The Helium-Neon laser
Theory
The following and the literature from the course.
Theory of modes in resonators
Fig. 1. Principal beam path for the transversal and modes.
The different modes of the laser correspond to different spatial distributions of the electromagnetic field in the cavity, Fig.1. The field is separated into components parallel to the optical axis (axial or longitudinal modes) and components normal to the optical axis (transverse modes). A given transverse mode can be brought to lase at several axial modes at the same time, and vice versa.
Fig. 2. The gain profile of
a HeNe-laser.
A laser mode is usually described by the transverse mode TEMlmn.
The mode parameters l and m state the number of nodes of the electrical field (i.e. positions where the field is zero) in a plane normal to the axis of the laser. The longitudinal parameter n states the number of nodes along the axis of the laser, i.e. the number of half-wavelengths between the mirrors minus one. Since the laser cavity is much longer than the wavelength of the emitted light, n will be a very high number, which is usually not written.
The transverse TEM00 mode is symmetric with respect to the longitudinal axis in contrast to the TEM01 mode, which has an asymmetric field distribution. One way to picture this, is that the optical beam is diverging from the laser axis. The higher values for l and m, the greater is the beam divergence from the central axis.
Every mode has a specific resonance frequency. A laser will normally lase at several different modes with different frequencies at the same time (it is, however, possible to suppress all but one mode). A gas laser will emit light at frequencies for which the Doppler broadened gain profile exceeds the losses in the resonator (see Fig. 2).
The frequency separation between two consecutive axial modes is given by:
(1)
Wherec = The speed of light in vacuum
ni= The index of refraction
L = The distance between the mirrors
This formula is valid for resonators with both plane and/or spherical mirrors.
The general resonance condition for a laser with spherical mirrors with radii R1 and R2 and the mirror distanceLis given by:
(2)
Changing l, m and n results in a frequency difference, :
(3)
For a confocal resonator R1 = R2 = L, which leads to:
(4)
Equation (4) shows the degeneration of the confocal resonator. If (1 + m) is increased by 2 and n decreased by 1 is there no change in frequency. A laser operating at a single transverse configuration TEMlm is often called a single mode laser. It usually radiates with several frequencies separated by A laser that only emits one mode and thus only one frequency is called a single frequency laser.
There are a number of ways to suppress the high order resonator modes and thus reduce the number of excited modes. One way to get a laser to operate in a single frequency mode is to reduce the optical pumping of the gain medium until only one axial mode is above the threshold for lasing. The drawback is that the remaining mode will be weak. A better method is to suppress all axial modes but one by adding another resonator to the laser, such a resonator could be a Fabry-Perot etalon or a simple glass plate. Introducing losses to all but one mode has the same effect as making the gain profile more narrow without reducing the peak gain.
Description of the laser
The laser tube used is from the American Company Melles Griot. A discharge tube is filled with He and Ne gas. The He-atoms are excited by a discharges in the tube and the excitation energy is transferred to the Ne-atoms through collisional processes. It is the Ne gas that is used for the lasing. The tube is sealed with a Brewster window at one end and a plane mirror at the other end. The tube is mounted on an optical bench and an external concave mirror can be placed in front of the Brewster window to produce a stable resonator. The voltage supplier can deliver a few kV without load. The voltage is reduced to 1.5 kV while the tube is working due to the internal impedance of the voltage supplier. There are three different concave mirrors for the laser: Two with a 1.0m radius of curvature, one has a reflectivity of 99.97% and the other is 98.3%. The third has a 0.45m radius of curvature and a reflectivity of 98%. To achieve such high reflectivities all the mirrors are dielectric mirrors made to reflect wavelengths centred at 632.8 nm. The mirrors can be adjusted horizontally and vertically using two micrometer screws at each mirror mount.
Description of frequency selection by laser etalon / glass plate
A laser etalon or glass plate only transmits certain frequencies. The principal physical mechanism for this can be seen in Fig.3. The incoming light is reflected many times inside the component. Every time the light hits a surface a part of it is reflected and a part of it is transmitted. For some frequencies the optical path between the two reflecting surfaces corresponds to an integer number of half-wavelengths. The corresponding waves are in phase and thus constructively interfering and are transmitted. For other frequencies the waves will be out of phase and interfere destructively. The transmission curve for a glass plate can be seen in Fig.4.
Fig. 3. Frequency selective Fig. 4. Transmissions maxima for a glass plate.
transmission of a glass plate.
(The angle of the plate is much
smaller in reality)
The free spectral range of the etalon, , separates the transmission maxima. is calculated in same way as 0 for the laser cavity. An etalon placed inside a cavity will block the frequencies that get to big losses due to the etalon. By choosing the right etalon monofrequency lasing can be obtained.
Description of the spectrum analyzer
The spectrum of the laser is analysed with a scanning Fabry-Perot interferometer (Spectra Physics Optical Spectrum Analyzer Model 470). This instrument can show the intensity distribution within a narrow spectral band on an oscilloscope (Fig.5).
Fig.5. Scheme for measuring with a scanning Fabry-Perot interferometer.
The analyser is a confocal Fabry-Perot-interferometer mounted in front of a photodiode. One of the mirrors is mounted on a piezoelectric material, so the distance between the mirrors can be changed. This is done with a saw tooth voltage pulse, which also is used to trigger the oscilloscope displaying the signal. The free spectral range of the interferometer (The frequency difference between two neighbouring transmissions peaks) is 2000 MHz. For a given distance between the mirrors the frequencies Nwill be transmitted where N is a big integer that corresponds to the optical frequencies. The distance between the interferometer mirrors is scanned using the saw tooth voltage pulse. This will shift the transmission maxima of the interferometer. The detector will only detect light if the incoming light has the same frequency as the transmission maxima of the interferometer. We get a frequency scale that depends on the total displacement of the plates. If the frequency scale is larger than the laser frequency will show up two or more times. The vertical displacement on the oscilloscope is proportional the laser irradiance at that frequency, and the peak position is determined by the frequency.
Preparation exercises
1.Calculate the power used by the laser if it the voltage is 1450 V and the current is 6.5 mA.
2.The quantum efficiency is defined as number of electrons that are generated by one photon. If the quantum efficiency for a photodiode is 0.5, what current, in mA, will the photodiode generate if you shine light with a wavelength of 633 nm and a power of 1.0 mW?
Hint: Power of monochromatic light 1.0 mW = 1.0.10-3J/s Number of photons/s.
3.What mirror distances are stable for a resonator with a plane mirror and a concave mirror with a 0.45 m radius of curvature?
4.Calculate the frequency difference between the TEM00-mode and the TEM02-mode for
L = 0.4m, ni= 1, R1 and R21m.
5.Fig.6 shows the oscilloscope picture similar to Fig.5.
Mark for the laser and FSRfor the Fabry-Perot Interferometer. Figure out which effects are caused by the Fabry-Perot interferometer and which the laser causes. Calculate the length of the laser cavity and determine, by using realistic assumptions, the radius of curvature of the two cavity mirrors.
Fig.6. Oscilloscope picture of a measurement with a Fabry-Perot interferometer
Lab exercises
1.Remove carefully the lasertube and the loose mirrors. Direct another laser by with two mirrors (why two?), so the beam is parallel to and centred on the optical bench. Adjust the lasertube and the loose mirror (R=0.45m) with the help of the laser beam. Turn on the lasertube and adjust the lasertube and mirror to maximum output laser power. The power can be measured with a photodiode, which delivers an output current to one milliamperemeter. This type of procedure is called alignment. The sensitivity of the photo diode is 0.4mA/mW. Measure the output power of the laser. The voltage over the operating tube is about 1.45kV and the current is about 6.5mA. Calculate the laser efficiency. Calculate the corresponding quantum efficiency of the detector.
2.Move the loose mirror and measure the output power for different resonator lengths. Compare the measurements with the stability diagram and write down how increasing the resonator length effects the position in diagram. Look especially at treshold for lasing. Note the output power for at least four different resonator lengths (use at least two lengths close to lasing).
3.Use a polariser to study the polarisation of the laserlight. Why is there a Brewster window in the lasercavity?
The discharge current for this particular laser is adjusted for maximal effect. How do you think that variation of the current affects the output effect? What happens if the current is greatly enhanced (hint: Look at figure 10.3 in Svelto)? State 2-3 effects that will affect the output power. Draw a graph that shows the main characteristics of the output effect as a function of the discharge current.
4.Use a lens and a screen to study the laser intensity profile. Place an iris or a haircross inside the resonator to study the tranversal modes. Draw a picture of some modes you get in each case and explain the pattern.
5.Mount a Scanning Fabry-Perot interferometer. The output signal is studied using an oscilloscope. The free spectral range of the interferrometer is 2GHz. What is the distance between the plates?
Study the signal from the interferometer when the laser beam is almost perpendicular to the mirrors of the interferometer. Adjust the laser so that only one transversal mode (TEM00) exists. Think about how it should look transversally (on the screen) and spectrally. Make a drawing of the oscilloscope screen. Measure the frequency difference between the axial modes and calculate the mirror distance. Compare with the measured mirror distance.
- Adjust the laser to get a mixture of two transversal modes, for example the TEM01 and TEM00. Make a drawing of the oscilloscope screen and mark the different modes on the graph. Determine the frequency difference and compare the result with a theoretical calculation. At the same time study how the beam looks on a screen. Do you see both modes?
7.Replace the moveable mirror with the 1 m radius of curvature and 99.97% reflectivity mirror. First place a glass plate near the lasertube and then align it so a single axial mode is generated. The laser now operates in single frequency mode. Place a laser etalon inside the cavity. What has changed compared to the glass plate? Why? Make a figure that describes how the single frequency lasing is obtained.
8.Use one of the two mirrors with a 1 m radius of curvature. Obtain maximum power and measure the output power. Do also measure the output power from the permanent end mirror (think in terms of systematic errors). This value should be used as a monitor value for the laser power in the cavity. Do the same with the other 1m radius of curvature mirror. How is the laser power inside the cavity affected? Why? What is the gain, in %, (per optical roundtrip) for both cases? What is the gain of the gain medium in dB/m?
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