Two lasers with very nearly the same wavelength can generate...

Two lasers with very nearly the same wavelength can generate a beat frequency if both laser beams illuminate a photodetector with a very fast response. In an experiment, one laser's wavelength has been stabilized at $780.54510 \mathrm{nm} .$ The second laser starts with a longer wavelength that is slowly decreased until the beat frequency between the two lasers is $98.5 \mathrm{MHz}$. What is the second laser"s wavelength?

Key Concepts

Beat Frequency

Beat frequency refers to the periodic variation in intensity that occurs when two waves of similar but not identical frequencies interfere with one another. In the context of lasers, if two beams have nearly the same frequency, the resulting interference pattern oscillates at a frequency equal to the difference between the two frequencies, making it possible to measure very small differences in laser frequency.

Frequency-Wavelength Relationship

The connection between frequency and wavelength is described by the equation c = f?, where c is the speed of light, f is the frequency, and ? is the wavelength. This relationship is fundamental when converting between wavelength changes and frequency differences, which is crucial for understanding how a change in the laser's wavelength results in a measurable beat frequency.

Photodetection

Photodetection involves using devices that are capable of sensing light and converting the optical signals into electrical signals. In experiments involving beat frequencies, a fast photodetector is used to capture rapid intensity fluctuations caused by the interference of two laser beams, allowing for the measurement of their frequency difference.

Laser Stabilization

Laser stabilization is the process of controlling the output wavelength or frequency of a laser so that it remains constant over time. This is important in precision experiments where one laser is fixed at a specific wavelength to serve as a reference, while another laser is tuned to generate a known beat frequency, thereby enabling accurate comparisons and measurements.

Transcript

00:01 The wavelength of one laser is 780 .5451510 nanometers.

00:21 The second laser has a longer wavelength and is decreased until you get a beat of 98.

00:48 5 megahertz.

00:52 And the wavelength is greater than the wavelength of the first one is what we're told.

01:03 All right.

01:05 What is the wavelength of the second laser? well, i know that speed of light is wavelength times frequency.

01:15 So the frequency of the first laser is the speed of light over the wavelength of the first laser.

01:23 The frequency of the second laser is the speed of light over the wavelength of the second laser.

01:30 And i know that the frequency of the second laser is the frequency of the first laser plus 98 .5 times 10 to the sixth power hertz.

01:49 So, speed of light over wavelength 1 equals speed of light over wavelength 2 plus 98 .5 times 10 to the 6th hour hertz.

02:07 We're trying to figure out wavelength 2.

02:11 So rearranging this and i'm going to rename this as f sub b for f beat.

02:27 C over lambda 1 minus f sub b equals c over lambda 2.

02:36 And so lambda 2 is going to be c over, c over lambda 1 minus f sub b.

02:51 So i can just put that into a calculator.

02:54 I can simplify it more, but i'm going to put it into a calculator.

02:56 3 times 10 to the 8th power, divided by 3 times 10 to the 8th power over lambda 1...

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