Nonlinear optics with semiconductor nanostructures. Alexey Belyanin Texas A&M University

Transcription

1 Nonlinear optics with semiconductor nanostructures Alexey Belyanin Texas A&M University

2 TAMU: Debin Liu (graduated in 005) Feng Xie (004-current) Don Smith (005-current) V.R. Chaganti (006-current) Dmitry Pestov U. Krishnamachari (summer exchange) External collaborations: Federico Capasso Dennis Deppe Claire Gmachl Franz Kaertner Jun Kono Oana Malis, Deborah Sivco Dave Reitze Acknowledgments Ed Fry Olga & Vitaly Kocharovsky Yuri Rostovtsev Marlan Scully George Welch Suhail Zubairy Harvard UCF-CREOL Princeton MIT Rice Bell Labs Univ. of Florida Support: NSF-CAREER AFOSR: FA NSF-MIRTHE FA NSF-PIRE NSF ECS

3 Ongoing projects Resonant nonlinear optics in multiple quantumwell structures Ultrafast dynamics and superfluorescence in magnetized electron-hole plasma PRL 96, (006); cond-mat/06070, PRB submitted Instabilities and ultrashort pulse generation in quantum cascade lasers PRL submitted Cavity QED effects in nanostructures, Unruh effect PRL 91, (003), 93, 1930 (004); PRA 74, (006), PRB in preparation. Nonlinear wave mixing in diode lasers

4 Background Outline - Electron states in quantum wells - Optical transitions in quantum wells - Nonlinear optics with intersubband transitions Motivation: infrared photonics and applications A zoo of nonlinear optical phenomena in nanostructures - Integration with quantum cascade lasers - Generation of harmonics - Raman laser - Terahertz sources - Coherent up-conversion detection - Transient phenomena Conclusions and outlook

5 PHYS 689: Physics of optoelectronic devices Spring 007 Overview of basic concepts: - lasers - nonlinear optics - photodetectors - semiconductor heterostructures - nanostructures with quantum confinement Physical principles of state of the art optoelectronic devices Integrated photonic systems and information technologies

6 Background: Heterostructures z Wide-gap semiconductor E g Narrow-gap semiconductor Wide-gap semiconductor E g1 E g.5.0 GaP AlAs AlAsSb Conduction band edge E g Eg1 Valence band edge z Energy Gap (ev) 1.5 AlInAs AlInAs GaAs InP 1.0 GaInAs 0.5 InAs Lattice Constant (A) Ga 0.47 In 0.53 As/Al 0.48 In 0.5 As/InP InAs/AlSb AlSb GaSb InSb

7 Electron states in Quantum Wells Particle in a box too simplistic AlInAs InGaAs AlInAs m b =0.076m 0 m w =0.043m 0 Energy e e 1 e E c e 1 E n ( p) ( p + p ); = 1,,... 1 = n n m eff hh 1 lh 1 hh E v p hh 1 z QW plane lh 1

8 Electron states in bulk semiconductors Note strong non-parabolicity 1.1 Ga 0.47 In 0.53 As 0. E (ev) k z (10 6 cm -1 ) Nonlocal pseudopotential method PRB 14,556 (1976) 8-band k p method (4 bands x spins)

9 k p method in a nutshell Schroedinger s equation for a single electron in a periodic potential V(r): (1) ψ = e ikr u n k (r) - Bloch functions Express unk (r) in terms of Bloch functions at k = 0: Obtain after integrating (1) over unit cell: * pnm = un0( r) pum0( r) dr unit cell Note the coupling between bands via k p term

10 The Luttinger-Kohn basis for u n0 (r) states: S,X,Y,Z are similar to S-like and P-like atomic states (lowest order spherical harmonics Y 00, Y 10, Y 11 etc.)

11 From bulk materials to heterostructures (a) Add slowly varying perturbation U(r) to the bulk Hamiltonian H 0 (b) Seek the solution as a product y ψ ( r) = f ( z) e u 0( r) ik x x + f(z) slowly varying envelope function ik y n Wide-gap semiconductor Narrow-gap semiconductor Wide-gap semiconductor z (c) Assume that u n0 (r) and k x,y are the same in each layer (d) Replace k z with i z and solve the resulting differential matrix equation for the column-vector f(z) Advantage of the method: everything is expressed in terms of several parameters that can be measured: E g, SO, m eff (k = 0)

12 Final touches Add strain (Bir-Pikus Hamiltonian) Add an external electric field Add Poisson equation and solve selfconsistently with Schroedinger equation to account for space charge effects Add other Coulomb interaction effects

13 Calculate electron states Use electron states to calculate optical matrix elements, electron-phonon scattering, resonant tunneling etc. Calculate optical modes for realistic device geometry Use all of the above for the analysis of nonlinear optical interactions, laser gain, photon statistics, etc.

14 Optical transitions in quantum wells 8 band k p calculations E, ev 1 E (ev) AlInAs GaInAs 80 A AlInAs Envelope functions f(z) z (Å) z, A Subband dispersion E(k ) Growth direction [001] E (ev) E, ev K k (10 6 ), cm Using Heterostructure Design Studio software

15 15000 Interband absorption Polarization [010] 1000 Absorption (1/cm) E (ev)

16 Optical transitions in quantum wells Intersubband transitions: sharp atomic-like lines No cross-absorption E, ev E (ev) K, k cm (10 6 cm -1-1 ) 10 7 Line broadening ~ 10 mev due to interface roughness and non-parabolicity (in narrow-gap semiconductors)

17 Intersubband transitions: selection rules 0.6 Energy, ev E3 E E1 Dipole matrix element: z, A * zmn fm ( z) fn( z) dz z f 1 and f 3 are even -> z 13 = 0

18 Asymmetric double quantum wells 0.6 All transitions become allowed 0.5 Energy, ev z, A Tailor-made optical response everything can be manipulated! Wave functions Dipole moments Transition frequencies

19 Resonant nonlinear optics with intersubband transitions Energy, ev ω MQW sapphire L ~ 5 mm d ~ 0.35 mm ω, ω Distance, A Nonlinearity on demand Potential for integration with electronic devices Saturation easily reached: Ω Rabi = eze / h > γ Large coherence ~ 1/ can be excited (compare to LWI, EIT etc.) ρ 1 Giant optical nonlinearities: χ () ~ 10 6 pm/v; compare to ~ 1 pm/v in KDP

20 Intersubband transitions typically lie in the mid- to far-infrared range: Wavelength λ ~ µm Target: new sources, detectors, modulators of the infrared radiation However: (1) Who would need lasers etc. in such a long-wavelength range? PRIMARY MOTIVATION: Atmosphere has transparency windows in the infrared range ALL molecules have STRONG spectral fingerprints in the infrared Other applications: infrared cameras, target pointers, countermeasures, telecommunications

21 HITRAN Simulation of Absorption Spectra ( & µm) CO : 4.3 µm COS: 4.86 µm CO: 4.66 µm CH O: 3.6 µm CH 4 : 3.3 µm NO: 5.6 µm NH 3 : 10.6 µm O 3 : 10 µm N 0, CH 4 : 7.66 µm Frank Tittel PQE006

22 Wide Range of Gas Sensing Applications Urban and Industrial Emission Measurements Industrial Plants Combustion Sources and Processes (eg. early fire detection) Automobile and Aircraft Emissions Rural Emission Measurements Agriculture and Animal Facilities Environmental Gas Monitoring Atmospheric Chemistry of C y gases (eg global and ecosystems) Volcano Gas Emission Studies and Eruption Forecasting Chemical Analysis and Industrial Process Control Chemical, Pharmaceutical, Food & Semiconductor Industry Toxic Industrial Chemical Detection Spacecraft and Planetary Surface Monitoring Crew Health Maintenance & Advanced Human Life Support Technology Biomedical and Clinical Diagnostics (eg. non-invasive breath analysis) Forensic Science and Security Fundamental Science and Photochemistry Life Sciences Frank Tittel PQE06

23 Frank Tittel PQE06 Air Pollution: Houston, TX

24 Non-invasive Medical Diagnostics: Breath analysis NO: marker of lung diseases Concentration in exhaled breath for a healthy adult: 7-15 ppb For an asthma patient: ppb NH 3 : marker of kidney and liver diseases Need fast and compact sensors Appl. Opt. 41, 6018 (00)

25 Existing Methods for Trace Gas Detection Non-Optical Mass Spectroscopy Chemical Gas Chromatography Optical Electro Chemical Non-Dispersive Dispersive Chemoluminescence Fourier Transform Gas Filter Correlation Microwave Spectroscopy Laser Spectroscopy Frank Tittel PQE06

26 Only semiconductor laser/detector technologies can provide fast (~ 1 sec), CW room-temperature operated, tunable, compact infrared sensors capable of detection at ppt level

27 Infrared semiconductor lasers Today s leaders: Diode/InP The gap QCL/InP QCL/GaAs Diode/GaAs Diode/GaSb QCL/InP strain compensated QCL- InAs/AlSb Pretenders: λ (µm) QCL- InAs/AlSb QCL - InGaAs/AlAsSb on InP QCL / GaN? ICL- InAs/AlSb Carlo Sirtori PW06

28 Problems with current sources: Lasers are not widely tunable, do not cover all wavelengths of interest, can operate CW at room-t only in the narrow spectral range, cryogenic at very short and very long wavelengths Nonlinear optical sources (OPO etc.) are bulky and expensive Is it possible to combine the advantages of both types of sources??

29 Energy, ev Resonant nonlinear optics with intersubband transitions Distance, A Saturation easily reached: Ω Rabi = eze / h > γ Large coherence ~ 1/ can be excited ρ 1 MQW sapphire Nonlinearity on demand Potential for integration with electronic devices ω L ~ 5 mm d ~ 0.35 mm ω, ω [Gurnick & De Temple 1983, Fejer et al. 1989; Sirtori et al. 1991, ] Giant optical nonlinearities: χ () ~ 10 6 pm/v; compare to ~ 1 pm/v in KDP

30 However, these advantages are usually inaccessible P NL ) (1) ( = χ E + χ EE +K 3 1 E SH 1 E p 13 Double resonance: χ () Either strong absorption at resonance or low efficiency far from resonance Either way, the figures of merit will be low N e d1d13d + )( γ ~ 3 h ( γ Resonance in absorption for both pump and the nonlinear signal: [ ] (1) N 1γ Im χpump ~ e d h( γ ) 1 )

31 4 3 Conventional nonlinear optics 13 Pump ω ω 1 All detunings are large: ~ ω >> γ; I SH 1 I p All frequencies are in the transparency region of the NLO crystals Absorption and nonlinearity are small; Need high power pump

32 Other problems specific for III-V V semiconductors Inefficient coupling of incident radiation with QWs; Only TM-polarization is allowed for intersubband transitions MQW sapphire L ~ 5 mm d ~ 0.35 mm Weak birefringence and ferroelectricity no convenient phase-matching scheme

33 Integration of injection lasers with resonant electronic nonlinearities We deal with semiconductors χ () ~ 10 5 pm/v PRA 001,00; PRL 90, (003); JQE 39, 1345 (003); APL 84, 71; APL 84, 751 (004), OE 1, 97 (004), EL 40, 1586 (004), Nature 433, 845 (005), APL 87, (005), APL 88, (006) I. II. Let s try to inject electrons, create population inversion and generate the optical pump right inside the nonlinear structure Active nonlinear medium: Laser field serves as a coherent optical pump for the nonlinear process One can approach resonance since resonant absorption is compensated by laser gain The tightest possible confinement and mode purity No problem with external pump; an injection-pumped device

34 Resonant nonlinear optics in the active laser medium Linear and nonlinear optical processes are of the same order P NL ) (1) ( = χ E + χ EE +K Resonant nonlinearity: χ ( n+ 1) χ ( n) E ~ ΩR ~ ω ΩR γ ~ I / I γt thr 1 1 ; Ω R = de h ; I = I thr laser threshold Low laser pump power at Ω R ~ γ : W ~ 100 mw Energy exchange with the medium: all fields are amplified, Manley-Rowe relations are violated Optical processes and electron transport are strongly entangled Coherent self-pulsations, ultrashort pulses

35 Challenges: Is it feasible at all? Need to combine high nonlinearity, high laser gain, and low losses Need independent control of all EM modes and electron states involved in lasing/nonlinear generation Phase matching of waveguide modes

36 First successful experiments with Quantum Cascade structures Integrated laser pump and nonlinear active region Collaboration with C. Gmachl (Princeton), F. Capasso (Harvard), Bell Labs and Agilent (MBE growth) Recent work by TU-Wien group on SHG and Paris-7 group on DFG Started collaboration with Rice (Kono) and Japanese groups (Sasa and Inoue) on nonlinear optics in antimonide structures

37 QC laser design e injector (n-doped) active region 3 injector (n-doped) active region 50 mev QC laser: width 3-0 µm, length 1-4 mm Voltage 5-10 V, current ~ A, max power ~ 1 W 60 nm J. Faist, F. Capasso, et al. Science 64, 553 (1994)

38 Monolithic integration of quantum-cascade lasers with resonant optical nonlinearities 5 4 I 5 energy 3 4 g 3 1 z active 1 region I. II. Maximizing the product of dipoles d 3 d 34 d 4 Quantum interference between cascades I and II χ () ~ 10 5 pm/v

39 Nonlinear polarization at second harmonic: 5 4 P 1 = Tr( dρ) V 3 1 I. II. ρ t k i = h [ H, ρ ] k + ρ t k col The leading term in χ () approximation: P ( ω ) = e 3 NeE h x ( ω ) z 3 z Γ 34 4 z 4 n3 n Γ n3 n Γ 3 + z 34 z Γ z 35 n4 n Γ n4 n Γ 43 3 Γ 4 = γ 4 + i(ω 4 -ω) etc. Double resonance: χ () Interference between cascades ( γ 3 N e z z34z4 )( γ )

40 Laser and SHG Spectra Wavelength (µm) Power (arb. units, off-set) * Wavelength (µm) Gmachl, Belyanin, Sivco, IEEE-JQE 003

41 Single-mode and tunable SH emission Fabry-Perot Laser Single-mode Laser 3.51 Intensity (a.u.) Intensity (a.u.) Wavelength (µm) Intensity (a.u.) Wavelength (µm) Intensity (a.u.) Wavelength (µm) nm/k Temperature (K) APL 84, 751 (004)

42 Third Harmonic Generation 1000 Power (arb. units) SHG THG Energy (mev) ω ω 3ω P 3ω ) P(ω ) I. II. Triple resonance ( ~ µm 5.5 µm 3.7 µm χ (3) ~ 10-7 esu T. Mosely, A. Belyanin, C. Gmachl, Optics Express 1, 97 (004)

43 W For second order nonlinearity s W () p Nonlinear efficiency () χ ( z) Η ε ( z, ω ) p p ( y, z) Η ( k + α ) x λ s s P NL ( y, z) dydz () ~ χ E p p pump s - signal α - effective losses ~ 3-10 cm -1 in the mid-ir Without phase matching: k x ~ 1500 cm -1 Phase matching and large nonlinear overlap are crucial Quasi phase matching by periodic Stark shift: APL 006 Modal phase matching: APL 84, 71 (004), EL 40 (004) Off-axis or surface emission mw power, 35 mw/w efficiency (> 1 W/W theoretical) O. Malis, A. Belyanin, D. Sivco, Electron. Lett. 004

44 Why one would need to double the frequency of a QC laser?

45 Short-wavelength infrared semiconductor lasers Today s leaders: Diode/InP 3-5 µm: Important spectral range for applications The gap QCL/GaAs QCL/InP Diode/GaAs Diode/GaSb cryogenic QCL/InP strain compensated QCL- InAs/AlSb Pretenders: λ (µm) QCL- InAs/AlSb QCL - InGaAs/AlAsSb on InP QCL / GaN? ICL- InAs/AlSb From Sirtori s talk at PW 006

46 Why QCLs cannot reach below λ ~ 4 µm e injector 3 active region injector Only ~ 50% of the conduction band offset is usable for laser transition: E 3 E ~ ½ E c active region 50 mev E c 60 nm InGaAs/AlInAs lattice matched to InP: E c = 0.5 ev, λ > 4.8 µm InGaAs/AlInAs strain compensated: E c < 0.8 ev, λ > 3.6 µm

47 Material systems for short wavelength QCLs wells In 0.53 Ga 0.47 As In 0.7 Ga 0.3 As In 0.53 Ga 0.47 As InAs barriers In 0.5 Al 0.48 As In 0.4 Al 0.7 As AlSb 0.44 As 0.56 AlSb substrate InP InP InP InAs (GaSb) comments lattice matched strain compensated lattice matched ~lattice matched E c ( Γ) 0.5eV 0.74eV 1.6eV.1eV L, X 0.5eV (X) ~0.6eV (X) 0.5eV (X) 0.73eV (L) m e * (m 0 ) From Sirtori s talk at PW 006 High band offset structures: InAs/AlSb, InAlAs/AlAsSb However, laser frequency is limited by E X,L or E g No QC lasers below λ ~ 3.5 µm exist

48 Second harmonic generation below λ ~ 4 µm Advantage: use of powerful, refined InP-based QC lasers in their sweet spot at λ ~ 6-7 µm; CW room-t operation guaranteed µm + 6 µm 3 µm Energy, ev Energy, ev Broad wells Position, A Matrix elements: z 13 = 13 A, z 34 = 4 A, z 14 = 1.3 A χ () = 5600 pm/v Conversion efficiency (without phase-matching): η = 16 µw/w Narrow wells Distance, A z 1 = 0 A, z 3 = 16 A, z 14 = 7 A Larger χ () = 10 5 pm/v

49 SHG in high band offset heterostructures InAs/AlSb, InGaAs/AlAsSb E Γ 3 E L.1 ev 3 E L 1 λ SHG = 3 µm 1 λ SHG can be pushed to ~ µm (limited by interband absorption)

50 .5 InAs/AlSb coupled quantum wells for SHG at 3 µm E (ev) z 1 z 13 z 3 ~ 1300 A 3 χ () = 10 4 pm/v Using Heterostructure Design Studio software z (Å) Collaboration with Kono (Rice), Sasa & Inoue (Osaka IT)

51 InAs/AlSb quantum wells: strong non-parabolicity and many-body effects predicted and partially observed Li et al., 003

52 Raman lasing and other coherent Triply resonant Raman lasing Lasing without inversion nonlinear phenomena 1 Slow light, intersubband polaritons, mixing with phonons, plasmons, s E t Beyond semiclassical picture: squeezing, entanglement Beyond rate approximation: instabilities, superfluorescence Density matrix: ρ ρ ρ ρ ρ ρ 1 3 ρ ρ ρ E p 3 E s E pρ E 1 p ρ1 0 t Quantum coherence E s

53 In most Raman amplifiers and lasers, both pump and Raman fields are very far from one-photon resonance ω p ω p, ω s Very large detuning to avoid absorption No real transitions to upper state 3 Raman shift ω 1 is fixed to be the phonon frequency Signal gain ω s -ω 3, mev 0 E p E s Gain at two-photon resonance: ω p - ω s = ω 1

54 Stimulated Raman scattering Raman inversion Raman gain I p ( N 1 ) 1 γ N ~ ω s Raman decoherence rate 3 Raman coherence ρ 1 << 1 (Except experiments by Sokolov, Harris et al.) I p I s Propagation of coupled Raman and pump fields 1 Manley-Rowe relation: I p I s + ω ω p s = const

55 Approaching resonance Both good and bad effects get enhanced Real one-photon processes become important Raman coherence ρ 1 also increases Raman gain increases strongly 3 ~ γ Absorption is increased E p E s t Es E pρ 1 E p E s 1

56 E p 3 E s ρ 1 1 Stokes gain at arbitrary detuning Gain, cm ~ γ ω s - ω 3, mev Γ Γ Γ = γ = γ = γ i( ω + i( ω + i( ω ω ) s ω ) p ( ω p ω )) Rabi frequency Raman gain is enhanced, but resonant absorption of the pump limits the interaction length s One-photon absorption ω d Ω ( n1 n ) 3 3 g Re s p ( n ) n * 3 * * Γ + Ω / Γ Γ Γ 3 p Two-photon gain γ ij Ω p Ω ~ 5 s = = 10 mev d 31 E p h d 3 E h s

57 Mid-IR Raman injection laser Raman shift is determined by intersubband transition and is tunable Energy Miniband mev Resonant Λ-scheme Miniband 1 Optical power (arb. units) Power (mw) Wavelength (µm) Wavelength (µm) Laser Stokes Current (A) Pump Stokes Very large Raman gain at resonance: ~ 10-4 cm/w Position M. Troccoli, A. Belyanin, F. Capasso, Nature 433, 845 (005) 40 mw Raman threshold 16 mw Stokes power

58 Note the similarity between our schemes and lasers without inversion (LWI) Ω p Ω s Ω p Ω s Gain Coherence term - Resonant absorption Λ-scheme V-scheme Resonant absorption N lower -N upper Ω p Ω s Ω s Ω p Ladder or cascade schemes Coherence term Ω p N pump γ coh Potential Payoff: Lasing on a short-lived transition Frequency conversion to a new spectral region AB, Olga Koch., M. Scully, et al. PRA (001)

59 Frequency down-conversion to the THz range λ ~ µm, f ~ THz Why THz range is important Three ways to achieve: Difference frequency generation Stokes Raman lasing Parametric down-conversion

60 THz spectroscopy and imaging T-rays allow you to see through any dry optically opaque cover: envelope, clothing, suitcase etc, and locate non-metallic things, even read letters. T-rays have enough specificity to distinguish big molecules; they can be used to detect explosives, drugs, etc. Three different drugs: MDMA (left), aspirin (center), and methamphetamine (right), have different images in T-rays K. Kawase, OPN, October 004 Q. Hu, QCL Workshop

61 Q. Hu, QCL Workshop

62 Stokes Raman lasing at THz frequencies 1 Potential benefits as compared to THz QC lasers When ω 3 0, it becomes difficult to provide selective injection to state 3 and selective depopulation of state. Also: backfilling of the lower laser state. All THz QC lasers are inevitably cryogenic. 3 Raman-type system can help in two ways: E p E s It can provide selective optical pumping to state 3 1 It creates Raman gain in the absence of inversion between states and 3 Seems to be feasible for room-t operation

63 Raman active region and waveguide for THz lasing Energy, ev Double-metal waveguide Effective optical confinement ~ 0.3 Modal gain ~ 100 cm -1 1 λ = 7 µm position, A Intensity λ = 100 µm 0. High gain, high losses distance, µm

64 Open issues and prospects New materials: antimonides, nitrides How far can we go into the THz range? Coherent instabilities: can they lead to mode-locking and femtosecond pulses? Can we generate the non-classical light through one of the nonlinear processes? Improvement in state of the art sources and detectors: tuning, wavelength agility etc.