## Abstract

Quadrature interferometry based on $3\times 3$ fiber couplers could be used to double the effective imaging depth in swept-source optical coherence tomography. This is due to its ability to suppress the complex conjugate artifact naturally. We present theoretical and experimental results for a $3\times 3$ Mach–Zehnder interferometer using a new unbalanced differential optical detection method. The new interferometer provides simultaneous access to complementary phase components of the complex interferometric signal. No calculations by trigonometric relationships are needed. We demonstrate a complex conjugate artifact suppression of $27\text{\hspace{0.17em}}\mathrm{dB}$ obtained in swept-source optical coherence tomography using our unbalanced differential detection. We show that our unbalanced differential detection has increased the signal-to-noise ratio by at least $4\text{\hspace{0.17em}}\mathrm{dB}$ compared to the commonly used balanced detection technique. This is due to better utilization of optical power.

© 2008 Optical Society of America

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### Equations (11)

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(1)
$${\mathbf{M}}_{{\mathbf{2}\mathbf{\times}\mathbf{2}}_{\mathbf{50}/\mathbf{50}}}=\left[\begin{array}{cc}\sqrt{0.5}& -j\sqrt{0.5}\\ -j\sqrt{0.5}& \sqrt{0.5}\end{array}\right]$$
(2)
$${\mathbf{M}}_{{\mathbf{2}\mathbf{\times}\mathbf{2}}_{9\mathbf{0}/1\mathbf{0}}}=\left[\begin{array}{cc}\sqrt{0.9}& -j\sqrt{0.1}\\ -j\sqrt{0.1}& \sqrt{0.9}\end{array}\right]$$
(3)
$${\mathbf{M}}_{\mathbf{3}\mathbf{\times}\mathbf{3}}=\frac{{e}^{-j2{K}_{\mathrm{cpl}}}}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& 1& 1\\ 1& 1& 1\end{array}\right]+\frac{{e}^{j2{K}_{\mathrm{cpl}}}}{3}\left[\begin{array}{ccc}2& -1& -1\\ -1& 2& -1\\ -1& -1& 2\end{array}\right],$$
(4)
$${\mathbf{E}}_{\mathbf{33}}(\phi )={\mathbf{M}}_{\mathbf{3}\mathbf{\times}\mathbf{3}}{\mathbf{M}}_{\phi}(\varphi ){\mathbf{M}}_{{\mathbf{2}\mathbf{\times}\mathbf{2}}_{\mathbf{90}/\mathbf{10}}}{\mathbf{E}}_{\mathbf{in}}\mathrm{.}$$
(5)
$${\mathbf{E}}_{\mathbf{22}\mathbf{1}}(\varphi )={\mathbf{M}}_{{\mathbf{2}\mathbf{\times}\mathbf{2}}_{50/5\mathbf{0}}}{\mathbf{E}}_{{\mathbf{in}}_{2\times 2}}(\varphi ),$$
(6)
$${\mathbf{E}}_{\mathbf{22}\mathbf{2}}(\varphi )={\mathbf{M}}_{{\mathbf{2}\mathbf{\times}\mathbf{2}}_{50/50}}{\mathbf{E}}_{{\mathbf{in}}_{2\times 2}}(\varphi )\mathrm{.}$$
(7)
$$P\propto {\mathbf{E}}^{*}\mathbf{E}\mathrm{.}$$
(8)
$${P}_{1}(\varphi )=\alpha {P}_{{33}_{1}}(\varphi )-{P}_{{22}_{1}}(\varphi ),$$
(9)
$${P}_{2}(\varphi )=\alpha {P}_{{33}_{3}}(\varphi )-{P}_{{22}_{2}}(\varphi )\mathrm{.}$$
(10)
$${P}_{\mathrm{RE}}(\varphi )={P}_{1}(\varphi ),$$
(11)
$${P}_{\mathrm{IM}}(\varphi )=\frac{{P}_{1}(\varphi )\mathrm{cos}(\mathrm{\Delta}\varphi )-{P}_{2}(\varphi )}{\mathrm{sin}(\mathrm{\Delta}\varphi )}\mathrm{.}$$