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This version reflects the comments of the core participants as reviewed and incorporated in accordance with CORD's FIPSE-supported Curriculum Morphing Project. MODULE 1-8
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of 258
MHz (Example E) and, if the fluorescent linewidth 
of the Nd:YAG laser is 30GHz, then the
number of longitudinal modes is calculated to 
(Example H).]Each of these longitudinal modes exhibits a spiking behavior independent
of the behavior of the other modes. The total output pulse is composed of thousands of
these short pulses.
| Q-Switching - Excellent Technical Article |
(8) Figure 2 shows a schematic diagram for a Qswitched laser. Several types of Qswitches are in common use, each type being suited to a particular type of laser and pulse domain. The Qswitch acts as a shutter within the laser cavity. When this shutter is closed, light passing through the active medium is blocked from reaching the HR mirror, or is reflected out of the cavity. Consequently, the highreflectivity (HR) mirror provides no feedback. The Qswitch introduces sufficient loss in the laser cavity to prevent lasing, which, in turn, allows the amplifier gain of the laser to increase far above the normal lasing threshold. When the Qswitch is opened that is, when feedback between the mirrors is restored lasing is initiated, and the energy stored in the active medium is subsequently released in one intense pulse.
Fig. 2 Q-switched laser schematic.
There are generally four types of Q-switches in use:
mechanical, acousto-optic, electro-optic, and dye.
(9) Figure 3 compares the operation of a pulsed laser in the Qswitch mode to the operation of the same laser in the normal pulsed mode. Without the Qswitch, the amplifier gain reaches the lasing threshold at t1, and lasing begins. The lasing process removes energy from the active medium in the form of the spiked output of a normal pulse. The amplifier gain and output power of the normal pulsed mode laser are indicated by dotted lines.
Fig. 3 Operation of a Q-switch
(10) The values for the Qswitched mode are indicated by solid lines. The Qswitch prevents internal feedback of the beam and maintains a loop gain value of zero until the energy stored in the active medium has reached a maximum value. At time t2 in Figure 3, the amplifier gain is many times the maximum gain value in a normal pulsed laser, due of course, to the large population inversion created. When the Qswitch is opened, loop gain rises rapidly to a large value – in some cases, the value may be several hundred. This large increase in loop gain can produce intense standing waves in many cavity modes, and all the stored energy is released in the resulting pulse. Qswitched pulses range in duration from a few seconds to several hundred nanoseconds. And the peak power of a Qswitched pulse may be several thousand times greater than that of the same laser without a Qswitch. While Qswitching reduces the total energy of the pulse, the pulse width is shortened even more.
(11) The "Q" in Qswitching stands for "quality factor" and is a carryover from electronics. The quality of a cavity is defined as the ratio of the amount of energy stored in that cavity in the form of a standing wave to the amount of energy lost for all reasons during a round trip of the cavity. When the Qswitch of a laser is closed, there is no feedback and thus no standing wave. The loss is very high and thus the quality factor is zero. When the Qswitch is opened, a strong standing wave is formed, causing the loss to be reduced. The Qswitch receives its name from the fact that it allows the "Q" of the cavity to be "switched" from (feedback blocked) a low value to a high value. (feedback restored) However, actual calculations of the quality factor are seldom made for laser cavities.
(12) No mechanical shutter can open fast enough for effective Qswitching. The simplest mechanical method of achieving Qswitching at the necessary rate is the rotation of the HR mirror. The HR mirror is mounted on the shaft of a motor that has a rotational rate of 30,000 rpm or greater. Once during each revolution, the mirror is aligned for nanoseconds and the laser pulse is produced. As indicated in the caption of Figure 2, one can use acousto-optic, electro-optic and dye switches, in addition to mechanical switches, to effectively Q-switch the cavity.
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MODELOCKED LASERS
| Lightwave Electronics Mode-Locked Laser |
(13) Figure 4 illustrates the output of a modelocked
laser. This output consists of a train of laser pulses, each pulse
having a duration of from picoseconds to a fraction of a nanosecond, depending upon
the laser. The separation of the pulses is equal to the time required for light to make
one round trip around the laser cavity, from mirror to mirror and
back again. If the distance between mirrors is l, then the roundtrip time is 
where c is the
speed of light in the cavity.
Fig. 4 Train of pulse output of a modelocked laser
(14) How is modelocking achieved? To understand the process, recall the work in Module 1-7, Optical Cavaities and Modes of Scillation, where we showed that many longitudinal modes (standing waves) exist in a cavity at the same time. In Figure 11 of Module 1-7 we showed how the number of modes found in the spectral distribution of the laser output depended on the width of the laser transition line, the cavity round trip gain, and the frequency spacing equation between the longitudinal modes.
(14a) In the drawing below, Figure 5, we show at a certain instant of time only three of the many modes that are oscillating. There are of course, the waves that bounce continually back and forth between the mirrors, forming standing waves with modes at the mirrors, and each mode with a whole number of half-wavelengths filtering exactly between the mirrors as we showed in Figures 6 and 7 of Module 1-7. (They are separated vertically in the drawing below only for clarity.)
Fig. 5 Three
longitudinal modes
–vertically separated only for clarity–
overlap and interfere constructively in the cavities
at the axial position labeled MAX and
destructively at the axial position labeled MIN.
(14b) If all the longitudinal modes were shown, the resultant would be an intensity profile of nearly zero amplitude at most locations with one or more positions where the resultant amplitude would be a maximum, as sketched in Figure 6.
Fig. 6 Longitudinal
modes interfere to
produce a maximum amplitude at a certain position, with nearly zero intensity everywhere
else. A modulelocker insures that the modes in the cavity (such as the three shown in
Figure 5) remain locked in phase so as to alwys produce the same maximum pulse. This pulse
travels back and forth between the mirrors with the speed c.
(14c) Now with an appropriate modelocker–acousto-optic, electro-optic or dye device–appropriately positioned in the cavity, the intensity profile shown in Figure 6 can be "locked in postion," maintaining the identical profile relative to the individual longitudinal modes from which it came. Just as the individual modes bounce back and forth between the two mirrors so does the resultant maximum pulse. But this first situtation happens only with a modelocker in place. Why? Because in a cavity without the modelocker–a so-called free running laser–the phases of the separate longitudinal modes (such as shown in Figure 5) would change relative to one another and the position of the maximum pulse would be constantly shifting, i.e., it would be "unlocked". If the modelocker is a dye switch for example, it would open (pause light) only when the high intensity of the pulse caused the dye to bleach and transmit the laser energy. Otherwise it would remain closed. In this way the modes remain locked in relative phase with one another, and the maximum pulse makes a cavity roundtrip in time equation, so that modelocked pulses appear in the ouput of the laser separately in time by an interval equation.
A cavity-dumped laser is just a different type of Q-switch laser. In the normal Q-switched laser, as we have already discussed, the population inversion is built to very high lead, then released all at once, giving rise to a large pulse of energy. This is achieved
CHARACTERIZATION OF PULSED LASER OUTPUTS
(15) Pulsed lasers may be divided into two further subclasses—(1) single-pulsed lasers and (2) repetitively-pulsed lasers. Single-pulsed lasers produce one pulse of light per laser operation. Repetitively pulsed lasers produce a train of pulses at equal spacing whenever the laser is in operation.
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SINGLEPULSED LASERS
(16) Figure 7 gives the power of a single laser pulse as a function of time. The maximum power of the pulse is Pmax. The total duration of the pulse at the base line is difficult to determine because the pulse dies out slowly toward zero power. The most convenient method of measuring the temporal length of the pulse is at the ha1fpower point (1/2 Pmax). "Pulse duration," or "pulse width," is the duration of the pulse at one-half the maximum power. This relationship sometimes is referred to as the fullwidth at halfmaximum (FWHM), and is represented by Dt1/2. (while we will use Dt1/2 here for clarity, others often use simply t, or T, for the pulse width)
Fig. 7 Energy of a laser pulse
(17) Since "power" is defined as "energy divided by time," energy is the product of power and time. In Figure 7, the total energy of the pulse is represented by the area under the power curve. The actual area can be determined through the use of calculus; but in most cases, an approximation is used. A triangle is drawn—its sides starting at the maximumpower point (A) and extending through the edges of the pulse at the ha1fpower points (B and C) to the base line (D and E). The area of this triangle is not exactly the same as that of the actual pulse, although it is a close approximation.
(18) The area of triangle ADE in Figure 7 can be determined from Equation 1.
A = 1/2 bh
| where: | b = Length of triangle base. h = Height of triangle. |
(19) The base of the triangle in Figure 7 is 2Dt1/2; therefore onehalf the base is the pulse duration, Dt1/2. The height of the triangle is the maximum power of the pulse Pmax. Substitution of these quantities into Equation 1 yields Equation 2.
E = (Dt1/2)(Pmax)
(20) The energy content of a laser pulse is the product of the maximum power and the pulse duration.
(21) In most practical situations, measurements of pulse duration and energy can be made. Measurements of pulse power cannot be made; therefore, the most useful form of Equation 2 is that for maximum power given in Equation 3.
(22) Example A demonstrates the use of Equation 3 in the solution of a problem.
| EXAMPLE A: MAXIMUM POWER OF A LASER PULSE | |
| Given: | The output pulse from a Q-switched ruby laser has a duration of 5 ns and an energy of 1 J. |
| Find: | Maximum power. |
| Solution: |  |
(23) In practice, the measurement of single laser pulses is accomplished with two measuring systems. A calorimeter is used to determine the energy of the pulse. This instrument consists of a sensor, which absorbs the energy of the pulse, and a display mechanism, which indicates how much energy has been absorbed. Pulse duration is determined when a small portion of the laser pulse is directed onto a fast photodiode. The photodiode converts part of the laser power to an electrical signal, which is displayed on an oscilloscope. This display is photographed, and the pulse duration is measured. Maximum power then is calculated from Equation 3.
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REPETITIVELY PULSED LASERS
(24) Figure 8 illustrates the output power of a repetitively pulsed laser as a function of time. The quantities Pmax, Dt1/2, and E are as defined previously. Pavg is the average power of the laser. The pulse repetition time (PRT) is the time interval between similar points on two consecutive laser pulses.
Fig. 8 Repetitively-pulsed laser output
(25) The pulse repetition rate is the number of pulses per second and is related to pulse repetition time by Equation 4.
PRR = 1/PRT
where: PRR = Pulse repetition rate.
(26) The shaded area in Figure 8 represents the product of the average power and the pulse repetition time. This area is the same as that of one of the laser pulses; therefore, Equation 5 can be used to determine the energy of a single pulse in a repetitively pulsed laser.
Equation 5
E = (Pavg)(PRT)
(27) The use of this equation is illustrated in Example B.
| EXAMPLE B: ENERGY PER PULSE | |
| Given: | A Q-switched Nd:YAG laser produces 5000 pulses per second at an average power of 20 W. |
| Find: | Energy of a single pulse. |
| Solution: |  |
(28) The "duty cycle" of a repetitivelypulsed laser is defined as the ratio of the time the laser is ON to the time the laser is OFF. The ratio is usually expressed as a percentage. Thus, a 10% duty cycle means that the laser is on for 10% of that period, while a 90% duty cycle means the laser is on for 90% of that period. Quantitatively, the duty cycle is equal to the ratio of pulse duration (Dt1/2) to pulse repetition time (PRT), thus is given by Equation 6.
DC = Dt1/2/PRT
where DC = Duty cycle.
From Equation 5—
From Equation 2—
(29) Substitution of these values into Equation 6 yields Equation 7.
Equation 7
(30) Example C illustrates the use of Equations 6 and 7 in the solution of a problem.
| EXAMPLE C: DUTY CYCLE AND MAXIMUM POWER OF A REPETITIVELY PULSED LASER | |
| Given: | A repetitively pulsed CO2 laser has an average power of 100 W, a pulse duration of 0.5 ms, and a pulse repetition of 500/sec. |
| Find: | Duty cycle and maximum power. |
| Solution: |  |
(31) In most cases, repetitivelypulsed lasers are characterized by measurement of the average power of the laser with a power meter and determination of pulse duration and pulse repetition time with a photodiode and oscilloscope. All other quantities then can be calculated as in Example D.
| EXAMPLE D: CHARACTERIZING A REPETITIVELY PULSED LASER | |
| Given: | A GaAs semiconductor laser produces an average power of 25 mW. The pulse duration is 2.5 ms, and the pulse repetition time is 1 ms. |
| Find: | Duty cycle, maximum power, and energy per pulse. |
| Solution: | Duty cycle:
Maximum power:
Energy per pulse:
|
See Idea Bank
LONGITUDINAL COHERENCE LENGTH
(32) The longitudinal coherence length is a measure of the temporal coherence of a laser beam and is the distance along the beam over which the laser light has sufficient coherence to produce visible interference fringes. Longitudinal coherence length is important whenever a laser beam is split and recombined to form an interference pattern. This principle is illustrated by the Michelson interferomoter of Figure 9. Light entering from the left strikes a beam splitter at point A and is split into two beams. The beam reflected from the splitter travels to the mirror at B and is reflected back to the beam at D. The beam transmitted through the splitter travels to the mirror at C and is reflected back to D. At point D, the two beams recombine. Part of the return beam from B is transmitted through the splitter to the screen, and part of the return beam from C is reflected from the splitter to the screen.
Fig. 9 Michelson interferometer
(33) This optical system contains two optical paths(1) A to B to D and (2) A to C to D. The optical path difference is the difference in length between these two paths. If the optical path difference is less than the longitudinal coherence length of the light, interference fringes are formed on the screen. If the optical path difference is greater than the longitudinal coherence length of the light, no interference fringes are formed. In most applications that involve interferometry, the longitudinal coherence length of the laser light must be known; and in many cases steps must be taken to extend the coherence length.
(34) The longitudinal coherence length of light is given by Equation 8.
| where: |  c = Longitudinal
coherence length.c = Speed of light. Dn = Total bandwidth of light. |
(35) Example E illustrates the use of this equation.
| EXAMPLE E: COHERENCE LENGTH OF A HeNe LASER | |
| Given: | The total bandwidth of a multimode HeNe laser is 1.5 GHz. |
| Find: | Coherence length. |
| Solution: |  |
(36) The coherence length of a typical HeNe laser is about 20 cm, which means that such a laser can be used with an interferometer to produce interference fringes if the optical path difference is less than 20 cm. For optical path differences of greater than 20 cm, no interference patterns can be formed.
(37) The longitudinal coherence length of laser light is inversely proportional to the bandwidth of the output laser light; therefore, the coherence length can be extended by reduction of the bandwidth. In some lasers, this reduction is accomplished by allowing only one longitudinal mode to oscillate within the laser cavity. This process reduces the bandwidth of the output beam from the multimode bandwidth (which is essentially equal to the full linewidth of the laser fluorescent transition) to the single-mode bandwidth of a cavity mode. The effect on the coherence length is illustrated in Example F.
| EXAMPLE F: COHERENCE LENGTHS OF ARGON LASERS | |
| Given: | An argon ion laser has a laser fluorescent linewidth of 10 GHz. The bandwidth of a single cavity mode is 7.5 MHz. |
| Find: | Coherence length with all possible cavity modes oscillating and coherence length if only one mode oscillates. |
| Solution: | If all modes oscillate, the bandwidth of the output is equal to the
total laser fluorescent linewidth:
If only one mode oscillates, the bandwidth of the output is the bandwidth of that mode:
|
(38) Single-mode operation can be achieved in many lasers by installation of an optical element called an "etalon" inside the optical cavity. The etalon acts as a secondary optical cavity within the primary cavity of the laser. Standing waves can be formed only at light frequencies that form standing waves in both optical cavities. The proper selection and installation of an etalon can achieve singlemode operation in any CW laser and in many pulsed lasers, as well.
- Define the following terms:
a. Pulse repetition rate.
b. Pulse repetition time.
c. Pulse duration.
d. Peak pulse power.
e. Longitudinal coherence length. - Draw and label graphs that relate output power as a function of time for
the following types of lasers:
a. Normal pulsed.
b. Qswitched.
c. Mode1ocked. - Draw graphs of amplifier gain, loop gain, and output power as a function of time for a Qswitched laser.
- Explain how modelocking is achieved.
- Explain the practical significance of the longitudinal coherence length.
- A Qswitched ruby laser emits 4.5 J in a pulse duration time Dt1/2 of 30 ns. What is the peak power?
- A Qswitched Nd:YAG laser with a pulse duration of 20 as has a peak power of 10 MW. What is the energy of the pulse?
- A repetitively Qswitched Nd:YAG laser has an average power of 10 W and a peak power of 12.5 kW. What is the duty cycle?
- The pulse duration of Dt1/2 of the laser in Problem 8 is 800 ns. Determine the PRT and PRR.
- A CO2 laser with an average power of 25 W has a pulse repetition rate of 250 per second. What is the energy per pulse?
- A Qswitched Nd:YAG laser has an average power of 22 W, a pulse duration
of 1.2 ms, and a pulse
repetition time of 250 ms. Find
the following values:
a. PRR.
b. Duty cycle.
c. Pmax
d. Energy per pulse. - A repetitively pulsed laser produces 47 mJ per pulse. The pulse
repetition time is 2.5 ms and the duty cycle is 0.08. Find the following values:
a. Pulse duration.
b. Pmax.
c. Pavg. - A ruby laser has a pulse repetition rate of 3 pulses per second. The
pulse duration is 0.5 ms, and the maximum power is 40 kW. Find the following values:
a. Duty cycle.
b. Average power.
c. Energy. - An Nd:YAG laser has a fluorescent linewidth of 30 GHz. What is the longitudinal coherence length if it lases over this entire frequency range?
- A pulsed ruby laser used for holography has a coherence length of 9 m. What is the frequency bandwidth of the laser output?
- An argon ion laser has a fluorescent linewidth of 9 GHz. The cavity length is 1.25 m. The transmission of the output coupler is 4%. Determine the coherence length with and without an etalon. (Hint: Refer to Module 17, "Optical Cavities and Modes of Oscillation," to calculate the bandwidth of a single mode.)
HeNe laser
Light chopper (or small electric motor with a rotary disk that has evenly spaced slots cut
out of it, as in Figure 10)
Optical power meter
Oscilloscope
Photodetector
Lab jack
See Idea Bank
See Idea Bank
MEASUREMENT OF OUTPUT PARAMETERS OF PULSED LASERS
In this experiment, the student will measure the pulse duration, pulse repetition time, and average power of a repetitively pulsed laser and will calculate the maximum power, pulse repetition rate, duty cycle, and energy per pulse.
- Set up the HeNe laser, light chopper, photodetector, and oscilloscope as
in Figure 10.
Fig. 10 Experimental arrangement for pulsed laser measurement
- Start rotation of the light chopper, making sure it is rotating at a uniform rate. Pulse width and pulse repetition time can be varied by changing the speed of rotation or by changing the size or number of slots in the chopper.
- Plug the lead from the photodetector into the vertical input of the
oscilloscope. Adjust the vertical gain and the horizontal time base to obtain a trace
similar to that depicted in Figure 11.
Fig. 11 Oscilloscope trace for measuring PRT
- Measure the distance in centimeters between two adjacent pulses, and multiply this distance by the time base of the oscilloscope in ms/cm to obtain the pulse repetition time. Record PRT in Data Table 1.
- Adjust the time base of the oscilloscope to obtain a trace of one pulse
as illustrated in Figure 12.
Fig. 12 Oscilloscope trace for measuring Dt1/2
- Measure the full width of the pulse at half the maximum height. Determine the pulse duration and record in Data Table 1.
- Replace the photodetector with the sensor of the optical power meter. Measure the average power and record in Data Table 1.
- Calculate the pulse repetition rate from Equation 4.
- Calculate the duty cycle from Equation 6.
- Calculate the maximum power by use of Equation 7.
- Calculate the energy per pulse from Equations 3 and 5. Both equations should yield the same value.
- Change the PRR by varying the speed of the light chopper or the number of slots. Repeat the procedure for two additional values of PRR. Record results.
DATA TABLE 1.
| Trial | PRR (pulses/sec) |
PRT (ms) | Dt1/2 (ms) |
Duty Cycle |
Pavg (mW) |
Pmax | E/pulse (mJ) |
| 1 | |||||||
| 2 | |||||||
| 3 | References |
Basov, N.G., ed. Temporal Characteristics of Laser Pulses and Interaction of Laser Radiation with Matter. New York: Plenum Publishing Corp., 1977.
Duley, W.W. CO2 Lasers: Effects and Applications. From the Series Quantum Electronics—Principles and Applications, edited by YohHan Pao. New York: Academic Press, 1976.
O'Shea, Donald; Callen, W. Russell; and Rhodes, William T. Introduction to Lasers and Their Applications. Reading, MA: AddisonWesley Publishing Co., 1978.
Pressley, Robert J., ed. CRC Handbook of Lasers, with Selected Data on Optical Technology. Cleveland, OH: The Chemical Rubber Company, 1971.
Ready, John F. Industrial Applications of Lasers. New York: Academic Press, 1978.
Ready, John F. Lasers in Modern Industry. Dearborn, MI: Society of Manufacturing Engineers, 1979.
Siegman, A.E. An introduction to Lasers and Masers. New York: McGrawHill Book Company, 1971.
Silicon Photodetector Design Manual. Santa Monica, CA: United Detector Technology.
Yerdeyen, Joseph T. Laser Electronics. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1981.
Wilson, Leroy E., et al, ads. Electronic Transition Lasers. Cambridge, MA: MIT Press, 1977.