Gain and Emission Cross Section Analysis of Wavelength-Tunable Si-nc Incorporated Si-Rich ${\rm SiO}_{\rm x}$ Waveguide Amplifier

Abstract

Multi wavelength strip-loaded waveguide amplifiers fabricated by growing Si-nanocrystal (Si-nc) incorporated Si-rich <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm SiO}_{\rm x}$</tex></formula> with detuning <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm N}_{2}{\rm O}/{\rm SiH}_{4}$</tex></formula> fluence ratio and RF plasma power are demonstrated, which show blue, yellow, and red multicolor amplified-spontaneous-emission (ASE) with gain coefficients of 157, 62, and 85.6 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">${\rm cm}^{-1}$</tex></formula> , and the corresponding products of Si-ncs emission cross section and Si-ncs radiative lifetime are 2.34 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\,\times 10^{-21}$</tex></formula> , 1.78 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\,\times 10^{-21}$</tex></formula> , and 1.28 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\,\times 10^{-21}~{\rm cm}^{2}\cdot{\rm s}$</tex></formula> , respectively, as deduced from the maximum gain-length product. Combining the time-resolved photoluminescence with the maximum gain-length product result, the Si-ncs cross section/carrier lifetime for the blue-, yellow-, and red-ASE <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm SiO}_{\rm x}$</tex></formula> : Si-nc samples are 1.37 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\,\times 10^{-14}$</tex></formula> /0.17, 6.84 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\,\times 10^{-16}$</tex></formula> /2.6, and 0.64 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\,\times 10^{-16}$</tex></formula> /20 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$({\rm cm}^{2}/\mu{\rm s})$</tex> </formula> , respectively. The high-gain blue-ASE sample exhibits a shorter saturation length of 0.25 mm with the highest loss coefficient due to scattering loss by Si-ncs of the highest density. The gain saturation of the strip-loaded <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm SiO}_{\rm x}$</tex></formula> :Si-nc waveguide is discussed.