Lec7 مبادئ

Standing Waves

• Laser light bounces within an optical cavity between two mirrors.
• Light waves travel in both directions simultaneously, causing interference
• This creates standing waves
• Standing waves dictate the properties of the laser light's frequency and wavelength

Fundamental and Resonant Frequencies

• The lowest vibration frequency that generates a standing wave is the fundamental frequency
• Resonant frequencies occur when standing waves are present
• The distance between successive nodes equals half a wavelength of the standing wave

Longitudinal Laser Modes

• Each longitudinal mode within an optical cavity forms a standing wave
• Nodes exist at each end of the cavity on the mirror surfaces, which is a condition that standing waves satisfy.
• The wavelength in diagrams can be disproportionate

Integer Wavelengths

• A 20 cm optical cavity emitting 0.5 micrometer visible laser light would have 400,000 integer wavelengths between the mirrors

Frequency (Mode) Spacing

• Frequency spacing (Δν) between longitudinal modes relies on the space between the mirrors (l)

Refractive Index

• n represents the refractive index of the gain medium

HeNe Laser Wavelength

• The bandwidth of a HeNe laser is greater than 750 MHz
• The output of a HeNe laser is not exactly 632.8 nm; it has a bandwidth (ΔλB.W.) and a frequency bandwidth (ΔνB.W.)
• Multiple longitudinal modes with spacing (Δν = c/2l) can fit within ΔλB.W. and exist at the same time

Gain versus Frequency

• Laser emission is amplified by stimulated emission of the laser transition
• The vq mode is at the center of the gain curve

Loop Gain

• With loop gain GL, longitudinal modes vq, vq–1, vq+1, vq–2, and vq+2 are present in the output
• Modes vq–3 and vq+3 are not present because they fall the gain curve threshold (GL=1)
• Intermediate frequencies do not have wavelengths that fit in the optical cavity of length L

HeNe Laser Example

• A He-Ne laser (n = 1.0) has a cavity length of 50 cm
• The output wavelength is 632.8 nm

Gas Lasers

• Gas lasers commonly have an index of refraction of 1.0
• Solid lasers require consideration of the laser rod's index of refraction

Mirrors

• When mirrors are deposited directly the index of refraction used for mode spacing calculations is the index of refraction of the laser rod.
• If the cavity includes a length of air (or other material) use the appropriate equation.

Nd:YAG Laser Example

• An Nd:YAG laser has a cavity length of 50 cm and a rod length of 10 cm.
• The index of refraction of Nd:YAG is 1.823.
• The remainder of the cavity is filled with air with an index of 1.0

Laser Output

• The longitudinal mode pattern of a laser output depends on factors like the active medium, temperature, and population inversion

Threshold Line

• The threshold line represents a loop-gain value of one
• The active medium provides sufficient gain for lasing at frequencies where the loop gain exceeds the threshold
• The number of modes with a gain of one depends on cavity losses
• Cavity losses come from optical distortion, surface flaws, transmission through the output coupler, and aperture size

Stimulated Emission

• The rate of stimulated emission depends on the strength of the stimulating signal
• Strong optical signals are built up in the laser cavity at frequencies that form standing waves
• Lasing occurs at frequencies corresponding to the cavity modes

Laser Output Beams

• Laser output is composed of coaxial beams with different frequencies and power

Understanding Wavelength Difference

• The wavelength difference between two adjacent modes in a He-Ne laser can be calculated.
• For a He-Ne laser with a cavity length of 50 cm and a mode spacing of 3.0 * 108 Hz where the wavelength of mode q is 632.8 nm, you can determine the wavelength of mode q-1.
• The wavelength difference between the two modes is 4 * 10–13 m, or 4 * 10–4 nm

Single Frequency

• Each laser mode is not a single frequency, but is composed of a range of frequencies
• The approximate bandwidth of a single mode: Δνbw = Δν(T + L)
• Δν = Mode spacing, T = Transmission of output coupler, L = Round trip cavity loss.

He-Ne Laser example

• A He-Ne laser has a mode spacing of 3.0 * 108 Hz and an output coupler with a transmission of 1.8%
• The round-trip loss is 0.4%.
• The bandwidth of a single mode: Δνbw = 6.6 MHz

Fluorescent Line Width

• The fluorescent line width of a laser is the width of the frequency range over which spontaneous fluorescence occurs
• The fluorescent line width is greater than the line width of the output laser beam and is expressed in frequency units
• The fluorescent line width of a typical He-Ne laser is approximately 1.5 GHz.
• The fluorescent line width of a typical Nd:YAG laser is about 30 GHz.
• The approximate number of modes in a laser output beam can be determined by dividing the laser fluorescent line width by the mode spacing

Number of Modes

• n = Δνlw / Δν
• n = Number of modes (an integer), Δνlw = Fluorescent line width of the laser, Δν = Mode spacing.

Nd:YAG Laser Modes

• The Nd:YAG laser from Example E has a mode spacing of 257.6 MHz
• The laser fluorescent line width of Nd:YAG is 30 GHz
• The approximate number of modes in the laser output is 117.