Research On Excess Noise Factor In The Output Mode Of Strip Off-axis Confocal Unstable Resonators

Strip off-axis confocal unstable resonators are widely used in solid-state and gas lasers.The space distribution characteristic of its output mode has been a hot area of research for several years.However,the excitation of the eigenmode and its connection with the output line-width has rarely been mentioned.The excess quantum noise is an important characteristic for the eigenmode of non-Hermitian optic system which used to describe the coupling between eigenmodes.The value of the excess quantum noise is actual the expression of output line-width in excess of the level predicted by the standard Schawlow-Townes formula.In this paper,an edge-wave method has been derived for quick analyzing of the excess quantum noise in the output mode of strip off-axis confocal unstable resonators.The specific research ideas and conclusions are as follows:(1)Based on asymptotic theory,an edge-wave method has been derived for quick calculating the output mode of strip off-axis confocal unstable resonators with large effective Fresnel-number.The analysis results point that:for positive-branch(PB),this method are adopted under cavity parameters condition of M>1.1 and Neff chosen between s+ 0.2 and s + 0.8(where s represent an integer);for negative-branch(NB),the valid of this method are given by a judgement formula.(2)According to the calculating results of eigenvector method,the eigenvalue of the lowest eigenmode dependence on Neff has been calculated for the off-axis confocal unstable resonators.The law of the distribution shows that,the mode crossing between the first two order eigenmodes occurres at Neff= s+ 0.08 for the PB and Neff =s+0.85 for NB.Need to be mentioned that,the Fox-Li iterative method is failure in the mode crossing point.(3)Numerical method of above has been employed in calculationg the excess quantum noise K for the lowest eigenmode of the off-axis confocal unstable resonators.Numerical results show different behavior in NB and PB cavity.In the situation of PB,the value of K factor shows a quasi-periodicity peak variation trend around ?Neff?1.The peak value occurs near Neff =s+0.85,which is the identical position of mode crossing point.When the magnification is chosen between region of[-1.9,-1.2]and the Neff changes between[-70,-10],the peak value of K factor is less sensitive to the variation of magnification but depend linearly on Neff;For NB,the value of K factor appears discontinuity at the mode crossing point in accordance with its distribution of eigenvalue.View from the continuity of eigenvalue,the mixed state curve composed by eigenvalue of each order explained the discontinuity of the v K alue of in PB structure.(4)Under the condition of slight misalignment,an equivalent model for output eigenmode calculation has been proposed,of which the equivalence between transverse movement misalignment(TM)and rotating inclination misalignment(RM)has been proved.Based on this equivalent model,the characteristic of excess noise K factor under slight misalignment has been studied.In the case of NB,when the value of TM changes between-0.01 and 0.01(the half-width of feedback mirror is 1),the value of K factor oscillates with a quasi-periodicity of 0.008.The peak value of the oscillation relates to the value of Neff,and the half-width of the "peak" are broaden with the increasing of magnification.In the practical design of resonator,when Neff =s+ 0.4,the resonator has a good anti-interference under misalignment tolerance between h'= 0.002;in the case of PB,when the misalignment is between-0.02 and 0.02,the value of K factor oscillates periodically with a quasi-periodicity 0.025,and the jumping of the peak value occurs in each period.The position of the jumping is related to the value of Neff.For the chosen of cavity parameters,one should prevent this jumping round the slight misalignment area(near h = 0),thus the value of Neff might be chosen near Neff=s+ 0.6.