Problem 47 - Fundamentals of Physics

Question

The active volume of a laser constructed of the semiconductor GaAlAs is only \(200 \mu \mathrm{m}^{3}\) (smaller than a grain of sand), and yet the laser can continuously deliver \(5.0 \mathrm{~mW}\) of power at \(a\) wavelength of \(0.80 \mu \mathrm{m}\). At what rate does it gencrate photons?

Step-by-Step Solution

Answer

The laser generates roughly \(1.0 \times 10^{16}\) photons per second.

Step 1: Determine Energy per Photon

Find the energy of a single photon using the formula for photon energy: \(E = \frac{hc}{\lambda}\), where \(h\) is Planck's constant \( (6.626 \times 10^{-34} \, \text{J} \cdot \text{s}) \), \(c\) is the speed of light \( (3 \times 10^8 \, \text{m/s}) \), and \(\lambda\) is the wavelength \( (0.80 \times 10^{-6} \, \text{m}) \). Calculate \(E\) by substituting these values.

Step 2: Calculate Power in Watts to Energy per Second

Remember that power in watts \((5.0 \, \text{mW})\) is energy per second. Convert \(5.0 \, \text{mW}\) to watts by dividing by 1000 to get \(5.0 \times 10^{-3} \, \text{W}\).

Step 3: Determine Rate of Photon Generation

The rate at which photons are generated is the total power divided by the energy per photon. Use \( \text{Power} = 5.0 \times 10^{-3} \, \text{W} \) and \( E \) from Step 1. The rate \( R \) is given by \( R = \frac{\text{Power}}{E} \). Calculate \( R \) using the values from the previous steps.

Key Concepts

Semiconductor Lasers

Semiconductor lasers are fascinating devices that convert electrical energy into light. This is achieved through a process called stimulated emission, where electrons and holes in a semiconductor material like GaAlAs recombine to emit light. These lasers are extremely efficient and compact, making them widely used in different technologies such as DVD players and fiber optic communications. They have an active region, often only a few micrometers in size, like the one in our exercise, which is only 200 µm³. This tiny volume can produce a continuous laser output of 5 mW, illustrating the power-packed performance of semiconductor lasers. The efficiency and size of semiconductor lasers make them indispensable in both everyday technology and advanced scientific applications.

Photoemission

Photoemission refers to the phenomenon where photons, or particles of light, cause the emission of electrons from a material. In the context of semiconductor lasers, photoemission is not directly involved in the laser's operation. However, understanding the energy of emitted photons, which is crucial for calculating the rate of photon production, has its roots in the principles of photoemission. The energy of a photon correlates with its wavelength, and this relationship is crucial in determining the characteristics of the emitted light. By applying the formula for photon energy \(E = \frac{hc}{\lambda}\), where \(h\) and \(c\) are constants, we calculate the energy that is intrinsic to emitted light, which can also mobilize electrons under the right circumstances.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, from gamma rays to radio waves. In our exercise, the laser emits light at a wavelength of 0.80 µm, which is in the infrared region of the spectrum. This part of the spectrum is not visible to the human eye but is crucial in applications like telecommunications and medical instruments. Each type of electromagnetic wave, defined by its wavelength, carries different energy levels and is suited to unique applications. The spectrum itself is essential for understanding the behavior of light and why certain wavelengths are chosen for specific technologies. For laser applications, choosing the right wavelength impacts efficiency, range, and safety, which makes understanding this spectrum vital in laser technology.

Optics

Optics is the branch of physics that studies the behavior and properties of light. It includes understanding how light interacts with different materials. In the case of semiconductor lasers, optics plays a crucial role in the design and functionality of the laser systems. The principles of optics allow engineers to manipulate light to deliver focused, coherent beams, which are essential for the high precision tasks that semiconductor lasers perform. As the emitted light travels through different media, understanding refraction, reflection, and absorption becomes key. Optics ensures that a laser's beam is directed precisely and maintains its intensity over distances, which is crucial whether the laser is used for cutting materials, in communication equipment, or in medicine.