Resonant Phase Modulators

FREE-SPACE RESONANTLY ENHANCED PHASE MODULATORS

Electro-optic phase modulators (PM) are devices that change the phase of an optical signal by applying an electric field to an electro-optic material. PMs can operate over a wide spectral range from ultraviolet (UV) to infrared (LWIR) with low optical loss, high optical power and modulation frequencies ranging from 50 kHz up to 20 GHz.

Phase Modulators can achieve high modulation depths with low driving voltages, making them attractive for various applications, including laser cooling, spectroscopy and spectral broadening. QUBIG offers Phase Modulators as bulk/free-space (PM), fiber-coupled (PM.FC) and surface-mount (PM.SMD) devices.

PHASE MODULATORS - bulk

KEY SPECS / FEATURES:

spectral range: 200nm - 12um | large crystals aperture
frequency range: 50kHz - 20GHz | high modulation efficiency
low insertion loss: typ. <2% (T>98%) | high ODT

TYPICAL APPLICATIONS:

laser frequency stabilisation - LFS (PDH, FM/MTS)
laser cooling | quantum state manipulation (Raman, Rydberg)
spectral broadening | coherence suppression

PHASE MODULATORS - fiber-coupled

KEY SPECS / FEATURES:

standard models for Rb, Cs, Ba+, Yb+, etc.
low insertion loss - IL(λ) | high ODT | long term stability
integrated single-mode PM fibres (FC-APC) for easy system integration

TYPICAL APPLICATIONS:

laser cooling and trapping of neutral atoms/ions/molecules
quantum state manipulation (e.g. Raman, Rydberg)
spectroscopy

PHASE MODULATORS - SMD

KEY SPECS / FEATURES:

wavelength range: 300 - 4000nm | low insertion loss - IL(λ) | high ODT
very compact and robust packaging | high modulation efficiency
50Ohms matched | implementation via soldering, glueing or wire-bonding

TYPICAL APPLICATIONS:

laser frequency stabilisation (PDH, FM/MTS)

Background Information

**Fig. 2** | *Characteristic features (Smith chart with Q-circle, S21) of a resonant system visualised with a vector.*

**Fig. 3** | *a) Optical spectrum of a phase modulated laser detected by a Fabry-Pèrot cavity. b) Bessel function spectrum of a phase-modulated laser. c) Test setup.*

Altered laser property: Phase

An important and easy to manipulate property of laser light that is commonly used for signal modulation is the phase. In general, optical radiation such as laser light is associated with electromagnetic waves which can be characterised with an amplitude and a phase. The phase determines in which part of an oscillation cycle the electric field is. Light where the optical phase evolves systematically and predictably in time possesses a high temporal coherence.

Coupling: Resonant

QUBIG’s resonant modulators consist of an electro-optic crystal that is coupled via a resonance circuitry to an RF input connector. This high-Q tank circuit is used to boost the input signal which eventually reduces the required RF power needed to achieve a desired modulation depth. An impedance matching network transforms the reactive crystal load to a 50Ohms input to allow for easy matching to standard RF drivers and function generators.

Effect on the laser light: Sideband generation

Resonant phase modulators are used to vary the phase of an optical laser beam. The induced sinusoidal phase variation f(t)=β*sin(Ω*t) at the modulation frequency Ω and peak phase change generates frequency sidebands at multiples of Ω about the central cw optical frequency, ω. The spectrum of a sinusoidally phase-modulated electric field after passing through the modulator is given by Bessel functions:

The amplitude in the m-th sideband at ω+m*Ω is proportional to Jm(β), where Jm is the m-th order Bessel function of the first kind. The amount of energy transferred from the fundamental J0(β) to the m-th sideband is proportional to the square of the electric field amplitude |Jm(β)|2. The modulation index β which describes how much energy is transferred from the carrier to the sidebands depends on many parameters such as the crystal material and its geometry, the laser wavelength as well as the applied RF power. The required value itself, which can be easily adjusted by tuning the RF level, varies a lot among the applications.

Typical Applications

High modulation efficiencies, large clear apertures for high power lasers, very low insertion losses (IL ~ %), a very broad spectral range (UV-LWIR) and strongly suppressed intrinsic disturbances (RAM) are typical characteristics of QUBIG‘s high-Quality free-space resonant phase modulators which make them suitable for a large range of applications such as:

**Fig. 1** | *Part of a LFS setup with characteristic oscilloscope traces of a phase modulated laser (yellow) and the PDH error signal (blue).*

**Fig. 2** | *Magneto optical trap (MOT) of neutral Lithium-7 atoms. Courtesy of UC Berkeley / Stamper-Kurn Group*

**Fig. 3** *The laser guide star in operation at the Very Large Telescope. Courtesy of the European Southern Observatory (ESO).*

**Fig. 4** | *Single ions trapped in a Paul trap under ultra-high vacuum are the building blocks of nowadays most precise optical frequency standards.*

Laser Frequency Stabilisation (LFS)

The linewidth (i.e. short-term stability) of “free-running” lasers is often not adequate for many applications. Powerful and elegant techniques such as Pound-Drever-Hall (PDH) and FM-/MTS are used in some of the most challenging precision measurements in modern optics and physics for controlling and stabilising the frequency of a cw laser to an ultra-stable reference such as high-finesse optical cavities or atomic transitions. Over the past several decades, especially precision spectroscopy, interferometry and the manipulation of quantum systems have directly benefited from the resulting improvement in cw laser stability.

Laser Cooling

Laser cooling is used to create degenerate ultra-cold gases for experiments in quantum physics. These experiments are performed near absolute zero where unique quantum effects such as Bose-Einstein condensates or degenerate Fermi-gases can be observed. The latter form the building blocks and basis for many future applications in Quantum Technology, such as Quantum Computers and sensors. Besides atoms and ions, recent progress has been made towards laser cooling of more complex systems, such as molecules and micro-mechanical objects.

Spectral Broadening

There are various applications that require laser beams with large linewidths. An efficient solution can be a strong phase modulation of a narrow-linewidth laser where the broadening is achieved by transferring energy from the fundamental J0(β) into many sidebands. The transport of high power cw laser beams in single mode optical fibers is very inefficient without spectral broadening due to stimulated Brillouin back-scattering (laser guide star - ESO). Other applications can be found in quantum science (laser cooling, white MOT) and spectroscopy (simultaneous excitation of several transitions).

Research & Science

Phase modulators (PM) are ubiquitous in atomic, molecular, and optical physics. They have played, and continue to play a major role in many fields of science. Optical clocks based on single ions or neutral atoms in optical lattices use phase modulators for quantum state manipulations, such as Raman transitions, optical repumper or phase demodulation. In metrology phase modulators placed in optical cavities are used for high resolution spectroscopy and the calibration of optical instruments like astronomical spectrometers. In laser science strong phase modulation is used as ultra-fast pulse-sources.