Chapter 1615: Direction of a Beam of Light

About ten minutes later, all members of Zhang Runing's research team, as well as representatives from the Torch Laboratory such as Li Yabo, sat in the conference room on the top floor of the Torch Laboratory.

Chang Haonan was standing next to the small podium in the front, with bruises clearly visible under his eyes, obviously from being overworked for days.

Fortunately, he seemed to be in high spirits and obviously in a good mood.

The display screen behind him, which took up most of the wall, was filled with densely packed formulas and symbols that were daunting.

Although all those present were senior researchers in the field of optics, they were still somewhat intimidated when faced with such a maze-like field of numbers and symbols.

Of course, this is also human nature.

As for math, if you don’t know how to do it, you don’t know how to do it.

Seeing everyone sitting down, he pointed directly to a matrix at the top of the screen without any greetings: "I believe everyone is familiar with this, right?"

A lighthearted laugh rang out in the conference room, erasing the solemnity just now.

"The Jones matrix that describes polarization aberration." He Xiujun pushed up his glasses and said, "For us opticians, it is the theoretical basis for our livelihood."

"Not bad." Chang Haonan nodded slightly, "Jones vector and Jones matrix are indeed used in the field of partial coherence imaging."

He pointed his laser pointer at the screen: "But the Jones pupil itself is not the best form to express polarization aberration."

These contents were not considered profound to everyone present, so Chang Haonan spoke very fast.

"The key point is that it does not explicitly give the specific values of phase delay and amplitude polarization in polarization aberration, so the Jones pupil needs to be decomposed."

At this point, he paused deliberately.

Sure enough, someone quickly responded, “The traditional method is to decompose the Jones matrix using the Pauli matrix basis to obtain four complex coefficients.”

Chang Haonan nodded, then found and circled the decomposition results directly on the screen.

“A very classic idea,” he commented.

But then he changed the subject:

"However, these four coefficients are essentially forced together through mathematical means, and each of them does not have a very clear physical meaning."

Zhang Runing sat up straight and said:

"In engineering practice, we usually believe that the real part of the a0 term in the decomposition result represents apodization (light intensity non-uniformity), and the imaginary part represents wavefront aberration, while the real part of the a1, a2, and a3 terms correspond to amplitude polarization, and the imaginary part corresponds to phase delay."

Chang Haonan was not an optical engineer, so he was slightly stunned after hearing this explanation.

Then he turned around and carefully checked the correspondence mentioned by the other party on the screen.

After a moment, he turned to the crowd again:

"It is indeed an approximate method that is feasible in engineering... But from a strict mathematical physics perspective, numerical equivalence does not mean physical equivalence... Moreover, in the results of Pauli decomposition, even the numerical values are only approximately equivalent, not strictly equivalent."

"Researcher Zhang, what I said should be correct, right?"

"That's right." Zhang Runing nodded, "But the difference in the values is very small. As far as I know, even the EUV lithography system will not be affected by the error."

Chang Haonan shook the page-turning pen in his hand:

"The problem is that without an equivalent physical meaning, it is simply impossible to analyze complex polarization systems."

During this month, Zhang Runing almost developed the habit of nodding subconsciously after Chang Haonan finished speaking.

But then I paid attention to the key point:

"A complex polarization system refers to..."

"We'll talk about this in detail later." Chang Haonan raised his hand and pointed in another direction on the screen.

There is a whole new set of mathematical expressions with a more sophisticated structure:

"I found a new way to decompose it."

The air in the conference room seemed to be stagnant, and everyone's eyes were focused on the unfamiliar formula.

"According to the polar decomposition theory," Chang Haonan said in a clear and steady voice, "any n-order complex matrix can be uniquely decomposed into the product of a Hermitian matrix and a unitary matrix - provided that the complex matrix is non-singular."

In polarization systems, a non-singular matrix means that it cannot contain an ideal polarizer.

In fact, there is no such thing.

So the conditions are not difficult to meet.

He paused to make sure everyone followed his train of thought: "Fortunately, for the Jones matrix that describes the polarization characteristics of the optical system, as long as the system itself does not have a singular point that causes complete loss of information, it satisfies this non-singular condition. Therefore, this decomposition is feasible and unique..."

"..."

The laser pointer's light kept jumping over the key parts of the formula.

Finally, we come to the conclusion in the lower left corner of the screen:

"The decomposition results can clearly point to five independent parameters with clear physical meanings!"

There was great certainty in Chang Haonan's tone.

"The first term, the transmission coefficient, describes the overall intensity loss or gain of light after it passes through the system."

"The second item is the wavefront phase, which is the traditional wavefront aberration and affects the imaging position and clarity."

"The third term, amplitude polarization, describes the variation in the intensity distribution of the electric field vector of the light wave in a particular direction..."

"..."

Even though he had deliberately slowed down the pace, most people were still able to keep up only at the beginning.

Halfway through, most people's eyes had begun to clear.

In the end, Zhang Runing was the only one still following the calculations with his head down.

He did not have theoretical mathematical knowledge, so it was impossible for him to complete the derivation from scratch, but it was enough to verify whether the process was correct.

"like……"

"Indeed!" Zhang Runing raised his head suddenly. "The eight complex coefficients are classified into five. Not only does it simplify the structure, but it also gives them corresponding physical meanings..."

Although others don’t know the specific process, since the two bosses have reached a consensus, it means that the conclusion on the screen should be correct.

"Then in this case..." He Xiujun's eyes gradually lit up, "Can the design of the objective lens group get rid of the past method of relying on experience and estimation, and then using the method of continuous trial and error iteration?"

"Well... at least the control of polarization aberration can be calculated directly, which can save a lot of effort..." Zhang Runing raised his head slightly and calculated in his mind, "The design cycle can be shortened to about half of the original... maybe about one third!"

He seemed to have seen a leap in design efficiency.

The sudden good news made him even forget the part he had just focused on.

But Chang Haonan didn't forget.

"It's not just a matter of efficiency." Chang Haonan showed a deeper smile on his face, "In physics, accurate description is generally equivalent to accurate control. In other words, we can freely control the polarization form of light within a certain range."

The crowd below was still processing the amount of information they had just received, and their reactions were a beat slower than usual.

It was not until about two breaths later that someone followed Chang Haonan's train of thought: "So the complex polarization you just mentioned, Academician Chang, means..."

"Conventional polarization control, in order to simplify the problem and ensure compatibility, often only uses a very limited part of the information in the polarization state of light."

Chang Haonan explained:

"Based on this theory, we can design a new multipolar light source, and it is no longer limited to simple X- or Y-polarization, but circular tangential polarization!"

As he spoke, he picked up the stylus and drew a diagram on the screen.

"In this mode, the direction of the electric field vector of the light wave is distributed in a ring around the optical axis, so the information pattern it carries is fundamentally different from traditional linear polarization."

He looked at Zhang Runing and He Xiujun: "Imagine that during the photolithography exposure process, the polarization state of each beam of light carries unique and precisely designed information. By utilizing the characteristics of tangential polarization, combined with the flexibility of multipolar light sources and the precise control capabilities of the new theory..."

Chang Haonan made a powerful gesture:

"We may be able to increase the amount of effective information that light signals can carry and transmit during the exposure process by a full order of magnitude!"