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
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
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(v)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dv范围内的光功率为P(v)dv，数学表示为P= P(v)dvP(v)的量纲?
• 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
量纲为[s]，Vo表g(v,vo)，引入谱线的线型函数示线型函数的P(v)g(v,vo) =中心频率，即Pg(v,Vo)dv = l·满足归一化条件Vo =(E2 -E)/h·线型函数在v=vo时有最大值，并在AVV=V+2时下降到最大值的一半，即△vg(Vo, Vo)△VV)= s+0)=g(vg(Vo +22，按上式定义的△称为谱线宽度
• 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 = = − +
Lineshape function If one performs a spectral analysis of theradiation emitted by spontaneous 2-→>1 transitions,one finds that the radiation is not strictlymonochromatic (that is, of one frequency) butoccupies a finite frequency bandwidth. Thefunction describing the distribution of emittedintensity versus the frequency v is referred to asthe lineshape function g(v,vo) (of the transition2-→>1) and its arbitrary scale factor is usuallychosen so that the function is normalizedaccording tog(v, vo)dv=1
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
. We can consequently view g(v,vo)dvas the apriori probability that a given spontaneousemission from level 2 to level 1 will result in aphoton whose frequency is between v and v+dv.. The separation △v between the two frequenciesat which the lineshape function is down to halfits peak value is referred to as the linewidth
• 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