深圳大学电子科学与技术学院 33谱线加宽和线型函数 基本概念 均匀加宽 自然加宽 碰撞加宽 晶格振动加宽 非均匀加宽 多普勒加宽 晶格缺陷加宽
深圳大学电子科学与技术学院 3.3 谱线加宽和线型函数 • 基本概念 • 均匀加宽 自然加宽 碰撞加宽 晶格振动加宽 • 非均匀加宽 多普勒加宽 晶格缺陷加宽
深圳大学电子科学与技术学院 谱线加宽与线型函数基本概念 由于各种因素的影响,自发辐射并不是单色 的,即光谱不是单一频率的光波,而包含有 一个频率范围,称为谱线加宽。 P()是描述自发辐射功率按频率分布的函数。 在总功率P中,分布在长计dV围内的光功 率为P(Vdv,数学表示为 P(ndv P()的量纲?
深圳大学电子科学与技术学院 • 由于各种因素的影响，自发辐射并不是单色 的，即光谱不是单一频率的光波，而包含有 一个频率范围，称为谱线加宽。 • P()是描述自发辐射功率按频率分布的函数。 在总功率P中，分布在~+d范围内的光功 率为P()d ，数学表示为 + − P = P()d P()的量纲？ 谱线加宽与线型函数基本概念
深圳大学电子科学与技术学院 ·引入谱线的线型函数g(v,v 量纲为[s],v表 示线型函数的 8(v,V) 中心频率,即 ·满足归一化条件」。3(v)lv=1 线型函数在v=v时有最大值,并在=(E2-ED)h 1。土 时下降到最大值的一半,即 △ 8(vo+,v)=8(v 3,v)(V,v) △ ·按上式定义的A称为谱线宽度
深圳大学电子科学与技术学院 • 引入谱线的线型函数 • 满足归一化条件 • 线型函数在= 0时有最大值，并在 时下降到最大值的一半，即 • 按上式定义的称为谱线宽度。 P P g ( ) ( , ) ~ 0 = ( , ) 1 ~ 0 = + − g d ( , ) ~ g 0 量纲为[s]，0表 示线型函数的 中心频率，即 0 = (E2 − E1 ) h 2 0 = 2 ( , ) ~ , ) 2 ( ~ , ) 2 ( ~ 0 0 0 0 0 0 g g g = = − +
深圳大学电子科学与技术学院 Lineshape function If one performs a spectral analysis of the radiation emitted by spontaneous 2->I transitions one finds that the radiation is not strictly monochromatic(that is, of one frequency) but occupies a finite frequency bandwidth. The function describing the distribution of emitted intensity versus the frequency v is referred to as the lineshape function g(v, vo)(of the transition 2>1 and its arbitrary scale factor is usually chosen so that the function is normalized according to g(v, vod=1
深圳大学电子科学与技术学院 Lineshape function • If one performs a spectral analysis of the radiation emitted by spontaneous 2→1 transitions, one finds that the radiation is not strictly monochromatic (that is, of one frequency) but occupies a finite frequency bandwidth. The function describing the distribution of emitted intensity versus the frequency is referred to as the lineshape function (of the transition 2→1) and its arbitrary scale factor is usually chosen so that the function is normalized according to ( , ) 1 ~ 0 = + − g d ( , ) ~ g 0
深圳大学电子科学与技术学院 We can consequently view g(v, vodvas the a priori probability that a given spontaneous emission from level 2 to level 1 will result in a photon whose frequency is between v and v+dv The separation Ay between the two frequencies at which the lineshape function is down to half its peak value is referred to as the linewidth
深圳大学电子科学与技术学院 • We can consequently view as the a priori probability that a given spontaneous emission from level 2 to level 1 will result in a photon whose frequency is between and +d. • The separation between the two frequencies at which the lineshape function is down to half its peak value is referred to as the linewidth. g(, )d ~ 0