Question

A I fs pulse of laser light would be \(0.3 \mu \mathrm{m}\) long. What is the range of wavelengths in a \(0.3\) lim long pulse of (approximately) \(600 \mathrm{~nm}\) laser light? \(\left(1 \mathrm{fs}=10^{-15} \mathrm{~s} .\right)\)

Short answer

The range of wavelengths in a 0.3 µm long pulse of approximately 600 nm laser light is 180 nm.

Step-by-step solution

Convert Units

Firstly, convert the laser pulse length and wavelength from µm and nm respectively to meters because the standard unit of measurement for that is meter (m). Thus, 0.3 µm = 0.3x\(10^{-6}\) and 600 nm = 600x\(10^{-9}\)

Calculate Pulse Duration in Seconds

It's given that the pulse duration is in femtoseconds (fs). For the calculation in next steps we need to convert this to seconds. As 1 fs = \(10^{-15}\) seconds, so the time interval of the pulse (∆t) will be ∆t = 0.3 µmx \(10^{15}\)

Apply the Heisenberg’s Uncertainty Principle

Using the Heisenberg’s Uncertainty Principle, which states that ∆λ x ∆ν ≥ c, where c is the speed of light and ∆ν is the frequency variation in the laser pulse, we can say ∆λ ≥ \( \frac{c}{∆ν} \) = \( \frac{c}{c/λ} \) = ∆t x λ

Calculation

Plug in the values into the formula. ∆λ = ∆t x λ = 0.3 x \(10^{-6}\) x 600 x \(10^{-9}\) = \(1.8 x 10^{-13}\). Convert the result back to nanometers by multiplying by \(10^{9}\) to get ∆λ = 180 nm.

Key concepts

Laser Pulse

A laser pulse is a short burst of coherent light energy emitted from a laser source. The pulse duration is the length of time the laser emits this burst of light. It is often measured in extremely small time units like femtoseconds (fs), where 1 fs equals \(10^{-15}\) seconds. This measurement reflects how quickly the energy is emitted by the laser. Understanding laser pulses is crucial, as it ties into the precision and applications of lasers in technology and research. Laser pulses are widely used in fields like telecommunications, where they carry data at high speeds, and in medical procedures that require precision.A key characteristic of laser pulses is their ability to focus energy in an incredibly short time duration, which can achieve significant power levels. This makes them ideal for tasks requiring precision and rapid processing.To work with laser pulses, especially in calculations involving their properties, it's essential to understand associated concepts like the wavelength of the laser light and how to convert units effectively to help in solving related problems.

Wavelength Calculation

Wavelength calculation involves determining the distance between consecutive peaks (or troughs) of a wave, such as light. In laser technology, the wavelength is critical as it determines the color and behavior of the laser light. For instance, in the given problem, the laser light has an approximate wavelength of 600 nm, which points to its position in the visible light spectrum, often associated with orange color. To calculate wavelength-related variations, such as shifts or ranges due to physical phenomena, understanding the relationship through formulas is vital. Specifically, Heisenberg's Uncertainty Principle becomes essential when examining the range of wavelengths emitted by a laser pulse. This principle connects the variations in wavelength (\(\Delta\lambda\)) with the time duration of the pulse (\(\Delta t\)).To compute the wavelength range for a laser pulse, you often need to:

• Identify the laser's central wavelength
• Use principles like Heisenberg's to account for uncertainties

Remember, accurate calculations hinge on precision with units and the understanding of light properties.

Unit Conversion

Unit conversion is an essential skill in physics to express measurements in a standardized form for ease of calculation and comparison. In our exercise involving laser pulses, we deal with units like micro-meters (µm) and nano-meters (nm) for length, and femtoseconds (fs) for time.Units like meters and seconds are often preferred in scientific calculations due to their universality in the International System of Units (SI). Therefore, converting from µm to meters or fs to seconds is necessary.Here are the common conversions needed:

• 1 µm = \(1\times10^{-6}\) m (micro to meters)
• 1 nm = \(1\times10^{-9}\) m (nano to meters)
• 1 fs = \(1\times10^{-15}\) s (femto to seconds)

When dealing with these conversions, keep consistent units throughout your calculations to avoid errors. For example, converting the laser pulse length from 0.3 µm to meters ensures that all subsequent calculations made with light properties, such as speed or wavelength calculations, are coherent and properly scaled.