Appl. Phys. B 81, 353–356 (2005) Applied Physics B DOI: 10.1007/s00340-005-1915-1 Lasers and Optics L.A. GOLOVAN ✉ V.A. MELNIKOV K.P. BESTEM’YANOV S.V. ZABOTNOV V.M. GORDIENKO V.YU. TIMOSHENKO A.M. ZHELTIKOV P.K. KASHKAROV Disorder-correlated enhancement of second-harmonic generation in strongly photonic porous gallium phosphide Physics Department and International Laser Center, M.V. Lomonosov Moscow State University, 119992 Moscow, Russia Received: 16 February 2005 / Revised version: 20 May 2005 Published online: 15 July 2005 • © Springer-Verlag 2005 ABSTRACT We report an order of magnitude enhancement of second-harmonic generation (SHG) from porous gal- lium phosphide relative to SHG in crystalline gallium phos- phide. Optical heterodyning measurements of photon free- path length reveal a correlation between SHG enhancement and disorder of the porous material. PACS 42.65.Ky; 61.46.+w 1 Introduction Interference phenomena and localization of light in photonic crystals and disordered, strongly scattering photonic media modify the structure of photonic bands, giving rise to new interesting regimes of nonlinear-optical interactions [1]. Photonic crystals have been shown to substantially enhance harmonic-generation and wave-mixing processes due to properly engineered phase matching [2, 3] and Fabry–Perot-type resonances in the density of modes [4–6]. Nanoporous structures, on the other hand, can phase match nonlinear-optical interactions due to the formation of birefringence [7–9] and through mesoscopic effects, manifested in the sensitivity of the nonlinear response to the sizes of pores and nanoclusters [10]. Local-field effects typically start to play an important role in the nonlinear optics of disordered media when the size of inhomogeneities becomes comparable with the wavelengths of optical fields. Multiple scattering of photons in such ran- dom media can result in an optical analog of Anderson local- ization [11], leading to a phase-transition-type change in the transport of light [12]. The criterion of localization is kl ∼ 1, where k = 2π n/λ is the wave vector, n is the refractive in- dex, λ is the wavelength, and l is the mean photon free-path length. The regime of strong localization when kl approaches 1 is of great interest for various applications, including en- hancement of nonlinear-optical interactions. Note that optical harmonic generation in disordered media has not been studied completely yet; the theory is developed mainly for the case of weak localization of light [13]. ✉ Fax: +7-095-939-15-66, E-mail: leo@vega.phys.msu.ru In this paper, we focus on second-harmonic generation (SHG) in porous gallium phosphide (por-GaP). Crystalline gallium phosphide (c-GaP) is transparent in the visible (red) region and characterized by a high refractive index (3.1 at 1200 nm, 3.46 at 600 nm [14]); besides, it has one of the highest values of quadratic dipole susceptibility among inor- ganic crystals [15]). Electrochemically etched pores and GaP nanocrystals are usually hundreds of nanometers in diameter [16]. These factors make por-GaP a very promising material for the investigation of light localization and its role in nonlin- ear optics. On the other hand, harmonic-generation enhance- ment can be one of the indicators of light localization. Indeed, a more than an order of magnitude rise of second-harmonic in- tensity in por-GaP in comparison with the crystalline one was reported [17–19]. Moreover, the SHG efficiency rises with a decrease in the ratio of the wavelength to the scatterer size. Thus, it seems to be very interesting to examine the correlation between the photon free-path length, which gives a measure of disorder in the medium, and SHG efficiency. In the paper, we report the results of such a study. 2 Experimental 2.1 Samples Films of por-GaP were formed by means of electro- chemical etching of crystalline n-type GaP:S (6 × 10 17 cm −3 ) in ethanoic HF (2 M) solutions. The surface orientation of the substrate was (111). To control disordering, samples of dif- ferent porosities were prepared. The porosity of the samples was controlled by varying the applied voltage (see Table 1). Porosities were estimated through charge-transport measure- ment. Atomic-force microscopy measurements show that for the por-GaP films the sizes of the pores and nanocrystals range from 250 to 500 nm [18, 19]. These sizes of inhomogeneity suggest strong light scattering and the obtained por-GaP sam- ples are indeed characterized by efficient scattering, which is rather Mie scattering than the Rayleigh one [19]. 2.2 Experimental setup To study the SHG efficiency versus the results of photon free-path length measurements we employed