Laser Fundamentals I | MIT Understanding Lasers and Fiberoptics

Summary

The video script offers an insightful introduction to the course 'Understanding Lasers and Fiber Optics'. It covers the fundamental properties of lasers, such as high monochromaticity and spatial coherence, and their applications in various fields. The instructor promises a simplified approach, focusing on basics over complex details, to make the course accessible to a wider audience. The script also delves into the unique properties of lasers, including their narrow spectral width and high temporal coherence, essential for applications like holography and fiber optic communication.

Takeaways

• 📚 The script is from a course on 'Understanding Lasers and Fiber Optics', aiming to cover various fundamental aspects of lasers and their applications.
• 🌟 It emphasizes the unique properties of lasers, such as high monochromaticity, high coherence, and the ability to produce an extremely narrow spectral width, which is vital for numerous applications.
• 🔍 The course will explore how lasers achieve such properties, starting with the basic principles of oscillators and extending to the concept of an optical oscillator, which is fundamental to laser operation.
• 🎓 The presentation style is simplified to make the material accessible to people without specialized backgrounds, focusing on fundamentals with minimal mathematical complexity.
• 🕊️ The script mentions a variety of applications for lasers, including barcode readers, CD players, laser printers, holography, sensors, fiber optic communication, materials processing, non-destructive testing, spectroscopy, military uses, and medical diagnostics.
• 🔑 The script introduces the concept of a resonator, which is crucial for determining the frequency of the laser and involves two mirrors to create standing waves for different modes.
• 💡 The importance of a light amplifier within the laser cavity is highlighted as it provides the necessary gain to overcome losses and maintain oscillation.
• 🔬 The course will delve into the practical aspects of laser operation, including the issues and problems associated with lasers and how they can be mitigated.
• 🌈 The variety of lasers and their specific characteristics will be discussed, including how different lasers are pumped and operate.
• 🌐 The basics of fiber optics will also be introduced, setting the stage for understanding the principles and applications of fiber optic communication.
• 🚀 The script promises to touch on future developments in both lasers and fiber optics, indicating the ongoing innovation and advancement in these fields.

Q & A

What is the main topic of the short course presented in the script?

The main topic of the short course is 'Understanding Lasers and Fiber Optics', covering various aspects of lasers, their properties, applications, and fiber optics basics.

Why are lasers of significant interest today?

Lasers are of significant interest due to their unique properties that enable a wide range of applications, from barcode readers and compact disks to medical diagnostics and military systems.

What are the key properties of lasers that make various applications possible?

The key properties of lasers include high monochromaticity, high coherence, high collimation, high spatial coherence, and the ability to produce high power, tunable wavelengths, and short pulse widths.

What is meant by the term 'monochromaticity' in the context of lasers?

Monochromaticity refers to the property of lasers emitting light of a single color or having a very narrow spectral width, which is essential for high-resolution applications.

How does the script describe the operation of a simple laser?

The script describes the operation of a simple laser by discussing the need for a resonator (laser cavity) and a light amplifier to overcome losses and achieve a continuous, coherent light output.

What are some of the practical issues and problems associated with lasers?

Practical issues with lasers include imperfections in their operation, potential problems if not treated properly, and the need to minimize or eliminate certain issues that can arise from their use.

What is the significance of the coherence time in lasers?

The coherence time in lasers is significant because it determines the duration over which the phase and amplitude of the laser light can be predicted accurately, which is crucial for applications like holography and interferometry.

How do the properties of lasers contribute to fiber optic communication?

The properties of lasers, particularly their high monochromaticity and coherence, contribute to fiber optic communication by allowing for the transmission of data over long distances with minimal distortion and high bandwidth.

What is the role of the light amplifier in a laser system?

The light amplifier in a laser system provides gain to the light oscillating within the laser cavity, overcoming losses and enabling the production of a continuous, coherent light output.

How does the script differentiate between continuous wave (CW) lasers and pulsed lasers?

The script differentiates between continuous wave (CW) lasers, which produce a constant, uninterrupted beam of light, and pulsed lasers, which emit light in short, discrete pulses of high power.

What is the purpose of using demonstrations in the course as mentioned in the script?

Demonstrations are used in the course to illustrate fundamental phenomena in lasers and fiber optics, making the concepts more understandable and engaging for people without specialized backgrounds.

What is the relationship between the spectral width of a laser and its coherence properties?

The spectral width of a laser is directly related to its coherence properties. A laser with a very narrow spectral width exhibits high temporal coherence, meaning it maintains a constant phase relationship over time, which is essential for applications like high-resolution spectroscopy.

How do the unique properties of lasers enable various applications such as barcode readers and laser shows?

The unique properties of lasers, such as high monochromaticity, coherence, and the ability to focus into a small spot, enable applications like barcode readers by providing precise light for scanning, and laser shows by allowing for the creation of bright, focused beams for visual displays.

Outlines

00:00

📚 Introduction to the Course on Lasers and Fiber Optics

The script introduces a course on 'Understanding Lasers and Fiber Optics' and outlines the topics to be covered. The instructor welcomes the audience and emphasizes the importance of lasers due to their unique properties that enable various applications. The course will delve into the reasons behind the widespread interest in lasers, their key properties, the operation of a simple laser, potential issues, types of lasers, and an introduction to fiber optics. The presentation style will be simplified to cater to a non-specialized audience, focusing on fundamentals with minimal math and plenty of demonstrations.

05:01

🌈 The Unique Properties and Applications of Lasers

This paragraph discusses the unique properties of lasers, such as high monochromaticity, which refers to their single color or narrow spectral width. It also touches on the high temporal coherence of lasers, which is related to the uninterrupted radiation time of atoms. The script provides examples of how these properties contribute to various applications, including barcode readers, compact disks, laser printers, holography, sensors, fiber optic communication, materials processing, non-destructive testing, spectroscopy, military applications, and medical procedures. The wide range of applications is a testament to the versatility and importance of lasers in modern technology.

10:01

🔬 Measuring Spectral Width and Temporal Coherence

The script explains how to measure the spectral width of light sources, such as spectral lamps and lasers, using a spectrometer. It contrasts the broad spectral width of a typical spectral lamp with the extremely narrow spectral width of a laser, which can be in the range of megahertz or even microhertz. The concept of high temporal coherence is introduced, relating it to the uninterrupted radiation time (tau) and its inverse relationship with the spectral line width (delta f). The paragraph also describes how the coherence time is limited to the duration of uninterrupted wavetrains and how this property is crucial for applications like communication, spectroscopy, interferometry, holography, and sensors.

15:01

📡 High Spatial Coherence and Collimation of Lasers

This paragraph delves into the concept of high spatial coherence and collimation in lasers. It explains how the laser beam's high degree of collimation allows for long-distance applications with minimal divergence. The script contrasts this with traditional light sources, which require smaller source sizes or longer focal lengths to achieve similar effects, often at the expense of light intensity. The paragraph also discusses the ability of lasers to produce a very small focus spot due to their diffraction-limited focusing, which is essential for applications like compact discs, laser printers, materials processing, and medical surgery.

20:04

🚀 Applications of Laser Properties in Various Fields

The script highlights the practical applications of laser properties in fields such as alignment, barcode scanning, long-distance communication, and space radar. It also discusses the importance of a laser's small focus spot and high intensity for tasks like cutting, welding, drilling, and medical procedures like retinal surgery. The paragraph emphasizes the advantage of lasers in creating intense, small spots that traditional light sources cannot achieve without losing intensity.

25:07

🔍 Exploring High Spatial Coherence and Its Implications

This paragraph explores the concept of high spatial coherence in lasers, which allows for the prediction of a wave's amplitude and phase at any spatial position at a given time. It contrasts this with traditional light sources that do not exhibit such stable spatial behavior. The script also touches on the ability to create collimated beams and focused spots with high spatial coherence, which is beneficial for applications where precise control of light is required.

30:07

⚡ High Power Capabilities of Lasers and Their Applications

The script discusses the high power capabilities of lasers, both in continuous wave (CW) and pulsed forms. It provides a range of power levels from milliwatts to exowatts, highlighting the versatility of lasers in producing extreme power levels. Applications mentioned include materials processing, fusion research, military uses, and nonlinear optics, which benefit from the high intensity that lasers can generate.

35:10

🌈 Tuning Range and Short Pulse Widths of Lasers

This paragraph covers the wide tuning range of lasers across the electromagnetic spectrum and their ability to produce very short pulse widths. It explains how lasers can be tuned to interact with specific atoms and molecules, study atomic and molecular structures, and be used in medical applications. The script also emphasizes the importance of short pulse widths for studying fast phenomena, high-resolution radar and imaging, and potential applications in optical computing.

40:11

🔧 How Lasers Achieve Their Unique Properties

The script shifts focus to explaining how lasers achieve their unique properties of monochromaticity and high temporal coherence. It introduces the concept of an optical oscillator and compares it with traditional oscillators. The paragraph sets the stage for understanding the workings of a laser by first reviewing the properties of oscillators and how they can be made to produce constant amplitude and narrow spectral width, which are key to the operation of a laser.

45:12

🔄 The Role of Resonators and Amplifiers in Lasers

This paragraph delves into the technical aspects of how lasers function as optical oscillators, highlighting the need for a resonator and an amplifier. It explains the concept of a resonator using two mirrors to create electromagnetic oscillations at specific frequencies. The script also discusses the role of an amplifier in providing gain to overcome losses within the resonator, which is essential for sustaining oscillation and producing the laser's characteristic output.

Keywords

💡Lasers

Lasers are devices that emit light through a process of optical amplification based on the stimulated emission of radiation. In the video, lasers are the central theme, with discussions on their unique properties and applications in various fields such as medicine, communication, and industry.

💡Fiber Optics

Fiber optics refers to the technology of transmitting information as pulses of light through a fiber made of glass or plastic. The script mentions fiber optics as a significant topic, highlighting its basics and issues, as well as its connection to lasers for communication purposes.

💡Monochromaticity

Monochromaticity is the property of having a single color, which in the context of lasers, refers to the high purity of the light's color and its narrow spectral width. The video explains how this property, crucial for applications like holography and spectroscopy, is achieved in lasers.

💡Temporal Coherence

Temporal coherence describes the predictability of a wave's phase over time. The script discusses how lasers have high temporal coherence, meaning the light waves maintain a constant phase relationship, which is vital for applications such as interferometry and holography.

💡Collimation

Collimation refers to the process of making a beam of light parallel. The video script emphasizes that lasers produce highly collimated beams, which is essential for applications requiring precise alignment or long-distance transmission, such as in laser pointers or fiber optic communication.

💡Spectral Width

Spectral width is the range of wavelengths emitted by a light source. The script explains that lasers have an extremely narrow spectral width, which is a key to their monochromaticity and high temporal coherence, and is crucial for high-resolution applications.

💡Demonstrations

Demonstrations in the script refer to the use of visual aids and experiments to illustrate fundamental phenomena in lasers and fiber optics. The instructor intends to use demonstrations to make the complex concepts more understandable and engaging for the audience.

💡Optical Oscillator

An optical oscillator is a system that generates a continuous, coherent beam of light by reflecting it back and forth between two mirrors. The script delves into the concept of an optical oscillator to explain how lasers produce their characteristic narrow spectral width and high coherence.

💡Resonator

A resonator is a part of a laser system that supports the formation of standing waves. The script describes the laser cavity as a type of resonator that defines the laser's frequency and mode, which is essential for achieving the laser's unique properties.

💡Gain

In the context of lasers, gain refers to the amplification of light as it passes through an active medium, overcoming losses in the laser cavity. The script mentions that gain is necessary for the laser action to occur, and it will be discussed in more detail in subsequent sessions.

💡Applications

Applications refer to the various uses of lasers and fiber optics. The script provides numerous examples of applications, such as barcode readers, laser shows, holography, sensors, fiber optic communication, and medical procedures, demonstrating the wide-ranging impact of these technologies.

Highlights

Introduction to the course 'Understanding Lasers and Fiber Optics' and its educational goals.

Explanation of the unique properties of lasers that enable a wide range of applications.

Discussion on how lasers have revolutionized various fields including data storage, printing, and medical procedures.

Overview of the course content, emphasizing the basics of fiber optics and future developments in the field.

Introduction to the concept of monochromaticity and its significance in laser applications.

Illustration of the narrow spectral width of lasers compared to traditional light sources.

Explanation of high temporal coherence and its relation to laser line width.

Demonstration of how to measure the spectral width of lasers using a spectrometer.

Discussion on the applications of high temporal coherence in communication, spectroscopy, and holography.

Introduction to the property of high spatial coherence and its implications for laser beams.

Comparison of laser beams to traditional light sources in terms of collimation and focusability.

Explanation of how laser properties enable precise control in applications like barcode readers and medical surgery.

Overview of the power levels achievable with continuous wave and pulsed lasers.

Discussion on the practical applications of high laser power in materials processing and military uses.

Introduction to the tunability of lasers across the electromagnetic spectrum.

Explanation of how laser tunability is utilized in spectroscopy and medical applications.

Discussion on the ability of lasers to produce extremely short pulse widths and their applications.

Summary of the key properties of lasers and their derivation from the function of an optical oscillator.

Introduction to the concept of an optical oscillator and its role in creating laser properties.

Transcripts

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good morning everyone

wherever you are

i'd like to welcome you to this short

course

entitled

understanding lasers

and fiber optics

and before i do anything

i'd like to

tell you

what sort of topics i'll be covering

i will start with

the many reasons why we're all

interested in lasers today

then

i would like to

talk about the key properties of lasers

that make all these applications

possible

then once we understand these key

properties then i would like to discuss

how these properties

excuse me come about

and then

we'll go describing the operation of a

simple laser and even show you a

demonstration how a simple laser works

what you need to make things happen

and then we look at variety of

properties of this

simple laser

then

we go look at

other issues and problems to do with

with lasers lasers are not perfect and

if you don't treat them right you know

they can give you give you some problems

and in some cases you can get rid of

these problems in some cases well you

try to minimize them

then i will discuss the the variety of

lasers and what makes them tick

because we have all kinds of lasers

today and it's nice to get a feel for

the variety of them and how they work

how they get pumped and so on

then i'm going to change topics and i

will

switch to the basics of fiber optics

and to to familiarize you with what's

going on in fiber optics what are the

issues and but mainly the emphasis on on

on basics and then finally i'll have a

few words to say about future

developments in in lasers and fiber

optics

now

the how will i present uh the material

well

i will be using a very simplified

treatment

and the reason is so that people without

specialized background can can follow

i will emphasize only fundamentals

and

not

not the details so that

the the understanding can be made

very easy

and i will use very little math

i will certainly not emphasize

mathematics because i would like to make

it very understandable and i don't want

to switch people

off

and most important i'll be using lots of

demonstrations

to

to illustrate some of the fundamental

phenomena in lasers and also in in fiber

optics

so now i think we're ready to to start

the course

and the uh

the first topic that i had is why is

there so much interest in in lasers

well

the

the reason why there's so much interest

is because

lasers have these unique properties that

we're going to discuss

and it and it's these unique properties

that make

all these applications happen

now these properties have created all

sorts of new devices

we'll mention a few of them briefly

and

also have improved

many existing

devices so the laser

has been

very nice

in in lots of lots of fields just to

give you some example of of uh just a

few applications

well let's just just look at them just

briefly the barcode readers everybody's

familiar today with barcode readers now

lasers certainly make that possible

and of course the compact disks computer

printers laser color copiers

all these depend on on some of these

properties of lasers that we'll be

discussing

then of course you've seen the laser

shows

and that certainly uses a specific laser

property then there is holography

that's the 3d imaging

the hologram that you see on

on credit cards

that's all due to

lasers then lasers are also used for

precise control of position and

motion

for example

sensors

lasers today can measure all kinds of

things

with fiber optics without fiber optics

or what have you

the

the big area

of today and the future is fiber optic

communication

and again it involves not only fiber

optics but also lasers so we'll see how

the properties of lasers are used for

fiber optic communication

then we have topics like materials

processing like cutting drilling welding

and so on in materials

there is a whole slew of

uh

techniques for non-destructive testing

this is the destruction the testing of

of systems without without having to

destroy them and lasers are quite

sensitive and they can do that without

the need to damage the the systems

then we go to spectroscopy and a variety

of spectroscopic techniques have been

opened up by by the laser

chemical process

then we get to the military application

military systems and we hear a lot about

the

laser

the use of lasers in in the military

and finally least

last but not least we have medical

procedures medical diagnostics using

using lasers

and all these applications come about

because of very few

unique properties of lasers and

certainly in this course we want to make

sure that that we understand those and

how they come about in fact the

we find lasers all over the place today

we find them in the home in the factory

in hospitals in laboratory in the the

military wherever it is in even in space

in the ocean and even in the in the

theater so you can see lasers are

playing a very important role in our

lives today

all right so now i would like to go

and to the next to the next topic and

that is the the unique properties of uh

of lasers

all right so what are these unique

properties

well let's start with

property number one

now some people refer to it as high

monochromaticity

what is monochromaticity well that means

it's one color

and we have to see what what people mean

by that others

refer to it as as a source of light that

has very narrow spectral width

again we want to see what what what it

means

and uh and and others may refer to this

property as high as a as something that

has a high temporal coherence and we

want to understand uh what all what the

meaning of all these things are

so let's start first with

with uh

with the narrow spectral width or the

single color here what i have and i hope

you can see it the colors of the

spectrum

i did the coloring myself and it's

pretty close to to the spectrum with

whatever colors uh i had

now

the the visible range as we all know

extends from about 4 500 angstroms to

about 6

500 angstroms in the in the red

which is about what two thousand

angstroms or so

and that's that's the visible

essentially that's the visible range

now when we compare

uh light sources

to this to this range for example the

spectral lamp that has a very narrow uh

line width or spectral width here it is

here's the typical output of a spectral

lamp let's say here in the yellow and

the width

over which there's this radiation could

be as low as one-tenth of an angstrom

okay or 0.1 angstroms or

in terms of uh frequency it's uh 10 10

gigahertz

and then you can get

some lamps that have smaller line widths

or you can even get them with broader

line width depending on on the

conditions of the discharge and so on

and when we come to to lasers

the line width is extremely narrow the

spectral width is extremely narrow and

it can be in the megahertz

but can also be in the micro hertz now

remember this is 10 to the minus 6 hertz

or even smaller so the laser

is an incredible kind of device device

when it comes to the spectral width

the line width can be extremely narrow

now i know in practice that's not what

one measures but but if you get rid of

some of the effects we'll talk about

external effects then you should be able

to see line widths as narrow as narrow

as that all right so so the laser then

is is extremely extremely narrow

the uh

let's see how now let's see how you

might uh

measure the uh the spectral width so you

don't have to take my word for it let's

see how you might measure it well if you

took a typical spectral lamp here and

then collect some of the light from it

and put it into a spectrometer or some

other device

device that measures the spectrum then

what you get you get a plot like this

intensity versus wavelength and here you

can either plot wavelength or you can

plot frequency depending on

the kind of work you do

and then you'll see some blob like this

and it has a certain width over which

the the the source radiates and we call

it either delta lambda for the width or

or delta f

now

when we compare it with a

with a laser again we'll do the same

thing we'll take the laser and feed it

into a spectrometer or some other device

the width here can be very narrow and

just like i said before can be

even as narrow as micro hertz

but these are only under special

conditions but even if it's uh megahertz

or tens of megahertz it's way narrower

than you get from from a from a lamp

so again if you're not sure then you

have to do the experiment and check

indeed that the laser does give you an

extremely narrow

narrow line width all right so that's

basically then the the the line width of

the of the laser

now the next thing is what about

high temporal coherence what has that

got to do with the line width of the

laser all right so now we need to

explain that topic

now

let's start first with with a wave with

a sine wave

okay now the sine wave let's say starts

from

minus infinity in terms of time and goes

all the way to plus infinity completely

uninterrupted a pure sine wave now if

you had a wave like this that has a

constant frequency and a constant

amplitude

then when you look at its spectrum on

the in the frequency in the frequency

domain

what you see you see something that's

let's say centered at at f zero f sub

zero with a width delta f here very

close to to zero all right now this is a

source

of radiation it's like a sun wave like

this that has

that has what we call perfect temporal

coherence or time coherence and that's

the best essentially the best that one

can have

now in in in practice

uh light sources

uh do not

radiate for such a long for a long time

without any phase interruption so let's

say we have a light source like this

that that radiates only for a time town

and then shuts off for example

now this one because it's it only

radiates for a time tau it's going to

have a line width in the frequency

domain it's going to it's not going to

be

a delta function like we had before and

this width if you do the calculation

this width in terms of frequency is

proportional to 1 over the the length of

this wave train tau

again i put approximate so that i don't

get into trouble about the exact numbers

but it's very close to delta f is one

over tau

so that if tau is very long if tau is

very long then delta f is small as we've

shown you before but if tau is short

then the

line width here will will grow

now

atoms

for example because this is where we get

our radiation from from atoms they

radiate in bursts

bursts like like this

now if they radiate in bursts like this

then then tau can be sometimes can be

quite short which means that the width

of the radiation will be will be uh

broader so the shorter this is then the

broader this this width and here i show

bursts from other atoms and when you put

them all together essentially that's

what you get you get a certain width

that's characteristic of the time of the

uninterrupted radiation of atom and here

we get an interruption therefore the tau

then is only when the wave is is

uninterrupted now some other atoms

will radiate in in decaying

sinusoids exponentially decaying sinus

so it doesn't matter the calculation is

a little bit

trickier but again you get a sort of

width and for the purpose of this course

uh all i'm after is is the uh is the uh

is the dominant width and i'm not

worried about little side bands down

here just just the width and again you

can say that the width here is of the

order of one over tau whether it's

exponentially decaying or it looks like

this or what have you

all right then then to summarize now

high temporal coherence means that the

radiation time

of the atoms without phase interruption

is very long because the line width is

one over tau

would be very small

and when you have

something that has a high temporal

coherence which means tau very long it

means that you can predict

the amplitude and the phase of the wave

at uh at any time every time because

it's a pure wave in fact if i go back to

to this uh plot over here so this is

where you have

infinite uh

coherence

it means that if i know the amplitude

and phase of the wave at this time

i can only with using a clock i can

predict exactly what the amplitude and

phase of the wave would be at some other

time later and the separation in the

time can be can be very long

when when we get to

uh

when we get into

into sources that radiate like this then

obviously within

this time

i can predict uh the the amplitude and

phase of the wave but if i stretch the

time a little further bigger than this

tau then i cannot

predict any more the amplitude in the

face because this is like another

another

waveform that is completely uncorrelated

with the first one so what we call the

coherence time now is going to be

limited only to this time during which

the the uh the uh

the wave is uninterrupted

then you might ask well what are typical

applications of of of this of this

unique property

well

the uh the fact that it has narrow line

with can be used in uh in communication

certainly that's a key key property here

in spectroscopy especially in high

resolution spectroscopy in

interferometry

uh holography and a variety of sensors

so that's a that's a key property for

for many many applications

now

what i'd like to do is discuss the

second what i call the second unique

property of uh of lasers

now here it is

the many ways of of describing it one

way is

that the laser is has a highly

collimated beam and we've seen that in

laser shows and what have you that the

laser has a highly collimated beam

other people

may use more better scientific language

and would call it a diffraction limited

collimation and we want to know what

that means

to sum

the fact that the laser has a very small

focus spot is a is this meaning of this

property

and others may call it again in a better

scientific language it's a diffraction

limited focus

all right so whether it's diffraction

limited collimation diffraction limited

focusing or even

as others might call it laser has high

spatial coherence they all mean

essentially the same thing and let's

find out now what uh what we mean by uh

by all these

uh words

all right let's go back and look at a uh

a typical uh a typical light source

let's say let's spectral lamp we have uh

electrodes here plus and minus we have

an arc here and then we collect the

light from the arc with the lens and

that's placed at the at the focus of the

lens here this distance here f is the

focal length of the lens so now we try

to collimate this uh this light source

well what sort of collimation do we get

you can see here that this point this

one end of the of the uh of the uh

discharge

or uh

is you you collect these two arrays from

here and you create a collimated beam in

this direction

uh the other end of this arc for example

the other extreme will give you a

collimated beam in this direction and

when you put them together you have this

this widely

diverging beam

now you can easily estimate the angle of

this beam in fact the angle of the

divergence of this beam theta is given

by h which is half

the

the size of the source here

in this case it's an arc it could be

discharge lamp or whatever

half the size of the of the source

divided by the focal length of the lens

and so so the

so if if you don't like if this angle is

too big then the only thing you can do

is either reduce the size of the source

or increase

the

focal length of the lens

now if you let's look at the increasing

the focal length of the lens if you

increase

the focal length of the lens means

you've got to put it

way far from from the source if you do

that you're going to lose a lot of light

so you may get a better collimation but

there's not going to be much light in it

the other

thing to work on is h the size of

of the source and clearly if you make it

smaller and smaller then the collimation

will be better and better

and that's how

pre-laser days that's how one got

collimated beams with a lot of light in

them because you try to generate sources

that have their very small socks

now let's see what's the best one can do

here

well the best one can do

is called diffraction limited

collimation

and here if you do the the

physics of it

uh if you have a beam

that's of diameter d

then the best you can do this is now a

perfect

optical beam light beam or what have you

beam electromagnetic radiation

diameter d i don't care whether it's

microwave optical

uv or whatever whatever then the best

you can do in terms of divergence angle

is lambda

divided by d lambda being the wavelength

of the light dividing by d as simple as

that and i make it approximate here

because it's just a small factor here

which i'm not going to worry about in

this in this course the critical thing

it depends on the ratio of lambda the

wavelength over d the shorter the lambda

the better the collimation the larger d

the better the collimation or this the

smaller is the divergence angle and it

doesn't depend on any source size or

anything because this is this is due to

basic physics of of electromagnetic

radiation that's why we call the

diffraction

limited collimation that's the best you

can do so keep that keep that in mind

now

let's compare

the

the output of a laser with this uh with

this diffraction limited beam here's a

laser source

and with some optics and what have you i

can create a beam that's diameter d and

if i go check

this its size further down i indeed see

that the angle here the angle of

divergence is very close to lambda over

d

just like the the perfect light source

that we talked about before

so you can say that laser is indeed

diffraction limited and and again the

divergence is just limited by the

wavelength divided by d while in the

case of the light source we had to worry

about the size of the source

and the other important thing here is

that all the laser light all the laser

light can be put into into that beam so

we don't need to lose any any light

because we're not collecting enough so

it's another fantastic kind of kind of

property

now the applications of this of this uh

property

uh

let's start with the collimation part

the the high degree of collimation can

be used of course for alignment you can

do go to large distances without the

beam

expanding too much certainly you see

these barcodes with the lights flashing

if if there was too much divergence you

wouldn't be able to to

scan the bars because the spacing is

very small between them

and certainly if you want to do long

distance communication especially in

space

radar what have you uh high degree of

condemnation is

is very very important

now the uh the next

thing here is that i mentioned before is

the very small focus spot or the

diffraction limited focus

now

where does that where does that

come from and and how does it compare

with what we can do without

lasers

well let's go back to basics back to our

arc lamp here

and then we collect the light as we did

before but now

instead of just collimating let's put

another lens and focus it down

and that's normally how we get intense

uh

spots

high intensity uh focused spots by again

taking light from a source and and

refocusing

now it turns out that because the source

has a certain size

you're not going to be able to create

anything here that's going to be

brighter than the source and again if

you don't believe me you have to go look

up basic physics and and it sort of

makes sense that it's very difficult

it's impossible to make this brighter

than here

so you cannot increase the brightness uh

as as dictated by uh by the source all

right now what about lasers all right

before we get to lasers what's the best

one can do let's go back to our

collimated beam of diameter d

that that was our perfect ideal beam now

if we take that put a lens here with a

focal length f and focus it down it'll

focus down to a very small spot

now the this is the smallest spot that

you can get and the spot size is given

by our lambda over d which we remember

from before multiplied by f the focal

length of the lens

now if f is approximately d

if you can choose f proximity d then we

have a spot size here that's of the

order the wavelength of light

so again without

having to study hard or remember heart

then we have two things the collimation

is just given the best collimation you

can get is lambda over d and the focus

spot size is lambda

and this is then assumes that it's a

perfect a perfect light source

all right so that

now let's compare with with what the

laser with the laser can do all right so

now we bring the laser up so here's our

laser giving us a beam a collimated beam

of diameter d put a lens here focus it

down

and i go measure the spot size

and it turns out that the spot size if

i'm careful is very close to the

wavelength of the of the light

so this means that the the laser beam is

as ideal and as close to perfect as one

can get both in collimation as well as

in focus

while with a while with a light source

it was difficult to to get something

that is that is extremely bright

you can make this of course the spot

size small here by putting apertures by

putting apertures here you can make this

spot size small but you cannot have a

small spot size with with very high

intensity like you can here in this case

you can put all that laser light and

we'll talk about all kinds of outputs uh

very soon and you can put all that into

at this tiny spot and that's how you can

get these huge

intensities

well you might say

what are the applications of some of

these small focus spots with high

intensities well there are all kinds of

applications there's compact discs

for example that rely on a on a tiny uh

small spot for the for the resolution

certainly for laser printers and again

for materials processing as i say for

cutting and welding and uh

uh

drilling and so on and also in medical

surgery

where the the spot size you know for

cutting and what have you has to be has

to be pretty small you don't want to

make a huge huge cut and also uh because

you have to deliver so much intensity

you need the uh spot size to be to be

small okay especially like for example

look at the example of retinal surgery

retinal welding where you try to weld

the retina the spot size is a key is a

key issue

because you can almost get any light

source to to spot weld the retina the

only problem is it's what wells the

entire retina but here with a tiny with

a tiny beam tiny focused beam you can

you can only weld

just just small areas of course they're

damaged areas and you hopefully you can

still see with the rest of the retina so

the the small spot size is is a key

thing to a lot of these applications

now

uh i mentioned earlier that uh

that some people refer to this property

of high collimation or or

a small focus spot to high spatial

coherence so let's see what uh what is

meant by uh by that

the uh

here is uh

high special coherence and and the and

the what we mean by that is that the

wave is well behaved in space

now before

we talked about

uh

waves that are well behaved with respect

to time

remember we showed that the wave

continues uninterrupted for for a long

period of time that's very well behaved

wave

into in time

now we're talking about a well-behaved

wave

in in space which means that we can

predict

its amplitude and phase at any position

at a given time

while before it was at the same position

at a different time but here at any and

any position now any spatial position

as a function

of time and also of course of space so

let's look at it

now

an ideal point source of radiation is

over here

and then it puts out you know these

spherical waves that we're probably used

to seeing if the source is is very small

then you have perfect

spherical waves

if uh i don't like a diverging beam and

i put a lens here then i can make this

into a collimated beam and this will be

perfectly collimated b

which means that uh for for what we call

high spatial coherence means that if i

know the amplitude and phase of the wave

here

in this position in space i can also

predict the amplitude and phase of the

wave in another uh position in uh in

space

and uh

and and uh and that's great

so whether it says diverging beam or a

collimated beam or so on if you tell me

what the amplitude and phase of the wave

here i can tell it i can tell you what

it's going to be over here because the

wavelength is is stable and the the

spatial

behavior is stable

well if this doesn't mean much to you

let's look at what a what the light

source uh puts out and it's back to our

spectral lamp here or in our clamp

now because we have so many atoms in the

source here that they're radiating that

we get a mess of a waveform that's uh

that's coming out so if even so if i

know the amplitude and phase over here

it's

pretty impossible for me to predict what

the amplitude and phase going to be at a

different location

in space

and even as a function of time because i

really have no control over uh these

light sources over here while in the in

the case of the laser i can get uh

pretty close to perfect

prediction anywhere i want in space but

in a in a in a

non-laser light source it's very

difficult

now i can improve things by making the

light source very small as we showed you

before i take lenses i focus them down

put small apertures and can sort of

create a tiny focused spot the only

problem is

there's not much light by the time i do

that while the laser you can put all the

laser

light into let's say collimated beam

with diverging beam that has a perfect

spatial spatial coherence

all right so these are two very key uh

properties now what i'd like to do is uh

is talk about few more a few more

properties

all right now here is the next one which

is high power

the laser as we know lasers have

uh incredible power all right so let's

let's see where that where that

comes from

here's again a picture of a laser and

putting out a beam of light

now there are two kinds of lasers

there's what we call cw or continuous

wave lasers and there's also pulse so if

the output is not continuous and it's

possible we call it pulse lasers some of

them can be very short and and so on

all right now let's see

what sort of power levels

that we can get from

from lasers

and these these numbers if you're not

familiar with them they're going to

really open your eyes out

to to what's going on now in terms of

continuous lasers

well we're all familiar i suppose with

the helium neon laser or semiconductor

lasers that put out a few milliwatts

all right some of us work with bigger

lasers that put out sort of watts

and uh not that many people uh

uh work with kilowatt lasers today these

are you can buy these lasers for all

kinds of applications and

you can also generate even megawatts of

of continuous lasers that's 10 to the

power 6 watts that's huge

huge uh

continuous power that comes out from

these lasers

now in terms of pulse lasers

well the numbers get really very big

here we're talking about in continuous

document tender six watts here we're

talking about anywhere from 10 to the

nine watts which is a or gigawatt

depending on where you come from and

then we also have can produce pulse

lasers with with

peak pulse power of 10 to the 12 watts

terawatts

and even 10 to the 15 watts and i don't

know if you've heard of this word here

petawatt and pitawatt means 10 to the 15

this case 10 to the 15 watts and also

recently we read that some people have

produced exowatt uh peak power which is

10 to the 10 to the 18 watts and these

fantastic fantastic power levels and

we'll see how they generate it soon and

and what we can use them for but for

here i'll just mention just a few

applications

of these peak powers certainly in

materials processing where you want to

do welding cutting and what have you

uh for

fusion today as we know there's a big

fusion program

for many years now uh that uses that's

based on on lasers called laser fusion

and the military of course would love to

use these high-power lasers where the

pulsed or cw and certainly a lot of

nonlinear optics application uh are

based on the fact that we have a lot of

uh a lot of power in these in these

lasers because it depends on the on the

intensity now the

next property that i want to mention is

the tuning range of

of lasers

lasers again are sources of radiation

and can have incredible uh tuning range

now let's see

over the spectrum

of electromagnetic radiation where

lasers are first of all

we have the visible lasers you know the

ones we we see are basically basically

over here

and

and you they may have a certain tuning

let's say from here to here

and

and we'll discuss them later i mean here

this is just in a pictorial form i want

to show you where the lasers are and

then maybe as we get into the infrared

there may be other lasers like this one

here some laser here let's say over here

is in the firing of getting close to the

final infrared some lasers that have

large large tuning range

we go from the visible we can go to the

ultraviolet or even to the vacuum

ultraviolet and today we've gone all the

way to to x-rays so lasers are found

all over the spectrum all over the

electromagnetic spectrum

but their tuning range or their widths

over with width the spectrum or the

spectral width

of the lasers or the tuning range of the

lasers can be can be quite broad

and then we'll discuss them later but

today we have lasers all over the

electromagnetic spectrum sure we may

have some gaps here and there but there

are techniques of filling these gaps by

by mixing techniques and so on that will

fill these gaps and today we really have

no excuse to say that i don't have a

laser at a specific uh wavelength

because all sorts of techniques to uh to

create lasers there if there aren't any

lasers there already

now the applications of

of

wide tuning range

could be in the interaction with

specific atoms and molecules where you

need to tune the light sources to be

able to interact with specific atoms and

molecules to reach their resonances and

so on

in

studying structure of atoms molecules

solids and so on you need a widely

tunable source

in the area of spectroscopy and then for

propagation uh sometimes uh you know if

you want to dodge certain molecules in

the atmosphere and the water and so on

you need to tune the laser away from

the absorption of these

molecules or atoms and in

in medical applications sometimes you

need to

uh to tune the laser so that it's at the

right wavelength for interacting with

tissue or or what have you uh and and

it's nice to have lasers that are uh

that are tunable now i have one more key

property and that's it it's going to be

just the fifth one

and and here it is that lasers can

produce very short

pulse width

now these these are incredibly short

pulse width much shorter than any any

electronic circuit can can generate and

here we are

here's a laser pulse that one can

generate and the pulse width

can be

well this is

big 10 to the minus nine seconds which

called nanosecond

uh certainly we can pre produce these on

a routine basis picosecond or 10 to the

minus 12 seconds

and today we're very close the record is

that we're very close to 10 to the minus

15 seconds

excuse me which is a femtosecond

that's incredible

because because even 10 to the minus 12

seconds very difficult impossible to

reach with electronic sources so already

from from below 10 to the minus 12 let's

say 10 minus 11 or so this is all lasers

because you can't do it

electronically all right so again

this this is fantastic property of uh

of lasers and and let's mention at this

stage what are some some applications of

very short pulses we can certainly use

them to study very fast phenomena

uh where the let's say the relaxation

time is so fast that normal uh

techniques don't work that cannot be

used to observe them because

too long all right so so in order to

study fast phenomena you need very short

pulsed lasers

then of course the exciting thing

about optical computers if they will

ever come about is to take advantage of

these very short pulses so you can have

can have faster clocks and

and so on

and for high resolution radar and

imaging these very short pulses can give

you again incredible

resolution

and so so there's lots of applications

of these short pulses and we'll have uh

something to say about them

later

now

i would like to to switch to to the my

my next topic

which is how

these properties how these properties uh

come about

and uh and again we'll start with uh

with the first with the first property

which is this monochromaticity uh

narrow spectral width and the high tempo

coherence which i hope you still

remember from from earlier

the question is

how does this property where does this

property come from

okay

so the answer is that the laser is an

optical oscillator

and

so some people might say well what's an

optical oscillator i know it comes out

like a sine wave but what's an optical

oscillator

well

the what's an optical oscillator is

the first in order to understand an

optical oscillator you have to

understand what an oscillator is so now

we're ready to talk about uh the

properties of an oscillator and we hope

then we can extend it to an optical

oscillator and then we can appreciate

where that first property of lasers

comes from so here we are let's review

the basic properties of oscillators i

know

a lot of you know about oscillators but

i have to start at some level so i'm

going to start right here so if we have

here black box that puts out this

sinusoidal oscillation this perfect

sinusoidal oscillation where the length

of this wave train as we've seen before

goes all the way from minus infinity

plus infinity very long uninterrupted

constant amplitude then in in the

frequency domain that as we've done

before that is that delta function

centered at some frequency here that

depends on the wavelength of this of

this radiation source

all right so that's what we generally

call an oscillator and especially

electrical oscillators we see them on an

oscilloscope we see this beautiful sine

wave on on on the oscilloscope and uh

and the the the the source of the

oscillation well we'll have to see how

that comes about in the case of lasers

and and the spectral width is is

extremely narrow and we see that

electrical oscillators all the time and

we don't even think about it

now

now i would like to

tell you a little bit about how an

oscillator is made

and once we understand oscillators made

then we can extend it to to the optical

domain and and then be able to explain

how a laser works okay so let's review

some background here in in oscillators

well there are all kinds of uh

oscillators i'm going to start with with

a pendulum

here's a simple pendulum length length d

and i let it i let it swing

what does it do when i let it swing well

it will go backwards and forwards just

like this will

generate an oscillation here of the

pendulum which will die down

and the frequency of this oscillation is

given by

1 over 2 pi the square root of

g the acceleration of gravity divided by

d the length of the of the pendulum

now

the uh so the the

longer d is the

smaller the the frequency of oscillation

but but as we can see this oscillation

dies down and the question why does it

die down well why does it die down

because there are some losses

and the losses for example come in this

pivot here comes pushing air around and

so on but basically it will die down

because it's difficult to get rid of

all these losses so we don't have that

constant oscillation that i showed you

before

now we go to the frequency domain

reminding you what we did before because

i have a dying oscillation like this

then if the time constant is is tau

then the line width is going to be

approximately uh delta f which is

approximately one over tau

and and that is proportional directly

proportional to the losses the higher

the losses the larger

larger is the line width and the shorter

is the uh the uh

the decay time

all right so that

if i improve the losses if i reduce the

losses then i can get this to narrow

down and i can get this to last to last

uh longer

now the um

if i as i just mentioned just now this

is in in pictorial form if i reduce the

losses if i'm clever in reducing the

friction in this pivot and so on i can

make the wave last

longer and this width gets

gets narrower but in order to make it

constant amplitude i have to do

something else

all right this is what i have to do i

have to call on this fellow here to to

push on this pendulum to push on this

pendulum so that

it stops it from from

dying down in a way what this fellow is

doing by doing his pushing at the right

time it's really overcoming the losses

whether at the the pivot here or pushing

air around and and so on so in order

instead of having just the dying

oscillation like this where i end up

with a constant amplitude because of

this fellow here is putting energy into

this system and compensating for

so as the amplitude here becomes becomes

constant then the line width here

starts the delta f starts to shrink and

goes close to zero so in this way i

produce a an oscillator and in this case

of course it's a it's a pendulum

oscillator that's used like a clock and

and so on but i do need

this energy source this person here to

overcome to overcome the losses

now this is not the only type of uh of

oscillator i have all kinds

uh let's say i have a mass spring system

i can make that into oscillator let's

say here i have a spring and there's a

mass connected to it and then if i pull

the mass away it's going to wobble

backwards and forward it's going to

oscillate

again it's going to be a dying

oscillation like this because of well

friction

mass friction has a friction between the

friction between the mass and and the

stable and losses in the spring and so

on the frequency here will be determined

by the

square root of the of the spring

constant k and divided by the mass

if i change the mass i change the

frequency and and so on and so so again

just like in the pendulum it's a dying

oscillation and has a in the frequency

domain has a certain width and the width

is proportional to

one over

one over tau and that's again

proportional to losses

if i look at a stretch string

here straight string if i hit it then it

it bobs up and down here in the middle

and then the frequency will be

determined by the speed of sound in the

material divided by by twice the

separation between the ends and again it

dies down okay this bubbling up and down

will die down

because again of losses and also we'll

have we'll have a width

and then finally here if i have an lc

circuit

inductor in a capacitor again if i if i

inject a pulse into it i see that again

i get an oscillation if i look let's say

the voltage across the capacitor here i

have this oscillation that dies down

and the frequency is given by in this

case by the square root of 1 over lc l

being the inductor c is the is the value

of the capacitance

and the this decay is due to losses now

in electrical circuit where the losses

come from well they come from ohmic

losses essentially dissipation in the in

the wires according to uh

ohm's law

so that

uh uh the

all these kinds of oscillators whether

pendulum or or uh mass spring and

vibrating string or electrical

oscillator they essentially they all

have specific frequencies all right they

oscillate at and but they all have

losses and to make them into into an

oscillator you have to overcome these

losses and as we as we saw that in the

in the case of the pendulum you need

somebody to push here you may also need

somebody to push over here you again you

you have to uh

you have to keep vibrating these things

to maintain oscillation and of course in

the electrical one we add a an amplifier

to overcome

to overcome the the losses now to uh to

then then summarize then we need to make

an oscillator

then we need a a resonator

that will determine the frequency for us

and we need a means of overcoming uh the

loss so if we have that then we can

then we can

get this

oscillation this nice oscillation that

that comes out from that black box i

showed you earlier now what about the

laser

okay how does the laser work

well

in in uh

in lasers because it lasers is an

oscillator we need a a resonator first

of all so let's look at how we can

create electromagnetic uh resonator

well

just like this is very similar to the to

the stretch string we need uh we need

two ends we need two nodes and here we

have uh to create this we have two

mirrors

uh here the two mirrors m and they're

spaced a certain distance l apart

now the

the lowest frequency that can fit

between these two modes and oscillate

backwards and forwards between these two

modes is the one where half the

wavelength where l is half half this

wavelength because the wave would be

would be about the size now such a wave

would be able to bounce backwards and

forwards between the two mirrors

and

and will

be at that frequency determined by in

this case will be determined by

uh f equals c over 2l because uh lambda

times uh times the frequency equals the

velocity of light

so either that the the wavelength is 2l

all right or its frequency is just c

over 2l okay so this is then the the the

lowest uh frequency that will be

supported in this kind of uh structure

with two reflectors or two nodes at the

ends just like in the vibrating string

now this oscillation will die down if i

injected some light in here and i get it

to

to oscillate like this it will die down

because of losses

and again in the frequency domain this

will have a width

question is what uh where are the losses

in this case

well the losses come from the reflection

in the

in the mirrors if the

reflectivity of the mirror is not

perfect

then then every time the light bounces

from one mirror to the other then the

amplitude will go down and very quickly

it will die down altogether

so in order to to make this then

oscillate or essentially lays

we need to overcome uh these losses but

before i get to this i want to talk

about uh other other

modes in in this kind of resonator

the uh

so far i've talked about this one where

only half the wavelength fits between

the two mirrors but i can also get a

condition where a full wavelength foot

fits between the two mirrors these are

sort of normal modes

of

of these resonators

now where lambda 1 was here was equal to

2l and f1 was c over 2l in this case

lambda 2

is is essentially l or i like to write

it as 2 l over 2 but i cancel to do the

twos and i get l

and the frequency is just 2 c over 2 l

so here we had 1 times c over 2 l here

is 2 c over 2 l and and so here i'm

spacing it along in the frequency uh

along the frequency scale here's my f1

and here's f2 and the separation is c

over 2l and each one has a width because

of the

of the losses now we can go a little

further here

and consider a few more of these uh

oscillations in this case uh well i have

one and a half waves that will fit

between the the cavity uh between the

two mirrors and or within the cavity and

then the wavelength will be 2l over 3

instead of 2l over 2

and the frequency will be 3 c over 2l

instead of 2c over 2l here so now again

you can see i'm going to stack them up

f1 f2 n3 and the separation is equal

between them which is c over 2l

and we can uh

go to many more and i'm jumping here to

to the what we call the qth mode lambda

sum q and just because the way i was

doing it uh previously you can see that

the wavelength will be 2l

divided by q this is the the q number

just like in here this was three two

two one and now in this case will be the

key

the qth mode

and the frequency will be just q c over

2 l just like here we have 3 c over 2 l

2 c over 2 l and so on so on the on the

on the frequency scale then we have all

these resonances that come from that i

can excite in in one resonator and can

we can be

as high as uh as you want it and the

width each one will have a width because

of the losses now not all the widths

will be the same because uh because not

all the losses will the sun losses will

depend on the wavelength or the

frequency you're at

so

since the mirrors can have loss but the

loss can depend on the wavelength and so

so these widths can

can vary

so now

this explains the the uh the uh

resonator and uh and and just the let me

summarize the uh

the uh information here we have a

typical now a laser uh cavity which is

again two mirror spaced by l in this

case i'm going to take l as a hundred

centimeters one meter if i choose for

the wavelength to be half a

micron or five times 10 minus 5

centimeters then q

comes out to be this q this integer we

talked about comes out to be uh 2l over

lambda from from the uh from this

formula here and it's 200 divided by 5

times 10 minus 5 which comes out to be

about 4 times 10 to the 6 which means

that q has the value of few million all

right which means there's lots of little

waves in here in a in a cavity of a 100

centimeters

separation the frequency associated with

that is against f sub q from here uh is

uh six times comes out to be six times

10 to 14 hertz

and the width will depend on the losses

uh which are uh mainly due to let's say

mirror losses and and so on which we'll

get into into later

so

so the uh so then to make a an optical

uh oscillator or like a laser we need

the resonator that we that we have

talked about but it has not just one

frequency but has many frequencies and

it has we have to have a a means of

overcoming the loss

and and that

uh is

is uh

that comes about with with a light with

a light amplifier

so the the light amplifier is the is the

key element uh in inlays in a laser

because without the amplifier you can

have all these cavities empty cavities

that do absolutely nothing for you but

in order to make create lasers out of

them then you have to put an amplifier

okay so here is then

then uh the laser

here's the cavity that we talked about

and then we have to insert this this

amplifier

and this amplifier which we will talk

about uh later in more depth this

amplifier then provides

gain

for the light that goes backwards and

forwards between these two mirrors to

overcome the losses wherever the losses

come from

and the whole idea is to make the losses

as small as possible so you don't you

need to use a big amplifier because in

order to generate this gain which we'll

talk about later

uh it costs a lot of effort a lot of

money and so on so so we want to

minimize the the uh the gain that's

needed

but we certainly have to have enough

gain to overcome uh the losses and uh

and here for example i have this this

amplifier this this gain of this

amplifier located at this particular

frequency and over here i have all the

modes of of the cavity that we talked

about before but if there is one of

these cavity modes under the bandwidth

of this amplifier

then if there is enough gain to overcome

the loss

then i can get this to to oscillate and

in fact

here it is as we know that this width of

the of the cavity comes about because of

the losses in the cavity but if i have

enough gain to overcome the losses

then i collapse this width to this delta

function that we had before and and the

output that comes out from this mirror

if i put some transmission in this

mirror here i leak a little bit of light

out then that light will will have this

spectrum this very narrow spectral width

or in terms of the time domain i have a

this this lovely

oscillation here that has a constant

frequency determined by this cavity mode

and a constant amplitude

so i think

uh

the

this will be a very fitting time to uh

to stop for this uh first session

because uh because i brought you just to

the stage where i think now you wanna

know where this uh where this gain comes

from that makes lasers possible so when

we come back we'll start exactly with

that with that topic