Slide 1 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

Proposal for a Solid State Carrier-Envelope-offset phase (CEP) detector

June 10 2008Cole Van Vlack, Stephen Hughes

Queen’s University, Kingston ON

Acknowledgements:S.T. Cundiff, J.E. Sipe, and M. Wegener

Slide 2 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

Motivation• Modern ultrafast laser techniques now allow precise control

of the absolute carrier envelope offset phase (CEP)

• Fundamentally interesting to look at the influence of the CEP on ultrafast carrier dynamics in semiconductors

• Solid state CEP detectors are highly sought after by the ultrafast laser community, but still remain elusive

• Note: Absolute CEP is different from relative CEP (eg. work by Cundiff, Sipe & co.)

CEP

Slide 3 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

Background• While the CEP has been measured previously in atomic

systems (e.g., Krausz group,... PRL `03 and T.Nakajima, et al, Opt. Lett. `06) there are several restrictions

• For semiconductors, several ideas have been proposed for measuring the CEP, eg. Wegener group, Opt. Lett `04, using carrier wave Rabi flopping (Hughes PRL `98)

– These high intensity regimes are not reliable for measuring the CEP (eg. Van Vlack, Hughes, Opt. Lett. `06)

• Although the CEP has also been measured in a solid state system using a gold cathode (Krausz group,... PRL `04), there are issues of geometrical averaging

Slide 4 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

Proposed Scheme for CEP detector

eg. [P. C. Planken et al., PRL `92]

GaAs thin film (20 nm)

Sapphire substrate

5 fs pulse

Emitted Dipole Field

Dipole Polarization

Slide 5 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

Theory• Solved with 1D FDTD, without using SVEA• Includes propagation effects

• Includes Surface SHG (Wegener & co, Opt. Lett. `04)

Slide 6 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

Material Equations• Field coupled to semiconductor Bloch equations, w/o RWA

• Employ two band approximation• Use tight-binding model for bands (w/ GaAs parameters)• Included intraband relaxation

Slide 7 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

Coulombic Effects

• Rabi frequency , ! E0=3 GV/m (corresponds to Ipeak ¼ 1 TW, or a 2.6 pulse)

Unscreened due to slow buildup of screening on ~10fs timescales (Haug & co., PR B. `94)

• Time dependent , which includes excitation induced dephasing (eg. Haug & co., PRL. `99)

Slide 8 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

Nonlinear Field Spectra and Ultrafast Carrier Dynamics

=0

=/2

Slide 9 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

=0

=/2

Nonlinear Field Spectra and Ultrafast Carrier Dynamics with excitonic contribution

Slide 10 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

Phase Map of Emitted Spectra

With excitonic interactionWithout excitonic interaction

Slide 11 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

Summary

• We have proposed a setup in which the effects of the CEP can be measured

• We have observed CEP effects at intensities low enough as to be below carrier wave Rabi flopping

• We have shown that they are fairly robust within a certain intensity range, and show no qualitative differences when excitons are included

• Future work: More sophisticated band structure

Slide 12 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

Beyond the two band approximation

Slide 13 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

2

Slide 14 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

Phase maps in regime of CWRF

2.5 pulse 5 pulse

Slide 15 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

Phase maps in regime of CWRF in transmission

2.5 pulse 5 pulse

Slide 16 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

Nonlinear Field Spectra and Ultrafast Carrier Dynamics for small amplitudes

=0

=/2

Slide 17 (of 11) C. Van Vlack et al., CAP Congress, June, 2008

Nonlinear Field Spectra and Ultrafast Carrier Dynamics for 10 fs pulses

=0

=/2