Can a pulse from a laser be treated as a Gaussian?

In summary, the results of the research show that it's important to take into account how the target reflects laser light when trying to estimate the range of a target.
  • #1
TL;DR Summary
I know a laser is generally treated as a coherent state (i.e. a plane wave). However, if a laser turns on and back off quickly, can the resulting light be treated as a gaussian?
I know a laser is generally treated as a coherent state (i.e. a plane wave). However, if a laser turns on and back off quickly, can the resulting light be treated as a gaussian multiplied by the plane wave that would have been emitted if the laser were continually active?
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  • #2
Depends on the laser. I assume you mean in the temporal sense? Q-switched lasers would often look like a fast exponential rise followed by a slower exponential fall. But anyway, they are complicated beasts that come in many flavors; it all depends on the details.

Plus I'm confused about the plane wave reference, that's a spatial profile, I guess? Lasers don't really make simple plane waves, more like diffraction limited TEM modes.

Anytime you hear people referring to plane waves they are intentionally choosing the simplest possible model, which is useful, but always wrong, somehow.
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  • #3
Anyway, your question is "is this a good model?" I guess we can't tell you that. It's not ridiculous, and it's simple enough (I think, still not sure about the details). All models are wrong, they are also simpler than reality, which is incredibly useful. The next step, the hardest part, is to evaluate if you care about the difference between your model and the real world; i.e. what you care about.

My favorite professor used to say: "Engineering is the art of approximation" - R. D. Middlebrook
  • #4
Concur with @DaveE.

We can divide commercial lasers, indeed many other EM emitters, as continuous with a wave as model (CW); and pulsed. Pulsed lasers allow fine control of the optical bandwidth and meaningful control of energy applied to the target. Energy from a CW laser concentrated within a short duration pulse, provide a glimpse of possibilities.

Pulse repetition frequency (PRF) adjustment provides many design and operational advantages over CW including more precise energy placement and improved retention of lasing material in the pulse-off period. As previously stated, laser design choice depends on application specifics, then cost and availability.

Pulsed lasers add interesting mathematics to basic wave model calculations. Aforementioned Q-switches permit very narrow pulse widths, and very rapid response.
  • #6
  • #7
The simplest model of a laser pulse is a carrier sine wave times a pulse envelope. A Gaussian envelope is a reasonable choice, but the fact that it never actual goes to zero can be problematic in some simulations/calculations. In that case, one can use a ##\sin^2## envelope, which has the nice property that the first derivative also goes to zero at the beginning and end of the pulse.

As others have mentioned, actual pulses have a more complicated shape that depends on the type of laser.
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  • #8
Alright, thank you for all of the responses! Out of curiosity, what's an example of a more complicated (but closer to reality) wave function for a light pulse?

Related to Can a pulse from a laser be treated as a Gaussian?

Can a laser pulse be approximated by a Gaussian function?

Yes, many laser pulses can be approximated by a Gaussian function, especially if the pulse shape is smooth and symmetric. This is because Gaussian functions are mathematically convenient and often provide a good fit for the temporal and spatial profiles of laser pulses.

Why is a Gaussian function used to describe laser pulses?

A Gaussian function is used because it simplifies the mathematical analysis and accurately models the behavior of many laser pulses. Gaussian pulses are characterized by their smooth, bell-shaped curves, which are commonly observed in real-world laser systems.

What are the key parameters of a Gaussian laser pulse?

The key parameters of a Gaussian laser pulse include the peak amplitude, the pulse width (often defined as the full width at half maximum, FWHM), and the temporal or spatial center. These parameters help define the shape and duration of the pulse.

Are there any limitations to using a Gaussian model for laser pulses?

Yes, the Gaussian model may not accurately describe laser pulses with complex shapes, such as those with multiple peaks or significant asymmetry. In such cases, other models like Lorentzian or super-Gaussian functions might be more appropriate.

How does the Gaussian approximation affect the analysis of laser pulses?

The Gaussian approximation simplifies the mathematical treatment of laser pulses, making it easier to predict and analyze their behavior. However, it is essential to validate that this approximation is suitable for the specific pulse being studied to ensure accurate results.

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