Residual Amplitude Modulation Research Articles

Coherent photo-thermal noise cancellation in a dual-wavelength optical cavity for narrow-linewidth laser frequency stabilisation.

Optical resonators are used for the realisation of ultra-stable frequency lasers. The use of high reflectivity multi-band coatings allows the frequency locking of several lasers of different wavelengths to a single cavity. While the noise processes for single wavelength cavities are well known, the correlation caused by multi-stack coatings has as yet not been analysed experimentally. In our work, we stabilise the frequency of a 729 nm and a 1069 nm laser to one mirror pair and determine the residual-amplitude modulation (RAM) and photo-thermal noise (PTN). We find correlations in PTN between the two lasers and observe coherent cancellation of PTN for the 1069 nm coating. We show that the fractional frequency instability of the 729 nm laser is limited by RAM at 1 × 10-14. The instability of the 1069 nm laser is at 3 × 10-15 close to the thermal noise limit of 1.5 × 10-15.

Field-programmable gate array-based residual amplitude modulation suppression and control for compact atomic clocks.

We designed a field-programmable gate array (FPGA) fabric to provide phase modulation techniques to lock lasers to optical frequency references. The method incorporates an active residual amplitude modulation (RAM) suppression scheme that relies on complex modulation. All the required servos to construct an optical atomic clock are incorporated into the same low-cost, commercial FPGA chip. We demonstrate a reliable, long-term RAM suppression of 60 dB with the remaining RAM level at -100 dBc and an improved stability of three decades when applied on a two-photon rubidium clock.

Synthetic FM triplet for AM-free precision laser stabilization and spectroscopy

The Pound–Drever–Hall (PDH) cavity-locking scheme has found prevalent uses in precision optical interferometry and laser frequency stabilization. A form of frequency modulation spectroscopy, PDH enjoys superior signal-to-noise recovery, large acquisition dynamic range, wide servo bandwidth, and robust rejection of spurious effects. However, residual amplitude modulation at the signal frequency, while significantly suppressed, still presents an important concern for further advancing the state-of-the-art performances. Here we present a simplified and improved scheme for PDH using an acousto-optic modulator to generate digital phase reference sidebands instead of the traditionally used electro-optic modulator approach. We demonstrate four key advantages: (1) the carrier and two modulation tones are individually synthesized and easily reconfigured, (2) robust and orthogonal control of the modulated optical field is applied directly to the amplitude and phase quadratures, (3) modulation synthesis, demodulation, and feedback are implemented in a self-contained and easily reproducible electronic unit, and (4) superior active and passive control of residual amplitude modulation is achieved, especially when the carrier power is vanishingly low. These distinct merits stimulate new ideas on how we optimally enact PDH for a wide range of applications.

Suppression of residual amplitude modulation in diffused-channel Ti:LiNbO3 optical waveguides by changing their geometry

Suppression of residual amplitude modulation in diffused-channel Ti:LiNbO₃ optical waveguides by changing their geometry

An ultra-stable laser based on molecular iodine with a short-term instability of 3.3 × 10−15 for space based gravity missions

Many space based gravity missions require frequency stabilized lasers with stringent requirements. Toward those requirements, we develop a compact frequency-stabilized laser which is referenced to the R(56)32−0: a1 transition of molecular iodine based on the modulation transfer spectroscopy technique. The stability of the laser is limited by the beam pointing noise, the electronic servo noise, and the residual amplitude modulation (RAM) noise. To improve the beam pointing stability, the system is constructed by gluing most components of the optical system on an ultra-low expansion glass base. We use a pre-amplifier to suppress the electronic servo noise, and use a wedged electro-optic phase modulator to suppress the RAM noise. The fractional frequency instability of the system is evaluated to be 3.3 × 10−15 at 2 s and 4 s averaging time, and is lower than 6 × 10−15 at averaging times from 1 s to 10 000 s. To our knowledge, this is the best short-term (1–4 s) instability reported so far for an iodine stabilized laser. The stability fully meets the requirements of next generation gravity mission and laser interferometer space antenna mission.

High band-width mid-infrared frequency-modulated Faraday rotation spectrometer for time resolved measurement of the OH radical.

We present a novel mid-infrared frequency-modulated Faraday rotation spectrometer (FM-FRS) for highly sensitive and high bandwidth detection of OH radicals in a photolysis reactor. High frequency modulation (up to 150 MHz) of the probe laser using an electro-optical modulator (EOM) was used to produce a modulation sideband on the laser output. An axial magnetic field was applied to the multi-pass Herriott cell, causing the linearly polarized light to undergo Faraday rotation. OH radicals were generated in the cell by photolyzing a mixture of ozone (O3) and water (H2O) with a UV laser pulse. The detection limit of OH reaches 6.8 × 108 molecule/cm3 (1σ, 0.2 ms) after 3 and falling to 8.0 × 107 molecule/cm3 after 100 event integrations. Relying on HITRAN absorption cross section and line shape data, this corresponds to minimum detectable fractional absorption (Amin) of 1.9 × 10-5 and 2.2 × 10-6, respectively. A higher signal-to-noise ratio and better long-term stability was achieved than with conventional FMS because the approach was immune to interference from diamagnetic species and residual amplitude modulation noise. To our knowledge, this work reports the first detection of OH in a photolysis reactor by FM-FRS in the mid-infrared region, a technique that will provide a new and alternative spectroscopic approach for the kinetic study of OH and other intermediate radicals.

Laser frequency stabilization in the 10 -14 range via optimized modulation transfer spectroscopy on the 87Rb D2 line.

We present a high-performance laser frequency stabilization method using modulation transfer spectroscopy (MTS) on the rubidium 87D2 transition line. A substantial improvement of the laser frequency stability was achieved by searching for the optimal diameter and intensity settings of the probe and pump beam. The frequency instability measured from the beat frequency of two locked external cavity diode lasers (ECDLs) reached a short-term stability of 4.5×10-14/τ and did not exceed 2 × 10-12 until 105 s, which is the best performance reported thus far with a D2 transition. The long-term stability is limited by the offset fluctuations of the baseline induced by the residual amplitude modulation (RAM), which can be further improved by reducing the current temperature variation of about 0.2 K by means of temperature stabilization or through a further reduction of the RAM.

Passive resonant laser gyroscope with improvement of the suppression of residual amplitude modulation effects through correlation analysis

Passive resonant gyroscopes (PRGs) utilizing the Pound-Drever-Hall (PDH) method are expected to have a lower shot-noise limit in rotational rate measurement. However, there are also many technical obstacles in the way to touch the intrinsic noise floor. In this article, we find that the residual amplitude modulation (RAM) effect in the phase locking process deteriorates the accuracy and stability of the output signal of PRGs, and becomes a dominant limiting factor, especially in the low-frequency range. Since the suppression is not good enough in the PRGs due to the strict requirements, we propose to use the Pearson correlation coefficient to evaluate the correlation between the RAM signal and the PDH signal to achieve a sufficient correlation before active servo control. With the implementation of this improvement, the RAM-induced fractional frequency stability for the 12 m optical ring cavity is reduced down to . The contribution of the RAM effect to the rotational sensitivity of our 3 m × 3 m PRG is lowered to 8.0 × 10−9 rad s−1 at 1 mHz, which is one order of magnitude better than the unconstrained situation. With this upgrade, a rotational resolution of rad s−1 of the PRG is achieved, which is the best performance among all PRGs so far.

Cavity locking with spatial modulation of optical phase front for laser stabilization

We study optical cavity locking for laser stabilization through spatial modulation of the phase front of a light beam. A theoretical description of the underlying principle is developed for this method and special attention is paid to residual amplitude modulation (RAM) caused by experimental imperfections, especially the manufacture errors of the spatial phase modulator. The studied locking method owns the common advantages of the Pound-Drever-Hall method and the tilt-locking one, and it can provide a more artful way to eliminate RAM noise in phase modulation for the ultimate stability of lasers. In situations where cost and portability are a practical issue, the studied method allows one to realize compact laser stabilization systems locked to Fabry-P$\acute{\mbox{e}}$rot cavities without use of expensive bulky devices, such as signal generators and electro-optic modulators.

Increased Spurious-Free Dynamic Range in Frequency Sweeping Interferometry by Suppression of Parasitic Amplitude Modulation

We propose an envelope detrending method to correct parasitic amplitude modulation (AM) in frequency sweeping interferometry (FSI). Parasitic AM arises from effects such as device spectral response and residual AM of laser. The periodic component in parasitic AM introduces spurious harmonics, which degrade the spurious-free dynamic range (SFDR) and interfere with information analysis. The proposed method employs a Hilbert transform to obtain a time-varying amplitude fluctuation curve from an auxiliary interferometer. This curve is then employed to detrend the parasitic AM in the main interferometric signal, thus restoring the point spread function and improving the SFDR. An optimal SFDR can be obtained when the optical path differences (OPDs) of the two interferometers are equal, while mismatched OPDs lead to a rapid degradation of the SFDR correction. Experimental results demonstrate the effectiveness of the proposed method and the optimal matching condition. A maximum SFDR of 90.2dB can be achieved when the OPD matching condition is satisfied. By applying the method to an optical frequency domain polarimeter, we realized a measured 81.1dB polarization extinction ratio. We believe that the proposed method can also help to improve the SFDR in other FSI systems.

Residual amplitude modulation induced error in resonant micro-optic gyroscope

A universal expression is proposed for evaluating the residual amplitude modulation (RAM) in a phase modulator. The different effects of the interference and linear terms of the RAM on the resonant micro-optic gyroscope (RMOG) are analyzed. It is found that the effect of RAM depends on the magnitude of RAM itself and the phase component. A theoretical model is then developed to calculate the RAM induced bias error in the RMOG. Finally, a technique for suppression of RAM is proposed and demonstrated, and the bias error of the separate-phase-modulation RMOG is successfully eliminated.

Application of additional high-frequency modulation to reduce influence of residual amplitude modulation LiNbO3 phase modulator on fiber optical gyroscope signal

Residual amplitude modulation in LiNbO3 phase modulator is one of the key factors that limit the accuracy of high-sensitive fiber-optical sensors. A fiber-optical gyroscope is an angular velocity sensor whose sensitivity is better than 0.001 °/h. Optical light intensity changes after phase modulator is a reason for wrong phase difference that introduces an error in the angular velocity signal. Most existing residual amplitude modulation suppression methods are based on reduction of back reflections between an optical fiber and integrated optical waveguide, absorbing groove to suppress or reduce reflection on the bottom face, and algorithmic compensation. In this paper, new approach to reduce residual amplitude modulation in LiNbO3 for fiber optical gyroscope application is presented. Method feature is an application of additional differential signal modulation with uniform amplitude distribution in the input signal voltage range of the phase modulator. The proposed method allows to suppress residual amplitude modulation of the multifunctional integrated optical circuit phase modulator more than 3 times using additional triangle signal modulation with the frequency f = 200.09 MHz and power P = 36 dBm. This method is suitable for improving fiber optical gyroscope accuracy. Moreover, it could be applied for any fiber-optic sensors based on LiNbO3 phase modulator. The paper will be of interest to specialists in the field of highly sensitive fiber optical sensors, fiber, and integrated optics.

Digital control of residual amplitude modulation at the 10-7 level for ultra-stable lasers.

The stabilization of lasers on ultra-stable optical cavities by the Pound-Drever-Hall (PDH) technique is a widely used method. The PDH method relies on the phase-modulation of the laser, which is usually performed by an electro-optic modulator (EOM). When approaching the 10-16 fractional frequency stability level, this technology requires an active control of the residual amplitude modulation (RAM) generated by the EOM in order to bring the frequency stability of the laser down to the thermal noise limit of the ultra-stable cavity. In this article, we report on the development of an active system of RAM reduction based on a free space EOM, which is used to perform PDH-stabilization of a laser on a cryogenic silicon cavity. A minimum RAM instability of 1.4 × 10-7 is obtained by employing a digital servo that stabilizes the EOM DC electric field, the crystal temperature and the laser power. Considering an ultra-stable cavity with a finesse of 2.5 × 105, this RAM level would contribute to the fractional frequency instability at the level of about 5 × 10-19, well below the state of the art thermal noise limit of a few 10-17.

A novel wavelength modulation spectroscopy gas sensing technique with an ultra-compressed wavelength scanning bandwidth

In a wavelength modulation spectroscopy (WMS) gas sensing system, a scanning ramp combined with a high frequency sinusoidal signal is applied to drive the laser source. Generally, a wide wavelength scanning bandwidth realized by voltage scanning ramp is required to fully cover the target gas absorption profile. In this paper, a novel WMS-based strategy is proposed and verified in a CH4 detection system. The wavelength scanning bandwidth is compressed from ∼659 pm to ∼166 pm, even narrower than the half width at full height (HWFM) of the CH4 absorption profile. In addition, the second harmonic signal that induced by the absorption is increased threefold by virtue of making full use of the dynamic range of the preamplifier circuit, and the waveform distortion that comes from the residual amplitude modulation (RAM) effect is eliminated as well. Benefiting from the compressed driving current range, the thermal stability of the laser diode is improved from the original level of 0.5 °C to 0.1 °C. As a result, a linear sensitivity of 75.2 ppb is achieved within 0–3000 ppm CH4 concentration range at 12.7 s time constant.

Suppressing backscattering noise of a resonant fiber optic gyroscope using coherent detection.

This paper provides a novel, to the best of our knowledge, method for suppressing backscattering noise of a resonant fiber optic gyroscope (RFOG) with a coherent detection technique. The light from the fiber ring resonator is mixed with a reference beam rather than being demodulated directly in traditional configurations, generating a coherent signal with a radio frequency. The central frequencies of the two reference lights used for the clockwise and counterclockwise waves are different to avoid the effect of backscattered waves. Besides, a common phase modulation is applied on the two counter-propagating waves to eliminate the parasitic effect due to the residual amplitude modulation in the phase modulator. Two demodulation schemes for the rotation rate detection from the coherent signals are then proposed and demonstrated, with performance on noise suppression tested. One is the beat-frequency demodulation, and the other is the self-mixing demodulation technique. The influence of backscattering intensity is reduced from 270°/h to 3°/h and 0.05°/h with the two demodulation techniques, respectively, showing a full suppression of backscattering noise.

Inhomogeneous spatial distribution of residual amplitude modulation in optical phase modulation using a bulk electro-optic crystal.

Residual amplitude modulation is one of the major sources of instability in many precision measurements using frequency modulation techniques. Although a transverse and inhomogeneous distribution of residual amplitude modulation has long been observed, the underlying mechanism is not well understood. We perform measurement and analysis of this spatial inhomogeneity using several electro-optic crystals of different types. Two distinct components are identified in the spatial distributions, and their detailed properties, some of which are previously unnoticed, are mapped out and analyzed, showing that the spatial inhomogeneity can be explained by acousto-optic interaction inside the crystal. Moreover, this spatial inhomogeneity can be further suppressed, improving the 1000-s stability of residual amplitude modulation to 3×10-7 (8×10-8) at modulation frequency of 11 MHz (120 kHz), corresponding to a frequency instability of 1×10-17 (3×10-18), estimated for a cavity-stabilized laser using a Pound-Drever-Hall discrimination slope of 1×10-4 V/Hz.

Resonant fiber optic gyroscope using a reciprocal modulation and double demodulation technique.

A resonant fiber optic gyroscope (RFOG) using a reciprocal modulation and double demodulation technique based on a single laser source is proposed and demonstrated. The effect of the residual amplitude modulation of the phase modulator is well suppressed thanks to the reciprocal modulation and demodulation. On this basis, the backscattering noise is also eliminated by the double demodulation process. The long-term bias stability of the RFOG is successfully improved to 0.2°/h for a test time of 45 hours.

Effects of Polarization Modulation Induced by Electro-Optic Modulators in Fiber-Based Setups

Using the Jones formalism, it is shown that electro-optic modulators used for phase modulation generate a modulation of the output polarization induced by the difference of phase modulation depth along the crystallographic axes of the modulator. We study two consequences of this polarization modulation in the fiber setups, limiting the performance of high sensitivity measurement devices. The first one is its partial conversion into a residual amplitude modulation (RAM) within any component presenting polarization dependent losses (PDL). The second one is a new effect that consists of the distortion of the signal detected at the output of a fiber cavity. The theoretical expressions of the detected signals are computed in each case.

Microring Optical Phase-Shifters With Low Driving-Voltage, Low Insertion Loss, and Small Residual Amplitude Modulation

Novel microring based optical phase-shifters on Si-photonic platforms for microwave photonic applications are demonstrated. By using an add-drop microring structure in combination with an additional multimode interferometer (MMI), pure phase modulation with an ultrahigh modulation efficiency can be realized. Comparison is made to the reference all-pass ring design with both the same radius (5 μm) and coupling coefficient (κ: ∼0.2). The demonstrated structure minimizes the residual amplitude modulation (0.9 vs. 1.8 dB) for nearly 2π phase shifting over a wide optical window (1520 to 1570 nm) at the expense of a larger insertion loss (0.06 dB) due to the additional MMI. The demonstrated phase shifter structure is implemented in a Mach-Zehnder interferometer (MZI) for further study of its dynamic and linearity performance. Under forward bias, it exhibits a low V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">π</sub> /I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">π</sub> (0.4 V/12.7 mA), fast rise-time (3 ns), low insertion loss (0.2 dB), low residue-amplitude-modulations (<0.9 dB), and can cover wide optical windows (1560–1568 nm) with a small footprint (37 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \times $</tex-math></inline-formula> 37 μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). The measured spurious-free dynamic range (SFDR: 70–75 dB) of our novel phase shifter-based MZI is comparable to that of the traditional traveling-wave MZI (∼75 dB) under reverse bias and tested using the same setup.

A Hollow-Core Photonic-Crystal Fiber-Optic Gyroscope Based on a Parallel Double-Ring Resonator.

A novel system structure of resonant fiber optical gyroscope using a parallel double hollow-core photonic crystal fiber ring resonator is proposed, which employs the double closed loop and reciprocal modulation–demodulation technique to solve the problem of the length mismatch between rings. This structure can suppress the residual amplitude modulation noise and laser frequency noise, essentially eliminating the influence of the Rayleigh backscattering noise and dramatically reduce the Kerr-effect-induced drift by three orders of magnitude. Thanks to its excellent noise suppression effect, the sensitivity of this novel system can approach the shot-noise-limited theoretical value of 8.94 × 10−7 rad/s assuming the length of the fiber ring resonator is 10 m.