28 Mode Locking

Devendra Mohan

Contents of this Unit

 

1.  Mode Locking

2.  Mode Pulling

 

Learning Outcomes

  • From this module students may get to know about the following:
  • Importance of mode locking in solid state lasers like Ruby/ Nd: YAG /Nd: Glass lasers

 

MODE LOCKING

 

Mode locking is the technique by which ultra short pulses (Picosecond or femtosecond pulses) are generated in a laser. As we have already noticed that there are large numbers of spikes because the modes associated with the laser output do not oscillate at the same time and their phases are random. In case the modes are forced to oscillate together with comparable amplitudes and with their phases locked, one gets mode locked operation of the laser. The output of the Q-switched Ruby or Nd-YAG laser consists of a pulse of duration over a range of ~10 to ~100 nanoseconds that is very short and results in outbursts of very high power .If the laser gives average energy of 1J and the pulse time is 20 ns, the average output power is 50 × 106 watts (~50 Megawatt). These pulses of nanosecond duration overlap thereby making pulses of even shorter durations of the order of ~1 to ~10 picoseconds (10-12seconds).

 

The technique of mode locking enables these pulses to be separated and a train of pulses of picoseconds duration are produced. The power in these extremely short pulses is very high. These pulses of very short duration are important as are being used as probes of short lived phenomenon like in photochemistry and photobiology.

 

Mode locking can be done by

 

Active mode locking Passive mode locking

 

The technique of active mode locking involves the periodic modulation of the cavity losses or of the round-trip phase change. This is usually done by using a modulator like acousto-optic or electro-optic or Mach–Zehnder based integrated modulator. The idea is to synchronize the modulation with the resonator round trip oscillations that leads to the generation of ultra short pulses.

 

A pulse with the “correct” timing is to pass the modulator at times where the losses are at a minimum. The wings of the pulse experience a little attenuation that effectively leads to pulse shortening in each round trip,

 

 

The passive mode locking is done by using saturable absorbers. One of the important lasers is an organic dye laser which has the ability to produce such ultrashort pulses. As the organic dyes play a significant role in picosecond pulse regeneration, so act as an active laser media. One of the important dye molecules is Rhodamine 6G that belongs to Xanthene class of dyes wherein the molecules are planar and contains conjugated bonds. As regards the interaction of light, it is only necessary to consider the two π-electron clouds, one above and the other below the plane of the molecule. The energy level diagram for a typical dye molecule considers singlet and triplet states. The absorption spectrum is of hundreds of wave number wide and possesses mirror symmetry with the corresponding fluorescence band that shifts towards longer wavelengths. As each molecule of the dye undergoes at least 1012 collisions per second with the surrounding solvent molecules, the relaxation among the rotation and vibrational levels of the electronic states occur very rapidly .Thus equilibrium is established in a picosecond domain. It is noteworthy that the life time of the fluorescence is in nanoseconds domain and therefore, for generating ultra short pulses, it is necessary to use a second dye called saturable absorber (the absorption of which falls in the emission band of first) and has a relaxation time, from the first excite singlet to the ground state, shorter than the round trip time inside the cavity.

 

Figure below gives a dye laser cavity arrangement for generation of ultra short pulses.

The laser cavity contains an absorber dye cell in contact with the 100% reflecting laser mirror. The saturable absorber absorbs at the wavelength at which the laser medium fluoresce. An interferometer like Fabry-Perot interferometer kept in the cavity permits control of the lasing frequency and bandwidth. Such a mode locked laser generates a train of pulses that are separated by the round trip time i.e. the double transit time of the laser resonant cavity to be considered. The pulses so generated are of duration of picoseconds or femtoseconds. The low power modes are absorbed by the dye molecules, and the energy which is contained in these modes bleaches the dye solution. There is a non- linear transmission function as the transmission increases with the increase in light intensity until a saturation level is reached. In this way, the very large spikes are transmitted and the smaller ones are absorbed.

 

However, the saturable absorber dye recovers in a time (cooling and healing due to inherent property of the dye) that is short compared with the duration of the pulse.

 

Comparison of the active and passive mode locking:

  • Active  mode  locking  generates  longer  pulses  as  there  is  the  need  for  an  optical modulator, the electronic driver and means for synchronization.
  • The Organic dye gain medium always operates in saturation and is four level laser systems as it has got advantages over the three level system.

 

Now- a- days saturable bragg reflector or semiconductor saturable absorber mirrors are being used for mode locking.

MODE Pulling

 

It has been established that a number of axial modes, separated by   , resonate within the Doppler Broadened line width of a given atomic transition. This was experimentally verified by Herriott in 1961 and later by Bennett in 1962. There were some interesting anomalies revealed by Bennett’s experiment. He found that the beat frequency is not equal to but is less than  by about 1 part in 800.

 

More interesting are the two observations Bennett made on increasing the power level: Firstly, the frequency of the c/2L beat increases with increasing power. This increase was anomalous. It is expected that the pulling is towards the line center to increase with the number of the excited atoms and the pulling would be less for a cavity resonance near the line center than for one further away from it. Hence the frequency separation between adjacent cavity resonances should decrease with increasing power.

 

 

 

 

 

Here n is the refractive index.

 

Now for w<w0  n (w) <n (w0) and hence  increases. That is frequencies on the left of w0 move to the right. On the other hand, frequencies on the right of w0 shift to the left because for w> w0, n (w)>n (w0). This implies that the frequencies on either side of w0 are pulled towards the center of the gain curve.

 

It is also observed that some nonlinear frequency dependent pulling mechanism exists that makes the spacing between adjacent resonant modes different. Assuming that no coupling effects exist between simultaneously oscillating modes through the line dependent non- linearity in the medium, the theory explains the dominant mode pulling effects.

 

The phase shift per transit through an evacuated tube of the length L is

Therefore, the dispersion for the evacuated cavity is

For a standing wave to build up, oscillation modes must correspond to a phase shift equal to an integral multiple of π.

 

Let E be the energy in the mode of interest and f the fractional energy loss per pass. The energy will decay with tie at the rate (c/L) fE.

 

The Quality factor Q of the cavity is

The quality factor is also defined as

The introduction of the medium changes the refractive index in the system therby altering single pass phase shift from that obtained in the evacuated case;

 

negative for the lower frequencies and the positive for higher frequencies . The equation suggests a shift in the direction of the line centre.

 

 

 

Using Kramers –kronig relations, Bennett obtained the following relation for

In case of inhomogeneous broadening, the relation becomes

 

References:

  1. W. R. Bennett. “Hole Burning Effects in a He-Ne Optical Maser”, Physical Review, 04/1962
  2. D. J. Bradley. “Some recent advances in lasers and opto-electronics”, Contemporary Physics,5/1/1975
  3. www.rp-photonics.com
  4. Mehta,. “Optical radiation and photonics “, Lasers and Holography, 1993.
  5. Springer Series in Optical Sciences, 1999.
  6. www.nimp.ro
  7. Michael Scharrer. “Ultraviolet lasing in high order bands of three-dimensional ZnO photonic crystals”, Applied Physics Letters, 2006
  8. G AGRAWAL. “Fiber Lasers”, Applications of Nonlinear Fiber Optics, 2001