Volume 62, number 6 OPTICS COMMUNICATIONS 15 June 1987 ENHANCED INCOHERENT SUM-FREQUENCY GENERATION BY GROUP VELOCITY DIFFERENCE * P. CHMELA ‘, Z. FICEK and S. KIELICH Nonlinear Optics Division, Institute ofphysics, A. Mickiewicz University, 60-780 Poznari, Poland Received 12 Feburary 1987 We propose a theoretical treatment of optical sum-frequency generation (SFG) by incoherent nonlinear mixing of two beams, the one coherent and the other chaotic. The efficiency of SFG is calculated in the second approximation of the iterative method solving the equations for parametric interaction of the three waves. It is shown that in the case of perfect phase matching the efficiency of SFG increases with increasing spectral width tl of the input chaotic radiation and increasing difference K between the group velocities of the sub-frequency modes. For small spectral widths of the chaotic sub-frequency radiation the efficiency of SFG is greater than for coherent interaction provided that zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG K is large. For large spectral widths, however, the efficiency of SFG is smaller than for coherent interaction irrespective of K. 1. Introduction The process of optical sum-frequency generation (SFG) is a nonlinear phenomenon of great practical impor- tance [ l-31, and moreover presents highly interesting theoretical aspects [ 41. The process consists in the gen- eration of photons at the higher sum-frequency o3 by fusing the photons at the lower frequencies o, and w2 (0, = w , + w2) by way of nonlinear optical interaction in a quadratic medium. The classical description of optical sum-frequency generation has been first given by Armstrong et al. [ 51 and observed experimentally by Bass et al. [ 61. The quantum description of this process was given by Agrawal and Mehta [ 71 and Peiina [ 81. The influence of the statistical and coherence properties of the generating radia- tions was first discussed by Ducuing and Bloembergen [ 91 and Akhmanov and Chirkin [ lo] in second-har- monic generation (degenerate sum-frequency generation) and by Chmela [ 111 in non-degenerate SFG. In frequency-conversion experiments one usually deals with single or multimode laser radiations, while the ampli- tudes can exhibit substantial light fluctuations. Therefore, it is important to understand the influence of the light fluctuations on nonlinear optical processes. The effects of phase and amplitude fluctuations in the gen- erating fundamental radiations on second-harmonic generation were studied in refs. [ 12-141. Eckardt and Reintjes [ 15 ] studied second-harmonic generation with phase modulation of the fundamental pulse. Chmela [ 1 l] considered SFG by incoherent nonlinear optical fusing of strong coherent radiation and another weak chaotic input beam with a finite spectral width. He has shown that the efficiency of SFG decreases with increas- ing spectral width of the input radiation and/or increasing dispersion of the medium and is independent of the difference between the group velocities of the interacting radiations. In this paper we study the influence of field amplitude fluctuations on the SFG process when the input radia- tions have arbitrary intensities. As we shall see later, in this case the efficiency of SFG is dependent on the difference K between the group velocities of the input radiations and increases with increasing spectral width 9, attains its maximum value for moderate 9, and then decreases for large QY We start from the set of first-order * This work was supported by Research Project C.P.B.P. 01.07. ’ Permanent address: Laboratory of Optics, Palack University, Leninova 26, Olomouc 77146, Czechoslovakia. 0 030-4018/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) 403