**by
Dr. Didar Islam,
Central Michigan Uuniversity Professor of
Physics**

__INTRODUCTION__

Laser cutters operate by directing large amounts of energy onto a very small surface area. A typical arrangement to achieve this is shown in Figure 1. By employing such an arrangement, the temperature of a small portion of a material object can be raised very quickly to a point where it melts or evaporates. Can you identify why this may be important?

Figure 1. Schematic diagram of a typical laser cutter. ("Lasers in Manufacturing", IFS Publications Limited, Birmingham, UK, pg. 52.)

The arrangement shown in Figure 1 can be used as a saw or knife to cut suitable materials. The power of the laser used depends on the material to be cut. Laser power is defined as the rate at which energy is delivered by the beam and is measured in units of Joules/second or Watts. For laser surgery typically the power is on the order of 10 W, and for cutting steel the power can be upwards of 2000 W. Some current applications of laser cutters are:

1. Laser cutting of metals, plastics and fabrics.

2. Laser surgery of the skin, the eye, internal organs, and other delicate tissues.

3. Laser etching of semi-conductors, crafts and lithography.

The above list represents only a few applications. Perhaps you can think of some ideas for new application after completing these lessons.

As in all applications of scientific knowledge, a quantitative analysis and understanding of the physical phenomenon is necessary to apply it in a controlled a predictable manner so that it can be used to achieve desired results. Physicists and engineers are constantly investigating the quantitative aspects of the problem so that newer and more efficient cutting tools can be developed. To see how these researchers think in developing such tools, let us do some quantitative analysis.

__ACTIVITY ONE__

**Goal****: To extract information from a graph using correct graphical analysis techniques and to apply the information in solving problems of power, specific heat capacity, latent heat of fusion, and conservation of energy. **

Consider the data given in Figure 2 which shows graphically the optimum rates at which lasers of different powers cut through sheets of mild-steel. This figure is rich in qualitative as well as quantitative information. This information can easily be understood if you read the graph in a systematic manner.

Figure 2. Cutting speeds for sheets of mild steel using CO_{2} laser.

An effective way of reading a graph is described next. First, read the graph title and figure caption to determine what physical information the graph represents. Then determine the physical meaning of the axes. Usually the independent variable is plotted along the horizontal axis. The parameter plotted along the vertical axis is then said to be a function of the variable in the horizontal axis. The plotted curves represent the functional relation between the two parameters. Try to understand clearly what physical information each curve represents in Figure 2. Did you notice that each curve corresponds to a different laser power? When you think you understand the graph, explain it to others in your team.

- You should be able to recognize the following:
- 1. The optimum cutting rate is related to both the sheet thickness and the laser power.
- For a given cutting rate, a higher laser power can cut through a thicker steel plate.

Similarly, for a given sheet thickness, a higher laser power can cut faster. You will now use the information above to perform the following activities and answer some interesting questions.

__Given Information __

In Figure 2 the cutting speed is given of various CO_{2} lasers of different power cutting sheets of mild steel.

Approximately ten percent of the incident laser power is absorbed by the metal surface.

The width of the cut is 2.0 mm.

The density of mild steel is 7.86 g/cm^{3}.

The melting point of mild steel is 1515 ° C.

The specific heat capacity of mild steel is 620 J/kg K (Averaged between 20 ° C to 1515 ° C).

The latent heat of fusion of the metal is 247 J/g.

Room temperature is assumed to be 20 ° C.

Finally, the conversion 1.0 inch = 2.54 cm.

When cutting a mild steel plate of thickness 0.25 in., a 1.5 kW CO_{2} laser is employed. The laser cutting speed is 50 in./min.

1. What is the optimum cutting speed with these parameters?

2. How much light-energy is delivered by the laser beam during the time it takes to cut out a circular piece of radius 2.5 ft ?

3. Determine the total mass of the metal that was cut out (or melted out) from the plate.

4. In step 3, how much energy is spent in raising the temperature to the melting point? Here, consider only the portion of the metal that melts.

5. Assume that the metal has reached its melting point and that the cutting occurs entirely by melting the metal. In step 3, how much energy is spent in melting the metal?

6. What fraction of the absorbed laser light is spent in raising the temperature of the metal to its melting point and melting it? Consider only the portion of the metal that melts.

7.The rest of the absorbed energy is dispersed by conduction into the surrounding metal, convection into the air, and as thermal radiation. Calculate the fraction of the incident light energy dispersed by these methods.

(Note: the above is a simplification of a more complex problem. In an actual cutter, a small jet of oxygen gas is blown directly onto the spot where the laser light strikes the metal, shown in Figure 1. The oxygen helps in oxidizing the hot metal and the cutting process is accelerated.)

__ADDITIONAL PROBLEMS__

1. Consider a sheet of metal which is 0.200 in. thick being cut first by a 1500 W laser beam and then by a 500 W laser beam. In each case, it is cut at optimum rates specified by the curves. Calculate the ratio of the mass of the metal cut through by a 1500 W laser beam and the mass cut by a 500W laser beam in any given time.

2. From a physical consideration, would you expect the ratio to be different for a sheet of metal 0.1-in. thick? Using the data in Figure 2, calculate the ratio and verify the validity of your expectation.

3. For a 1500 W laser beam cutting at a rate of 100 in./min, how much energy is delivered in the time taken to cut a square hole of sides 3.00 in through a 0.200 in thick plate?

4. What is the total amount of heat absorbed by the metal. Remember that it absorbs approximately 10 % of the laser light incident on its surface.

5. For simplicity, and for purposes of rough estimates, assume that the cutting takes place exclusively by melting the metal. Starting at room temperature, calculate the total amount of heat absorbed by the portion of the metal that melts. At optimum cutting rates, assume that the temperature of the melted metal does not exceed the melting point.

__ADDITIONAL ACTIVITY__

Using the data in Figure 2, answer the following.

1.Estimate what laser power must be employed to cut a 0.2 in. thick mild steel plate at the rate of 180 in./min?

2.Estimate what laser power must be employed to cut a 0.4 in thick mild steal plate at the rate 45 in./min?

Hints:

For Problem 1, select a plate-thickness of 0.2 in. from Figure 2. Using the data, plot the cutting speed as a function of laser power. Draw a smooth curve through the data points extending beyond the data points on either side. Can you now estimate what laser power must be employed in cutting a 0.2 inch thick mild steel plate at the rate of 180 in./min?

__ACTIVITY TWO__

**Goal****: To use information from laser surgery and solve problems concerning specific heat capacity, latent heat of vaporization, laser light intensity and laser cutting speeds. **

Lasers have successfully been used to conduct delicate surgery with pinpoint accuracy. This is a growing area of research and of applied laser technology. The principles behind the successful implementation of this technology are basic concepts in physics. These concepts are: energy, power, absorption coefficient, temperature, boiling point, specific heat capacity and latent heat of vaporization.

Some of you may not be familiar with the concept of "absorption coefficient", usually represented by the symbol (a ) and measured in units of cm^{-1}. The absorption coefficient tells us how the intensity of light diminishes as it passes through a given material. It is therefore a material dependent (intrinsic) property. For any given material, the absorption coefficient is a function of the frequency of the incident light.

For ordinary body tissue, the absorption coefficient is small compared to burned or the so-called "carbonized" tissue. Once a layer of carbonized tissue is formed, the energy absorption rate increases. The carbonized layer is formed within a small fraction of a second from the moment the laser beam hits the tissue. About six (6%) of the incident energy of the laser is absorbed by carbonized tissue. The rest of the energy is reflected or scattered.

Another interesting feature of a quantitative analysis of laser surgery is that body tissue is mostly water. So the specific heat capacity and the latent heat of vaporization of the tissue is very close to that of water.

This activity is centered on basic concepts of physics. Let us quantitatively "dissect" laser surgery. The following formula can be used to determine the cutting rate for laser surgery. This formula is used in determining the cutting speed of the laser.

???????Equation 1

(Note: this equation was provided by Dr. Steven L. Jacques, Oregon Medical Laser Center, Portland, Oregon.)

Where:

??*v* = cutting speed (m/s)

*I* = the laser power incident per unit surface area (watt/m^{2})

a = Absorption coefficient of carbonized tissue (~ 122 cm^{-1} for l = 1064 nm) *
d* = average carbonized layer thickness (m)

q

The parameter *q* is related to the specific heat capacity and latent heat of vaporization of water, and is given by the relation

??????Equation 2

Where:

r = Density of water (1 g/cm^{3}) *
c _{p}* = specific heat capacity of water (4190 J/kg.

H

D

The values of the different parameters involved for body tissue are very close to that of water as indicated above. Therefore, the cutting speed is given by,

??????Equation 3

(Note: that this formula works only when the laser intensity is sufficiently high, as in actual laser surgery.)

1.Normal body temperature is around 37 ^{o}C. Using this information calculate the energy needed to raise the temperature of 1.5 g of body tissue to the boiling point of 100 ° C.

2. Calculate the thermal energy needed to vaporize the same amount of tissue at 100 ^{o}C.

?3. What fraction of the absorbed energy is spent in vaporizing the tissue?

4. A 10.0 W NdYAG laser (l = 1064 nm) has a circular beam-cross-section of 3.0 mm diameter.

(a) Using units of W/cm

(b) Suitable thin lens can be used to narrow down the beam cross-section to raise the intensity. By what fraction must the beam diameter be reduced in order to increase the beam intensity by a factor of 9?

5. A typical thickness of the tissue that is carbonized in a sweep of the focused laser beam is of the order of 5.0 m m. With the enhanced intensity, calculate a cutting speed of this laser scalpel.

** **

Questions? Comments??