On the role of shot noise in carrier‐envelope phase stabilization

This paper represents a systematic investigation of detection shot noise in carrier-envelope phase (CEP) stabilization. Numerical simulations are conducted to calculate the influence of shot noise in laser oscillators. These results are compared with experimental results for Ti:sapphire lasers. It is found that shot noise imposes a limitation for obtaining sub-100 mrad CEP jitters. Careful interferometer design is necessary to push this limit toward 10 mrad. In contrast to oscillator stabilization, shot noise appears to play a much more restrictive role in amplifier stabilization. Using spectral interferometry together with spectral broadening in sapphire, it already appears practically challenging to reach sub-100 mrad jitters. Adaption of the optical nonlinearity in the broadening step appears key to further improvements of the CEP jitter of amplified systems. We believe that these improvements open a perspective for currently unfeasible applications of CEP stabilized pulses. Moreover, our considerations can be easily adapted to CEP stabilization of other laser types beyond Ti:sapphire.

[1]  See Leang Chin,et al.  Ultrafast white-light continuum generation and self-focusing in transparent condensed media , 1999 .

[2]  J Burgdörfer,et al.  Observation of light-phase-sensitive photoemission from a metal. , 2004, Physical review letters.

[3]  H. Takada,et al.  Single-shot measurement of carrier-envelope phase changes by spectral interferometry. , 2001, Optics letters.

[4]  M. Takeda,et al.  Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry , 1982 .

[5]  A. Zheltikov,et al.  Ultrabroadband, coherent light source based on self-channeling of few-cycle pulses in helium. , 2008, Optics letters.

[6]  Jun Ye,et al.  Colloquium: Femtosecond optical frequency combs , 2003 .

[7]  Eberhard Riedle,et al.  Femtosecond continuum generation in bulk laser host materials with sub-μJ pump pulses , 2009 .

[8]  Anton Husakou,et al.  Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers , 2002 .

[9]  W. Schottky.  Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern , 1918 .

[10]  Mark S. Bowers,et al.  Numerical models of broad-bandwidth nanosecond optical parametric oscillators , 1999 .

[11]  R. Windeler,et al.  Fundamental noise limitations to supercontinuum generation in microstructure fiber. , 2002, Physical review letters.

[12]  H. Pollak,et al.  Amplitude distribution of shot noise , 1960 .

[13]  I. Walmsley,et al.  Analysis of ultrashort pulse-shape measurement using linear interferometers. , 1994, Optics letters.

[14]  F. Kartner,et al.  Carrier-envelope phase dynamics and noise analysis in octave-spanning Ti:sapphire lasers , 2006, 2006 Conference on Lasers and Electro-Optics and 2006 Quantum Electronics and Laser Science Conference.

[15]  P. D. Drummond,et al.  Quantum noise in optical fibers. II. Raman jitter in soliton communications , 1999, quant-ph/9912096.

[16]  Jianhua Liu,et al.  Scaling laws of femtosecond laser pulse induced breakdown in oxide films , 2005 .

[17]  T. Hänsch,et al.  Optical frequency metrology , 2002, Nature.

[18]  G. Steinmeyer,et al.  Agile linear interferometric method for carrier-envelope phase drift measurement. , 2012, Optics letters.

[19]  R. Kienberger,et al.  Precise, real-time, every-single-shot, carrier-envelope phase measurement of ultrashort laser pulses. , 2011, Optics letters.

[20]  P. Corkum,et al.  Method for single-shot measurement of the carrier envelope phase of a few-cycle laser pulse. , 2000, Optics letters.

[21]  Y. Shen,et al.  Spectral broadening of ultrashort pulses in a nonlinear medium. , 1984, Optics letters.

[22]  R. Holzwarth,et al.  Attosecond control of electronic processes by intense light fields , 2003, Nature.

[23]  S. Rice.  Mathematical analysis of random noise , 1944 .

[24]  Jun Ye,et al.  Long-term carrier-envelope phase coherence. , 2002, Optics letters.

[25]  F. Krausz,et al.  Long-term carrier-envelope-phase-stable few-cycle pulses by use of the feed-forward method. , 2012, Optics letters.

[26]  R. Kienberger,et al.  Single-shot carrier-envelope phase measurement of few-cycle laser pulses , 2009 .

[27]  Günter Steinmeyer,et al.  Performance comparison of interferometer topologies for carrier-envelope phase detection , 2009 .

[28]  J. Gordon,et al.  Negative dispersion using pairs of prisms. , 1984, Optics letters.

[29]  F. Krausz,et al.  Electron emission from metal surfaces by ultrashort pulses: determination of the carrier-envelope phase. , 2003, Physical review letters.

[30]  U. Keller,et al.  Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation , 2004 .

[31]  Günter Steinmeyer,et al.  Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation , 1999 .

[32]  Steven T. Cundiff,et al.  Phase stabilization of ultrashort optical pulses , 2002 .

[33]  T. Taira,et al.  High-power blue generation from a periodically poled MgO:LiNbO3 ridge-type waveguide by frequency doubling of a diode end-pumped Nd:Y3Al5O12 laser , 2003 .

[34]  A. Baltuska,et al.  Measurement of the phase of few-cycle laser pulses. , 2003 .

[35]  Hartmut G. Roskos,et al.  Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy , 2006, physics/0603134.

[36]  Günter Steinmeyer,et al.  Carrier-envelope offset phase-locking with attosecond timing jitter , 2003 .

[37]  Albrecht Bartels,et al.  Offset frequency dynamics and phase noise properties of a self-referenced 10 GHz Ti:sapphire frequency comb. , 2011, Optics express.

[38]  Alexander Dreischuh,et al.  Dispersion control in a 100-kHz-repetition-rate 35-fs Ti:sapphire regenerative amplifier system , 2002 .

[39]  Peter Hommelhoff,et al.  Attosecond control of electrons emitted from a nanoscale metal tip , 2011, Nature.

[40]  T. Hänsch.  Nobel Lecture: Passion for precision* , 2006 .

[41]  Ferenc Krausz,et al.  Self-stabilization of carrier-envelope offset phase by use of difference-frequency generation. , 2004, Optics letters.

[42]  A Poppe,et al.  Route to phase control of ultrashort light pulses. , 1996, Optics letters.

[43]  C. Radzewicz,et al.  Collinear interferometer with variable delay for carrier-envelope offset frequency measurement. , 2009, The Review of scientific instruments.

[44]  Hall,et al.  Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis , 2000, Science.

[45]  Ady Arie,et al.  Periodic, quasi‐periodic, and random quadratic nonlinear photonic crystals , 2010 .

[46]  G Korn,et al.  Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers. , 2002, Physical review letters.

[47]  J. Dudley,et al.  Supercontinuum generation in photonic crystal fiber , 2006 .

[48]  P. D. Drummond,et al.  Quantum noise in optical fibers. I. Stochastic equations , 1999 .

[49]  Self-channeling of ultrashort laser pulses in materials with anomalous dispersion. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[50]  Günter Steinmeyer,et al.  Fast f-to-2f interferometer for a direct measurement of the carrier-envelope phase drift of ultrashort amplified laser pulses. , 2008, Optics letters.

[51]  Thomas Udem,et al.  Attosecond control of optical waveforms , 2005 .

[52]  A Husakou,et al.  Carrier-envelope phase stabilization with sub-10 as residual timing jitter. , 2011, Optics letters.

[53]  Günter Steinmeyer,et al.  Bandwidth-independent linear method for detection of the carrier-envelope offset phase. , 2007, Optics letters.

[54]  C. Nam,et al.  Carrier-envelope phase stabilization of femtosecond lasers by the direct locking method , 2012 .

[55]  Mansoor Sheik-Bahae,et al.  Infrared to ultraviolet measurements of two-photon absorption and n/sub 2/ in wide bandgap solids , 1996 .

[56]  Günter Steinmeyer,et al.  Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise , 2010 .

[57]  J. Marburger,et al.  Self-focusing: theory , 1975, International Quantum Electronics Conference, 2005..

[58]  U. Kleineberg,et al.  Single-Cycle Nonlinear Optics , 2008, Science.

[59]  A. Schill,et al.  Single Shot Carrier Envelope Phase Stabilization of a 10 kHz, 10 W Regenerative Amplifier , 2012 .

[60]  T. Fortier,et al.  Carrier-envelope phase-controlled quantum interference of injected photocurrents in semiconductors. , 2004, Physical review letters.

[61]  T. Hänsch,et al.  Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime , 2004 .