Principles of laser席鹏北京大学工学院生物医学工程系

Outline Principle of laser Laser modes Features of laser

Energy levels and transition粒子的能级与辐射跃迁 The ground state corresponds to having the

atom's single electron in the lowest possible orbit. An excited state is any state with energy greater than the ground state.

By giving the atom additional energy (for example, by the absorption of a photon of an appropriate energy), the electron is able to move into an excited state (one with one or more quantum numbers greater than the minimum possible). If the photon has too much energy, the electron will cease to be bound to the atom, and the atom will become ionised.

Decay, Lifetime The lifetime of a system in an excited state is

usually short: spontaneous or induced emission of a quantum of energy usually occurs shortly (ps level) after the system is promoted to the excited state, returning the system to a state with lower energy (a less excited state or the ground state).

This return to a lower energy level is often loosely described as decay and is the inverse of excitation.

Long-lived excited states are often called metastable state (ns level).

Question: where is the energy?

Section 1一．粒子的能级与辐射跃迁 1 ．粒子的能级

　组成物质的原子、分子等粒子总是处于一定的能态或能级，能量最低的能态称为基态，其它能量较高的状态称为激发态。基态是最稳定的状态，通常多数粒子处在基态上，当一粒子获得一定的能量跃迁到某一激发态时，它在激发态上停留的时间一般很短，其平均寿命大约在 10-7 秒量级。有些粒子的某些激发态寿命较长，平均寿命大约可达 10-2 秒量级，这样的激发态称为亚稳态。

Atom absorbts energy from photon

基态ground state

激发态excited state

Units 1 10-3 : milli- 10-6 : micro- (μ) 10-9 : nano- (n) 10-12 : pico- (p) 10-15 : femto- (f) 10-18 : atto- (a)

2 ．辐射跃迁的三种基本过程　光与物质的相互作用有三种基本过程，这就是光的吸收、自发辐射和受激辐射。 1) 吸收：假设 E1 、 E2 为某个粒子的两个能级，如图所示。一个处在较低能级 E1 上的粒子，吸收一个能量 hn= E2-E1 的光子，跃迁到较高的能级 E2 上，这一过程称为光的吸收。

Emission of light

基态

激发态

1) Spontaneous emission is the process by which a light source in an excited state undergoes a transition to the ground state and emits a photon. It plays an essential role in many phenomena in nature and forms the basis of many applications, such as fluorescent tubes, older television screens (cathode ray tubes), plasma display panels, lasers (for startup - normal continuous operation works by stimulated emission instead) and light emitting diodes.

The propagation direction, and initial phase are random in spontaneous emission.

Feature

1) 自发辐射：处在高能级上的粒子可以自发地辐射光子而跃迁到较低的能级，这种过程称为自发辐射。如图所示，自发辐射光子的能量 hn= E2-E1 。

自 发 辐 射 发 出 的 光 子 的 传 播 方向、初相位彼此无关。

特点

2) Stimulated emission is the process by which an atomic electron (or an excited molecular state) interacting with an electromagnetic wave of a certain frequency may drop to a lower energy level, transferring its energy to that field.

A photon created in this manner has the same phase, frequency, polarization, and direction of travel as the photons of the incident wave.

特点

2) 受激辐射：处在高能级 E2 上的粒子，在一个外来的能量为 hn= E2-E1 的光子的诱发下，跃迁到能量较低的能级 E1 ，同时释放出一个与诱发光子完全相同的光子的过程称为受激辐射。

受激 辐射 发 出 的 光 子的 频 率、 传 播方向、初相位与诱发光子相同。

特点

Principle of laser 受激辐射过程

(Stimulated Emission Radiation, SER)

基态

激发态：寿命10-7s

亚稳态 :寿命 10-3s

二．粒子数按能级分布 1.Boltzmann distributionIn thermal equilibrium state, the atom number for each energy level

obeys Boltzmann distribution　Where ni in the number of atomic energy levels by Ei, gi is the level degeneracy of Ei, and k is the Boltzmann constant. According to the Boltzmann distribution, under thermal equilibrium conditions, the number of particles on a higher energy level is always less than the number of particles on the lower level. For example: according to the Boltzmann distribution , the 3s excited state of neon atom versus the ground state at room temperature (T = 300K), the ratio of particles number of two energy level is

　　　　　　　 N2/N1=e-653 <<1

　　 This indicates that, under conditions of thermal equilibrium, the vast majority of the particles are at the ground state. The higher the energy level , the less the particle number.

kTE

ii

i

egn

二．粒子数按能级分布 1. 玻尔兹曼分布

在热平衡状态下，原子数按能级分布服从玻尔兹曼定律　其中 ni 为处在 Ei 能级的原子数， gi 为 Ei 能级的简并度， k 为玻尔兹曼常数。根据玻尔兹曼分布，在热平衡条件下，处在高能级上的粒子的数目总是少于低能级上的粒子的数目。例如：根据玻尔兹曼分布计算得知，氖原子 3s 激发态与基态在常温下 (T=300K) ，两能级的粒子数之比为　　　　　　　 N2/N1=e-653 <<1

　　这说明，在热平衡条件下，绝大多数的粒子都处在基态，能级能量越高，粒子数越少。

kTE

ii

i

egn

激光产生基本原理

光放大 (Light Amplification, LA) 光放大的条件：粒子数反转 (population

inversion)

一象棋盘大米的故事 传说国际象棋是舍罕王的宰相西萨 . 班 . 达依尔发明的。他把这个有趣的娱乐品进贡给国王。舍罕王对于这一奇妙的发明异常喜爱，决定让宰相自己要求得到什么赏赐。 西萨并没有要求任何金银财宝，他只是指着面前的棋盘奏道：“陛下，就请您赏给我一些麦子吧，它们只要这样放在棋盘里就行了：第一个格里放一颗，第二个格里放两颗，第三个格里放四颗，以后每一个格里都比前一个格里的麦粒增加一倍。圣明的王啊，只要把这样摆满棋盘上全部六十四格的麦粒都赏给你的仆人，他就心满意足了”，舍罕王听了，心中暗暗欣喜：“这个傻瓜的胃口实在不算大啊”。他立即慷慨的应允道：”爱卿，你当然会如愿以偿的！”但当记麦工作开始后不久，舍罕王便暗暗叫苦了，因为尽管第一袋麦子放满了将近二十个格子，可是接下去的麦粒数增长的竟是那样的快，国王很快意识到，即使把自己王国内的全部粮食都拿来，也兑现不了他许给宰相的诺言了！ 舍罕王由于失算而欠了西萨一大笔债，他为顾全面子而选择了什么样的善后措施我们已不得而知，但计算一下他的债务确是一件很有趣的事。

我们知道，这位聪明的宰相所要求的麦粒总数，实际上是等比数列 :1,2,4,8... 的前六十四项和，即二的六十四次方减一，为一个二十位的大数：18,446,744,073,709,551,615 。 这些麦粒究竟是多少呢？如果一升小麦按150 ， 000 粒计算，这大约是 140万亿升小麦，按目前的平均产量计算，这竟然是全世界生产两千年的全部小麦！！

经济小常识 假如你从现在开始每个月存

200元到银行，银行每年发一次利息（本金的 5%），这样的话 40年后你有多少钱？ 30万。 假如你从现在开始每个月投资

200元到某股市，股市年回报率为 10% ，这样的话 40年后你有多少钱？（依据：中国GDP 增长约为 8%）。

117万。

总资产

0

200000

400000

600000

800000

1000000

1200000

0 5 10 15 20 25 30 35 40

单位

：元

与物理的联系想要在股市赚钱的一个必要条件：年回报率

>0 。形成激光的必要条件：粒子数反转 ( 增益系数

>0) 。

激光腔的构成Main components of Laser cavity

Gain medium ： medium for population inversion

Pump: provide energy for population inversion

Mirror: provide oscillation

基态

激发态： Excited state寿命 10-7sMesostatic state 亚稳态 : 寿命 10-3s

增益介质：为粒子数反转提供媒介 泵浦源：为粒子数反转提供能量 反射镜：提供震荡

1964 Nobel Prize in Physics

Mainmann and his Ruby laser

On June 22 of 1960, Maiman sent a paper to the Physical Review Letters about his achievement, but received a letter of rejection stating that the publisher was no longer interested in maser related papers. Next, he sent a short version of his paper to the British journal "Nature". Consequently, the first scientific report about the first laser appeared on August 6, 1960 not in the USA but in Great Britain. The paper was titled "Stimulated Optical Radiation in Ruby" (Nature, 1960, v.187, P.493).

1927-2007

Lamp pumped laser灯泵浦的激光器结构图Streak lamp

Laser output

Ruby Total reflection

Partialreflection

Small-signal gain and gain saturation When the laser intensity is very small initially,

there are sufficient inversion particles to enhance the laser in the oscillator. In such a case, the gain coefficient is only related to the frequency of the light, irrespective of the light intensity. Such a gain is called small signal gain.

After a while when the laser is not so weak, therefore to the large amount of photons, the gain will decrease. Finally, the gain and loss will gradually reach a balance, such balance is called gain saturation.

小信号增益和增益饱和 在振荡器内激光信号很小的时候，有足够的反转粒子支持信号得到增强，在这样的情况下，增益系数仅与光的频率有关，而与光强无关，这样的增益叫做小信号增益。 在经过一定增益后，光强对于工作介质所能提供的反转粒子数不再是一个很小的量，通过增益与损耗将逐渐达到一种平衡，这种平衡叫做增益饱和。

Theory of standing wave in laser When light waves reflected back and

forth in the cavity mirrors, the incident and the reflected waves interfere. To form a stable oscillation in the cavity requires that the lightwave due to the interference to be strengthened and that the light waves in the cavity from the Total phase shift of an integer multiple of 2. Therefore, only the specific frequencies of the light which satisfy the resonance condition can meet the oscillate condition:

， q 为整数qLcf

=2

激光腔驻波原理 当光波在腔镜中来回反射时，入射波和反射波会发生干涉。为在腔内形成稳定的震荡，要求光波因干涉得到加强，即光波在腔内往返一周的总相移为 2 的整数倍。因此，只有特定频率的光才能满足谐振条件：

， q 为整数qLcf

=2

Mode of the laser (1): longitudinal mode

qLcf

=2 L

c2

=Frequency spacing

Frequency

Realistic：Ideal ：

激光的模式（ 1）：纵模qL

cf

=2 L

c2

=模式间隔频率对于一般的增益介质：

理想状况：

Mode of the laser (1): longitudinal mode

qLcf

=2 L

c2

=模式间隔频率 The wave inside the laser has to be standing

wave: qL =2

Different longitudinal mode pattern represents the monochromatics of a laser

激光的模式（ 1）：纵模2cf qL

= Lc

2=模式间隔频率

由电磁波理论可知，激光腔内的波必须是驻波，即满足条件 qL =2

不同纵模模式代表了激光器的单色性

Mode of the laser (1): longitudinal mode

The longitudinal mode representatives the monochromatics of the laser

Homogeneously broadened medium, the mode of competition will bring a decline in the overall gain, making only one longitudinal mode oscillates - single longitudinal mode operation

Most of the media are non-homogeneously broadened medium, which requires other techniques to deliver single longitudinal mode operation.

增益阈值

激光的模式（ 1）：纵模 纵模代表了激光的单色性 在均匀加宽工作介质中，模式竞争会带来整体增益下降，使得只有一个纵模震荡—单纵模运转 大部分介质为非均匀加宽介质，需要其他技术来实现单纵模运转

增益阈值

激光的模式（ 1）：纵模

In the inhomogeneous broadening gain medium, the laser radiation will cause "gain hole burning" effect

在非均匀加宽增益介质中，由于激光的辐射会造成“增益烧孔”效应。

He-Ne laser application example In a normal He-Ne laser, the central fluorescence

frequency of the Ne atom (wavelength 632.8nm) is , its linewidth

Set q=1, to a cavity length L=30cm laser,

Therefore, we can have 3 longitudinal modes. There corresponding wavelengths are:

Hz1074.4 14=Hz105.1 9= f

Hz105.0 9=

=

f

c

He-Ne 激光器应用实例 在普通的 He-Ne 激光器中， Ne 原子辉光放电荧光光谱中心频率 (波长

632.8nm) ，其线宽 设 q=1, 对于腔长 L=30cm 的激光器，

因此，可出现 3 个纵模。其波长分别为：

Hz1074.4 14=Hz105.1 9= f

Hz105.0 9=

=

f

c

Laser mode (2): transversal mode When the laser oscillates in the resonant cavity, as it is

reflected by the resonator back and forth, the mirror border diffraction effect after a certain number of times will cause the transverse field distribution of the light beam reaching a balance. This distribution is referred to as the transverse mode of the laser beam.

=

211cos11

2ggnmq

Lc

mnq n

=

211cos121

2ggnmq

Lc

mnq n

11 1

RLg =

22 1

RLg =

A stabled cavity output:(square mirror)

(round mirror)

，L is the cavity length of the resonant cavity; R1, R2 is the radius of curvature of the two spherical mirrors; m and n are the ordinal number of the transverse modes; q is the ordinal number of the longitudinal mode; η is the refractive index for laser working medium.

Where are the parameters of the cavity.

激光的模式（ 2）：横模 当激光在谐振腔内震荡的时候，由于谐振腔的来回反射，以及腔镜限制引起的衍射效应，在经过一定次数后，光束的横向场分布便趋于平衡。这一分布被称为激光的横模。

=

211cos11

2ggnmq

Lc

mnq n

=

211cos121

2ggnmq

Lc

mnq n

11 1

RLg =

22 1

RLg =

稳定腔的输出频率特性为：( 方形镜 )

(圆形镜 )

，

L 为谐振腔的腔长； R1 、 R2 为两个球面反射镜的曲率半径；m 和n 为横模序数； q 为纵模序数； η 为激光工作介质的折射率。

其中： 为腔参数；

Laser mode (2): transversal mode

Transverse mode intensity distribution of the squar mirror

Except those with special needs, generally the fundamental transverse mode should be used, as it has the following characteristics: high brightness, small divergence angle, more uniform light intensity distribution in the radial cross section of the laser beam, equal phase at the cross section points, and best spatial coherence.

Transverse mode intensity distribution of the round mirror

激光的模式（ 2）：横模

方形镜一些低阶模式的光强图样； 圆形镜一些低阶模式的光强图样。 除有特殊需要外，一般都选择基横模输出，因为基横模有以下特点：亮度高 、发散角小 、在激光光束的横截面上径向光强分布较均匀 、横截面上各点的位相相同，空间相干性最好。

Gaussian beam along the z-axis is a variant of the center of curvature and radius of curvature of the spherical wave. At the waist and infinity the wavefront is flat, in which the radius of curvature is infinite; in ，

Gaussian intensity distribution

The general stability of the spherical cavity can be found in its sole corresponding equivalent confocal cavity. Stable cavity light field of a Gaussian beam.

fz =

0W

f =

fR f 2=（ is the confocal parameter),

there exists the minimal curvature radius

http://202.113.13.85/webclass/gdzjsh/experiments/notes/13.doc

Gaussian intensity distribution

一般稳定球面腔都可以找到与其唯一对应的等价共焦腔。稳定腔的光场为高斯光束。 fz =

0W

f = fR f 2=

高斯光束沿 z轴是一个变曲率中心和曲率半径的球面波。在束腰和无穷远处的波阵面是平面 ,曲率半径无限大 ; 在 ，（ 为共焦参量 ), 曲率半径有最小值

http://202.113.13.85/webclass/gdzjsh/experiments/notes/13.doc

Gaussian beamSize of the beam W(z)changes with z with hyperbolically:

12

2

20

2

=fz

WzW

LWz

zWze

2222lim

0/1 2 ===

0)( 1)(2 = nmnm

012 = nmmn

z=0, W(0) reaches min, called waist, written as W0

Corresponding high-order modes divergence angle: ( 方镜 )

(圆镜 )

The far-fielddivergence angle (full angle) of a confocal cavity fundamental mode

高斯光束光斑尺寸W(z)随坐标 z 按双曲线规律变化 :

12

2

20

2

=fz

WzW

LWz

zWze

2222lim

0/1 2 ===

0)( 1)(2 = nmnm

012 = nmmn

其中 z=0 处的 W(0) 最小 , 称为束腰 ,记为 W0;

相应高阶横模的远场发散角 ( 方镜 )

(圆镜 )

共焦腔基模远场发散角（全角）

M2 factot

2

0 0

The product of the actual beam waist spot radius and far-field divergence angleThe product of the fundamental mode beam waist spot radius and far-field divergence angle

mn mnWMW

= =

2

00 =W 21)(2)()( = nmW nmnm

212 = nmW mnmn

where , (square mirror)

The fundamental mode Gaussian beam having the smallest M2 value (M2 = 1). he beam waist radius and the angle of divergence is also minimized, to achieve the diffraction limit. high-order, multi-mode Gaussian beam or other non-ideal light beam (such as wavefront aberration) M2 values are greater than the the M2 values can characterize the actual beam deviates from the extent of the diffraction limit, so called diffraction magnification factor M2 larger the value the faster the divergence of beam diffraction.

(round mirror).

The beam diffraction magnification factor M2 is widely accepted as parameter to evaluate the quality of the laser beam in space. It is defined as:

M2因子00

2

WW

M mnmn==径与远场发散角的乘积基模高斯光束的腰斑半

远场发散角的乘积实际光束的腰斑半径与

2

00 =W 21)(2)()( = nmW nmnm

212 = nmW mnmn

其中 , , ( 方镜 ),

由以上论述可知 , 基模高斯光束具有最小的 M2值 (M2=1), 其光腰半径和发散角也最小 , 达到衍射极限高阶、多模高斯光束或其他非理想光束 ( 如波前畸变 ) 的 M2值均大于 1. M2值可以表征实际光束偏离衍射极限的程度 ,因此被称为衍射倍率因子 . M2值越大 , 光束衍射发散越快。

(圆镜 ) 。

目前国际上普遍将光束衍射倍率因子 M2 作为衡量激光光束空域质量的参量 . 其定义为 :

Measure the divergence angle experimentally

Laser CCD

1m

FilterM1

M2

M3

M41

2

First adjust to guarentee that between 1 and 2, the optical path is greater than 8 meters (4 bounds). With the CCD the beam profile is measured at the position 1 (z1) and position 2 (Z2) to obtain the spot radius W (z1) and W (z). Using the formula

12

122zz

zWzW

=The far-field divergence angle can be estimated.

测量激光发散角实验Laser CCD

1m

FilterM1

M2

M3

M41

2

首先调整位置 1 和 2 之间的光程大于 8 米 (4次往返 ), 分别用 CCD 在位置 1(z1) 和位置2(z2) 处测量出光斑半径W(z1) 和 W(z2),利用公式

12

122zz

zWzW

= 可以估算出该模式的远场发散角。

Different laser types (by the gain medium) Gas laser气体激光器： He-Ne, Ar+, CO2 Solid-state laser固体激光器： Nd:YAG,

Ti:Sapphire Dye laser染料激光器 Diode laser半导体激光器 Fiber laser 光纤激光器

He-Ne Laser

Working principle: the gas discharge; energy to the He atom; energy transfer from He to Ne atom; laser

Wavelengths: 632.8nm,1.15um,3.39um Medical application: the continuous wave laser output with

power of 5 ~ 50mw, wavelength 632.8nm, as a "light-needle” and irradiated tools, has a good effect on the treatment of the ulcer.

http://www.walshcomptech.com/repairfaq/sam/onebrew3.gifhttp://www.chinalaser.com.cn/CN/News/2004-12-27/5584.shtml

He-Ne Laser

工作原理：气体放电 -将能量传给 He 原子 -Ne 原子 - 产生激光 波长： 632.8nm,1.15um,3.39um 医疗上常用的是输出功率 5~50mw 的连续激光，主要波长是

632.8nm ，用作“光针”和照射的工具，对溃疡的治疗有较好的疗效。http://www.walshcomptech.com/repairfaq/sam/onebrew3.gif

http://www.chinalaser.com.cn/CN/News/2004-12-27/5584.shtml

When natural light is incident to the surface of the medium, the reflected light refracted light is partially polarized.

i1n2n

When the light incident from medium 1 with the refractive index n1to a medium 2 with refractive index n2, when the incident angle satisfying:

1. Polarization in reflection and refraction

In reflected light, those vibration direction perpendicular to the incident plane is dominant over those parallel to the incident plane.

In refracted light, the vibration parallel to the direction of the incident plane is dominant over the component perpendicular to the incident plane

1

2tgnnib =

2. Brewster’s Law

当自然光入射到介质表面时，反射光和折射光都是部分偏振光。i

1n2n

光从折射率为 n1 的介质射向折射率为 n2 的介质时，当入射角满足 :

一、反射和折射的偏振光

反射光中振动方向垂直入射面的成分比平行于入射面的成分占优势； 折射光中振动方向平行入射面的成分比垂直于入射面的成分占优势；

1

2tgnnib =

二、布儒斯特定律

1

2tgnnib =

bi

1n2n

bi

0r

2

= rib

From the law of refraction

1

2

sinsin

nn

rib = and Brewster’s

law

The reflected light becomes completely polarized light, with vibration direction perpendicular to the incident. The refracted light is still partially polarized.

is called Brewster’s angle

biBrewster’s law

1

2tgnnib =

It can be proved: When the angle of incidence equals ib, reflected light and refracted light is perpendicular to each other. Namely:

1

2tgnnib =

bi

1n2n

bi

0r

2

= rib

由折射定律1

2

sinsin

nn

rib = 和布儒斯特定律

反射光就变为振动方向垂直于入射面的完全偏振光。而折射光仍为部分偏振光。称为布儒斯特角bi

布儒斯特定律

1

2tgnnib =

可以证明：当入射角等于 ib 时，反射光和折射光相互垂直。即：

• Glass n2=1.5 ， = 3.56biBrewster’s angle• Water n2=1.33 ， = 1.53bi注意：

1 ） When the angle of incidence is the Brewster angle, the reflected light is polarized light, and the vibration direction perpendicular to the line of the incident surface and refracted light Remaining components are dominant vibration direction parallel to the incident surface of partially polarized.2 ） Note the difference between the Brewster’’s angle and the angle of total internal reflection:Different conditions. Total internal reflection happens when n1>n2 (inside medium); Brewster angle has no such requirement.

Total reflection occurs when the incident angle is greater than the angle of total reflection, but only when the angle of incidence is the Brewster’s angle, the reflected light can be completely linearly polarized.

• 玻璃n2=1.5 ， = 3.56bi布儒斯特角• 水n2=1.33 ， = 1.53bi注意：

1 ）当入射角为布儒斯特角时，反射光为振动方向垂直入射面的线偏振光，而折射光仍为振动方向平行于入射面的成分占优势的部分偏振光。2 ）要注意布儒斯特角与全反射角的区别： 两者条件不同。全反射时对 n1 、 n2 有要求；而布儒斯特角无此要求； 入射角大于全反射角时都会发生全反射，但只有入射角为布儒斯特角时反射光才是完全线偏振光。

The use of glass stack can produce a strong reflection of polarized light.

0r

bi bi

Theory and experiments have proved that: the linear polarized reflection accounted for only 7.4% of the total energy of the incident natural light, while about 85% of the vertical component remains in the refraction.

To obtain a larger intensity linear polarized light, a stack of glass plate can be used. A bouquet of natural light from the declination 56.30 incident on the 20-layer plate glass

In the lower layer of the glass plate, the incident angle of 33.70 satisfies the Brewster’s angle from the glass directed to the air from the polarization angle, so the reflected light is still perpendicular to the incident plane polarized light vibrating.

利用玻璃片堆可产生较强的反射偏振光。0r

bi bi

理论实验表明：反射所获得的线偏光仅占入射自然光总能量的 7.4% ，而约占 85% 的垂直分量和全部平行分量都折射到玻璃中。 为了获得强度较大的线偏振光，可采用玻璃片堆的办法。一束自然光以起偏角 56.30 入射到 20 层平板玻璃上， 在玻璃片下表面处的反射，其入射 33.70 也正是光从玻璃射向空气的起偏振角，所以反射光仍是垂直于入射面振动的偏振光。如图：

He-Ne Laser

http://www.walshcomptech.com/repairfaq/sam/onebrew3.gifhttp://www.chinalaser.com.cn/CN/News/2004-12-27/5584.shtml

CO2 Lasers

The carbon dioxide gas laser is the most efficient gas laser, with a power conversion rate of 20%. The operating wavelength is located 10.6um. Carbon dioxide laser of the fixed wavelength has been used widely in industry, with intensity as high as tens of KW.

二氧化碳激光器是最有效的气体激光器，功率转换率达到 20% 。工作波长位于 10mm附近，很多工业作业用的是固定波长的二氧化碳激光器。工业上使用的二氧化碳激光器输出功率最高可以达到几十千瓦的量级。

固体激光器 Solid-state laser

• Nd:YAG 1.06um (Frequency double:532nm)• Ti:Sapphire: 800nm

http://www.nasa.gov/centers/langley/images/content/69852main_LaserTech-fig2.gif

Tunable Dye LaserMany organic dyes can be used as the laser medium. One of the most common is the Rhodamine 6G, dissolved in methanol or ethylene glycol.

Transitions of the upper and lower states are split into continuous energy bands due to interactions with the solvent. After excitation, the molecules are relaxed to the lowest level of the excited band quickly with non-radiative transition, then transmit to the ground state energy level and thus produce fluorescent radiation. The radiated fluorescence spectrum does not vary with the excitation light source.

Tunable Dye Laser

很多有机染料可以被用作激光介质。其中最常见的是若丹明6G（ Rhodamine 6G），溶于甲醇或者乙二醇。跃迁上下能级由于和溶剂的相互作用而分裂为连续的能带。分子被激发到上能带后迅速无辐射弛豫到上能带的最低能级，并由此向基态各能级跃迁，产生荧光辐射。辐射荧光曲线不随激发光源的改变而改变。

If a small chamber filled with the dye solution was placed in the laser cavity with sufficient pump energy, it can emit laser light. If a broadband laser mirrors is employed, stimulated emission occurred near the fluorescence emission vertex for several tens of Å. For single wavelength output, reflective grating can be used instead, to reduce the radiation bandwidth down to 0.5 Å. By rotating the grating, allows the laser output can cover the whole range of the fluorescence emission band. A flash light can be used as a pump to obtain a laser pulse with duration of 1ms, repetition frequency of 1Hz, and a few kW peak power output. A fixed wavelength laser can also be used as a pump, for example, nitrogen molecular laser, excimer laser, a copper vapor laser, or multiplier after Nd: YAG laser.

如果将充有染料溶液的小室放置于激光腔内，并提供足够的泵浦能 量，则可以放出激光。如果使用宽带激光反射镜，受激辐射在荧光发射曲线顶点的周围几十个 Å附近发生。可以把反射镜用光栅代替。激发辐射带宽降低到 0.5 Å 。通过转动光栅，可以让激光在整个荧光发射带范围内调节。泵浦可以用闪光灯来实现，得到的激光脉宽 1ms ，峰值功率大概几 kW，重复频率 1Hz 。也可以用固定波长激光器，例如氮分子激光器，准分子激光器，铜蒸气激光器或倍频后的 Nd: YAG 激光器。

Semiconductor LasersTypical semiconductor laser medium is the doped GaAs. The laser is generated between the medium from the p-type dopant and n-type doped. The applied electric field causes the electrons and the holes are close to the middle, which is formed in the conduction band relative to the valence band holes inversion. Can produce energy equivalent to the band gap energy by stimulated emission of photons. The semiconductor laser can be very compact, with which a typical size of less than 1mm.

Limited by the diffraction and size, the spatial mode of a LD is generally not good, with an output spot of large aspect ratio.

Semiconductor Lasers典型半导体激光器介质是掺杂 GaAs 。激光是从 p型掺杂和 n型掺杂的介质之间发出。外加电场使得电子和空穴都向中间靠近，从而在导带形成相对于价带空穴的粒子数反转。可以产生能量相当于带隙能量的受激发射光子。半导体激光器可以做的非常小，典型尺寸小于 1mm 。

受到尺寸的衍射限制，半导体激光器的空间模式一般不好，光斑纵横比较大。

The semiconductor laser may be used for the red light, in particular the infrared band. Most of the media need to use with cooling, but GaAs can be used for room temperature. By changing the temperature, tunable lasers with output between 800 to 900nm can be obtained with LD.Using several different media, LD can cover the range of about 40um of the infrared spectral band.

半导体激光器可以用于红光，特别是红外波段。多数介质需要在使用的时候进行冷却， GaAs则可用于室温。通过改变温度，可以在 800 到900nm 之间调谐激光器。使用几种不同的介质，可以覆盖红外光谱波段 40mm左右的范围。

激光的特性 Monochromatic: the spectral width of the

laser light (0.1nm) is better than ordinary light source 2-3 orders of magnitude.

Collimation: the divergence angle of the laser (mrad) is only ~1/1000 of general light source (2pi radians)

Brightness: small divergence angle, leading to the laser intensity 108-1010 times than the ordinary light sources.

http://www.fou.uib.no/fd/1996/h/404001/kap04.htm

激光的特性单色性：激光的光谱宽度 (0.1nm) 比普通光源好

2-3 个数量级。准直性：激光的发散角 (mrad)仅是一般光源 2pi弧度的千分之几 高亮度：由于激光的发散角小，其亮度比同强度普通光源高 108-1010 倍。 相干性好

http://www.fou.uib.no/fd/1996/h/404001/kap04.htm

激光的特性 Coherence: The natural light has a random phase, so the

overall diffraction effect is averaged, therefore it is called non-coherent light. Because the wave of laser is generated by stimulated emission of radiation, it maintains the same phase; and therefore interference can be easily observed.

相干性：一般光源发出的波列位相是杂散的，整体上观察不到衍射效应，因此称为非相干光。激光由于其波列由受激辐射产生，因此保持了同样的位相，因而很容易产生干涉效应。

CW and Pulsed laser

T

平均功率重复频率 repetition rate脉冲宽度 pulse width (duration)脉冲功率 pulse intensity占空比 aspect ratio峰值功率 peak power

t

平均功率Average power

A Ti:Sa laser with output of 500mW ， pulse duration of 100fs ， 100MHz repetition rate, calculate its peak power and pulse energy. A Nd:YAG 532nm ， pulse duration 10ns ， repetition rate of 10Hz ， 100mJ/pulse laser ， calculate its average power and peak power.

1. 峰值功率 =500mW/占空比 =5x10^4W ，脉冲能量=500mW/100MHz=5nJ

2. 平均功率=100mJx10Hz=1W峰值功率 =1W/(10ns*10Hz)=10^7W

连续激光与脉冲激光

T

平均功率重复频率脉冲宽度脉冲功率占空比峰值功率t

平均功率

A Ti:Sa laser with output of 500mW ， pulse duration of 100fs ， 100MHz repetition rate, calculate its peak power and pulse energy. A Nd:YAG 532nm ， pulse duration 10ns ， repetition rate of 10Hz ， 100mJ/pulse laser ， calculate its average power and peak power.

为什么生物医学要使用脉冲激光？High peak intensity( effectively use of the

photons in a short time; multi-photon effect; opto-mechanical effect)

Low average power (to protect the sample)

高脉冲能量（在短的时间过程有效利用光子；多光子效应；产生光机械作用）低平均功率（保护样品）

Q: How to create a large water flow from a river?

A: Build a dam.

Magic material: saturation absorber (to

low intensity it is opaque, but to high

intensity it is transparent)

Basic principles of ultrafast lasersComponents of ultrafast laser system

Pump

HRGain

OCMode-locking

Mechanism

Dispersion

Compensation

Cavity modes

n = 2 L/n f = c/2 L

Concepts of Mode Locking

Out of phase

RANDOM phase for all the laser modes Irradiance vs. Time

Time Time

Out of phase Out of phaseIn phase

LOCKED phases for all the laser modes

Mode locking is a method to obtain ultrafast pulses from lasers, which are then called mode-locked lasers mode

Basic principles of ultrafast lasersBandwidth vs Pulsewidth

narrow spectrum

continuous wave (CW)

broader spectrum

pulses (mode-locked)

broadest spectrum

shortest pulses

bandwidthn

durationt

nt = const.

Active mode-locking Acousto-optic modulator Synchronous pump mode-locking

Passive mode-locking Saturable absorber (dye, solid state) Optical Kerr effect

Mode-locking Mechanisms

Pow

er

Time

Pow

er

Time

cw cw MLP

ower

Time

Q-switch Pow

erTime

Q-sw.ML

Types of Laser Output

Low-intensity beam

High-intensity ultrashort pulse

Focused pulse

Kerr medium (n = n0 + n2I)

Kerr-Lensing

Intensity dependent refractive index: n = n0 + n2I(x,t)

Spatial (self-focusing)• provides loss modulation with suitable

placement of gain medium (and a hard aperture)

Temporal (self-phase modulation)• provides pulse shortening mechanism with

group velocity dispersion

Optical Kerr Effect

Refractive index depends on light intensity: n (I)= n + n2 I

self phase modulation dueto temporal intensity variation

self-focusing due totransversal mode profile

Optical Kerr Effect

Optical pulse in a transparent medium stretches because of GVD

Group Velocity Dispersion (GVD)

• v = c / n – speed of light ina medium

• n –depends on wavelength, dn/dl < 0 – normal dispersion

• High-intensity modes have smaller cross-section and are less lossy. Thus, Kerr-lens is similar to saturating absorber!

• Some lasing materials (e.g. Ti:Sapphire) can act as Kerr-media

• Kerr’s effect is much faster than saturating absorber allowing one generate very short pulses (~5 fs).

Prism compensator

Wavelengthtuning mask

“Red” component of the pulse propagates in glass where group velocity is smaller than for the “blue” component

GVD CompensationGVD can be compensated if optical pathlength is different for “blue” and “red”

components of the pulse.

Components of an Ultrafast Laser

Pulse shortening mechanism• Self phase modulation and group velocity

dispersion

Dispersion Compensation

Starting Mechanism

Regenerative initiation• Cavity perturbation• Saturable Absorber (SESAM)

Cavity configuration of Ti:Sapphire laser

Tuning range 700-1000 nmPulse duration < 20 fs Pulse energy < 10 nJRepetition rate 80 – 1000 MHzPump power: 2-15 W

Typical applications:

• time-resolved emissionstudies• multi-photon absorptionspectroscopy • imaging

Amplification of fs Pulses

Oscillator Stretcher Amplifier Compressor

• Stretch femtosecond oscillator pulse by 103 to 104 times• Amplify• Recompress amplified pulse

Concept:

Chirped pulse amplification

• Femtosecond pulses can be amplified to petawatt powers• Pulses so intense that electrons stripped rapidly from atoms

Homework

Use Matlab to simulate a laser cavity, and see how the standing wave forms after multiple times of reflection. Hints:1. How to simulate the amplitude of a light wave?2. How to describe reflected wave?3. How to describe the total intensity?4. Is the cavity length important to the form of the

standing wave?

Homework共焦腔 He-Ne 激光器中， L=30cm ，波长

632.8nm ，则全角发散角为 2.3x10-3rad.

LWz

zWze

2222lim

0/1 2 ===

总结 激光： Light Amplification Stimulated

Emission Radiation 产生激光的条件：粒子数反转谐振腔+ 工作物质 +泵浦源纵模：激光波长有关横模：激光的方向性有关 激光的特性：单色性、准直性、高亮度、相干性

推荐课后读物：上帝掷骰子吗——量子史话 http://book.sina.com.cn/nzt/liangzishihua/