Light & Coherence part 1: Temporal Coherence

Summary

本视频深入探讨了光的波粒二象性，从历史角度回顾了光作为粒子和波的争论起源，并详细解释了光的量子化概念，即光子。通过分析光电效应和光的发射过程，视频阐述了光子作为能量量子化的表现，并非实际的粒子。此外，视频还探讨了光的相干性，包括时间相干性和空间相干性，并通过实验展示了如何测量光源的相干长度。最后，视频指出光的非均匀能量分布是波现象的直接结果，尤其是与相干性相关的波现象。

Takeaways

• 🌟 光既表现出粒子性质也表现出波动性质，这是量子物理学中的波粒二象性。
• 👀 历史上，关于光是波还是粒子的争论由来已久，从17世纪末开始，经历了牛顿和惠更斯的不同理论。
• 📚 托马斯·杨通过双缝实验展示了光的波动性，而麦克斯韦的工作进一步证明了光是一种电磁波。
• 🌐 爱因斯坦通过光电效应实验提出了光量子假说，即光由不可分割的能量量子（即光子）组成。
• 🔬 光电效应实验表明，光的能量是分立的，并且与光的频率直接相关，而不是光的强度。
• 💡 光子不是爱因斯坦发明的概念，而是由吉尔伯特·路易斯提出，用以描述辐射过程中不可或缺的假想原子。
• 🌈 光的粒子观由于爱因斯坦的再引入而引起了许多混淆，但光的本质可能更多地与波动现象相关。
• 🕒 时域相干性与光的颜色或频率有关，而空域相干性则与光源的几何形状和波长等有关。
• 🔍 通过米歇尔逊干涉仪实验可以观察和测量光源的相干长度，这有助于理解光的时域相干性。
• 📊 实验显示，激光二极管在不同的工作模式下（自发辐射与受激发射）具有显著不同的相干长度。
• 🚀 视频的目标是通过波动现象来解释光的性质，而不是单纯依赖粒子模型，以期达到更深入的理解。

Q & A

光是由什么构成的？

光由一种称为光子的离散能量包组成，表现出波粒二象性，即同时具有波动性和粒子性。

什么实验首次证明了光的波动性？

托马斯·杨的双缝实验首次证明了光的波动性。

光的粒子性是如何被重新认识的？

通过阿尔伯特·爱因斯坦关于光的生产和转换的论文，他提出光是由空间定位的能量量子组成，这些观点基于光电效应的实验结果。

什么是光电效应？

光电效应是指当光照射到金属表面时，能够将电子从金属表面逸出的现象。这一现象表明光的能量是量化的。

什么是光子，并且谁首次引入了这个概念？

光子是表示光的能量量子的术语，最初由吉尔伯特·路易斯在1926年引入，用于描述在任何辐射过程中发挥基本作用的假想新原子。

为什么会说光具有波粒二象性？

因为光既表现出波动性（如双缝实验中的干涉现象）又表现出粒子性（如光电效应中的量子化能量转移），因此光被认为同时具有波动和粒子的特性。

什么是相干性以及光的相干性有哪两种基本类型？

相干性描述了波动在空间和时间上的同步程度。光的相干性有两种基本类型：时间相干性和空间相干性。

时间相干性是什么意思？

时间相干性与波源发射的光的频谱带宽有关，描述的是波动在时间上的同步程度，即在特定时间间隔内波的频率保持不变的特性。

空间相干性是什么意思？

空间相干性描述了在波前的横向方向上，波的相位或振幅在空间上的一致性，即不同位置的波动是如何同步的。

什么是米氏干涉仪，它是如何用来测量光的相干性的？

米氏干涉仪是一种实验设备，通过分裂光束并让其沿不同路径传播后再次合并，来观察由于路径差引起的干涉图样。通过改变两条路径的长度差，可以测量光源的相干长度，从而了解光的时间相干性。

Outlines

00:00

🌟 光的波粒二象性

本段介绍了光的波粒二象性，即光同时具有波动性和粒子性。从历史角度出发，讲述了自17世纪末以来关于光的本质是波还是粒子的争论。牛顿支持光的粒子说，而惠更斯支持波动说。托马斯·杨通过双缝实验展示了光的波动性，麦克斯韦的电磁理论进一步支持了光的波动说。然而，爱因斯坦通过光电效应的解释，重新引入了光的粒子观点，提出了光量子（即光子）的概念。

05:04

🔬 光电效应与光子

这段内容深入探讨了光电效应实验，该实验展示了光的能量是分立的，支持了光的量子化观点。爱因斯坦的研究成果表明，光的能量并非连续分布，而是由不可分割的能量量子组成，这些量子被称为光子。此外，还提到了光子这一术语是由吉尔伯特·路易斯提出的，用以描述辐射过程中的基本粒子。

10:04

🌈 光的相干性

本段讨论了光的相干性，包括时间相干性和空间相干性。时间相干性与光谱带宽有关，而空间相干性与发射器的几何形状、波长和距离有关。通过解释相干性的基本概念，本段为理解光的波动性质提供了理论基础，并预告了将在后续视频中更深入地探讨这些概念。

15:10

📏 相干长度与光源

这一部分通过实验来测量不同光源的相干长度。使用迈克耳孙干涉仪，可以观察到当两束光的路径长度相等时，会产生干涉图样。通过改变光源的类型，比如从白光LED到激光二极管，可以观察到相干长度的巨大差异，从而展示出光源的相干性对其发射光波的影响。

20:13

🚀 激光与自发辐射

本段通过实验比较了激光二极管在不同工作模式下的相干性。在低电流下，激光二极管表现为普通LED，主要进行自发辐射；而在高电流下，激光二极管开始激光，即受激发射。实验结果显示，受激发射模式下的光源可以产生非常窄的光谱分布，从而在数米的距离上保持相干性，这与自发辐射模式下的相干性有着显著的差异。

Keywords

💡光子

光子是光的基本量子，表现为能量的离散包。在视频中，光子被描述为光的能量量子，它们不可分割，只能作为一个整体被吸收或发射。例如，爱因斯坦的光电效应实验表明，光的能量不是连续分布的，而是由一系列能量量子组成，这些量子就是光子。

💡波粒二象性

波粒二象性是指光同时具有波动性和粒子性的特性。这一概念在量子物理学中非常重要，因为它解释了光在不同实验条件下表现出的波动或粒子行为。在视频中，波粒二象性被用来解释光的复杂行为，如双缝实验中的干涉现象。

💡双缝实验

双缝实验是量子力学中的一个经典实验，用来展示光和其他粒子的波粒二象性。在这个实验中，光通过两个紧邻的缝隙，然后在屏幕上形成干涉条纹，显示出波动性。视频中提到了双缝实验，用以说明光的波动性质。

💡光电效应

光电效应是指当光照射到金属表面时，能够引发电子从金属中逸出的现象。这一效应为光的粒子性提供了证据，因为电子的逸出与光的频率有关，而与光的强度无关。爱因斯坦因解释光电效应而获得了诺贝尔奖。

💡量子物理学

量子物理学是研究物质和能量在微观尺度上的行为的物理学分支。它揭示了在原子和亚原子水平上，自然界遵循的规律与我们日常经验中的物理规律截然不同。视频中提到的光子、波粒二象性和双缝实验都是量子物理学的重要概念。

💡电磁波

电磁波是电场和磁场的波动，它们可以传播能量。光就是一种电磁波，它表现出波长和频率等特性。在视频中，光被描述为电磁波，这涉及到光的波动性质。

💡频率

频率是指波在单位时间内完成振动的次数，通常以赫兹（Hz）为单位。在光学中，频率与光的颜色和能量有关。视频中提到，光电效应中电子的最大动能与光的频率有关，这说明了光的粒子性质。

💡干涉

干涉是波动现象中的一种，当两个或多个波相遇时，它们的振幅可以相互加强（构成干涉）或相互抵消（破坏干涉）。在视频中，干涉用来解释光波如何形成特定的图案，如双缝实验中的干涉条纹。

💡时间相干性

时间相干性是指波在时间上的一致性或同步性。具有良好时间相干性的波在一段时间内保持稳定的相位关系。在视频中，时间相干性与光谱带宽有关，窄带宽的光源（如激光）具有较长的时间相干性。

💡空间相干性

空间相干性是指波在空间上的一致性或同步性。具有良好空间相干性的波在特定区域内的各个点上表现出相同的振幅和相位。在视频中，空间相干性与光源的尺寸、波长和距离有关，影响光场的均匀性。

💡光谱带宽

光谱带宽是指光源发出的光覆盖的频率范围。窄带宽意味着光源发出的光具有单一或少数几种频率，而宽带宽则意味着包含多种频率。视频中提到，光谱带宽与时间相干长度成反比，影响光的干涉和相干现象。

Highlights

光实际上是由小粒子，即光子组成的。

根据普朗克和爱因斯坦的理论，光以离散的能量包形式存在，称为光子。

光的波粒二象性意味着光同时具有粒子和波的特性。

自17世纪末以来，光是波还是粒子的问题一直存在激烈的争论。

牛顿在1704年出版的书中解释了光的行为，将其视为小快速移动的粒子。

托马斯·杨在1801年通过双缝实验展示了光的波动性质。

麦克斯韦的工作为光作为电磁波提供了强有力的证据。

爱因斯坦在1905年的著名论文中提出，光的能量不是在空间中连续分布的，而是以“空间局部化的能量量子”存在。

光电效应实验结果支持了光子概念，即光由不可分割的能量量子组成。

“光子”这个术语是由吉尔伯特·刘易斯在爱因斯坦的论文21年后提出的。

爱因斯坦重新引入的光的粒子观点至今仍引起许多困惑，并根本上影响了我们对光的看法。

视频制作者希望通过后续视频，尝试纯粹从波动现象的角度解释光及其属性。

相干性是一个复杂的概念，尤其是与光的相干性相关的时间和空间相干性。

通过实验可以观察和测量光源的时间相干性。

视频中将探讨相干性如何在波动现象中表现，例如表面波的同步性。

视频中讨论了时间相干性，这与光谱带宽有关，即光中存在的不同颜色或频率。

电磁波的光场是许多小波的线性总和，这些小波由激发态原子或分子的发射组成。

光子实际上是发射器发射一定量辐射能量的过程，这个过程是量子化的。

光源发出的光总是包含多个波长或频率，这是由于多种原因造成的。

通过米歇尔逊干涉仪实验可以测量不同光源的相干长度。

实验中使用的空间相干白光源展示了白光的时间相干性质。

激光二极管在不同工作模式下的相干长度差异显著，这通过干涉仪可以观察到。

Transcripts

“Today I’m going to be showing you that light is actually made out of small little

particles” “Some of it’s just due to just the photons

hitting the surface” “From Planck and Einstein, we learned that

light comes in discrete little packages of energy, called a photon”

“That means that each photon should have to decide whether it’s going through one

slit or the other” “Now how could they interfere with each

other because there is only one in the device at any one time?”

“Welcome to Quantum Physics!”

“We now have to accept that light obeys wave-particle duality, meaning it is both

a particle and a wave at the same time.

Confused?

You should be.”

Hey everyone.

I guess I was confused.

In the past I assigned particle properties to light.

But apparently, I’m not the only one.

So why is everyone confused?

Well, to find out, let’s start by looking at history and see where most of the confusion

about particle-wave duality originated from.

Whether light was a wave or a particle has been a subject of fierce debate since the

end of the 17th century.

When Christiaan Huygens published a paper on the wave theory of light in 1690, most

scientists of his time did not agree to his views.

Among which was one of the most prominent scientists of that time: Sir Isaac Newton.

In 1704, about 14 years later, Newton published a book in which he explained the behavior

of light in terms of small fast-moving particles.

And for about 100 years, both the particle and the wave description had their own fanbase.

However, in 1801, Thomas Young demonstrated that light behaves like a wave and that the

colors of light are in fact related to wavelength.

He did this by performing what is now generally referred to as the double slit experiment.

And again, about 60 years later, the work of James Clerk Maxwell showed strong evidence

that light should in fact be an electromagnetic wave.

So, at the very beginning of the 20th century, there really wasn’t much to debate any more:

light consists of waves.

So where did things get confusing again?

Well, in 1905 Albert Einstein wrote a now famous paper on the “production and transformation

of light”.

In this paper, he combines experimental data from various sources, connects them and discusses

some of the theoretical consequences.

And one of his conclusions is that the energy contained in light is not “continuously

distributed” in space but as he states it consists of a finite number of “spatially

localized energy quanta”.

He proposes that these quanta “are indivisible and can only be absorbed and emitted as a

whole”.

And the arguments to support his claims are mainly based on the results of an experiment

that is now better known as the “photo-electric effect”.

To understand how Einstein came to his conclusions, let’s take a take a quick look at the essence

of the photoelectric effect and what exactly points to quantization of radiation.

The experiment is generally performed in a high vacuum with 2 electrodes.

One of the electrodes is covered with a layer of a specific metal, for example Cesium.

When we irradiate this metal with UV-light, electrons can be expelled from it.

We know this because we can measure that a potential difference arises between the 2

electrodes.

Basically, because the negatively charged electrons go from one electrode to the other.

And so, we can do various experiments on this system, like vary the wavelength of the light

while measuring voltages and currents or deliberately change the potential to see at which field

values the flow of current stops.

Now the thing is that this phenomenon only occurs when the frequency of the light used

for irradiation, is above a certain value.

For example, the effect exists for UV-light, but not for visible light or infra-red.

Not even if the intensity of the latter radiation is very high.

When the frequency of the radiation is above a specific threshold however, we can measure

the effect even at very low radiative power.

By changing the potential difference between the two electrodes, we can also measure the

maximum kinetic energy of the emitted electrons.

And it turns out that this maximum kinetic energy is dependent on the frequency of the

light and increases with higher values.

So now we are faced with the following: we observe emission of electrons, so discrete

entities, from the metal by irradiation.

In order for these electrons to escape from the metal surface, each of them needs a certain

amount of ionization energy, which is more or less a constant.

But apparently, they are also left with a certain kinetic energy, which is directly

dependent on the frequency of the light.

This suggests that the total energy needed for this, is supplied to the electron as one

discrete package with a certain amount of radiative energy: part of it is used to escape

the metal, and the part that is left over remains as the kinetic energy of the electron.

And so, the experiment strongly suggest that light consists of small chunks of energy,

rather than a continuous stream.

Now, it’s these energy quanta in light proposed by Einstein that are referred to as “photons”

by many people today.

You might now think that the name “photon” is an invention of Einstein, but it’s not:

the name “photon” was introduced 21 years later by Gilbert Lewis, who used it as the

name to describe a “hypothetical new atom that plays an essential part in every process

of radiation”.

I guess that is how it sticks in everybody’s mind, including mine: a photon apparently

being some kind of light particle.

I guess partly also because of the name it was given Lewis: electron, proton, neutron,

photon.

The corpuscular or particle view on light reintroduced by Einstein, still causes a lot

of confusion and influences fundamentally how many of us look at light.

Drawings of emission- and absorption processes show discrete little waves packets.

Complex experiments with light are explained in terms of photons moving through slits and

prisms and then hitting detectors.

Stimulated emission, is described in terms of light particles: 1 photon in, 2 photons

out.

The corpuscular description of light is literally everywhere and almost every science video

about light on YouTube is about light being a particle at some level.

But is it correct?

In this video and the follow-up video, I want to leave the corpuscular- or particle view

behind me and try to explain light and its properties purely as the result of wave phenomena.

The reason I made this video is that hopefully it can lead to better understanding, initially

for myself but of course also for others.

Personally, I do think that the energy in light is in fact “discontinuously distributed

in space”, as Einstein initially concluded.

But not because light itself consists of packages or photons, but because of a direct result

of wave phenomena, in particular those related to coherence.

As will become apparent, coherence is actually a pretty complex subject to explain in simple

terms.

So that is why I want to use at least videos to explain it.

There are 2 fundamentally different types of coherence behavior: Temporal coherence

and spatial coherence.

In the current video, I’ll mainly talk about temporal coherence, a phenomenon related to

spectral bandwidth.

So in the case of light, temporal coherence is about which colors or “frequencies”

are present.

And later in the video I will demonstrate experimentally how we can observe and measure

temporal coherence in light sources.

In video 2, I’ll discuss spatial coherence, which is about the geometry and how aspects

like the size of the emitter, the wavelength and the distance from a source can create

a spatially uniform field in a specific area.

And of course, I want to take a few side tracks to see if we can get a tiny step closer to

understanding the particle-like behavior of electromagnetic radiation.

When we talk about coherence in wave phenomena, for example surface waves, we refer how strongly

points on the surface move in sync with each other, both in space and time.

Waves aren’t static entities but move at a velocity over the surface in a certain direction.

Now, I’m not much of an animator and this is of course a static image but the idea here

is that these waves shown here are moving from left to right.

This here is an example of a very regular linear wave.

If we look in the direction of propagation, every point on the surface moves with exactly

the same frequency.

So apart from any phase differences, the movements of all points are synchronized and so they

are directly related.

We call this wave temporally coherent, because it does not change in time.

Also, if we look in the direction transverse or perpendicular to the direction of wave

propagation, we see that all points move in unison.

This means that this wave is also spatially coherent, because spatial coherence is specifically

about the relation between points in the direction transverse to wave propagation.

So, if we were to keep track of a particular wave on the surface along the direction of

propagation, it will be here at a specific time, and at a later time the same wave will

be some distance further.

And of course this distance depends on the propagation velocity.

This illustrates how in temporal coherence distance and time are related.

Especially if we ignore damping or friction for now.

Okay, this is a pretty boring wave, let’s make things a bit more interesting.

Here we again have a linear wave moving in the same direction but now the wave has a

variable frequency.

If we observe at one specific point in space again, we see that the frequency changes in

time.

Same if we compare the waves at different positions along the direction of propagation.

And if we were to compare movements of points on the surface in this direction, we would

observe that these are actually not in sync any more.

In other words: because there is more than one frequency present in the wave, we have

lost temporal coherence.

But this wave is still completely spatially coherent because in the transverse direction,

all points are still moving in sync.

If that were not the case for example in this peculiar looking wave, if we move in the transverse

direction, we also lose coherence at every point on the surface.

And so this wave is both temporally and spatially incoherent.

Let’s return to the spatially coherent wave.

Now, you might argue that for this particular wave the degree in which temporal coherence

is lost, depends on the time interval during which we observe the wave at a particular

location.

And that is indeed correct: If this time interval is small enough, we might actually not see

any significant differences in amplitude or frequency.

The same of course is true if we compare the waves only over very short distances on the

surface.

So, for temporal coherence, there is a time and corresponding length at which we can say

that any loss of coherence or synchronization is acceptably small.

And these values are generally referred to as the coherence time and coherence length.

Now for spatial coherence, we actually have something similar.

If we just examine a tiny fraction across the wavefront, we will still of course observe

phenomena due to temporal incoherence.

But due to the fact that this area is very small, the wave behavior within that specific

area will actually be uniform.

So, whereas the degree of temporal coherence can be quantified by a coherence time and

length, the degree of spatial coherence can be quantified by an area of coherence.

I’ll dive deeper into the subject of area of coherence in the second video.

In this video thought, I will assume perfect spatial coherence in all the examples.

The main reason for strictly separating the two is convenience.

Because for spatially coherent waves, whether they are two- or three dimensional, the behavior

can always be described in 1D-plots.

And so, by assuming perfect spatial coherence, we can simplify things quite a bit when we

want to discuss the essence of temporal coherence.

Now this temporally incoherent wave contains sort of a frequency gradient and therefore

contains multiple frequencies.

However, this is not a very good depiction for the electromagnetic waves of light.

For one, because the electromagnetic field will be something that propagates in 3D space.

Also, there will be an electric and magnetic component to it and a polarization direction.

But if we consider perfect spatial coherence also in light, all of this added complexity

is actually irrelevant.

Because the field passing any area of coherence will be the same for all points in that area.

And so we can still describe the behavior in one or more 1-dimensional plots.

The electromagnetic field in light is actually the linear sum of many individual smaller

waves.

And that is because this field at any point in space is the sum of emissions by excited

state atoms or molecules that fall back to a lower electronic state.

When they do, they can emit a small electromagnetic wave, which adds to the total field.

Now, this schematic image might give the impression that waves actually interact with each other

or melt together, but that is not the case.

In a linear medium, waves don’t interact, they just momentarily interfere.

For example, take the case of 2 temporally coherent laser beams: their fields might show

interference in a specific area when they cross paths, meaning that their fields add

up of cancel out for a brief moment, but after that, the waves will go their own way unaltered

as if nothing happened.

Okay, so what is a photon in this depiction?

Well, it is actually the emission of a certain amount of radiative energy by the emitter.

Just to be clear: I’m not referring to the resulting electromagnetic wave as “the photon”,

I’m referring to conversion process to electromagnetic energy.

This process is actually quantized and is governed by the difference in the energy levels

allowed within the emitter itself.

So in emission, a photon is just the creation of a certain amount of electromagnetic energy.

As for the electromagnetic field emitted: this immediately becomes part of the total

field and will generally become inseparable from the total soup of electromagnetic field

waves that may already be present.

Now, I drew the emission processes as occurring in all directions, which is not necessarily

true, because it can be sort of directional.

But due to the nature of the electromagnetic field, it cannot be purely unidirectional

either.

It has to spread out in space as it propagates.

And a logical question you might have now is: how can we absorb a discrete amount of

energy if waves spread out in space like this?

Well, we’ll leave the explanation to that question for video number 2.

An intrinsic aspect of light is, that it always contains multiple wavelengths or frequencies.

There are several reasons for this, and I will just name a few of them.

For example: emitters like excited state molecules are always moving.

In a gas for example, their velocity is general several km/second and this causes a doppler

shift in the frequency of the emitted radiation.

Also, there are considerations related to the Heisenberg uncertainty principle for time

and energy.

Short emissive processes have by definition a higher uncertainty in energy and therefore

in wavelength.

But maybe I’m getting ahead of myself.

The only important thing to remember is that every source, even the fanciest laser, emits

multiple frequencies.

If only because every emission process occurs in a finite time interval.

Let’s focus on what temporal coherence looks like if we just consider the linear addition

of waves in one dimension, in other words in the case of spatial coherence.

Here you see a hypothetical infinitely long harmonic wave, with just has one single frequency.

If we look at the spectrum, it actually has just one line corresponding to this frequency.

Now, let’s see what happens if we consider two waves with a slightly different frequency.

Here you see how the individual waves look and here you see what happens to the linear

sum of these two waves: At points where the two are in phase we get the highest peak to

valley differences, but as the waves gradually go out of phase, we observe destructive interference,

which causes the amplitude to go down.

At some point however, they will get in phase again and so what we observe is a beat frequency

that is the difference between the 2 original frequencies.

Now, let’s add a few more frequencies to this, in this case 7 regularly spaced frequencies.

At points where all the frequencies are in phase, we get constructive interference again,

and we see the same kind of regular pattern appear of areas where all waves are either

in or out of phase.

Now, as a next step, let’s weigh the contributions of these frequencies such that their amplitude

become smaller as they get further away from the central frequency.

What you observe now is that the interference pattern consists of these little separated

waves packets with very little activity in between.

Now this is where I want to take a big step and consider the following: what would happen

to this interference pattern if we did not just use 7 frequencies, but a continuous Gaussian

distribution of frequencies and add all of these up.

Well, if we do that, we would arrive at the following wave pattern: Just one single isolated

wave packet, only at the one point where all waves are in phase.

Now, some of you might be surprised and think: where have all the waves gone?

Some of you more into math and cats may think: Ahh look: Fourier transform kittens.

So cute.

And those of you who have seen the most recent Physics Explained video on the uncertainty

principle will probably say: yeah of course.

I knew that.

In the case of a Gaussian frequency distribution, the coherence length is related to the half

width of the spectral distribution by the following formula.

What this formula basically points out is that the coherence length is inversely proportional

to spectral band width.

Just a quick illustration of why this is: if all frequencies involved are very close

together like in a laser, it will take a long time for the waves to go out of phase and

so the waves will be coherent over a long distance.

Whereas if we have a very wide distribution of frequencies, the distance over which the

waves are in phase, is actually only a few wavelengths long.

Now when you casually look at these images you may think: Are you now trying to tell

us that radiation automatically comes in discrete packets because of spectral band width and

decoherence?

Well, actually no, I wasn’t.

I was only trying to prepare you for an experiment in which we can measure the coherence length

in light.

But it is of course a tempting thought: very long packages in coherent radiation from for

example a laser, very short packages for broadband radiation.

But that would be looking for particles where there actually aren’t any: because this

type of behavior is purely the result of wave principles.

Anyway, about the experiment that I just mentioned: with it we can measure the coherence length

of various light sources.

For the experiment, I’ll use a Michelson interferometer, shown here schematically.

Light from a spatially coherent source is directed towards a beam splitter where it

is split into two paths.

The light then hits two mirrors, which reflect it back to the beam splitter where it’s

is recombined and projected on a cmos sensor.

One of the mirrors has a fixed position and the other one has a variable position, which

allows us to change the difference in length between the two paths.

Here is the actual setup I built, quite simple.

Here is the light source pointing into the beam splitter.

These are the 2 mirrors and to the left is the CMOS sensor.

One of the mirrors is placed on a linear translation stage, so that the length of this path can

be varied.

For the first experiment, I built a spatially coherent white light source.

This sounds special but it is not that difficult to make.

It just consists of a white LED, a tiny pinhole in front of it, a collimation lens and an

aperture.

Because of the spatial coherence, the beam exiting this source has a uniform field across

the beam area.

As a consequence, the light from this source looks kind weird because very parallel over

long distances.

Now with this spatially coherent source, we can look at the temporal coherence properties

of white light.

Here you see the camera image when the lengths of the 2 arms of the interferometer are exactly

equal and we can observe a clear interference pattern.

Now, getting this image is not trivial because the accuracy required for matching the 2 path

lengths is only a few wavelengths.

This is because the light is spectrally broad and the contained frequencies will get out

of phase very quickly.

The reason that we observe an interference pattern is the following: if the arms of the

interferometer are equal, every electromagnetic wave from one arm, regardless of frequency

or phase, is basically in phase with the wave from the other arm.

And therefore, this will lead to visible constructive and destructive interference around the point

where the arms have equal length.

And the reason why we can observe this pattern directly from the CMOS-sensor is that the

2 mirrors in the interferometer are slightly tilted with respect to each other.

And this causes the interference patterns due to temporal coherence to spread out over

the CCD sensor area.

You can clearly see how the different wavelengths start to go out of phase quickly when we move

away from the point of equal path length.

In fact, by using narrow-band interference filters, we can look at the separate frequencies

or colors present in the pattern.

We see that every frequency has its own interference periodicity: The blue light with the shortest

wavelength has the smallest spacing, the red light with the longest wavelength has the

widest spacing.

And the white light interference pattern is basically the sum of all frequencies or colors.

Now this is a screen shot again of the interference pattern that we observe.

If we now discard the color information of the camera for a moment and just look at the

intensity, the image will look something like this.

This image allows us to extract approximate intensity information and plot it as a function

of distance.

You see that we can now very roughly determine the coherence length from the image.

With the average wavelength of the light being around 500nm or 0.5 microns, the coherence

length of the white light is just about 2 wavelengths long so about 1um, so extremely

short.

Okay, now let’s try a different light source, in this case a laser diode.

Now, stimulated emission only takes place at high field intensities in the laser cavity,

in other words, at relatively high operating powers.

However, if we operate the device at very low currents, it basically works like a normal

LED and only shows spontaneous emission.

So let’s take a look at both operating modes using the Michelson interferometer.

We’ll start out with a low operating current.

The diode now operates as a normal LED, so no stimulated emission.

And here you see the camera image again, when the two arms of the interferometer are set

to equal length.

In the images, the interference lines are spaced much closer together and that is because

I placed the two mirrors under a larger tilt, so we can look at decoherence over a larger

distance.

And you can observe that coherence extends over a larger number of wavelengths.

We can do the same measurement of the coherence length here: we can take a screen shot of

the interference pattern, convert it to an intensity plot and then estimate the coherence

length.

And now it’s almost 4.5 microns, which is more than 4 times longer than in the case

of the white light from the LED.

Let me show you what happens if we increase the current through the laser diode to the

point where it actually starts to lase.

So, here I’m turning up the current; because the intensity of the light output is much

higher now, we either need to decrease the shutter time of the camera, or attenuate the

light by means of a neutral density filter.

But look what happened to the interference pattern: now suddenly it is everywhere.

Whereas in the previous cases it was tricky to find the interference pattern, I can now

go wild on the micrometer of the linear stage and never lose the interference from sight.

We can actually extend the difference in distance between the two paths from centimeters up

to several meters.

This can be achieved by carefully setting the current of the laser diode to a value

of very stable operation.

And so this illustrates the extreme difference in coherence length between a source operating

in spontaneous emission mode and stimulated emission mode.

In the latter case, the source can evidently create a spectral distribution so very narrow

that coherence is preserved over distances of several meters, which is a million times

longer than in the case spontaneous emission.

So I want to pause my presentation here and I will continue in a second video.

In which I will, among other things, discuss spatial coherence in more detail.

And I will of course continue the discussion on how phenomena related to coherence and

interference can create a non-uniform distribution of energy in space.

I can assure you: it is going to be fascinating.