The schematic diagram of this method is shown in Fig. 1. The light beam coming from a laser diode LD passing through a polarizer P and an electro-optic modulator EO incidents on a beam splitter BS. The transmitted light enters a modified Michelson interferometer and is divided into two parts by a polarization beam splitter PBS: the reflected s-polarization light and the transmitted p-polarization light. The former is normally reflected by a mirror M1, and then is reflected by the PBS and the BS again. And it passes through an analyzer AN and is detected by a photo detector PD. It acts the reference light in this interferometer. The latter is normally reflected by another mirror M2 and returns along its original path. After being reflected by the BS, it passes through the AN and also enters the PD. It acts as the test light in the modified Michelson interferometer. If the amplitudes of the reference light and the test light are Er and Et, PD measures the interference intensity of Er and Et, that is, l= |Er+Et|2.
For convenience, the +z axis is chosen along the propagation direction, the x-axis is along the horizontal direction and only the light of the wavelength λi is considered. et the transmission axis of the P be at 45˚ with respect o the x-axis, then the Jone vector of the light incidenting on the BS can be written as
If the fast axis of the EO is along the x-axis, and an external saw tooth voltage signal with frequency f and amplitude V is applied to the EO, then the retardation produced by the EO can be expressed as[3,4]
where V is the associated half-wave voltage of the EO at λi. And if the transmission axis of the AN is 45˚ with respect to the x-axis, then we have
where ϕi is the phase difference being corresponding to the optical path difference between the test light and the reference light, i.e.,
Therefore, the interference intensity is given by
Because the light coming from a laser diode contains many continuous spectrums, the interference intensity measured by the PD can be expressed as
where n is an integer, and ai is the bias intensity of wavelength λi. From Eq. (7), it is obvious that we can obtain the summation signal of many cosine signals on the oscilloscope OSC. Then, moving M2 in steps until the contrast of the signal on the OSC is nearly equivalent to zero. At the time, the optical path difference between the test light and the reference light is the coherence length.
In order to show the validity of this method, a laser diode (HHL6720G) manufactured by Japan Hitachi Ltd. is tested. It operated at 25 °C with electric current 35 mA and its central wavelength is 670.57 nm. An EO modulator (4002) fabricated by New Focus, with half-wave voltage 220 V at 670.57 nm, is used in this test. A saw tooth signal, with frequency 2 kHz and amplitude
220 V, is applied to the EO modulator. Fig. 2 are the interference signal on the OSC as the optical path difference is about (a) zeromm, (b) 27mm, (c) 42mm, respectively. According Fig. 2, we obtain its coherence length is about 42mm. In addition, we also measure its coherence length with the conventional Michelson interferometer. We obtain the same result.
The half-voltage of the EO is varied as the wavelength is varied. In our test, the tested LD has narrow spectral bandwidth, the condition V ≌ Vi exists in Eq. (7). So our measured result has the same result as the conventional method. If a light source with wide spectral bandwidth or several separate spectral lines, is tested, the half-voltage is different for different wavelength. Consequently, the measured result with this method will be smaller than that of the conventional method. We also measure two He-Ne lasers (GLG 5369 and GLG 5730) manufactured by Japan NEC Ltd. The half-voltage 146.4 V at 632.8 nm is applied to the EO. Their measured results are 256 mm and 378 mm (with this method), and 305 mm and 450 mm (with the conventional method), respectively. Therefore this method is suitable only for the light source with narrow spectral bandwidth. In addition, either mirror does not move as the contrast of the interference signal is monitored in the process of this method, so this method has some merits such as high stable signal, easy operation, and high accuracy.
This study was supported in part by the National Science Council, Taiwan, under contract NSC 93-2215-E-009-021.