JPH04107892A - Simulation apparatus for pulse laser - Google Patents

Abstract

PURPOSE:To realize excellent simulation through gradual fall of pulse like the actual measurement by adding non-linear loss term to the differential equa tion of laser oscillation. CONSTITUTION:A differential equation of laser oscillation of a pulse laser, for example, CO2 pulse laser of atmospheric pressure is expressed by the equa tion (8) adding the non-linear term Cfunc(Inu) to the conventional equation (7). Here, Cfunc(Inu) is expressed, for example, by the equation (9). Inu is intensity of laser beam within the light resonator; while nuL(1) the number of vibrations of laser beam; c, velocity of light; h, Planck's constant; N is inverted distribution density; W, quantity related to transition probability of light. Moreover, 7c is life expectation of laser beam within the optical resonator which is given, for example, by the relation, tauc=-(2L/c).lnRo. Moreover, N001 is upper level density of laser and PLA is a constant releted to the self-generating transition probability. Moreover, Inu,c is a constant determined by structure and size of experiment apparatus and experimient condition and a light intensity of the limit generating sudden attenuation within the optical resonator.

Description

DETAILED DESCRIPTION OF THE INVENTION OBJECTS OF THE INVENTION (Industrial Field of Application) The present invention relates to a simulation apparatus used in the simulation of pulsed lasers, particularly atmospheric pressure CO2 pulsed lasers.

(Prior Art) A simulation code for an atmospheric pressure CO2 pulse laser simulation device.

The "CPC Program Library" widely published at Queen's University in the UK is well known. There, the first
The following equation is given for the five-temperature model shown in the figure (Reference: Computer P hys-ics Community
cations t YoO (1975) ppH7
-132).

Tortoise-E,”(T,)% =Ne(t)’NNi”hv*’Xs**3(
T) To criticize = Na(t)・(1-f)・h・hga・Maruichi E= (NN, + Nco, + 1NHs)・kT where EL-Ez, Ez-E4- Es is CO, The energy level associated with laser oscillation, El.

E, ,E, are the symmetrical, bending, and asymmetrical vibrational modes of Co2, respectively. Also, E4 and E are the lower vibrational level of N2 and the lower vibrational level of CO, respectively - Ne(t) is the time change of electron density, (1-f) is the decomposition rate of CO2, and h is a blank constant. ν□, )2. ν are the above, E, , respectively.
It is the frequency of the vibration mode corresponding to E, ,E, and the drop,
, 乍, similarly have vibration mode E4. It is the frequency corresponding to E. Also, Ei” (T), “’ i” (Tv T j
), Eie (Tt Tjt Th) **Vibration mode i
The thermal equilibrium energy is, respectively, when the gas temperature is T, when the gas temperature is T and the j level is Tj, when the gas temperature g is T and the j level is Tj, and when the level is Tk. Also, τ1゜(T), τ, 2 (setting τ□(T= Ti, “ra), τ2
゜(T), τ1□(T, ), τ λ(T 9 TII
T2)(λ=3.5), τ4ko(T)−τ5λ(
T, Tλ) (L = 3.4), etc. are relaxation times that give the speed of the relaxation process shown in each equation.

In order to oscillate laser light, an equation related to light is also required, which is the following equation.

dIV Ic=-1+c・ν,・h・ΔN"W"Iy+C'h'S
'L'Noax"PLA"・■dt τNiko where Iν is the laser beam intensity within the optical resonator, νL is the frequency of the laser beam, C is the speed of light, h is the blank constant, Δ
N is the population inversion density, and W is a quantity related to the transition probability of light. Further, τC is the lifetime of the laser beam within the optical resonator and is given by the following equation.

τc = (2L/c)・QnR Furthermore, No. , is the laser upper level density and PLA
is a constant related to the spontaneous transition probability.

These seven equations are the basis of this simulation.

(Problem to be solved by the invention) Simulation of this CPC library.

Although the code is widely distributed and often cited,
In reality, it is not always possible to simulate the phenomenon satisfactorily1
For example, GO, /N, /Ho = 1/1/8 and lat
A comparison of experiments and simulations regarding the laser gas of 100% is as shown in FIGS. 2(a), (b), and (c). Second
Looking at Figure (a), it can be seen that the relationship between the mirror reflectance R in the laser resonator and the laser pulse output Pj is in good agreement with the actual measurement. On the other hand, the laser output waveform when the mirror reflectance is changed is as shown in Figure 2 (b) and (c).
It can be seen that they do not match very well, and the difference from the actual measurements becomes significant, especially when the reflectance R of the mirror becomes small.

The present invention grasps the essence of this well-known problem in the simulation code, improves the code, and makes it a code that matches reality well.The present invention provides a code for pulsed laser equipment equipped with a simulation code that is useful for pulsed laser development. The purpose is to provide a simulation device.

[Structure of the invention]

(Means for Solving the Problem) The inventors have determined from the comparison between the simulation and the actual situation,
It has been found that when the laser light intensity exceeds a certain level within the optical resonator, there is a nonlinear term that undergoes rapid attenuation. Therefore, a nonlinear loss term Cfunc (Iv) is added to the laser oscillation differential equation (2) to form the following equation.

+c-hshiL"Noo 1・PLA CfunJv)
...<8) (effect) When the intensity of light inside the optical resonator increases, this nonlinear term becomes
We believe that this is because there are cases where two or more photons are absorbed at the lower level (100) of the CO laser at the same time.

In other words, inside the laser beam resonator, as shown in Figure 3, light with energy corresponding to the difference between the upper and lower levels of CO2 in the optical axis direction generates stimulated emission by colliding with upper level CO8 molecules and enters the cavity. Emit light with the same phase and wavelength as light (laser action).

However, when the light intensity level inside the laser cavity increases,
This causes a situation in which two pieces of light simultaneously collide with the CO2 molecules at the upper level. At this time, CO.

Since the molecule emits only one photon, the light amplification is lower than in the case where the light intensity is low (so-called gain saturation).

In addition to this gain saturation, the inventors discovered the following new light attenuation process. That is, as the laser light intensity increases, there is a possibility that two or more photons will collide with CO2 molecules located at a lower level at the same time.

If it is one photon, the lower level CO2 molecule will just go up to the upper level, so there will be no loss of laser light (■ in Figure 4).However, if two or more photons act at the same time, the lower level CO2 molecule will rise to the upper level. I was in a co.

The molecules are excited to a level even higher than the upper level (■ in Figure 4).The CO□ molecules present at the level above the upper level of the laser are unrelated to laser oscillation, and other It loses energy through collisions with wavelengths of light and other molecules.

Therefore, a rapid attenuation effect is exerted on the light. In this way, the inventors discovered the nonlinear loss term Cfunc(
The validity of Eya) becomes clear.

Since a nonlinear loss term is added to the differential equation of laser oscillation,
When the laser intensity inside the optical cavity increases beyond the level of
Due to the rapid attenuation effect, the light cannot increase any further. Therefore, since the peak of the light is limited by the value, the 002 molecules present at the upper level of the laser are not consumed too much at the peak of the pulsed laser light, and the falling edge of the pulse is compared to the simulation as in the actual measurement. This makes it possible to perform better simulations.

(Example) In view of the above, in the present invention, the conventional simulation formula
At ω, the differential equation (2) regarding optical oscillation is modified as shown in the following equation.

+C”h vL”N0II,・PLA Cfunc(I
v) Here, Cfune(Iv) is a nonlinear correction term of the present invention, and is given, for example, in the form of a linear equation.

Cfunc(Iy)=C1・(r,/L+t.)”
4v Eya here. is a constant determined by the structure, dimensions, and experimental conditions of the experimental equipment, and is the critical light intensity that causes rapid attenuation in the optical resonator. This is the key point of the 0-line simulation, but in this simulation, we further estimate the optical lifetime. in. We also modified the following equation by considering the loss τ within the optical resonator.

Due to this, the characteristics of the optical resonator become even better.

In the example, since the discharge chemical reaction is the same as in the conventional example, C
The temporal change in vibration level density associated with laser oscillations such as O2, N2, and CO would proceed in the same way as in the absence of laser oscillation. When laser oscillation occurs, the laser light intensity within the optical resonator is a constant I vvC determined by the experimental equipment and experimental conditions.
If it is below, the laser beam is emitted to the outside as in the conventional case. However, the laser light intensity within the optical resonator is constant. As mentioned above, the increase in laser light is strongly restricted due to the rapid attenuation, and the laser light intensity I
The peak of V is suppressed. Therefore, since the consumption of CO2 at the upper level of the laser is suppressed, the fall of the laser light becomes more gradual than in the conventional example, and as shown in Fig. 5 (a) and (b), the simulation results are in good agreement with the actual measurement. can get.

In this way, the present invention has a simulation code based on multi-photon absorption, a fundamental physical process that has not been considered in conventional CO2 lasers, so that it can be obtained by simply curve fitting. It can be seen that good agreement between experiment and simulation was achieved.

In the embodiment of the present invention, a term proportional to the square of the laser light intensity I9 in the optical resonator is introduced as the nonlinear loss coefficient c fune, but the present invention is not limited to such a case. A term of the first power, a term of the third power, or even a term in which the increment of the laser beam becomes zero at the level of Iv as shown in FIG. 6 may be used.

Further, although the present invention has been mainly described with reference to a C02 pulse laser, it is natural that the nonlinear loss term due to rapid attenuation based on absorption of two or more photons at a lower level can also be applied to other lasers.

〔Effect of the invention〕

As described above, in the present invention, a nonlinear loss term is added to the differential equation related to laser oscillation based on the basic concept of multiphoton absorption, and therefore, it has been found that the simulation simulates the experiment well.

[Brief explanation of the drawing]

FIG. 1 is a comparison of the well-known 5-temperature results of a CO2 laser and an experiment, and FIG. 3 is a diagram explaining the laser action, gain saturation, and loss process. Figure 4 is a similar explanatory diagram from above the energy level diagram,
FIG. 5 shows simulation results using the simulation code of the present invention, and FIG. 6 shows nonlinear gain characteristics employed in other embodiments. Agent Patent Attorney Noriyuki Chika Figure 1 Mirror reflectance k (''/,) Figure 2 Figure 2 Total reflection mirror Output mirror CO2 molecules (upper level 002 molecules) Figure 3 Figure 4 (a) ( b) Figure 5 Figure 6

Claims (3)

[Claims] (1) In a pulsed laser simulation device,
A pulsed laser simulation device characterized by introducing a nonlinear term into the optical amplification equation. (2) A simulation device for an atmospheric pressure CO_2 pulsed laser, characterized in that a nonlinear term whose loss term is a square or more is introduced into the atmospheric pressure CO_2 pulsed laser. (3) A simulation device for a pulsed laser in which, in an optical amplification type of pulsed laser simulation, the optical gain suddenly drops to zero when the optical intensity level in the optical resonator exceeds a certain value.