Solution ( a ) Mode Locking in a Laser :

Mode locking is a method which is used in optics. It helps the Laser in the production of pulses of light which have a very small duration ( pico seconds or femto seconds ) [ 1 ]. The concept behind this method is the induction of a fixed phase relation amongst the longitudinal modes of the resonant cavity of the Laser [ 2 ]. The pulse train can be produced by the Laser light because of constructive interference between the above mentioned modes [ 3 ].

Solution ( b ) Design of edge – emitting semiconductor Laser :

1.5 um

It generates a 40 GHz pulse stream.

Length of the cavity = ? = 1.25 mm

Refractive index of the material = ? = 1.53

Other dimensions of the device have also been mentioned.

Number of wavelengths the cavity length corresponds to = 830

A monolithic mode – locked Laser can be designed operating at a wavelength of 1.5 um. An active Laser, having a repetition frequency of 40 GHz, has a pulse width of 4 ps, wavelength of 1462 nm, the number of waveguides is 2, the cavity configuration is G – W ( Gain – Passive Waveguide ) and bulk well is present in the gains section. The time bandwidth product is 1.4.

Solution ( c ) Numerical Model :

The equation used is :

Here, ω0 = Resonant frequency of the cavity which is chosen arbitrarily.

Also,

Plot of E ( t ) and P (  t ) :

The value of intensity has been plotted against the time ‘t’ in Figure 1.

Figure 1

The figure 2 shows the plot of Power with respect to the wavelength.

Figure 2

Addition of several longitudinal modes leads to the formation of pulses :

The optical or resonant cavity in the Laser consists of basically 2 plane mirrors which face one another [ 4 ]. The light ( as wave ) bounces between the 2 mirrors present in the cavity. The light interferes with itself constructively as well as destructively [ 5 ]. This leads to standing waves or modes formation between the 2 mirrors. Hence, discrete frequencies are generated called the longitudinal modes [ 6 ].

Solution ( d ) If the phase angles of the modes are all set to zero :

In such a case, the various Laser modes interfere constructively with each other periodically and lead to the production of an intense pulse of light [ 7 ].

Solution ( e ) If the modes have random phase angles :

In case of random phase angles, there is interference between various modes [ 8 ]. This can lead to beating effect at the Laser output and a fluctuating intensity. However, if the number of modes is very high , then output intensity is almost constant [ 9 ].

Solution ( f ) If the modes have different amplitudes :

A phenomenon called Mode beating [ 10 ] is observed if different amplitudes are present and if the ratio of intensity of the primary and secondary modes is greater than or equal to 100.

References

[1] M.K. Smit, J. van der Tol and M.T. Hill, “Moore’s Law in Photonics”, Laser & Photonics Reviews, 6, 1, pp. 1–13 (2012).

[2] J. Summers et al., Monolithic InP-Based Coherent Tansmitter Photonic Integrated Circuit with 2.25 Tbit/s Capacity, Electronics Letters Vol. 50, pp. 1150-1152, 2014.

 [3] F. Kish et al., “System-on-Chip Photonic Integrated Circuits”, IEEE Journal of Selected Topics in Quantum Electronics, 24, 1, Jan.-Feb. 2018.

[4] J.J.G.M van der Tol., Jiao,Y., Shen, L., Millan-Mejia, A.J., Pogoretskiy, V., van Engelen, J.P. & Smit, M.K., “Indium Phosphide Integrated Photonics in Membranes”, IEEE Journal of Selected Topics in Quantum Electronics. 24, 1, 9 p., 6100809, 2018.

[5] J.J.G.M. van der Tol, Y. Jiao, K.A., “InP Photonic Integrated Circuits on Silicon”, Silicon Photonics, Lourdudoss, S., Chen, R. T., Jagadish, C. (eds.). Elsevier, p. 189-219 23 p. (Semiconductors and Semimetals; vol. 99), Sep 2018.

[6] M.K. Smit et al., An Introduction to InP-Based Generic Integration Technology”, Semiconductor Science and Technology, Volume 29, Number 8, http://iopscience.iop.org/article/10.1088/0268-1242/29/8/083001, 2014.

[7] JePPIX roadmap 2018, “The Road to a Mulit-Billion Euro Market in Integrated Photonics”, the JePPIX consortium, www.jeppix.eu/roadmap2018.

[8] L.M. Augustin, R. Santos, E. den Haan, S. Kleijn, P.J.A. Thijs, S. Latkowski, D. Zhao, W. Yao, J. Bolk, H. Ambrosius, S. Mingaleev, A. Richter, A. Bakker, T. Korthorst, “InP-Based Generic Foundry Platform for Photonic Integrated Circuits”, IEEE Journal of Selected Topics in Quantum Electronics, 24, 1, 6100210, 2018.

[9] J. Bolk, H. Ambrosius, R. Stabile, S. Latkowski, X. Leijtens, E. Bitincka, L. Augustin, D. Marsan, J. Darracq, K. Williams, ‘ “Deep UV Lithography pProcess in Generic InP Integration for Arrayed Waveguide Gratings”, IEEE Photonics Technology Letters, 30, 3, pp. 1222-1225, 2018.

[10] D. Pustakhod, K. Williams, X. Leijtens, “Fast and Robust Method for Measuring Semiconductor Optical Amplifier Gain”, IEEE Journal of Selected Topics in Quantum Electronics, 24, 1, 9, 8004439, 2018.