Laser principles—lecture - 5

The amplitude of a light beam is increased in a laser by multiple passes of coherent light waves through the active medium. The process is accomplished by an active medium placed between a pair of mirrors that act as a feedback mechanism. During each round trip between the mirrors, the light waves are amplified by the active medium and reduced by internal losses and laser output. A number of different combinations of mirrors, such as plane and curved, have been utilized in practical lasers. The pair of mirrors, axially arranged around an intervening volume, sometimes is called an "optical cavity," or a "laser resonator." Only certain frequencies of EM radiation will set up standing waves within this volume. These allowed frequencies of oscillation are referred to as "axial," or "longitudinal," modes of the cavity.
This module discusses the optical cavity of a laser, gain and loss in optical cavities, cavity configurations, standing waves in optical cavities, and the effects of all these factors on laser operation and output. In the laboratory, the student will align the optical cavity of a He-Ne laser.
OPTICAL CAVITIES:
A laser is essentially an amplifier placed between two mirrors. The presence, shape, and separation of the mirror surfaces determine the spatial distributions of the electromagnetic fields inside the laser. An optical cavity is a volume bounded by two or more reflective surfaces. The optical cavity of a typical laser is depicted in Figure 1. The optical axis is a line perpendicular to the mirror surfaces at the center of the optical cavity. The aperture is the element within the cavity that limits the size of the beam. In most cases, the aperture is at the end of the active medium; but in some lasers, an additional aperture is installed in the cavity to limit the beam to a desired diameter.

Fig. 1 The optical cavity of a laser
LOSS AND GAIN IN OPTICAL CAVITIES:
A laser contains an amplifying medium and an optical cavity. Spontaneous emission of photons, some of which takes place along the direction of the optical axis, begins the formation of the laser beam. The beam is reflected backward and forward between the two mirrors. During each round trip of the cavity, the beam passes through the active medium twice and is amplified; some of the light passes through the output coupler to form the output beam, and some of the light is removed from the beam due to losses in the cavity. The remaining portion of the light energy is reflected back into the optical cavity. All these factors must be considered in the design of a laser optical cavity.
LOSS IN OPTICAL CAVITIES:
The following factors contribute to losses within the optical cavities of lasers:
1-Misalignment of the mirrors: If the mirrors of the cavity are not aligned properly with the optical axis, the beam will not be contained within the cavity, but will move farther toward one edge of the cavity after each reflection.
2-Dirty optics: Dust, dirt, fingerprints, and scratches on optical surfaces scatter the laser light and cause permanent damage to the optical surfaces. Instructions for the cleaning of laser optics are presented later in this module.
3-Reflection losses: Whenever light is incident on a transparent surface, some portion of it always is reflected. Brewster windows and antireflection coatings greatly reduce this loss of light but cannot eliminate it entirely.
4-Diffraction loss: Part of the laser light may pass over the edges of the mirror or strike the edges of the aperture and be removed from the beam. This is the largest loss factor in many lasers.
When a light beam passes through a limiting aperture, the waves at the edge of the beam bend outward slightly, causing the beam to diverge. This phenomenon is termed "diffraction." When laser light moves from left to right (Figure 1), diffraction occurs at the aperture, and the beam diverges. When the beam returns to the aperture after reflection from the HR mirror, its diameter is larger than the diameter of the aperture; and the edges of the beam are blocked. The portion of the beam that does pass through the aperture is diffracted again and experiences additional loss on the next pass.
LOOP GAIN:
The loop gain of a laser is the ratio of the power of the beam at any point in the cavity to the power at the same point one round trip (loop) earlier through the cavity.
The power of the beam at point 1 in Figure 2 is P1. When the light passes through the active medium at point 2, it is amplified to a power of P2 = GaP1. After reflection from the HR mirror, the power is P3 = R1GaP1. This light passes through the active medium again and is amplified to have a power of P4= GaR1GaP1. After reflection from the output coupler at point 5, the power is P5 = R2GaR1GaP1. This loop accounts for all modifications on the initial beam except for losses. If the round-trip loss is L, the power remaining at point 1 after one complete circuit of the optical cavity is P6 = P5(1-L), or P6 = R2GaRlGaPl(1-L). Point 6 is identical with point 1 and signifies the completion of one loop.


Fig. 2 Loop gain of a laser
The loop gain of the laser, then, is the ratio of P6 to Pl, as indicated by Equation 1.
Equation 1


Given: A ruby laser has the following characteristics (refer to Figure 2):
Ga = 3.0
R1 = 0.995
R2 = 0.50
L = 0.08
Find: Loop gain.
Solution: GL = G2R1R2(1 – L)
GL = (3.0)2(0.995)(0.50)(1 – 0.08)
GL = (9.0)(0.995)(0.50)(0.92)
GL = 4.12


Given: The following are characteristics of the components of an argon ion laser:
• Reflectivity of HR mirror: 99.8%
• Transmission of output coupler (T): 4.2%
• Scattering and absorption loss of output coupler (S + A): 0.05%
• Round-trip loss (excluding mirror loss): 0.8%
• Amplifier gain: 1.05
Find: Loop gain.
Solution: Determine reflectivity of output coupler:
R2 = 1 – (T + S + A)
R2 = 1 – (0.042 + 0.0005)
R2 = 1 – (0.0425)
R2 = 0.9575
Write remaining quantities as decimal fractions:
R1 = 0.998
Ga = 1.05
L = 0.008
Calculate the loop gain:
GL = Ga2R1R2(1 – L)
GL = (1.05)2(0.998)(0.9575)(1 – 0.008)
GL = (1.1025)(0.998)(0.9575)(0.992)
GL = 1.045
If the loop gain of a laser is greater than one, the laser output power is increasing. If the loop gain is less than one, the output power is decreasing. If the loop gain is exactly one, the output power is steady.
GAIN IN CW LASERS:
Figure 3 relates loop gain and output power of a CW laser as a function of time from the moment the laser is turned on. The excitation mechanism begins to operate at time t0. At time t1, a population inversion is established, and the amplifier gain is one. However, lasing does not begin at time t1 because the losses in the cavity result in a loop gain of less than one. At time t2, the loop gain reaches unity, and lasing begins. Both loop gain and output power increase until loop gain reaches a maximum value at t3. At this point, the laser output power is increasing at its maximum rate, and the maximum condition of population inversion exists.

Fig. 3 Loop gain and output power in a CW laser
As lasing continues past t3, stimulated emission moves atoms from the upper lasing level to the lower lasing level faster than the atoms can be replaced. This process reduces the population inversion; consequently, both amplifier gain and loop gain are decreased. At t4, the laser stabilizes with a steady output power and a loop gain of one.
The loop gain of a CW laser in steady state operation is always one. The amplifier gain may be found by the substitution of this value for loop gain into Equation 1 and by the solving for amplifier gain, as in Equation 2.
Equation 2




Given: A CW Nd:YAG laser contains mirrors R1 = 0.998, R2 = 0.980 and a round-trip loss of 0.5%.
Find: Amplifier gain during CW operation.
Solution:
If the power of the excitation mechanism is increased, the laser output power may increase; but a new steady state condition will be reached with a loop gain of one. The amplifier gain will be the value that produces a loop gain of one.
The amplifier gain measured in Module 1-6, "Lasing Action," is called the "small signal gain," which is the gain of the active medium for optical signals that are so small that their amplification does not significantly reduce the population inversion. The actual amplifier gain of CW lasers is less than the small signal gain because the power removed by the laser beam does reduce the population inversion. This reduced value of amplifier gain is referred to as "saturated gain."
GAIN IN PULSED LASERS:
The instantaneous power of the pulsed laser excitation mechanism far exceeds that of CW lasers. Much greater population inversion and much higher values for both amplifier gain and loop gain are achieved in pulsed lasers. Figure 4 graphically shows the loop gain and output power of a pulsed laser as a function of time. At t1, the loop gain has reached a value of one, and lasing has begun. Loop gain continues to increase to some maximum value at t2, and output rises accordingly.