BASE LEGAL

In Sections 2.1 and 4.1, the equations for the OPLL and OIPLL configurations were presented, respectively, and the contribution of the DC term produced by the

Chapter 5; Optical and Electrical D esign

photodetection process, which is related to the laser incident powers, was neglected in the analysis of the systems after eq. (2.1.7). In heterodyne architectures, this approach is valid as the region of main interest for the loop control is located around the AC term of the photocurrent, at a frequency corresponding to the beat frequency o f the lasers, and DC terms can be filtered out. However, for homodyne applications, the beat frequency between the lasers is zero and it is not possible for the loop to distinguish between the contribution due to the laser incident power and the contributions of the actual phase error signal. As already described in Sections 2.1 and 4.1, the slave laser frequency tuning is a result of the control of the slave laser frequency by the phase error signal detected and processed by the loop. Therefore, any variation in the total optical power reaching the photodetector by means of intensity noise and/or bias tuning would cause the tracking circuit to misinterpret the intensity changes as detected phase error and the locking process could be severely compromised.

A balanced detector system [5.16-5.19] is a way to solve the problems arising from the variation of the optical power of the lasers. The schematic diagram o f the balanced opto-electronic receiver used in the OIPLL experiment is shown in Fig. 5.18.

Q H n n PBS L .ISO =r Rp.ams 1—1 LJ ! Incoming Laser Beams from NBS Loop Filter PH2

Fig. 5.18 - Balanced receiver for a single-facet homodyne OIPLL system. Q: quarter-

wave plate; H: half-wave plate; PBS: polarising beam splitter; NBS: neutral beam

splitter; PHI and PH2: photodetectors; L: lens; ISO: isolator.

The system was designed for the particular case of the single-facet homodyne OIPLL experimental set-up of Fig. 5.2, The polarising beam splitter output signal in Fig. 5.2 comprises of two orthogonally polarised beams, one from the m aster laser, the other from the slave laser, as explained in more detail in Section 5.1. The neutral beam splitter divides the m aster and slave laser beam intensity equally betw een the transmitted and reflected outputs, conserving their polarisation state. Using a similar approach to that described in Appendix F for the mixing of the two orthogonally polarised outputs o f the hi-bi fibre, a balanced receiver can be designed. The

photodetectors chosen were two TL-IOOL from ILX, both with sim ilar bandwidth (around 1.2 GHz) and responsivity (around 0.9 AAV). The association o f the quarter- wave plate, half-wave plate and polarising beam splitter creates the condition for the signals reaching the photodetectors to be phase-shifted by K in relation to each other. The photodetectors are connected to produce opposite sign photocurrents to the operational amplifier used in summing configuration. Thus, the output o f the amplifier results in a signal containing mainly the term carrying the phase error information, and the contribution from the laser incident powers is practically eliminated. Because of imperfection in the optical components and the slight difference in responsivity for the two photodetectors used, it was necessary to adjust the half-wave plate to ensure the n

phase shift of the signals reaching the photodetectors and to misalign the isolators to match the intensity of the DC contribution of each photodetector for the signal at the output of the system. W hen the balanced detection condition was established, the suppression of the DC term of the signal was better than 30 dB, measured from the ratio between the maximum DC signal produced by the photodetection and the minimum scale precision of the instrument (0.5 |iA) used to measure the output signal.

In section 5.1, no mention has been made regarding the alignment process that leads to the mixing of master and slave laser signals on the active area of the receiver photodetectors (Fig. 5.18) and coupling of the beams into the fibre that takes both signals to the Fabry-Perot interferometer and lightwave signal analyser (Fig. 5.2). Also, it has been assumed that the beams are perfectly overlapped throughout the set-up. In eq. (2.1.5), a term was introduced to account for the problem of the lack of polarisation matching and wavefront alignment between master and slave laser signal. In fact, although the optical components are not perfect, the outputs of polarising beam splitters can ensure good agreement for the polarisation states of the beams. The main problem arises from the w avefront matching [5.9]. In reality, the degree o f beam overlap achieved during the alignment process described in Section 5.1 is good enough to guarantee the injection locking part of the OIPLL system, but it may not be sufficient for the detection system and the fibre coupling, which leads to the degradation of the phase-lock contribution to the OIPLL. From Fig. 5.2 and 5.3, it is possible to see that any variation in the position of the master and slave lasers can lead to a decrease in the level of the power injected into the slave laser cavity. Therefore, it is not possible to correct the beam overlap by adjusting the lens positions without degrading the injection level. The only component that could offer ways of correcting the beam overlap is the mirror M (Fig. 5.2) through angular tilting of its positioner.

In order to study the beam overlap problem. Fig. 5.19 shows a representation of the wavefronts of two laser electric fields reaching, for simplicity, the square active area

Chapter 5: Optical and Electrical Design

of a photodetector of side L. It is assumed that the wavefront of the laser 1 is parallel to the photodetector active area region whilst the wavefront of laser 2 is misaligned by k and that there is no misalignment in the direction

In Appendix G, the wavefront mismatch between the master and slave laser signals is studied with the assumptions of Fig. 5.19. Assuming that the photodetector is loaded with a resistance r, the average dissipated power relative to the DC and AC parts of the photocurrent are given by, respectively (Appendix G):

P o c i ^ ) = + P i cos"(k-)]‘ (5.3.1) Pa cM = 2 r R ^ {k) sin ^ s in (K -) 71L . . . Ao k

L

XT

It is possible to see from eq. (5.3.1) and (5.3.2) that the misalignment between the wavefronts can compromise the beam coupling and degrade the output signal of the photodetector. For the OIPLL and OPLL systems, the term of interest is the amount of AC signal that can be obtained during the mixing of the two signals.

laser 2

laser 1

photodetector active region

In order to illustrate the implications of no overlapped wavefronts, Fig. 5.20 shows the degradation of the dissipated power Fac(^)/^/\c(0) (dB) as a function of the of the wavefront misalignment, for a load resistance r = 50 Q, responsivity R = 0.9 AAV, optical powers P] = P2 = \ 0 0 pW , laser wavelength A2 = 1.55 pm and photodetector

length L = 100 pm. 00 ■D CL C

I

I

0

2

6

8

W avefront A lignm ent (deg)

Fig. 5.20 - Degradation of the dissipated power fo r the AC term o f the photocurrent as a function o f wavefront misalignment.

It can be seen from the plot that variations of 0.4° and 0.65° in the angle /cfrom perfectly overlapped wavefronts ( k = 0) can cause a power degradation around 3 dB and ju st under 10 dB, respectively. One should keep in mind that effect o f the wavefront alignment over the efficiency of the signal mixing is even worse than the results shown by Fig. 5.20 as all the calculations assumed perfect matching in the x direction of Fig. 5.19 and that one of the laser wavefront planes was coincident with the photodetector active area. In order to solve the wavefront misalignment, the laser beams should be combined far way from the sources (over 1 m) before being mixed on the active area of the photodetector. For a misalignment of 1 mm and distance between the sources and the observation point of 1 m, the angle K = 0.06°, and very good matching is possible in direction y of Fig. 5.19. In Fig. 5.2, the mirror M mount was fitted with piezoelectric drives to provide fine angular adjustm ent. A fter adjustm ent, the wavelength overlap efficiency defined in eq. (2.1.5), was measured to be between 0.5 and 0.6.

Chapter 5: Optical and Electrical D esign