## Abstract

We report the first observation of enhanced third-order nonlinear effects in AlGaAs nanowires. AlGaAs nanowaveguides with widths varying from 100 to 600nm were fabricated and characterized. Nonlinear phase shifts of ~π were experimentally observed at 1.55µm with peak powers of 30–40W in 600µm long, 550nm wide guides.

© 2006 Optical Society of America

## 1. Introduction

The development of single-mode nanowaveguides (or nanowires) is today an issue of great research interest [1]. Advances in fabrication technology over the last decade have made it possible to fabricate devices with sub-micron and nano-scale transverse dimensions. In the future, these sub-wavelength waveguides may find applications as compact information conduits between microchip devices or as sensors in biotechnology [2]. In general, optical nanowaveguide structures are capable of providing superior light confinement (because of their strong index contrast) and are thus ideal for nonlinear optics applications [3]. To date, silica glass waveguides and fibers have been fabricated with sub-micron modal diameters and have been used to observe super-continuum generation and soliton compression among other nonlinear effects [4–6]. In addition, other nonlinear glasses such as lead silicate, tellurites, and bismuth have been employed in similar ways [7–11]. Lately self-phase modulation has also been observed experimentally in silicon nanowires [12–14]

Quite recently we have explored the fabrication of high index-contrast AlGaAs nanowires. Given the fact that at 1.55µmAlGaAs exhibits an ultrafast Kerr nonlinearity that is three orders of magnitude higher than that of silica [15, 16], the prospect of realizing sub-µm^{2} cross-section nanowires may eventually lead to low-power nonlinear devices with *sub-millimeter* interaction lengths operating at *Watt power levels* [17]. We note that second harmonic generation in AlGaAs optical nanowaveguides has also been recently demonstrated [18] and nonlinear micro-ring resonators have been realized in this same material system [19, 20].

In this paper we report the first observation of self-phase-modulation enhancement due to strong confinement in 550 nm wide, Kerr nonlinear AlGaAs nanowaveguides. We have successfully fabricated and tested prototype AlGaAs optical nanowires for all-optical applications. The prototype structures fabricated were a few hundred nanometers wide and up to 700*µm* long. To facilitate in-coupling and out-coupling from such narrow waveguides, tapers were also fabricated for efficient excitation and output collection. The propagation losses were evaluated and the spectral broadening or self-phase-modulation (SPM) and nonlinear three photon absorption were measured and compared to that of conventional waveguides of the same length. Large enhancements in SPM compared to standard ridge waveguides were observed. Our experimental results were in excellent agreement with theoretical predictions based on the bulk value for n_{2} [15, 16]. Furthermore, the three photon absorption coefficient in these nanowires as determined from nonlinear absorption measurements was also comparable to that in the bulk [21].

## 2. Nanowaveguide Fabrication

The nanowires were fabricated by deep etching of a multilayer MBE structure on a GaAs wafer. The nanowaveguide structure and the required fabrication steps in the vertical direction are shown in Figure 1.

The substrate is GaAs on top of which was deposited sequentially a 4200nm cladding layer of Al_{0.7}Ga_{0.3}As, a 500 nm core of Al_{0.2}Ga_{0.8}As, a 300 nm upper cladding of Al_{0.7}Ga_{0.3}As and a cap layer of 100nm GaAs. The layer structure was etched down to a depth of 2300 nm, (as shown in the SEM picture of Fig. 2), to form a single mode waveguide at 1550 nm.

The structure of each completed waveguide, as viewed from the top is shown in Fig. 3. The total length of each device was 1.8mm. The length L of the nanowire was varied from 0 to 700µm in 100µm steps to facilitate the measurement of the nanowire losses. Although a large variety of nanowire widths W was successfully fabricated, all of the experiments were performed with W≅550nm guides.

In order to analyze the modal vector field structure of such high index contrast waveguides a finite element method was used. Since the aluminum content is known in every layer, the corresponding refractive index can be obtained [22] and the resulting field distributions for the lowest TM and TE modes at 1550 nm can be computed as shown in Fig. 4 below.

As Fig. 4 shows, strong modal confinement is obtained for the TM mode. The modal area of the single mode guide is in this case ~0.3 µm^{2}. This value is approximately two-orders of magnitude lower when compared with typical weakly guiding channel waveguides with modal areas of the order 10–15µm^{2} [23].

#### 3. Linear and nonlinear transmission measurements

Rough estimates for the propagation loss for different nanowire lengths were first obtained by measuring the transmission of the devices at low powers as a function of the nanowire length L. Typical results are shown in Fig. 5 for a nanowire of width 550nm. Assuming constant values for the in-and out-coupling efficiencies and the tapered regions, the total measured loss for the fundamental TM mode was found to vary with length L. For the TM polarized mode the average loss value of the nanowire was estimated to be ~19 cm^{-1}. On the other hand, the TE modes exhibited a higher loss in the nanowire section, presumably because in this case the fields are perpendicular to the boundaries (as compared to the TM case, see Fig. 4) and hence are more sensitive to waveguide surface roughness etc.

Although a number of channels of different channel lengths were investigated, here we focus first on the case L=0 to obtain the coupling efficiency and the losses in the input, output waveguide sections. In experiments with a cw laser, the contrast in the Fabry-Perot fringes due to multi-reflections between the sample facets yielded a loss coefficient of 4cm^{-1} for the structure. In subsequent calculations, since the short tapers were designed to be adiabatic transformers, i.e. non-radiative, the 4cm^{-1} measured loss was attributed to the total length of the structure. Furthermore, using the throughput measurements for L=0 and the Fresnel losses at the two interfaces (29% each), a coupling efficiency due to field overlap of 29% was deduced and used in subsequent calculations.

Since the nanowire effective area is only 0.3µm^{2}, the intensities easily approach 3 GW/cm^{2} with peak powers of just 10W. Hence multi-photon absorption was expected to be significant at high intensities. The apparatus used for measuring the nonlinear transmission (and spectral broadening) is shown in Figure 6 below. The optical source was a Pritel fiber laser that was first temporally broadened by a chirped fiber grating, next amplified by a broad area KEOPSYS erbium-doped amplifier and finally compressed by a grating pair to produce 8ps long pulses at a 5MHz repetition rate. The pulses were approximately transform-limited and the maximum peak power output was 4 KW.

Detailed measurements of the TM throughput between the two sample facets are shown below for 550nm wide nanowire samples with L=0 and L=400µm as a function of the input power just inside the input facet. It is clear from Fig. 7 that at powers of 10W nonlinear absorption is already important. In general, the peak waveguide intensity with propagation distance can be written as

where *α*
_{1}, *α*
_{2} and *α*
_{3} are the one (linear), two and three photon absorption coefficients respectively. Because the photon energy used is sufficiently less than half the semiconductor’s band gap energy, two photon absorption was neglected. The contributions to the transmission loss of the net power *P _{in}*=

*P*(0) just inside the entrance facet to just inside the exit facet

*P*were taken into account by the equation:

_{out}where *A _{eff}* is the effective waveguide cross-section area of each of the three segments of the waveguide: nanowire section and the input and output waveguide sections. The calculated waveguide transmission in Fig. 7 of the L=0 sample (blue line) was based on the measured coupling efficiency, Fresnel losses, the propagation losses just discussed and the literature value for α

_{3}. The linear regime of the throughput curves for the L=400µm nanowire was then used to evaluate the nano-wire loss coefficient and a value of 19cm

^{-1}was deduced, in good agreement with the estimates from Fig. 5. Note that the overall agreement between experiment and theory is indeed very good, vindicating the assumption of nonlinear loss via three photon absorption.

## 4. Self-phase-modulation measurements

A single-mode fiber was used to couple the output from the composite waveguides to the spectrum optical analyzer (SOA). The spectrum obtained at the output is shown in Figure 8 for the L=0 and L=600µm nanowire lengths with W=550nm. (The choice of L=600µm was made to optimize the SPM of the nanowire relative to the input and output sections: The L=700µm nanowire had a damaged input facet.) Although the combined length of the input and output channels is about 2 times that of the nanowire, the nonlinear phase shift in the nanowire clearly dominates the spectrum.

The modeling for the frequency spectrum is complicated because there are both linear and higher order absorption mechanisms that must be taken into account when evaluating the nonlinear phase shifts experienced by the propagating field *U(z,T)*. The pertinent equations are:

where *U(0,T)* is the input field and *S*̃(*z,ω*) is the frequency power spectrum of the output pulse from the waveguide structure. As Fig. 8 indicates, there is very good agreement between the experiment and the simulation for a total peak nonlinear phase shift of 0.9π.

Fig. 9 shows the change in the frequency spectrum measured at the waveguide output for two different input power levels, namely 8W and 38W (calculated after the input facet of the structure). Again the agreement between experiment and simulation is very good.

## 5. Summary

In summary, we have fabricated AlGaAs nanowaveguides with very strong confinement. In spite of high losses, these prototype nanowires were orders of magnitude more efficient in producing a nonlinear phase shift (and hence spectral broadening) than the more conventional waveguides which have been used previously for all-optical devices such as nonlinear directional couplers [15,16]. Such tightly confined waveguides may be used in the future to realize all-optical switching devices operating at greatly reduced (>2 orders of magnitude) power levels that can also be integrated at much higher packing densities.

This research was sponsored in the United States by NSF, in Canada by NSERC, in the UK by EPSRC.

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