thermo-optic effect (original) (raw)

Author: the photonics expert (RP)

Definition: changes in refractive index caused by temperature changes

Categories: article belongs to category general optics general optics, article belongs to category physical foundations physical foundations

Related: refractive indexthermal lensing

Formula symbol: ($\partial n/\partial T$)

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DOI: 10.61835/mih Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn

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Contents

What is the Thermo-optic Effect?

Thermo-optic effects are generally understood to be effects on light propagation caused by thermal effects. The typically relevant effect is that the refractive index of a transparent medium is temperature-dependent, and this is usually called the thermo-optic effect.

This effect is often relevant in situations with non-uniform temperature. Here, one also often has substantial mechanical stress in materials, which may also have optical effects (called photoelastic effects) of similar magnitude. Although these are definitely also temperature-related optical effects, the thermo-optic effect is considered only to relate to the direct temperature influence on the refractive index, not including photoelastic contributions.

Thermo-optic Coefficient

As the dependence of refractive index on temperature is usually linear in a wide temperature range, it is natural to quantify the effect with a thermo-optic coefficient, which is the derivative of a refractive index with respect to temperature: ($\partial n/\partial T$). As the refractive index is dimensionless, that coefficient has units of K−1. From a temperature-dependent Sellmeier formula, one can obtain the thermo-coefficient by numerical differentiation.

Values of that coefficient for typical optical materials are normally on the order of 10−5 K−1. However, the coefficient can be well more than 10−4 K−1 for semiconductors, for example, and it can be negative for some materials, especially for polymers, but also for certain glasses and crystals. Negative coefficients can result from thermal expansion (reducing the density with increasing temperature) and from a decrease in polarizability.

For birefringent materials, the refractive index is generally polarization-dependent, and the thermo-optic coefficients for the different polarization directions can also vary substantially. This is relevant for non-critical phase matching of nonlinear interaction, for example. It can even happen that coefficients have different signs for different polarization directions.

Consequences of the Thermo-optic Effect

Thermal Lensing for Laser Beams

The thermo-optic effect is often the main reason for thermal lensing, e.g. in laser crystals. Typically, the thermo-optic coefficient is positive, and in combination with the higher temperature on the beam axis leads to a focusing lens effect. However, there can also be contributions to thermal lensing from stress effects and from the bulging of endfaces.

The dioptric power of a thermal lens is generally proportional to the thermo-optic coefficient, as long as the thermo-optic effect is dominant. Note, however, that it is also inversely related to the thermal conductivity because better thermal conduction reduces temperatures gradients. Therefore, “benign thermo-optic properties” of laser gain media include not only a low thermo-optic coefficient, but also a high thermal conductivity, and possibly also weak stress-related effects.

See the article on thermal lensing for more details.

Thermally Induced Phase Shifts

Optical phase shifts from propagation through a transparent medium are generally temperature-dependent. This can be utilized for thermo-optic switches, a kind of optical switches using such phase shifts inside a Mach–Zehnder interferometer.

Temperature Tuning of Resonance Frequencies

The resonance frequencies of optical resonators are often affected by the thermo-optic effect, i.e., they become temperature dependent. This is often an undesirable influence, e.g. when frequencies of laser emission are affected, but it can also be exploited for intentional temperature tuning, e.g. of micro-ring resonators or monolithic solid-state lasers such as nonplanar ring oscillators.

Thermal effects on optical resonance frequencies can also lead to interesting nonlinear phenomena such as optical bistability.

Temperature Effects on Diode Lasers

The mode frequencies of laser diodes are also temperature-dependent. However, the peak wavelength of the gain in the semiconductor is even more strongly temperature-dependent. Therefore, the temperature coefficient of the emission wavelength is often substantially larger than expected from the thermo-optic effect alone.

Temperature Effects on Fiber Bragg Gratings

Fiber Bragg gratings often exhibit spectrally narrow reflection features. Due to the thermo-optic effect, these can move substantially. That can be detrimental, but it is also utilized in fiber-optic temperature sensors.

Mode Profile Changes in Fibers

The modes of optical fibers and other types of waveguides are determined by refractive index profiles. The thermo-optic effect makes them temperature-dependent. While for most fiber devices that effect is negligibly weak, in some high-power fiber lasers and amplifiers it has significant effects because temperature gradients can be substantial and large mode area fibers are generally more sensitive to lensing effects. It can even happen that a fiber which is normally single-mode supports additional modes at high enough power levels. Also, the effective mode area can shrink, giving rise to more intense nonlinear optical effects.

Thermal Mode Instability in Fiber Amplifiers

High-power fiber lasers and amplifiers often exhibit the so-called thermal mode instability above a certain threshold power. Here, the output beam quality is substantially degraded, and strong fluctuations of mode powers occur.

The thermo-optic effect is an essential ingredient of that effect: Periodic spatial temperature variations, which can arise from interference effects, are leading to refractive index gratings which can reflect light.

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