advantage of 2N-OCWOC for type-I CPM SH beam
quality
10-OCWOC sample circular SH shape
Type-I (ooe) blue SHG with BBO-OCWOC
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IV. Enhancement resonator operationtheoretical
background

• Cavity equations for the FF and SH fields
• Exact propagation model
• Simplified mean-field model (quasi-stationary)

• b) Thermal effects limitations
• thermal lensing
• nonlinear losses (BLIIRA, GRIIRA, TPA)

c) Optimal focusing or loose focusing ?
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Exact propagation model for cavity-enhanced SHG

• Ring-cavity model

? cavity round-trip length ? cavity
round-trip time ?n cavity detuning

• Iterative solutions until convergence (numerical
  split-step method)
• single or double resonance

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Plane-wave mean-field model
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Stationnary simplified (MF) model Ashkin et al,
IEEE J. Quant. Electron. QE-2 (1966)
Evaluate cavity enhancement factor Pc/Pin
mode-matched input power
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Singly-resonant SHG result Kozlovsky et al,
IEEE J. Quantum. Electron. 24, (1988)
In addition to FF field passive RT loss, one has
to account for nonlinear loss
From this stationnary, zero-detuning equation ?
conversion efficiency
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Doubly-resonant SHG results Ou et al, Opt.
Lett. 18, (1993)

• DR-SHG is useful for the conversion of low power
  laser sources

( resonance of SH ? nonlinearity enhancement )
For T1, e1 ltlt 1, SR-SHG ???
For T1,2, ?1,2 ltlt 1, DR-SHG ???
where

• 6?10-5 W-1 ?1 0.017

DR-SHG difficulty simultaneous control of FF and
SH cavity resonance
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b) Thermal effects limitations Douillet et al,
J. Opt. Soc. Am. B 16 (1999)

• Strong focusing often results in deleterious
  thermal effects due to residual absorption by the
  crystal

• Radial temperature gradient

• Thermo-optic effect

• Moving cavity resonance

Thermo

• Dynamic cavity fringe shape

d0
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This opto-thermal coupling can lead to curious
passive resonator length self-stabilization
effects on the contracting length side of the
triangular hot fringe

• Analysis of the hot cavity dynamics shows that
  any acoustical noise dithering the optical path
  is corrected by the thermo-optic effect, with a
  passive (proportional) servo gain of G D.

d effective cavity detuning with respect to
laser frequency
d
g
Gain is maximum at the inflexion point of the
Lorentzian fringe and nil on top bistability
at the maximum intracavity power!
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Thermal lensing

• The absorption of power Pabs awLcPc induces a
  thermal lens power

( even for aw lt 1/cm, lens focal length a few
cm )
which dynamically modifies the cold cavity
mode-matching conditions
Part of the input laser power is reflected by the
cavity
Crystal facets
Thermal lensing can be partially compensated for
by a proper cavity design
For a linear symmetric resonator, there is a
critical power for beam collapse
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• To contend thermal lensing avoid too strong
  cavity focusing when G is large as in PPKTP or
  PPLN

• Example PPKTP (20mm) for SR_SHG _at_ 922nm

• With PP materials, it is detrimental to focus at
  optimal focusing ! Better use a longer crystal
  and loose focusing to obtain nearly identical
  theoretical conversion efficiency.

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Other thermally-induced phenomenon

• BLIIRA Blue induced IR absorption. Absorption of
  blue photons induces absorption loss at the
  pump (KNbO3)
• GRIIRA Green induced IR absorption (LiNbO3)
• Photo-refraction ( in most of the ferro(electric
  compounds, except KTP). Absorption of VIS at room
  temp. Solution heating.
• TPA 2-photon absorption (mostly in pulsed
  regime). Rules
• 2w photon energy must correspond to energy
  much lower than the material bandgap energy
  (UV cutoff wavelength)

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V. Enhancement resonator design

• Estimate RT passive loss e from mirror coatings
  specification and known crystal loss (including
  AR loss)

• Linear or ring cavity? Ring design should be
  preferred because minimizes RT passive loss and
  avoid phase interference effects in the nonlinear
  process.

• Mirror design
• Using ABCD formalism, once w0 is determined from
  above, evaluate required curved mirror ROC and
  total resonator length L. Check that w0 can be
  varied within 50-100 by changing the cavity
  geometrical distances.
• Curved mirrors meniscus shape preferred for SH
  beam divergence.

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• Mirror coatings design
• Output meniscus dual-band AR (HR_at_ w and HT_at_2w)
• Dual-band AR _at_ w, 2w for all front sides.

• NLO crystal sample parallelepipedic or Brewster
  cut?
• Avoid if possible Brewster cut and opt for a
  dual-band AR-coated sample. Small error in
  Brewter angle can be dramatic ! (e.g. additional
  spurious loss).
• Calculate PM angular bandwidth and check
  compatibility with focused beam divergence Dq gt
  d0 .
• Minimize transverse extension r0 of sample to
  repel onset of thermal lensing.
• Prefer PP material to bulk CPM material if
  possible.
• Bulk BPM material prefer type-I over type-II (if
  not possible, RT phase compensation between o and
  e waves must be implemented)

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Type-II BPM intracavity phase-compensation
Zondy et al, J. Opt. Soc. Am. B 11 (1994)
Intra-cavity Wave Plate(s) jRT(e) - jRT(o) 2kp
WOC arrangement also allows birefringence phase
compensation
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Resonator length active servo

• The cavity length must be stabilized with respect
  to laser resonance to counter-act external
  perturbations ( mechanical, acoustical, thermal)
  of the cavity optical path length. Locking
  schemes

• Hänsch-Couillaud Hänsch et al, Opt. Commun. 35,
  (1980) optically phase-sentitive, takes
  advantage of the medium birefringence to derive a
  dispersive error signal. Simple but fails under
  strong thermal effects.
• Pound-Drever-Hall Drever et al, Appl. Phys. B
  31, (1983) phase modulation of the laser.
  Advantage wide servo bandwidth. Expensive and
  more complex.

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• AM-FM lock simple to implement, robust,
  recommended.

• dither cavity length or laser frequency at a
  frequency 100 kHz (10 times required BW)
• demodulate amplitude using a lock-in amplifier
• provide a dispersive error signal when d is
  scanned (derivative of the fringe signal)

wL
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Conclusions

• basic methodology for optimizing a nonlinear
  laser source based on cavity-enhanced SHG
  described.
• Techniques for enhancing NLO materials
  nonlinearity (WOC).
• Operation at optimal focusing as predicted by
  focused beam SHG theories not necessarily
  relevant.
• Conversion efficiency gt 70 for G gt 10-4 W-1
• For smaller G (BBO, LBO,), impedance matching is
  critical and may lead to modest efficiencies
• Efficiency ultimately limited by deleterious
  thermal effects.
• Same methodology for SFG of 2 laser sources.