Abstract

We revisit the problem of the optimization of a silicon-nanocrystal (Si-NC) waveguide, aiming to attain the maximum field confinement inside its nonlinear core and to ensure optimal waveguide performance for a given mode power. Using a Si-NC=SiO 2 slot waveguide as an example, we show that the common definition of the effective mode area may lead to significant errors in estimation of optical intensity governing the nonlinear optical response and, as a result, to poor strength evaluation of the associated nonlinear effects. A simple and physically meaningful definition of the effective mode area is given to relate the total mode power to the average field intensity inside the nonlinear region and is employed to study the optimal parameters of Si-NC slot waveguides. © 2012 Optical Society of America OCIS codes: 190.4400, 230.1150, 230.7370. Silica (SiO 2 ) embedded with silicon nanocrystals (Si-NCs) is considered a promising nonlinear material, as it exhibits a strong ultrafast Kerr effect and can also be used with the current complementary metal-oxidesemiconductor technologies where S z E × H ·ẑ is the time-averaged z component of the Poynting vector,ẑ is the unit vector along the waveguide axis, and the integration is over the entire x − y plane. In the weak-guidance approximation, implying that the refractive index varies slowly in the transverse direction, this definition leads to the well-known expression [4,6,8] jFx; yj 4 dxdy; Of primary importance for a nonlinear waveguide is the average field intensity I NL inside its nonlinear constituent, as it determines the efficiency of all nonlinear effects developing inside the waveguide. Without loss of generality, we focus on a quasi-TM mode with the dominant component of the electric field being in the x direction (so that F ≈ E x ). It turns out after some reflection that neither Eq. (1) nor Eq. (2) can be used to relate I NL to the total power P of this mode, as none of them explicitly contains the lateral dimensions of the waveguide. The equality I NL P=A eff would hold only if S z (or E x ) was uniform inside the nonlinear region and zero outside of it, in which case A eff is simply equal to the region's cross-section area a NL . It is not hard to construct a proper factor relating P and I NL , and we introduce a new EMA in the form where NL denotes integration over the nonlinear region. Since the surface integrals in this expression give the total mode power (numerator) and the power P NL transmitted through the nonlinear part of the waveguide (denominator), we can write I NL P NL =a NL P=a eff . Hence, while the effective area given in Eq. (1) or Eq. (2) determines the relative efficiency of the nonlinear effects within the framework of the NLSE, the quantity in Eq. (3) allows one to estimate the actual intensity of light inside the nonlinear waveguide. These equations are inapplicable to plasmonic waveguides, where S z has different signs inside metal and dielectric, and thus the total power flow may vanish. To better understand the difference between the preceding definitions, consider an optical fiber with a highly nonlinear core (e.g., a silicon-core fiber) and assume that June 15, 2012 / Vol. 37, No. 12 / OPTICS LETTERS 2295 0146-9592/12/122295-03$15.00/0