Random Lasers - Physics & Application

Transcription

1 Random Lasers - Physics & Application HuiCao Depts. of Applied Physics & Physics, Yale University Group members Jonathan Andreasen Yong Ling Bo Liu Heeso Noh Brandon Redding Xiaohua Wu Junying Xu Alexey Yamilov Jin-Kyu Yang Northwestern Univ. Robert P. H. Chang Eric Seelig Xiang Liu Yale Univ. Michael Choma Doug Stone, Li Ge Michael Rooks

2 Laser Essential components for a laser Gain medium Cavity Light amplification Coherent feedback Mirror Gain medium Mirror R 1 2gL R e 2 Threshold R R 1 Resonance 1 2e 2 L 2 m k c

3 Laser Essential components for a laser Gain medium Cavity Light amplification Coherent feedback Mirror Gain medium Mirror R 1 Scattered light R 2

4 Laser Essential components for a laser Gain medium Cavity Light amplification Coherent feedback Mirror Gain medium Mirror R 1 Many scatterers R 2

5 Laser Essential components for a laser Gain medium Cavity Light amplification Coherent feedback Gain medium Mirrorless laser

6 Outline Why? What? So what?

7 Laser Essential components for a laser Gain medium Light amplification Cavity Coherent feedback Mirror Gain medium Mirror R 1 R 2 Lasing frequency 2 L 2 m k c

8 Laser with Scattering Reflector Scattering medium Ruby crystals Mirror Nicolay Basov Non-Resonant Feedback Lasing Threshold 2gL 1 2e g R R 1 Ambartsumyan, Basov, Kryukov, and Letokhov, IEEE J. Quantum Electron (1966) Vladilen Letokhov

9 Photonic Bomb Instability for Amplification of Spontaneous Emission (ASE) Average path length of photon exceeds amplification length Photon multiplication Letokhov, Sov. Phys. JETP 26, 1109 (1968)

10 Lasing in Diffusive Mode ), ( ), ( ), ( t r W l v t r W D t r W Diffusion equation t l v D B n n g n e r a t r W ) ( 2 ) ( ), ( ), ( ), ( l t g Solution n 0 ), ( ), ( 2 t r B t r n n n Diffusive mode Smallest eigenvalue L B 1 ~ g l t l g l v D B Critical volume 3 3 g t V cr L

11 Laser Paint Lawandy, Balachandran, Gomes & Sauvain, Nature 368, 436 (1994)

12 Light Diffusion, Absorption, Emission, and Amplification Pump light and probe light in 4-level atomic media Wiersma & Lagendijk, Phys. Rev. E 54, 4256 (1997)

13 Biological Random Laser Random laser action in dye-treated animal tissues Siddique, Yang, Wang, & Alfano, Optics Commun. 117, 475 (1995)

14 ZnO Nanorods 1m HC et al, Appl. Phys. Lett. 73, 3656 (1998); Phys. Rev. Lett. 82, 2278 (1999)

15 Field/Amplitude Feedback After multiple l scattering, light returns to a coherence volume it visited before. Interference of backscattered light determines the lasing frequencies. Feedback for lasing is phase sensitive (coherent) and therefore frequency dependent (resonant).

16 Electromagnetic Mode Maxwell s equations ), ( 1 ), ( 0 t r E t t r H ), ( ) ( 1 ), ( 2 0 t r H r n t t r E t ) ( Complex refractive index i n r in n Boundary condition: only outgoing waves HC et al, Phys. Rev. E, 61, 1985 (2000)

17 Lasing in Quasi-Mode Rate equations for 4-level atoms dn dt dn dt dn dt N 1 2 WpN N N N N E dp l dt E dp dt l Pump W p Laser Transition ω l dn dt N 4 4 WpN1 43 Polarization equation 2 d P dp 2 l l P 2 dt dt N 2 N 3 E Jiang & Soukoulis, Phys. Rev. Lett. 85, 70 (2000)

18 Localized Modes Mode Pattern Spectrum Vanneste & Sebbah, Phys. Rev. Lett. 87, (2001)

19 ZnO Powder Average particle diameter ~ 100 nm C E C E (x) ( x) E * ( x') E( x x') dx' Exponential decay length hd = m x (m) HC et al, Phys. Rev. E 66, R25601 (2002)

20 Porous GaP k l t 6 van der Molen et al, Phys. Rev. Lett. 98, (2007)

21 Dependence of Lasing on Amount of Scattering PMMA doped with rhodamine dye and TiO 2 particles J) mp pulse eshold ( cident pum rgy at thr Inc ener = 620 nm Numbe er of lasing modes l (m) l Ling et al., Phys. Rev. A 64, (2001)

22 Weak Scattering System Dye solution with scattering particles k l 1 Amplification of spatially extended modes in random media Mujumdar et al, Phys. Rev. Lett. 93, (2004)

23 Overlapping Resonances Thouless number N T 1 Excitation spectrum of a passive system Resonances are strongly overlapped spatially and Spectra al Intensity (a.u u.) spectrally Wavelength (nm)

24 Coherent Lasing Mode Lasing spectrum Lasing Mode Pattern Max ensity (a.u.) Spectral Int Wavelength (nm) Laser Field Amplitude Min Vanneste, Sebbah & HC, Phys. Rev. Lett. 98, (2007).

25 Amplification Enhances Interference Effect Returning field E = E 1 + E 2 + L 1 In the absence of gain L 1 < L 2 E 1 > E 2 L 2 Weak interference In the presence of gain Longer path, more amplification E 1 ~ E 2 Stronger interference

26 Lasing in Extended and dlocalized dmodes Microscopically defined fields of ZnO nanoparticles Spectrally and spatially emission Fallert et al., Nature Photonics, 3, 279 (2009)

27 1D Localization Laser pump p emission Milner & Genack, Phys. Rev. Lett. 73, (2005)

28 Short-Range Disorder Short-range, abrupt change of refractive index scatters light Wave optics

29 Long-Range Disorder Long-range, smooth variation of refractive index deflects light Geometric optics - ray trajectories Open trajectory Closed trajectory Exp Vardeny, Polson, Tulek et al. Theory Apalkov, Raikh & Shapiro kl 2 m k 2 L

30 What is new? How random lasers differ from conventional lasers?

31 Non-Uniform Pumping Absorption outside pump region reduces effective size of random structure by suppressing feedback from unpumped region, creating localized lasing modes. Yamilov et al., Opt. Lett. 30, 2430 (2005)

32 Creation of New Lasing Mode 1D weakly scattering random structure No absorption outside the gain region Neglect gain saturation and mode competition Andreasen & HC, Opt. Lett (2009); Phys. Rev. A 81, (2010)

33 Directional Output Diffusive system Ballistic system Use spatial inhomogeneous pumping p profile to achieve desired output directionality in the weakly scattering samples. Li Ge, PhD thesis, Yale (2010)

34 Directional Laser Emission Local pumping of weakly scattering samples Cone shaped pump volume Angular distribution of output t intensity it Integra ted Emission Inten nsity (a. u.) Laser emission 100 m 0 Spontaneous emission Detection Angle (degree) Wu & HC, Phys. Rev. A 74, (2006)

35 How coherent is random laser emission? First order coherence field correlation Second-order order coherence intensity correlation

36 Temporal Coherence δz Temporal coherence length is determined by spectral bandwidth of laser emission 2 2ln2 z ct c Noginov et al, Opt. Mater. 12, 127 (1999); Papadakis et al, J. Opt. Soc. Am. B 24, 31 (2010)

37 Young s double slit experiment Spatial Coherence

38 Tailoring Spatial Coherence by Varying Pump Region MFP=500 μm d=215 μm γ = μm Wavelength (nm) MFP=500 μm d=290 μm γ = μm Wavelength (nm) MFP=500 μm d=390 μm γ = μm Wavelength (nm)

39 Tailoring Spatial Coherence by Changing g Scattering Strength Weaker scattering MFP=500 μm d=215 μm γ = μm Wavelength (nm) MFP=50 μm d=215 μm Stronger scattering γ = μm Wavelength (nm) B. Redding, M. Choma, & HC, Opt. Lett. 36, 3404 (2011).

40 Second-Order Coherence Emission intensity or photon number fluctuations G 2 I 2 2 I I Single-mode coherent light: G 2 1 Single-mode chaotic light: G 2 2

41 Emission Statistics of Nonresonant Feedback Laser Fluctuation of total emission is suppressed by gain saturation. ti Intensity fluctuation of a single mode remains large due to mode coupling. G 2 2 Ambartsumyan et al. Sov. Phys. JETP 26, 1109 (1968)

42 Photon Statistics of Diffusive Random Laser A collection of low-q cavities coupled by photon diffusion gain spectrum Florescu & John, Phys. Rev. Lett. 93, (2004); Phys. Rev. E 69, (2004)

43 Photon Statistics of Random Laser with Resonant Feedback ngth (nm) Wavele G Time (ps) P/P th HC et al. Phys. Rev. Lett. 86, 4524 (2001); G. Zacharakis et al. Opt. Lett. 25, 923 (2000).