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TECHNICAL NOTES Measurement of the coherence length of a laser using a holographically generated phase-conjugated wave front C. Bhan, K. Syam Sundara Rao, and P. C. Mehta The authors are with the Instruments Research & Devel- opment Establishment, Dehra Dun, India 248008. Received 1 June 1990. 0003-6935/91/304282-02$05.00/0. © 1991 Optical Society of America. A simple and quick method is reported for measurement of the coherence length of a laser by using a holographically generated phase-conjugated wave front employing real- time recording material. Michelson defined the temporal coherence length of a source in terms of the visibility of interference fringes between two beams derived from the source as a function of the optical path difference. 1 The Fabry-Perot interferome- ter has also been used for determining the coherence length by measuring the linewidth of the source. 2,3 This method gives the correct value of the coherence length for those sources whose accurate distribution of spectral components is known. Wuerker and co-workers 4 have demonstrated a holographic method for measuring directly the complete temporal coherence function of a pulsed laser. The method is based on the recording of a two-beam hologram of an inclined diffusing card. The reconstructed image of the card reveals the coherence property of the source. We report a simple method for the measurement of the coherence length of a laser using a holographically gener- ated phase-conjugated wave front employing a Fe-doped LiNbO 3 crystal. The method requires no critical alignment. The object beam and reference beam record a phase grating in the crystal, and the reconstruction beam produces the phase conjugate of the object beam in real time. 5,6 The experimental arrangement is shown in Fig. 1. The laser beam (argon-ion, 514 nm, with an étalon) is split into two parts by a beam splitter BS 1 (a wedged glass plate). The transmitted beam forms the reference beam R, while the reflected beam acts as the object beam 0. The path of the object beam can be varied by incorporating a beam splitter BS 2 and a mirror M 2 in the path as shown in the figure. The two beams record a phase hologram in a crystal (Fe-doped LiNbO 3 20 × 20 × 3 mm), which is reconstructed by the beam R 1 . The beam R 1 is the transmitted reference beam that passes through the recording crystal and is reflected back by the mirror M 3 . The reconstructed conjugate object beam O* is taken out by the beam splitter BS 3 and observed on a screen. Initially the object beam path is made approximately equal to the reference beam path. Then the path length of the object beam is continuously increased by moving the mirror M 2 until the conjugate object beam disappears on the screen. The path difference between the object beam and reference beam in this condition gives a direct measure- ment of the temporal coherence length of the laser. For the argon-ion laser we measured a coherence length of 1.9 m. Figure 2 shows a plot of the intensity of the conjugate beam as a function of the position of M 2 , i.e., the path difference. The beam intensity first falls off rapidly and then becomes almost constant before gradually becoming zero. From the curve the path length can be selected for, say, 50% coherence. For path lengths from 0.4 to 1.4 m the intensity remains ~ 50% of the peak value. The main advantage of the method is that it is quick and involves no critical or accurate alignment of optical compo- nents. We have only to see the presence of a laser point on the screen rather than to observe interference fringes as in the Michelson method. Vibration isolation is also not necessary, because, even if there are vibrations, continuous writing and reading of the hologram will take place, and there will always be a reconstruction, although it may be of poor quality. The experiment can be performed with a direct laser beam without expansion. The method is also applicable to laser sources other than those in the visible wavelength region. In such a case hologram writing may be done at the desired wavelength; the reconstruction beam R 1 may be derived from a He-Ne laser, so that on the screen a red point is observed. However, the recording crystal must be sensitive to the desired wavelength application. For the measurement of short coherence lengths, such as those of pulsed lasers, accurate path length matching is required as in the case of other methods. Alternatively we can replace the beam splitter BS 2 and mirror Mg with an inclined graduated card, as used by Wuerker et al 4 How- ever, this requires additional optics for illuminating the card and for collecting the scattered light for recording the hologram in real time. Fig. 1. Schematic diagram of the experimental setup for measure- Fig. 2. Variation of the conjugate beam's intensity with the path mont of the coheronce length of a laser. difference. 4282 APPLIED OPTICS / Vol. 30, No. 30 / 20 October 1991
