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Lecture 4 The role of QuasiPhaseMatching in Parametric Devices plus Brightness enhancement via param

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Title: Lecture 4 The role of QuasiPhaseMatching in Parametric Devices plus Brightness enhancement via param


1
Lecture 4The role of Quasi-Phase-Matching in
Parametric DevicesplusBrightness enhancement
via parametric amplification
  • David Hanna
  • Optoelectronics Research Centre
  • University of Southampton
  • Lectures at Friedrich Schiller University, Jena
  • July/August 2006

2
Phase matching for second harmonic (SH) generation
z l
z 0
z
Fundamental field (?1) at z
SH (?2 2?1) polarisation of the medium, at z
SH field, at z l radiated by SH polarisation
at z
If all SH field contributions, for z from 0 to l
, are to add in phase, one needs ?k k2 2k1
0 (phase-matching)
ie n1 n2
3
Calculation of total field, ESH, at exit (z l)
from nonlinear medium
Here ?kz p, so SH field generated at z is p out
of phase with SH field generated at z 0
Non phase- matched
z
ESH(z)
Phase-matched
ESH
Phase-matched
Length of each phasor
Non phase-matched
Phase angle, relative to SH wave launched at z 0
z
3lc
lc
2lc
4lc
4
Principle of quasi-phase-matching
Ensure that the contribution to generated field
from each coherence length does not cancel with
that from preceding lc e.g. modulate c(2) between
adjacent coherence lengths
ESH
5lc
ca cb ca cb ca cb
3lc
4lc
lc
lc
period 2lc
2lc
l
lc
2lc
3lc
z
ca gt cb
5
Some quasi-phase-matching schemes
  • Periodic E field (via segmented electrode)
    field-induced ?(2)
  • Frozen-in field-induced ?(2), in optical fibres
  • Periodic destruction/reduction of nonlinearity,
    eg via ion-implantation through a
    mask
  • Overgrowth on a template having periodic
    modulation of substrate orientation
    (orientation-patterning, eg OPGaAs)
  • Periodic modulation of pump intensity (eg use
    corrugated capillary waveguide for High Harmonic
    Generation)
  • Fresnel birefringence via periodic TIR in a
    thin plate
  • Periodic-poling of ferroelectrics, switching
    ?(2) ? - ?(2)

6
Quasi-phase-matching condition
Grating period is D, hence grating wave-vector,
DkG, is
Nonlinear grating of period 2lc
period 2lc
(Phase- mismatch)
ie. Quasi-phase-matching requires Dk DkG So,
instead of making Dk zero, we make Dk Dk
DkG 0
Generalisation If any nonlinear parametric
process has a phase-mismatch Dk, impose (somehow)
a periodic modulation on the nonlinearity, with
wavevector, DkG such that NDkG Dk where N
is the QPM order
7
Higher order QPM
4lc, 6lc
3rd order
lc, 3lc, 5lc
period
3lc
3lc
3lc
3lc
period
One period (6lc) produces the net effect of 2lc
3x smaller ceff
Advantage larger scale pattern, easier to
fabricate Disadvantage effective nonlinear
coefficient for Nth order QPM is reduced by N
8
Quasi-phase-matching condition
?
If has 50/50 duty cycle
then
If
where
i.e. Dk 0 , QPM condition
9
Quasi-phase-matching condition
Nonlinear process Conventional phase-match
condition Phase-mismatch QPM condition (Nth
order QPM)
?3 ?2 ?1
k1
k2
k3 k2 k1
k3
?k k3 - k2 - k1
k1
k2
N?kG
?k N ?kG
k3 k2 k1 N?kG
k3
Note if QPM grating is tilted, eg to tune its
effective period, the interaction is necessarily
non-collinear e.g. SHG 1st order
k2
?kG
k1
k1
10
Some benefits of QPM
  • Access materials having too low a birefringence
    for
  • phase-matching, e.g. LiTaO3, GaAs
  • Ability to phase-match any frequencies in the
    transparency range,
  • freedom to choose ideal pump for an OPO
  • Non-critical (90) phase-matching,
  • allows tight (confocal) focussing
  • Access to largest nonlinear coefficient,
  • e.g. d33 in LiNbO3

11
Fabrication of Periodically Poled Lithium Niobate
Lithium niobate crystal
Photoresist
Conducting gel
Constant current HV source
0.51mm
50mm
12
Attractions of photolithography for QPM grating
fabrication
  • Precise control over grating period
  • Fast processing over whole wafer
  • Allows complex grating patterns
  • fan-out gratings
  • different gratings on same wafer
  • tandem gratings
  • controlled distribution of deff
  • aperiodic, e.g. chirped gratings
  • 2-D gratings

13
Periodically Poled Lithium Niobate Crystal
Acknowledgements to Peter Smith, Corin Gawith and
Lu Ming ORC, University of Southampton
14
PPLN tuning via grating period and temperature
31
?p 1047nm, crystal length 2cm
PPLN grating period (µm)
30
Tuning of gain peak from 140ºC to 180ºC FWHM
bandwidth at 160ºC.
29
2.0
2.1
1.6
1.7
1.8
1.9
1.5
Wavelength (µm)
15
Various grating designs
Angle-tuned cylindrically polished crystal
Multiple grating
Fan-out grating
GQPS (Generalised Quasi-Periodic-Structure) APOSL
(Aperiodic Optical Superlattice)
Tandem gratings, sequential processes
?2??3?
???2?
16
Various grating designs
Nonlinear physical optics with transverse-patterne
d QPM gratings
Transverse modulation of deff
Chirped grating
2-D nonlinear photonic crystal, e.g. HXLN
Odd waveguide mode QPM with angled staggered
gratings
17
Frequency-conversion efficiency and parametric
gain in PPLN
SHG conversion efficiency, confocal focus (l b
2p wo2n1/?) (?1? 2?1) 16p2P(?1)d2eff
l/c?0n1n2 ?13
SHG, 1064nm ? 532nm or Parametric gain
532nm ? 1064nm
2/ Wcm (deff 17pm/V)
(Waveguide enhancement by l?/2nw2 102 -103
gt1000/ Wcm2) Parametric gain, 1µm ? 2µm,
0.25 / Wcm (PPLN) 2µm ? 4µm, 0.5 / Wcm
(GaAs)
18
Minimum pump energy for 1µm pumpedPPLN
parametric devices
  • CW SRO 1-3W
  • Nanosecond-pumped OPO 5 µJ
  • Synchronously-pumped OPO 100pJ
  • (10 mW _at_ 100 MHz)
  • Optical parametric generator 100nJ (fs/ps)
  • 100µJ (1 nsec)

130 dB gain
All power/energy values scale as (d2/n2?3 )-1
19
cw singly-resonant OPOs in PPLN
  • First cw SRO Bosenberg et al. Opt.Lett., 21,
    713 (1996)
  • 13W NdYAG pumped 50mm Xtal, 3W threshold,
    gt1.2W _at_ 3.3µm
  • cw single-frequency van Herpen et al.
    Opt.Lett., 28, 2497 (2003)
  • Single-frequency idler, 3.7 ? 4.7 µm, 1W ? 0.1W
  • Direct diode-pumped Klein et al. Opt.Lett., 24,
    1142 (1999)
  • 925nm MOPA diode, 1.5W threshold, 0.5W _at_ 2.1µm
    (2.5W pump)
  • Fibre-laser-pumped Gross et al. Opt.Lett., 27,
    418 (2002)
  • 1.9W idler _at_ 3.2µm for 8.3W pump

20
Some results from PPLN ps/fs parametric devices
  • Low threshold SPOPO
  • 7.5 mW (av), 1047nm pump, 4ps, _at_120 MHz
  • 21mW, pumped by Yb fibre laser
  • High gain devices (at mode-locked rep. rate)
  • Widely-tuned SPOPO, idler gt7µm
  • OPCPA, 40 dB gain, mJ output
  • OPG operated at 35 MHz, 0.5W signal
  • High average power femtosecond SPOPO
  • 19W (av) signal _at_ 1.45 µm, 7.8W _at_ 3.57 µm

21
Nanosecond QPM OPOs
  • Threshold of few micro joules for PPLN
  • Wide tunability, idler gt5.5 µm in PPLN
  • Few hundred µJ output typical
  • (30 mJ demonstrated with PPLN stack)
  • QPM GaAs 2-9 µm covered so far
  • threshold 16 µJ

22
Why GaAs?
  • Large nonlinearity, d14 100pm /V
  • Extensive transparency, 0.9 µm - 17 µm
  • Mature technology
  • But, how to make a QPM structure ?

23
Orientation-patterned GaAs OPGaAs
Patterned photoresist
Etch through Ge layer
GaAs growth of opposite orientation
Remove photoresist
Ge buffer layer
Regrowth of GaAs matching the underlying GaAs
orientation
Oriented GaAs substrate
24
Difference-frequency generation of 8 µm
radiation in orientation-patterned GaAs
O.Levi et al Optics Letts, 27 2091, (2002)
  • QPM GaAs 20x5x0.5 mm
  • period 26.3 µm, for first-order QPM
  • estimated loss 0.05 cm-1
  • Experiment mix cw 1.3 µm and 1.55 µm,
  • to generate 8 µm
  • Result agreement within factor of 3 between
    measured
  • output power and calculation based on d14
    105pm/V

25
OPO in QPM GaAs
Threshold 16 µJ in 6 nsec gt50 photon conversion
slope efficiency
Vodopyanov et al., Optics Letts., 29,1912, (2004)
26
Optical parametric generation of a mid-IR
continuum in orientation-patterned GaAs
OPG output spectrum, 3.28µm pump,1ps,1.4µJ
Very broad gain band-width via phase-matching for
degeneracy, with pump-wavelength ?/2 where ?
corresponds to the GV max., i.e. where d2k/d?2 is
zero
Kuo et al Optics Letts., 31, 71, (2006)
27
QPM waveguide devices
  • Blue SHG at high conversion efficiency in
    MgOLiNbO3
  • 852nm ? 426nm, 1500/Wcm2 in 10mm guide
  • 55mW ? 17.3mW
  • Sugita et al Optics Letts. 24, 1590 (1999)
  • High Efficiency SHG in 1550nm communication band
  • 1536nm ? 768nm, in 3.3cm PPLN guide
  • 150/Wcm2, 1600/W
  • Parameswaran et al Optics Letts. 27, 179
    (2002)
  • Predict 10dB signal gain at 1550nm, for
  • 115mW of pump at 775nm in 6cm guide

28
Multiple-channel wavelength-conversion via
engineered QPM structures in LiNbO3 waveguides
Chou et al, Optics Letts 24, 1157 (1999)
?in
?out1
?P1/2
Phase reversal sequence
Uniform QPM grating
Multiple channel QPM structure
?P2/2
?out2
More channels via extra phase-reversal sequences
and tailored duty cycle
29
Engineerable fs pulse-shaping by SHG with Fourier
synthetic QPM gratings
Imeshev et al Opt. Letts. 23, 864 (1995)
Autocorrelation signal
(a)
(a)
(b)
(b)
(c)
(c)
-10
-5
0
5
10
Time (ps)
30
Pulse compression during second harmonic
generation in aperiodic quasi-phase-matched
grating
Arbore, Marco Fejer, Optics Letts. 22, 865
(1997)
I2(z)
I1(z)
Chirped QPM grating
Z
Z
  • Leading edge converts to SH at grating entrance,
    and so travels more slowly than trailing edge
    which converts near exit.

31
Generation of sub-6-fs blue pulses by frequency
doubling with QPM gratings
310mm PPLT crystal
Nonlinearly-chirped grating, Periods from 6.5mm
to 1.8mm 405nm SH pulse, 5.3fs Conversion,
0.5 /nJ
12.7fs
Cross-correlation
-60
-40
-20
20
40
60
0
Delay (fs)
Gallman et al Opt. Letts. 26, 614, 2001
32
Tandem-chirped OPA grating design for
simultaneous control of group delay and gain
control
  • Chirped grating 1 produces idler with
    frequency-dependent group delay
  • Idler from grating 1 acts as signal for grating
    2, hence idler from 2 has frequency of
    original signal
  • Grating 2 compensates group delay dispersion of
    grating 1

Charbonneau-Lefort et al., Opt. Letts.,
30,634,(2005)
33
Future agenda for QPM
  • GaAs, GaN etc.
  • Power scaling, eg with fibre laser pumps
  • Larger transverse dimensions
  • UV materials

34
Brightness enhancement via parametric processes
  • A range of pump-wave directions can drive a
    single signal-wave in a specific direction, i.e.
    a multi-transverse mode pump can drive a single
    transverse mode signal
  • This offers the possibility of brightness
    enhancement, or brightness-scaling, i.e. the
    signal can be brighter than the pump
  • Since there is, in principle, no heat input to
    the medium, what sets a limit to the practical
    extent of scaling.
  • Here we first establish the angular acceptance
    range of the pump and relate this to the M2
    value of the pump
  • Then we examine some estimates of performance
    potential

35
Angular acceptance of pump I
Angular acceptance determined by the
phase-mismatch, ?k, that can be tolerated
?k
kp
ki
?
ks
ki
kp
  • ?kL p sets limit to ?
  • Next relate ?k to ?

?k
36
Angular acceptance of pump II
  • Set ?kL p to find ? max
  • If ?p ?s ?i 3 2 1,
  • internal angle
  • ie. external angle
  • This is the acceptance (half-) angle for the pump

37
Beam quality M2
  • Divergence of TEMoo mode is ? /pwo
  • Divergence of overall beam is M ? /pwo M2(?
    /pWo)
  • Divergence is M2 greater than for a
    diffraction-limited beam

38
Confocal focussing for a multimode beam (M2)
  • To focus a gaussian beam confocally, in a medium
    of length L,
  • set the waist spot size, w0, to satisfy
  • 2pw02n/? L
  • To confocally focus a multimode beam (M2), in
    length L of medium ,
  • set the waist size, W0 (Mw0), to satisfy,
  • 2pW02n/M2? L
  • i.e. beam diameter, D (2W0), is given by
  • D2 M2(2L?/pn)

39
Allowable pump M2 for a parametric process
  • If pump beam diameter Dp, divergence for
    diffraction-limited
  • beam is (?p/Dp), hence allowable pump M2 is
    ?max,ext/(?p/Dp)
  • This gives
  • Equivalently this equation gives the minimum pump
    diameter that
  • allows the entire pump power to drive a sigle
    signal mode, i.e.
  • Dp2 (M2p,3,2,1)2 (3L?p/2n)
  • Note this is not confocal focussing it
    corresponds to a spot-size which is M times the
    confocal (multimode ) spot-size

40
Effect of pump M2 on OPO threshold I
  • Threshold Dp2 provided Mp2 does not exceed
  • But this max. M2 scales as Dp
  • so minimum threshold pump brightness,
    Pp/(M2)2?p2,
  • needed to reach threshold, is independent of Dp

41
Effect of pump M2 on OPO threshold II
  • If some particular pump enables OPO threshold to
    be achieved,
  • a combination of identical, mutually incoherent
    pump beams,
  • side-by-side, will also reach threshold for a
    single-mode signal extending over the entire
    composite pump beam.
  • (Composite beam has same brightness as
    individual beams)
  • Recipe for power-scaling of OPO
  • But no heat input

? Recipe for brightness-scaling
42
Prospects for brightness-scaling via cw OPO
  • Example paper exercise
  • Scale from results of Gross et al, for a cw
    fibre-laser-pumped OPO
  • (Optics Letts., 27, 418, (2002))
  • Actual experimental performance
  • Yb fibre laser, 1µm wavelength
  • PPLN crystal, 40mm long
  • Maximum pump beam diameter 200 µm
  • Threshold 3.5W
  • Maximum output 2W (idler, 3µm ) for 8.3W pump

43
Power- and brightness-scaling of a cw PPLN OPO
paper exercise
8W fibre laser, 250µm diameter beam, 40mm PPLN ?
2W _at_ 3.2µm
1mm x 1mm PPLN aperture would allow 16x power
scaling 3mm x 10mm PPLN slab would allow 500x
power scaling ie 1kW _at_ 3.2µm from 4kW pump ?T for
idler absorption 0.1/cm, 0.5oC
(?Tacceptance 5 oC)
Need 4(M2)2W of pump power to reach threshold
For slab, this needs 2kW pump, with M2(12) x
M2(40).
4kW pump _at_1µm, M2(40x12) ?1kW _at_ 3µm, M2(1x1)?10x
Brightness
44
Brightness enhancement via pulsed OPO/OPA
  • Pulsed operation allows high gain from a
  • wide range of nonlinear materials
  • Nanosecond pulsed operation of OPO resonator
  • designed to select large signal TEMoo mode
  • Can use multimode fibre as pump source
  • Use multimode ps/fs pulses to drive
  • synchronously pumped OPO, or OPA

45
Brightness enhancement via pulsed OPA
  • For short pulse amplification, need short pump
    pulse
  • (commensurate duration, pump and signal)
  • For high energy need long pump pulse
  • Solution stretch (chirp) the signal pulse to
    match
  • the pump pulse length
  • Optical Parametric Chirped Pulse Amplification
  • OPCPA

46
Parametric chirped pulse amplification
Amplified signal
(multimode) Pump
Compressor
OPA
Compressed diffraction-limited signal
1nsec 250µJ, M23
20mm PPLN
M21, 60µJ (106 gain)
Pulse stretcher
fs laser
Stretched (chirped) signal pulse
10-10J
Galvanauskas IEEE J Sel Topics in QE, 7, 504,
(2001)
47
Concluding comment
  • The absence of thermal input in parametric
    processes is potentially one of the strongest
    attractions.
  • However this potential still remains largely
    unrealised.
  • The true capability for power-scaling and
    brightness-scaling via parametric devices needs
    to be subjected to experimental scrutiny, for a
    wide range of operating conditions and materials
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