Harald Schneider Institute of Ion-Beam Physics and Materials Research Semiconductor Spectroscopy Division Rosencher s Optoelectronic Day Onéra 4.05.011 Optical Nonlinearities in Quantum Wells Harald Schneider Helmholtz-Zentrum Dresden Rossendorf Institute of Ion-Beam Physics and Materials Research Dresden, Germany
Outline Introduction Optical Rectification Harmonic Generation & Two-Photon Absorption Difference-Frequency Generation Conclusion
Optical nonlinearities in QW: Classification Our focus today: Resonant intersubband (intraband) nonlinearities Not covered (but also interesting): Interband optical nonlinearities CB e e1 Electro-optical effects e.g., quantum-confined Stark effect intensity and phase modulators Excitonic nonlinearities Marginally covered: Mixed interband/intersubband nonlinearities hh1 lh1 hh lh VB 3
Optical nonlinearities involving intersubband transitions Second-order Optical rectification E. Rosencher et al., APL 55 1597 (1989) Second-harmonic generation M.M. Fejer et al., PRL 6, 1041 (1989) Difference-frequency mixing C. Sirtori et al., APL 65, 445 (1994) Sum-frequency mixing H.C. Liu et al., IEEE JQE 31, 1659 (1995) Third-order Four-wave mixing D. Warlod et al., APL 59, 93 (1991) Third-harmonic generation C. Sirtori et al., PRL 68, 1010 (199) Dc Kerr effect A. Sa ar et al., APL 61, 163 (199) Two-photon absorption E. Dupont et al., APL 65, 1560 (1994) 4
ITQW Conference 1991 Cargèse 011 Badesi 5
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often used for nonlinear wavelength conversion integrated with quantum cascade lasers 7 Nature 391, 464 (1998)
Outline Introduction Optical Rectification Harmonic Generation & Two-Photon Absorption Difference-Frequency Generation Conclusion 8
Nonlinear susceptibility () 0,max q T 3 0 N1 N 1 1 T dephasing time 1 1 z 1 z 1 z 1 More than 10 3 higher nonlinearity than in bulk GaAs Additional contribution due to T 1, which is ~10x longer than T! 9
Sainte Chapelle, Paris Little devil who holds the electron at its place, thus preventing it from returning back to the ground state 10
Semiclassical "rectification efficiency" () 0,max 3 q T 0 T dephasing time storage time N1 N 1 1 More than 10 6 higher efficiency than in GaAs! 11
1 Several periods with thick inter-well barriers
From rectification to detection Thin inter-period barriers dc photocurrent! 13
Optimization high absorption strength high escape probability high capture probability small tunneling probability Low-noise QWIP 1: excitation zone : drift zone 3: capture zone 4: tunnel barrier zone no tunneling no thermal re-emission high tunneling probability 14
ENERGY (mev) Parameters and subbands 0 periods 4.8 nm GaAs:Si 4x10 11 cm - 45.0 nm AlGaAs x=0.6 1 excitation zone drift zone 1.8 nm GaAs 3 1.8 nm AlGaAs x=0.6 capt ure 3.0 nm GaAs zone 0.6 nm AlAs 4 1.8 nm AlGaAs x=0.6 t unnel 0.6 nm AlAs barrier 3.6 nm AlGaAs x=0.6 zone 50 00 150 100 50 1 3 4 0 0 0 40 60 80 100 10 POSITION (nm) 15 Appl. Phys. Lett. 71, 646 (1997)
CURRENT (A) Response at 300 K background temperature Photovoltage due to thermal background radiation 10-7 10-8 cold shield T B =300 K, 45 facet T B =300 K, grating (expected) Background limited performance 10-9 10-10 10x10 µm 65 K -4-3 - -1 0 1 BIAS VOLTAGE (V) 16
DETECTIVITY (cmhz 1/ /W) Low-Noise QWIP same D * as for conventional QWIPs both polarities demonstrated other polarity carrier density PC QWIP 8 x 10 10 cm - Low-Noise 4 x 10 11 cm - Photoconductive QWIP " Low-Noise" QWIP in PC mode fit to all data 10 10 77 K 45 facet geometry 0 periods 8.6 8.7 8.8 8.9 9.0 9.1 9. 9.3 9.4 9.5 LONG WAVELENGTH CUTOFF (µm) Physica E 7, 101 (000) 17
640 x 51 Low-Noise QWIP FPA NETD = 9.6 mk 7.4-9. µm f/, 30 ms, 60 K 18 H. Schneider and H. C. Liu, Quantum Well Infrared Photodetectors, Springer 007 AIM
Outline Introduction Optical Rectification Harmonic Generation & Two-Photon Absorption Difference-Frequency Generation Conclusion 19
Nonlinear susceptibility for SHG N1 N 1 3 31 (),max ~ T Dipole moments µ 1, µ 3, µ 31 0 Need asymmetry SHG in step QWs Up to 3 orders of magnitude more efficient than in bulk GaAs 0
High-efficiency SHG conversion possible provided that we can beat the losses 1
Nonlinear susceptibility () 3,max ~ NT1T3T34 1 3 34 41 µ 1, µ 3, µ 34 µ 41 0 T 1, T 3, T 34 dephasing times
Intracavity SHG and THG in quantum cascade lasers 3 T. Moseley et al., Opt. Express 1, 97 (004) C. Gmachl et al., IEEE JQE 39, 1345 (003)
50 µw 80 K 98 K 6 µw Efficiency 0.13 mw/w (RT), 0.04 mw/w (80K), 19 mw/w (theory) Deviation due to higher lateral modes, detuning from resonance, 4
Two-photon absorption TPA coefficient ~, max N D 1 3T 1 ( 3) T dephasing time 1 T e dephasing time associated with state 3 Independent of µ 31 (in contrast to SHG) TPA works with a symmetric QW structure! T e E E 1 E 3 E 3 Semiclassical (analogy with opt. rectification) "Sequential TPA" N D step,max ~ 1 34 1 T 1 lifetime for 1 T 1 T T e E E 1 5
QWIPs with quadratic power dependence Resonant two-photon QWIP 3 1 E 3 - E = E - E 1 Standard QWIP 1 Photocurrent (power) ² stronger signal if two pulses overlap in time photocurrent power density 6
norm. Photocurrent Time Resolution of Two-Photon-QWIP Autocorrelation measurements using 170 fs mid-ir pulses 8:1 peak-to-background-ratio nearly ideal autocorrelation for small delay times Sub-ps time resolution Influence of intermediate state on detector response Oscillations decrease exponentially phase relaxation T Exponential behavior of the "wings intersubband relaxation T 1 8 6 4 0 8 6 4 0-1 0 1 Delay Time (ps) = 10.4µm Bias = 1V T = 77K ideal autocorrelation of 165 fs pulse IR Phys. Technol. 47, 18 (005) 7
Photocurrent (a. u.) Photocurrent (a. u.) Determining T 1 and T by numerical fits 8 6 well doped experimental numerical fit 8 6 modulation doped experiment numerical fit 4 = 10.4 µm Bias = 1 V T = 77 K 4 =10.6µm Bias = 0. V T=70K 0 0.0 0. 0.4 0.6 0.8 1.0 1. Delay Time (ps) well doped mod. doped T 1 530 fs 750 fs T 10 fs 40 fs 0 0.0 0. 0.4 0.6 0.8 1.0 1. Delay Time (ps) 8 Appl. Phys. Lett. 91, 191116 (007)
Signal (arb. units) Signal (arb. units) Quadratic Autocorrelation at Room Temperature 6 4 interferometric intensity autocorrelation 300 K InGaAs/AlGaAs 6. nm QW = 5.4 µm 6 4 EXP FIT 0 0-4 - 0 4-0.0 0.00 0.0 0.04 0.06 Time (ps) Time (ps) Interferometric autocorrelation 6:1 (ideally 8:1) Intensity autocorrelation.:1 (ideally 3:1) Fringes (1-cos) shape FWHM 3.7 ps FEL pulse width.6 ps 9 H. Schneider et al., Appl. Phys. Lett. 93, 101114 (008)
Photocurrent (arb. u.) THz Two-Photon QWIP 8 6 4 Interferometric autocorrelation Intensity autocorrelation = 4 µm 9.5 K, 0.5 V 18 nm GaAs/AlGaAs QWs 6 4 0-0.4 0.0 0.4 0-10 -5 0 5 10 Time Delay (ps) Operation below the Reststrahlenband at 4 µm (7 THz) FWHM 6. ps 4.4 ps FEL pulse width 30 H. Schneider et al., Opt. Express 17, 179 (009)
Interferometric autocorrelation of modelocked QCL C. Y. Wang et al., Opt. Express 17, 1931 (009) Pulse diagnostics Pulse width Chirp Photon correlation 31
3 Autocorrelation of amplified spontaneous emission source
Outline Introduction Optical Rectification Harmonic Generation & Two-Photon Absorption Difference-Frequency Generation Conclusion 33
34 DFG at around 60 µm
3 stacks: DFG region, QCL1 (8.4 µm), QCL (9.5 µm) 100 nw output power (0.5 µw/w external efficiency) at 78 K Up to 100 µw expected after further optimization 35
intensity (counts) THz/NIR nonlinear optics with exciton levels in quantum wells THz sideband generation TiSa NIR FEL FEL Sideband energies sample n = NIR ± n FEL n = 0,±1,±, 15000 100000 75000 50000 5000 n=- *100 n=-1 *1000 FEL energy 8.9 mev NIRlaser /1000 -NIR wavelength 791.9nm -NIR power 30 kw/cm² -FEL-power 13 kw/cm² -efficiency here 0.03% n=+1 *1000 n=+ n=+4 n=+3 *1000 *1000 0 1540 1550 1560 1570 1580 1590 1600 1610 energy (mev) Best efficiency if THz energy is resonant with 1s-p intraexcitonic transition 36 M. Wagner et al., Appl. Phys. Lett. 94, 41105 (009)
Absorption (-log(t)) hh(1s) hh(s/p) lh(1s) High-field physics with FEL: Excitons dressed by THz beams Autler-Townes (AT) effect for intra-excitonic transitions e weak. strong THz field e 1 hh 1 lh 1 exciton 9 mev hh(p) ħ THz hh(1s) hh-exciton Rabi frequency E 1 / Observation of AT splitting interband absorption under intense THz pumping of hh(1s) hh(p) transition 3 1 0 3 NIR Energy (mev) 1560 1580 1600 0 130 0 330 650 THz Peak Intensity (kw/cm²) 37 M. Wagner et al., Phys. Rev. Lett. 105, 167401 (010)
NIR photon energy (mev) energy splitting (mev) Dependence on THz frequency and intensity 157 1568 130 kw/cm² 4.4 kv/cm 6 4 measured linear fit 1564 1560 4 6 8 10 1 14 16 18 0 THz photon energy (mev) Anticrossing experiment model unperturbed exciton As expected from the two-level model also quantitatively! Deviations at very high intensities 0 0 5 10 15 0 5 30 (THz peak intensity) 1/ (kw/cm ) 1/ On-resonance energy splitting (THz peak intensity) 1/ electric field 38 M. Wagner et al., Phys. Rev. Lett. 105, 167401 (010)
Conclusion QW = great system for constructing huge optical nonlinearities Dipole moments on the order of the QW width Model system with taylorable (), (3) Custom-design of resonances for enhanced nonlinearity But still much room for improvements New geometries, e.g., photonic crystal structures for higher efficiency? New concepts, e.g., shorten the "radiatíve lifetime" using a microresonator? Other nonlinearities, e.g., two photon emission? Jamais la nature ne nous trompe; c est toujours nous qui nous trompons. Jean-Jacques Rousseau 39