Theoretical Study of Nonlinear Fabry-Perot

Interferometer for Few-cycle Pulses

Buyanovskaya Elizaveta and Egor Kryshkovets National Research University of Information Technology, Mechanics and Optics

st. Petersburg, Russia lee.buyanovskaya@gmail.com

Abstract- In this work we aim to theoretically investigate transmission of few-cycle pulses by Fabry-Perot interferometer created by a nonlinear dielectric between two metal mirrors.

Keywords-few-cycle pulses; nonlinear interferometers

1. INTRODUCTION

Nowadays one of the main problems of nonlinear optics of few cycle waves is the search for useful applications of obtained theoretical and experimental results. Due to the lack of destruction of optical media in the field of intense extremely short pulses, nonlinear processes including optical harmonic generation can be significant even in case of short nonlinear media. Here we theoretically investigate the transmission of few cycle pulses by nonlinear interferometer Fabry-Perot (TFP) with equal reflective coefficients of the mirrors.

11. THEORETICAL STUDY

In accordance with previously developed technique that takes in the account multiple rereflections inside the Fabry­Perot interferometer by examination of two superimposed waves we obtained expression that describe peculiarities of transmission of few-cycle light pulses by interferometer in the following form:

E (I L)=E(O)(I L)+GE(I)(I LJ=F-1 { (1-R)F{E",(O,I)} }+ "'", ",," ",,' ' l-R·exp(-iro·2L) (1)

FR F + [ -1 {F(.,_(',L)+I_ ("L)} +-!iiF (', ("L)+I, (',L))} • +GvR' R-exp(-im·2L)-1

+S_(I,L)+I_(I,L)

where

This work was supported by Government of Russian Federation (Grant 074-U01) and RFBR Grant No. 14-02-31367.

qt,L)=- -- -3( I )3 a [(E'�:!(I +L))' [,LE.\::! (r-2L) dT+ 1 2 � at + (E.\::! (t+L))[JE,\;:! (r-2L))' dr

G = 4n21 I No (here n, - coefficient of nonlinear refraction

index; 1 - radiation intensity), R - mirrors reflection coefficients, L is the distance between mirrors. The first term in RHS of expression (1) describes peculiarities of few-cycle waves transmission by linear IFP and the second term accounts for media nonlinearity and describes joint effects of self-action of the input light pulse - s_(t,L),s+(t,L) and its interaction

with radiation reflected from the mirror - 1+ (t,L)J_ (t,L) . We

do not take dispersion and saturation into consideration.

Fig. 1. Spectrum of total transmitted by Fabry-Perot interferometer radiation

Numerical simulation of (1) showed that in linear case, as expected, we observe changes just in amplitudes of spectrum harmonics (spectrum modulation) that in time domain corresponds to sequence of subpulses. Tn case when intensity is high enough for media inside interferometer to express nonlinear behavior on the output we observe generation of triple, sextuple and etc. harmonics (See fig.1).

REFERENCES

[1] M. Wegener, "Extreme Nonlinear Optics: An Introduction", Springer­Verlag, Berlin, 2005.

[2] Buyanovskaya E. M., Kozlov S. A. "Dynamics of the fields of counter­propagating light pulses of a few oscillations in nonlinear dielectric media", JETP Letters, 2007, 86(5), p. 297