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Journals >Chinese Optics Letters >Volume 13 >Issue 6 >Page 060604 > Article

Chinese Optics Letters
Vol. 13, Issue 6, 060604 (2015)

Generation of ultra-flat optical frequency comb using a balanced driven dual parallel Mach–Zehnder modulator

Jian Wang^1、2, Haiwen Cai^1、*, Dijun Chen¹, and Ronghui Qu¹

Author Affiliations

¹Shanghai Key Laboratory of All Solid-State Laser and Applied Techniques, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

²University of Chinese Academy of Sciences, Beijing 100049, China

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DOI: 10.3788/COL201513.060604 Cite this Article Set citation alerts

Jian Wang, Haiwen Cai, Dijun Chen, Ronghui Qu. Generation of ultra-flat optical frequency comb using a balanced driven dual parallel Mach–Zehnder modulator[J]. Chinese Optics Letters, 2015, 13(6): 060604 Copy Citation Text

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Abstract

We propose and experimentally demonstrate an ultra-flat optical frequency comb (OFC) generator by a balanced driven dual parallel Mach–Zehnder modulator. Five- and seven-tone OFC with exactly equal intensity can be generated theoretically. Experimentally obtained five- and seven-tone OFC with flatness of 0.6 and 1.26 dB are demonstrated, respectively, which agrees well with the theoretical results.

E_{out} = \frac{E_{in}}{4} {\exp (j \frac{π}{V_{π}} V_{bias 1}) \exp [j \frac{π}{2 V_{π}} V \sin (ω t)] + \exp [- j \frac{π}{2 V_{π}} V \sin (ω t)] + \exp [j \frac{π}{V_{π}} V_{bias 3}] {\exp (j \frac{π}{V_{π}} V_{bias 2}) \exp [j \frac{π}{2 V_{π}} V \sin (ω t + φ)] + \exp [- j \frac{π}{2 V_{π}} V \sin (ω t + φ)]}}

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E_{out} = \frac{E_{in}}{4} {\sum_{n = - \infty}^{\infty} [\exp (j V_{a}) + {(- 1)}^{n}] J_{n} (β) \exp (j n ω t) + \exp (j V_{c}) {\sum_{n = - \infty}^{\infty} [\exp (j V_{b}) + {(- 1)}^{n}] J_{n} (β) \exp [j n (ω t + φ)]}},

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{\begin{matrix} I_{n = 2 k} = \cos^{2} (\frac{1}{2} V_{a}) J_{n}^{2} (β) + \cos^{2} (\frac{1}{2} V_{b}) J_{n}^{2} (β) + 2 \cos (\frac{1}{2} V_{a}) \\ * \cos (\frac{1}{2} V_{b}) J_{n}^{2} (β) \cos (\frac{1}{2} V_{a} - \frac{1}{2} V_{b} - V_{c} + n φ) \\ I_{n = 2 k - 1} = \sin^{2} (\frac{1}{2} V_{a}) J_{n}^{2} (β) + \sin^{2} (\frac{1}{2} V_{b}) J_{n}^{2} (β) + 2 \sin (\frac{1}{2} V_{a}) \\ * \sin (\frac{1}{2} V_{b}) J_{n}^{2} (β) \cos (\frac{1}{2} V_{a} - \frac{1}{2} V_{b} - V_{c} + n φ) φ = π / 2 . \end{matrix}

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\frac{1}{2} V_{a} - \frac{1}{2} V_{b} - V_{c} = l π, (l = 0,1, \dots)

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α = \frac{I * (d ϕ / d t)}{d I / d t}

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\sin^{2} (\frac{1}{2} V_{a}) J_{1}^{2} (β) + \sin^{2} (\frac{1}{2} V_{b}) J_{1}^{2} (β) = \cos^{2} (\frac{1}{2} V_{a}) J_{0}^{2} (β) + \cos^{2} (\frac{1}{2} V_{b}) J_{0}^{2} (β) + 2 \cos (\frac{1}{2} V_{a}) \cos (\frac{1}{2} V_{b}) J_{0}^{2} (β) .

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\cos^{2} (\frac{1}{2} V_{a}) J_{0}^{2} (β) + \cos^{2} (\frac{1}{2} V_{b}) J_{0}^{2} (β) + 2 \cos (\frac{1}{2} V_{a}) \cos (\frac{1}{2} V_{b}) J_{0}^{2} (β) \cos (\frac{1}{2} V_{a} - \frac{1}{2} V_{b} - V_{c}) = \cos^{2} (\frac{1}{2} V_{a}) J_{2}^{2} (β) + \cos^{2} (\frac{1}{2} V_{b}) J_{2}^{2} (β) + 2 \cos (\frac{1}{2} V_{a}) \cos (\frac{1}{2} V_{b}) J_{2}^{2} (β) \cos (\frac{1}{2} V_{a} - \frac{1}{2} V_{b} - V_{c} + π) .

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\frac{{[\cos (\frac{1}{2} V_{a}) + \cos (\frac{1}{2} V_{b})]}^{2}}{(1 + 2 \cos (\frac{1}{2} V_{a}) \cos (\frac{1}{2} V_{b}))} = \frac{2 J_{1}^{2} (β)}{(J_{0}^{2} (β) + J_{1}^{2} (β))},

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\frac{2 \cos (\frac{1}{2} V_{a}) \cos (\frac{1}{2} V_{b})}{\cos^{2} (\frac{1}{2} V_{a}) + \cos^{2} (\frac{1}{2} V_{b})} = \frac{(J_{0}^{2} (β) - J_{2}^{2} (β))}{(J_{0}^{2} (β) + J_{2}^{2} (β))} .

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{\begin{matrix} \cos^{2} (\frac{1}{2} V_{a}) + \cos^{2} (\frac{1}{2} V_{b}) = \frac{2 m}{2 + n - 2 m n} = k_{1} \\ \cos (\frac{1}{2} V_{a}) * \cos (\frac{1}{2} V_{a}) = \frac{m n}{2 + n - 2 m n} = k_{2} . \end{matrix}

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{\begin{matrix} \cos (\frac{1}{2} V_{a}) = \frac{\pm \sqrt{k_{1} + 2 k_{2}} \pm \sqrt{k_{1} - 2 k_{2}}}{2} \\ \cos (\frac{1}{2} V_{b}) = \frac{\pm \sqrt{k_{1} + 2 k_{2}} \mp \sqrt{k_{1} - 2 k_{2}}}{2} . \end{matrix}

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J_{1}^{2} (β) = J_{3}^{2} (β) .

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Jian Wang, Haiwen Cai, Dijun Chen, Ronghui Qu. Generation of ultra-flat optical frequency comb using a balanced driven dual parallel Mach–Zehnder modulator[J]. Chinese Optics Letters, 2015, 13(6): 060604

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