# Jones vectors and electric field of a wave

• Lindsayyyy
In summary, the conversation discusses the use of Jones vectors and matrices to calculate the electric field of a right circular polarized wave. It is mentioned that there are other approaches, such as using Stokes parameters, but Jones vectors are considered the best approach. The conversation also touches on the differences between the Stokes and Jones approaches, and the advantages and disadvantages of each. The conversation concludes with a discussion on the use of mirrors and quarter wave plates to manipulate polarization. There is a question about whether knowing the polarization state of a wave implies knowing the E field, to which the response is no, as the E field is also affected by the field magnitude and waving part of the wave.
Lindsayyyy
Hi everyone,

I have a question. Let's say we have a right circular polarized wave (created by a lamba/4 plate which is reflected in a mirror and send back through the lambda/4 plate.

Is the only way to calculate the electric field via the Jones vectors or is there any other possibility to calculate the electried field vector?

I hope I'm in the right board for this question.

Using Jones vectors and matrices is probably the best approach to track polarization vectors, but it is not the only approach. You could also use http://en.wikipedia.org/wiki/Stokes_parameters" .

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Thanks for the help, I'll check this out.

chrisbaird said:
Using Jones vectors and matrices is probably the best approach to track polarization vectors, but it is not the only approach. You could also use http://en.wikipedia.org/wiki/Stokes_parameters" .

The .pdf file was ok, but it's important to remember that the Stokes/Mueller and Jones calculi are conceptually very different. The Stokes vector can treat randomly polarized light, while the Jones vector cannot, for example.

The Mueller calculus has the advantage of being based on measurable parameters (intensities), as opposed to the fields themselves. The disadvantage of the Mueller calculus is the increased complexity, because polarization is expressly treated as a statistical property of the electromagnetic field.

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Andy Resnick said:
The .pdf file was ok, but it's important to remember that the Stokes/Mueller and Jones calculi are conceptually very different. The Stokes vector can treat randomly polarized light, while the Jones vector cannot, for example.

Yes, thank you for making this distinction. The Stokes are Jones approach are fundamentally different as the Stokes approach deals with a statistic ensemble of many polarization states and the Jones approach deals with a single polarization state. But if one makes the assumption that there is only a single polarization state present, which the original poster implied, one can still apply the Stokes approach and then transform between the two approaches.

If you know the polarization state of the wave, do you not know, by definition, the E field of the wave? In other words, by saying that the wave is RHCP, does that not imply certain characteristics about the E field?

Jones and Mueller matrices are formalisms that aid in calculations when you pass certain polarization states through various optical systems.

Claude.

Claude Bile said:
If you know the polarization state of the wave, do you not know, by definition, the E field of the wave? In other words, by saying that the wave is RHCP, does that not imply certain characteristics about the E field?

Jones and Mueller matrices are formalisms that aid in calculations when you pass certain polarization states through various optical systems.

Claude.

I'm not sure I understand your question. For example, how would you specify the E field given a Stokes vector of (1,0,0,0)?

The mirror itself serve as a half-wave plate if your light fall perpendicular to its surface. Light that pass two times through the quarter wave plate serves as a half wave plate.

Claude Bile said:
If you know the polarization state of the wave, do you not know, by definition, the E field of the wave? In other words, by saying that the wave is RHCP, does that not imply certain characteristics about the E field?

Jones and Mueller matrices are formalisms that aid in calculations when you pass certain polarization states through various optical systems.

Claude.

No. The polarization is only one part of a plane electromagnetic wave. The E field is a product of the polarization vector, the field magnitude, and the waving part (cos(kx - ωt))

## 1. What is a Jones vector?

A Jones vector is a mathematical representation of the polarization state of an electromagnetic wave. It consists of two complex numbers, known as the amplitude and phase, which describe the magnitude and orientation of the electric field vector of the wave.

## 2. How is the electric field of a wave related to the Jones vector?

The Jones vector represents the electric field vector of a wave. The amplitude and phase values in the Jones vector determine the magnitude and direction of the electric field at any point in space and time.

## 3. How is the Jones vector used in optics?

The Jones vector is commonly used in optics to analyze and manipulate the polarization of light. It is particularly useful in studying the behavior of polarized light as it passes through various optical elements, such as polarizers and waveplates.

## 4. Can the Jones vector be used for non-linearly polarized light?

Yes, the Jones vector can be used to represent any polarization state, including non-linearly polarized light. In such cases, the Jones vector will have different amplitude and phase values for the two complex numbers, indicating the varying magnitude and orientation of the electric field vector.

## 5. How is the Jones vector different from the Stokes vector?

While the Jones vector represents the polarization state of an electromagnetic wave using two complex numbers, the Stokes vector uses four real numbers to describe the polarization state. Additionally, the Jones vector is more commonly used for coherent light sources, while the Stokes vector is used for partially polarized or unpolarized light.

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