Imagine that we chop a continuous laserbeam (assumed to be...

Imagine that we chop a continuous laserbeam (assumed to be monochromatic at $\lambda_{0}=632.8 \mathrm{nm}$ ) into 0.1 -ns pulses, using some sort of shutter. Compute the resultant linewidth $\Delta \lambda$, bandwidth, and coherence length. Find the bandwidth and linewidth that would result if we could chop at $10^{15} \mathrm{Hz}$.

Key Concepts

Linewidth and Bandwidth Relationship

Linewidth refers to the spectral width of a light source at a specific wavelength, while bandwidth represents the range of frequencies present in a pulse. They are related through the dispersion relation, where a change in frequency corresponds to a change in wavelength based on the central wavelength and the speed of light. This relationship is central to determining how chopping a laser beam into pulses will affect its spectral properties, including the resulting linewidth and overall bandwidth.

Time-Bandwidth Uncertainty Principle

This principle states that the product of a pulse's temporal duration and its spectral bandwidth is bounded from below, reflecting a fundamental limit on simultaneous precision in time and frequency. In optics, this means that short pulses must have a correspondingly broad spectrum, while a narrow spectral linewidth implies a long pulse duration. This concept is crucial when chopping a continuous beam into pulses, as modifying the time duration directly affects the frequency spread.

Fourier Transform Relationship

The Fourier transform links the time and frequency domains by decomposing a time-dependent signal into its frequency components. In the context of pulsed lasers, applying a time window (such as a shutter or pulse modulation) results in a convolution in frequency space, leading to a broadened spectral profile. Understanding this relationship is essential for predicting how modulation of pulse duration influences bandwidth and linewidth.

Coherence Length

Coherence length is a measure of the distance over which a light wave (or laser beam) maintains a predictable phase relationship and is inversely proportional to the spectral bandwidth of the source. When the pulse duration is reduced, resulting in a broader frequency spectrum, the coherence length decreases. This concept is important in applications like interferometry, where phase stability over distance is critical.

Transcript

Please give Ace some feedback