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jc_168

木虫 (正式写手)

[求助] 关于强激光激发的电磁场问题

The laser beams can produce electromagnetic fields whose intensity can reach very high values, beyond what is possible with other sources of electromagnetic radiation. In principle, it becomes possible to probe the fundamental properties of matter and verify the theories of physics under extreme conditions.

In this exercise, you are asked to calculate the parameters of a laser beam as the maximum value of the energy density of the electromagnetic field corresponds to that associated with the energy density of matter at rest under relativistic (i.e. the formula mc^2). For your calculation, use the water density is 1 g/cm^3. Suppose that the laser beam is Gaussian transverse profile, the electric field of this beam is given by the following expression in the plane where it is



a)        Find the expression of the magnetic field associated with this beam. Neglect the longitudinal field components, i.e. along the axis z.

b)        Find the expression of the energy density of the electromagnetic field produced by this beam. Find the parameters of electric and magnetic fields that produce an energy density equal to that of matter at rest. Rate these extreme values of electric and magnetic fields, as well as the magnetic induction.

c)        Express the electromagnetic field in phasor notation. Find the expression of the average power per unit area (i.e. the intensity). What is the maximum intensity?

d)        What is the average power of this beam? Suppose a wavelength λ = 1 μm and a beam size w = 10 μm.

e)        In practice, we can not attain power with a continuous laser. It is necessary to use a pulsed laser. What is the energy of the laser pulse if its duration is 1 picosecond (1 ps = 10^-12 s)?

f)        What is the volume of medium required to produce the laser pulse is extracted if averaged 10^18 photons/cm^3 in this environment?

[ Last edited by 华丽的飘过 on 2012-9-22 at 21:53 ]
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吾博而不好學,特而不善長,不曾見過世面,一市井小民耳……
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jc_168

木虫 (正式写手)

没人知道么?水的密度和质能公式怎么用啊?
吾博而不好學,特而不善長,不曾見過世面,一市井小民耳……
2楼2011-10-04 00:30:23
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狗屁狗

铜虫 (正式写手)

太难了,麻烦楼主先翻译成中文吧
3楼2011-10-04 16:02:05
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0272323

金虫 (小有名气)

【答案】应助回帖

jc_168(金币+1): 有那么点意思,但是为啥要用水去转化能量呢?仅仅就是一个打比方的假设而已? 2011-10-08 23:04:46
不是太肯定,好像是用水的密度和质能公式来计算:要把多少体积的水转换成能量,才能制造一个激光脉冲,并且脉冲的光子数密度要达到10^18 photons/cm^3
4楼2011-10-08 10:06:39
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0272323

金虫 (小有名气)

引用回帖:
4楼: Originally posted by 0272323 at 2011-10-08 10:06:39:
不是太肯定,好像是用水的密度和质能公式来计算:要把多少体积的水转换成能量,才能制造一个激光脉冲,并且脉冲的光子数密度要达到10^18 photons/cm^3

我猜是这样,题目中提到的物质只有水了
5楼2011-10-10 00:33:45
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liluplanet

新虫 (初入文坛)

【答案】应助回帖

jc_168(金币+1): 鼓励一下~ 2011-11-17 01:17:39
这个很简单,1um的光子对应1.24ev能量
光束直径w=10um,平均密度10^18光子/厘米^ 3
1皮秒脉冲,对应长度是0.3mm即300um,也就是体积是23561um^ 3
光子数量是2.4x10^10,总能量是2.92x10^10ev,对应4.67x10^-9J
这个可以求出光子数,进而求出总能量E=4.67x10^-9J
水的能量E=mc2,可以得出水的质量m=E/c2=?
这个单位不会换算了,大家自己看着办吧
6楼2011-11-16 22:16:30
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