Statistics of backscattering in optical waveguides Francesco Morichetti, 1,2, * Antonio Canciamilla, 1 and Andrea Melloni 1 1 POLICOM—Dipartimento di Elettronica e Informazione, Politecnico di Milano, Via Ponzio 34/5, 20133, Milano, Italy 2 Fondazione Politecnico di Milano, P.zza Leonardo da Vinci 32, 20133 Milano, Italy *Corresponding author: morichetti@elet.polimi.it Received March 18, 2010; accepted April 2, 2010; posted April 23, 2010 (Doc. ID 125645); published May 19, 2010 The statistics of backscattering induced by sidewall roughness in dielectric optical waveguides is experimentally investigated. We demonstrate that waveguide backscattering is a wavelength-dependent random process, whose sta- tistics follows the rules of single scattering systems, independently of shape, size, and refractive index contrast of the waveguide, and of the light polarization state. The intensity of backscattering is distributed according to an exponen- tial probability density function, and its mean delay corresponds to a reflection at half the effective length of the waveguide. © 2010 Optical Society of America OCIS codes: 230.7370, 290.1350, 130.2790. Scattering processes in optical guiding structures can be originated by either volume or surface imperfections. In optical fibers, Rayleigh scattering due to volume inhomo- geneities is the dominant scattering process, resulting in the main source of propagation loss. Rayleigh backscat- tering generates along the fiber a distributed coupling between counterpropagating guided modes, whose sta- tistics have been the subject of in-depth theoretical and experimental studies [1,2]. Differently from fibers, in in- tegrated optical waveguides, the main source of propaga- tion loss and backscattering is the sidewall surface roughness produced by selective etching processes [3–5]. In recent contributions, we provided experimental evi- dence that backscattering can reach surprisingly high le- vels in subwavelength high-index-contrast waveguides [6], especially if enhanced by resonant structures [7]. In this Letter, we derive from experiments the statistics of backscattering induced by sidewall roughness in di- electric optical waveguides based on total internal reflec- tion (TIR), that, to the best of our knowledge, have never been reported. Our study reveals that rough waveguides behave as single scattering systems, independently of shape, size, and refractive index contrast of the wave- guide, and independently of the light polarization state. The statistics of the process are analyzed in detail, point- ing out that the mean, standard deviation, and correlation strictly depend on the waveguide length L w . These re- sults provide key instruments for an accurate modeling of realistic optical waveguides and integrated circuits. The statistics of waveguide backscattering were mea- sured by using the frequency-domain interferometric technique described in [6], which allows the measure- ment of both amplitude and phase of the local back- scattering distributed along a waveguide. Referring to Fig. 1(a), we measured in the space (time) domain the complex amplitude h R ðzÞ of the backscattering gener- ated by an arbitrary waveguide section of length dz lo- cated at a distance z from the input (z ¼ 0). The power spectral density (PSD) jH R ðλÞj 2 of the cumulative backscattering at the input of a waveguide of length L w is directly derived by Fourier transforming h R ðzÞ. As a first example of optical waveguides, we measured silicon-on-insulator (SOI) nanowires (core refractive in- dex n Si ¼ 3:45) buried in a SiO 2 cladding (n SiO 2 ¼ 1:45). The waveguides have a rectangular cross section with a height of 220 nm and width w, and were fabricated ac- cording to the procedure described in [8]. Figure 1(b) shows the measured jH R j 2 (normalized to unitary input power) of an SOI waveguide with L w ¼ 1 mm and w ¼ 490 nm for both TE and TM input polarization. The higher TE backscattering level depends on the higher sensitivity to sidewall roughness [5,6]. All over the 60-nm-wide mea- sured wavelength range (1520–1580 nm), jH R j 2 shows the wavelength dependence typical of a white noise. The mean backscattering level hjH R j 2 i versus L w is shown in Fig. 2 for three silicon waveguides with w ¼ 300, 350, and 490 nm and for TE polarization. For small L w , hjH R j 2 i increases linearly, with slopes of H 0 ¼ 3:95 × 10 −2 , 1:28 × 10 −2 , and 0:41 × 10 −2 mm −1 , re- spectively, that decreases versus w. The higher backscat- tering of narrower waveguides is related to the higher sensitivity of the guided mode effective index to w pertur- bations ð∂n eff =∂wÞ 2 [6]. This initial linear dependence in- dicates that backscattering adds incoherently along the waveguide until propagation loss (equal to 13, 7, and 2:5 dB=cm in the three waveguides of Fig. 2) becomes sig- nificant. The backscattering increases according to the re- lation hjH R j 2 i¼ H 0 ½1 − expð−4αL w Þ=4α, where α is the field propagation loss. The mean backscattering hjH R j 2 i becomes higher than the transmitted power for Fig. 1. (a) Schematic of a rough optical waveguide, (b) mea- sured PSD of the backscattering of a 1-mm-long SOI waveguide with w ¼ 490 nm for TE (solid curve) and TM (dotted curve) input polarization. June 1, 2010 / Vol. 35, No. 11 / OPTICS LETTERS 1777 0146-9592/10/111777-03$15.00/0 © 2010 Optical Society of America