G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, "Nonlinear envelope equation modeling of sub-cycle dynamics and harmonic generation in nonlinear waveguides," Opt. Express 15, 5382-5387 (2007).

[CrossRef]
[PubMed]

P. Kinsler, S. B. P. Radnor, J. C. A. Tyrrell, and G. H. C. New, "Optical carrier wave shocking: detection and dispersion," Phys. Rev. E 75, 066603 (2007).

[CrossRef]

A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, and Á. Montero, "Forward-backward equations for nonlinear propagation in axially invariant optical systems," Phys. Rev. E 71, 016601 (2005).

[CrossRef]

J. C. A. Tyrrell, P. Kinsler, and G. H. C. New, "Pseudospectral spatial-domain: A new method for nonlinear pulse propagation in the few-cycle regime with arbitrary dispersion," J. Mod. Opt. 52, 973-986 (2005).

[CrossRef]

P. Kinsler, S. B. P. Radnor, and G. H. C. New, "Theory of directional pulse propagation," Phys. Rev. A 72, 063807 (2005).

[CrossRef]

M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional optical pulse propagation equation," Phys. Rev. Lett. 89, 283902 (2002).

[CrossRef]

Y. J. Ding, J. U. Kang, and J. B. Khurgin, "Theory of backward second-harmonic and third-harmonic generation using laser pulses in quasi-phase-matched second-order nonlinear medium," IEEE J. Quantum Electron. 34, 966-974 (1998).

[CrossRef]

Y. J. Ding and J. B. Khurgin, "Backward optical parametric oscillators and amplifiers," IEEE J. Quantum Electron. 32, 1574-1582 (1996).

[CrossRef]

L. W. Casperson, "Field-equation approximations and amplification in high-gain lasers: numerical results," Phys. Rev. A 44, 3291-3304 (1991).

[CrossRef]
[PubMed]

K. J. Blow and D. Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 25, 2665-2673 (1989).

[CrossRef]

S. E. Harris, "Proposed backward wave oscillation in the infrared," Appl. Phys. Lett. 9, 114-116 (1966).

[CrossRef]

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).

[CrossRef]

G. Rosen, "Electromagnetic shocks and the self-annihilation of intense linearly polarized radiation in an ideal dielectric material," Phys. Rev. A 139, A539-A543 (1965).

S. E. Harris, "Proposed backward wave oscillation in the infrared," Appl. Phys. Lett. 9, 114-116 (1966).

[CrossRef]

Y. J. Ding and J. B. Khurgin, "Backward optical parametric oscillators and amplifiers," IEEE J. Quantum Electron. 32, 1574-1582 (1996).

[CrossRef]

Y. J. Ding, J. U. Kang, and J. B. Khurgin, "Theory of backward second-harmonic and third-harmonic generation using laser pulses in quasi-phase-matched second-order nonlinear medium," IEEE J. Quantum Electron. 34, 966-974 (1998).

[CrossRef]

K. J. Blow and D. Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 25, 2665-2673 (1989).

[CrossRef]

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).

[CrossRef]

J. C. A. Tyrrell, P. Kinsler, and G. H. C. New, "Pseudospectral spatial-domain: A new method for nonlinear pulse propagation in the few-cycle regime with arbitrary dispersion," J. Mod. Opt. 52, 973-986 (2005).

[CrossRef]

G. Rosen, "Electromagnetic shocks and the self-annihilation of intense linearly polarized radiation in an ideal dielectric material," Phys. Rev. A 139, A539-A543 (1965).

P. Kinsler and G. H. C. New, "Few cycle pulse propagation," Phys. Rev. A 67, 023813 (2003).

[CrossRef]

P. Kinsler, S. B. P. Radnor, and G. H. C. New, "Theory of directional pulse propagation," Phys. Rev. A 72, 063807 (2005).

[CrossRef]

S. B. P. Radnor, L. E. Chipperfield, P. Kinsler, and G. H. C. New, "Carrier wave self-steepening and application to high harmonic generation," submitted to Phys. Rev. A .

L. W. Casperson, "Field-equation approximations and amplification in high-gain lasers: numerical results," Phys. Rev. A 44, 3291-3304 (1991).

[CrossRef]
[PubMed]

A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, and Á. Montero, "Forward-backward equations for nonlinear propagation in axially invariant optical systems," Phys. Rev. E 71, 016601 (2005).

[CrossRef]

P. Kinsler, S. B. P. Radnor, J. C. A. Tyrrell, and G. H. C. New, "Optical carrier wave shocking: detection and dispersion," Phys. Rev. E 75, 066603 (2007).

[CrossRef]

M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional optical pulse propagation equation," Phys. Rev. Lett. 89, 283902 (2002).

[CrossRef]

T. Brabec and F. Krausz, "Nonlinear optical pulse propagation in the single-cycle regime," Phys. Rev. Lett. 78, 3282-3285 (1997).

[CrossRef]

P. Kinsler, "Theory of directional pulse propagation: detailed calculations," arXiv:physics/0611216.

If the forward field has a wave vector k0 and evolves as exp(+ik0z), the generated backward component will evolve as exp(−ik0z). This gives a very rapid relative oscillation exp(−2ik0z), which will quickly average to zero.

S. B. P. Radnor (Department of Physics, Imperial College London, London, personal communication, 2006).

G. B. Whitham, Lectures on Wave Propagation (Wiley, 1979).

P. Kinsler, "Pulse propagation methods in nonlinear optics," arXiv:0707.0982.