- #1

- 368

- 5

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter semc
- Start date

In summary, as a physics student, you can decompose a periodic function into sine functions with different frequencies using Fourier transform. However, when generating ultra-short pulses, you need many frequencies, which is why Fourier transform is applicable in this case. Passing monochromatic light through an optical chopper introduces higher harmonics and follows the uncertainty principle, resulting in a spread of wavelengths. This can be further understood through the concept of Gibbs phenomenon and the relationship between time and frequency domains in Fourier transforms.

- #1

- 368

- 5

Physics news on Phys.org

- #2

- 1,948

- 201

semc said:I would therefore like to ask what happens if I pass my monochromatic light through a optical chopper. Is Fourier transform not applicable in this case since ultra short pulse generation does not require many frequencies?

Ultra short pulses DO require many frequencies. Fourier transform theory applies

- #3

- 3,442

- 1,233

- #4

Science Advisor

Gold Member

- 2,833

- 513

- #5

- 734

- 171

- #6

- 368

- 5

dauto said:Ultra short pulses DO require many frequencies. Fourier transform theory applies

I am aware that you need many frequencies to get short pulse. That's what Fourier transform tells us. In my example, I specifically said I only have single wavelength as source.

A single frequency like a pure sine wave is only a single frequency if it starts at the beginning of time and goes on forever.

So if I turn on and off my laser I introduce higher harmonics as well?

Ain't this just the math? I am confused how higher frequencies are generated.

- #7

Science Advisor

Gold Member

- 2,833

- 513

- #8

- 368

- 5

marcusl said:

Don't really understand how this comes about. Is there any reference to explain in detail about this?

- #9

- 1,948

- 201

semc said:I am confused how higher frequencies are generated.

That's an application of the uncertainty relation. When you chop down the beam you are making a measurement of the photon location. By the uncertainty principle the photon momentum becomes uncertain creating a spread on the wavelength. In other words, the uncertainty principle is the physical principle that expresses the spread in wavelength required by the mathematics of waves which can be studied and understood through Fourier transforms.

- #10

Science Advisor

Gold Member

- 2,833

- 513

"Quote by dauto

Ultra short pulses DO require many frequencies. Fourier transform theory applies

I am aware that you need many frequencies to get short pulse. That's what Fourier transform tells us. In my example, I specifically said I only have single wavelength as source."

Once you modulate the carrier (pure sine) with an envelope, you no longer have a pure sine of single wavelength. You have a time-varying envelope that may have a rich spectrum, as I indicated earlier.

- #11

- 22

- 0

Fourier decomposition of a (periodic) signal will give you a long string of harmonics along with their amplitudes that when added together will give you your original signal back. If the wave is square then you will only get odd harmonics. In practice you may well get low amplitude even harmonics as well.

- #12

Mentor

- 35,156

- 13,382

You might start here http://en.wikipedia.org/wiki/Gibbs_phenomenonsemc said:Don't really understand how this comes about. Is there any reference to explain in detail about this?

A square wave has an infinite spread of frequencies. Gibbs ringing is what happens when you try to approximate a square wave with a finite spread of frequencies.

- #13

Science Advisor

- 1,479

- 26

Claude.

A Fourier transform is a mathematical technique that is used to decompose a complex signal into its individual frequency components. It converts a signal from its original time or space domain into a frequency domain representation.

A Fourier transform is useful because it allows us to analyze and manipulate complex signals in terms of their frequency components. This can help in various applications such as signal processing, image and sound analysis, and data compression.

A Fourier transform is used for continuous signals while a Fourier series is used for periodic signals. The Fourier series decomposes a periodic signal into a sum of sinusoidal components, while the Fourier transform decomposes a non-periodic signal into a continuous spectrum of frequencies.

Fourier transform has many applications in science, including signal processing, image and sound analysis, data compression, and solving differential equations in physics and engineering. It is also used in chemistry to identify and analyze the composition of molecules.

While Fourier transform is a powerful tool, it has some limitations. It assumes that the signal is periodic or infinitely long, which may not always be the case in real-world applications. Additionally, it cannot accurately capture sudden changes or discontinuous signals.

Share:

- Replies
- 47

- Views
- 1K

- Replies
- 3

- Views
- 1K

- Replies
- 13

- Views
- 1K

- Replies
- 1

- Views
- 1K

- Replies
- 7

- Views
- 2K

- Replies
- 16

- Views
- 768

- Replies
- 29

- Views
- 3K

- Replies
- 3

- Views
- 947

- Replies
- 3

- Views
- 838

- Replies
- 1

- Views
- 853