Source: http://aoot.osa.org/oe/abstract.cfm?uri=oe-25-26-33143
Timestamp: 2019-04-24 12:24:45+00:00

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We report the observation of second-harmonic generation (SHG) in stoichiometric silicon nitride waveguides grown via low-pressure chemical vapor deposition (LPCVD). Quasi-rectangular waveguides with a large cross section were used, with a height of 1 µm and various different widths, from 0.6 to 1.2 µm, and with various lengths from 22 to 74 mm. Using a mode-locked laser delivering 6-ps pulses at 1064 nm wavelength with a repetition rate of 20 MHz, 15% of the incoming power was coupled through the waveguide, making maximum average powers of up to 15 mW available in the waveguide depending on the waveguide cross section. Second-harmonic output was observed with a delay of minutes to several hours after the initial turn-on of pump radiation, showing a fast growth rate between 10−4 to 10−2 s−1, with the shortest delay and highest growth rate at the highest input power. After this first, initial build-up (observed delay and growth), the second-harmonic became generated instantly with each new turn-on of the pump laser power. Phase matching was found to be present independent of the used waveguide width, although the latter changes the fundamental and second-harmonic phase velocities. We address the presence of a second-order nonlinearity and phase matching, involving an initial, power-dependent build-up, to the coherent photogalvanic effect. The effect, via the third-order nonlinearity and multiphoton absorption leads to a spatially patterned charge separation, which generates a spatially periodic, semi-permanent, DC-field-induced second-order susceptibility with a period that is appropriate for quasi-phase matching. The maximum measured second-harmonic conversion efficiency amounts to 0.4% in a waveguide with 0.9 × 1 µm2 cross section and 36 mm length, corresponding to 53 µW at 532 nm with 13 mW of IR input coupled into the waveguide. The maximum equivalent χ(2)-susceptibility amounts to 3.7 pm/V, as retrieved from the measured conversion efficiency.
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Fig. 1 (a) Calculated effective refractive index vs. waveguide width, w, for the IR fundamental mode (E11) with quasi-horizontal polarization (red curve), and for various transverse modes at 532 with quasi-horizontal polarization. The waveguide height is fixed at 1 µm. (b) Analogous calculation of dispersion for quasi-vertically polarized modes. The black circles indicate where modal phase matching is expected, namely with w = 0.65 µm or 0.68 µm.
Fig. 2 Schematic of the experimental setup used for second-harmonic (SH) generation in Si3N4 waveguides. The infrared pump laser with a wavelength near 1 μm is sent through two half-wave plates (HWP), through a telescope arrangement (TA), and a polarizing beam splitter (PBS) and focused into a waveguide sample with an aspheric lens (AL). Output from the waveguide is collected with a microscope objective (MO). A polarizing beam splitter (VIS PBS) for the SH light and transparent for the IR pump light is used as analyzer and to separate the SH output from the IR pump light. The SH output is directed to a photodiode (PD VIS) via a dichroic mirror (DM1) for further suppression of any residual IR pump light. The transmitted IR pump light, together with about 1% residual transmitted SH light, is directed towards a infrared power meter (PM IR). Part of the transmitted IR pump power is sampled (16%) by a dichroic mirror (DM2) and send into an infrared spectrometer (IR) using a collection lend (CL) and a large mode area fiber. A second dichroic mirror (DM1) separates the residual transmitted SH light from the IR path and sends it to the spectrometer for visible light (VIS).
Fig. 3 (a) to (d). Initial growth of the second-harmonic output power vs. time (green traces) in four waveguides of different widths, w, and lengths, L. The red traces show the average infrared pump power in the waveguide. The dashed curves are least-square fits of the exponential function f (t) (see main text) to the experimental data. (e). Shown is the rate of growth, R, where the SH output has reached a 1/e-fraction of its steady-state value, as retrieved from the fits to the data in (a–d), vs. the waveguide-internal pump power. The triangular and square symbols represent growth rates as obtained with waveguide widths of w = 0.9 µm and 1.2 µm, respectively. The dashed curve is a linear least-square fit to the data.
Fig. 4 Measured second-harmonic (SH) output as function of input infrared pump power. The used waveguide has a width of 0.9 µm, a height of 1.0 µm and a length of 22 mm. The dashed line is a quadratic fit curve (slope m = 2).
Fig. 5 Power spectra of the generated visible radiation (green trace) compared with the autocorrelated infrared pump power spectrum (red trace) in a logarithmic plot, with peak values normalized to 0 dB. The SH was generated in a waveguide with a 0.6 × 1 µm2 cross-section and a length of 36 mm, with a waveguide-internal pump power of 4.8 mW.
Fig. 6 Far-field intensity pattern formed by the second-harmonic output beam, normalized to the maximum intensity, recorded with a CCD behind an immersion objective (a) and calculated normalized intensity pattern for the waveguide modes E13 (b), E21 (c) and E31 (d). The waveguide has a width of 0.7 µm and a height of 1 µm. The SH output and waveguide modes are horizontally polarized.
Fig. 7 (a) Measured second-harmonic (SH) output power for different waveguide widths with a fixed input power of 10 mW, horizontally polarized (squares) and vertically polarized light (triangles) for a waveguide length of 36 mm. (b) Measured second-harmonic power for different waveguide lengths with a fixed input power of 10 mW, for a waveguide with 0.9 × 1 µm2 cross-section.
Fig. 8 Normalized charge distribution in the waveguide core induced by the coherent photogalvanic effect. The generating optical fields are assumed to be the fundamental mode E 11 ( ω ; r → ) for the IR field and the E 13 ( 2 ω ; r → ) mode for the SH field, both polarized along the x-direction. For clarity only charge values with |ρ| above 80% of the maximum value are plotted, where red and blue represents positive and negative charge, respectively. The sign of the effective χ(2) is then given from blue to red. The horizontal arrow indicates the coherence length for SHG, ℓ c = π Δ k, in absence of quasi-phase matching.
Fig. 9 QPM period required for SHG in the various different modes shown in Fig. 1 with the infrared pump power in the E11 mode. All modes are horizontally polarized. As can be seen, E13 has the largest period for the range of waveguide widths discussed in Fig. 1.
Fig. 10 Nonlinear coupling (orange markers) and equivalent χ eq ( 2 ) (blue markers) as a function of the length of the waveguide. The core of the waveguide has a cross-section of 0.9 × 1 µm2. The shown error bar (0.2 pm/V half-width) seen at the highest data points represents the statistical uncertainty of the fit in Fig. 4 and the experimental uncertainty in measuring the output coupling efficiency at the waveguide exit facet.
(2) E ( 2 ω ; r → ) = A 2 ( z ) E ( 2 ω ; x , y ) cos ( k ( 2 ω ) z + φ 2 ) .
(3) P D C ( 3 ) ( 0 ; r → ) = 3 8 ϵ 0 χ ( 3 ) ( 0 = ω + ω − 2 ω ) E ( ω ; r → ) E ( ω ; r → ) E * ( 2 ω ; r → ) .
(5) ϵ 0 χ ( 1 ) ℰ D C = − ϵ 0 χ ( 1 ) E D C = − P D C ( 3 ) ( 0 ; r → ) .
(7) P ( 3 ) ( 2 ω ; z ) = 3 8 ϵ 0 χ ( 3 ) ( z ) ℰ D C ( r → ) E ( ω ; r → ) E ( ω ; r → ) .
(8) χ eff ( 2 ) ( r → ) = 3 χ ( 3 ) ℰ D C ( r → ) .
(9) χ eq ( 2 ) = 2 ( κ ϵ 0 ) 2 2 ( n ( ω ) eff ) 2 n ( 2 ω ) eff ( 2 ω ) 2 ( μ 0 ϵ 0 ) − 3 / 2 S eff .

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