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In understanding the nature of electromagnetic wave transmission, a fundamental concept is the relationship between bandwidth and frequency. Imagine a highway: the wider it is (the greater the bandwidth), the more cars (information) can travel simultaneously. Similarly, in telecommunications, bandwidth refers to the range of frequencies over which a system can transmit signals effectively. The frequency of an electromagnetic wave is akin to the individual car speeds. Higher frequency waves, like those used in laser telephone transmission, can carry more information because they can be modulated more quickly, akin to a multi-lane freeway that supports high-speed vehicles.

According to the Shannon-Hartley theorem, the maximum data rate that can be transmitted with a certain level of noise, over a given bandwidth, is determined by the formula \( C = B \log_2(1 + S/N) \), where \( C \) is the channel capacity in bits per second, \( B \) is the bandwidth in hertz, \( S \) is the signal power, and \( N \) is the noise power. Thus, a higher frequency band (resulting in a higher \( B \)) will enable a higher rate of information transmission, given that other factors such as signal-to-noise ratio are well-managed.

This principle supports the reality that laser communications, using light waves at the visible spectrum, offer higher bandwidth and thus a much greater capacity for data transmission compared to traditional wire-based communications.

When delving into laser telephone transmission, we step into the world of modern communication marvels. Lasers emit light at visible frequencies, and this technology harnesses the power of these waves to transmit information at incredibly high rates. Just like a beam of light can be seen across vast distances, laser communication can send vast amounts of data over long optical fibers with minimal loss. Moreover, optical fibers are immune to electromagnetic interference which often plagues electronic transmissions.

Laser telephone systems make use of the vast bandwidth available in the optical spectrum to modulate signals. This allows a multitude of conversations, or data streams, to occur simultaneously. Each individual conversation can be thought of as a different color of light, and many colors can be combined to travel down the same optical fiber, a concept known as wavelength-division multiplexing (WDM).

The efficiency of this method is profound, as it provides a much larger capacity for information compared to conventional electronic data transmission methods, enabling high-speed internet and telephone connections that can handle more users and more data-intensive applications at any given moment.

Communicating with submerged submarines presents unique challenges. Extremely Low Frequency (ELF) radio communication is one of the few methods that can penetrate deep seawater to reach these vessels. ELF radio waves have much longer wavelengths and lower frequencies than other parts of the electromagnetic spectrum used for communication.

Due to their lower frequency, ELF waves have a significantly lower bandwidth, which restricts the amount of information they can carry. Consequently, while a submarine can receive ELF signals, the data rate is so low that only short, simple messages can be sent. This typically includes strategic commands or emergency signals, as opposed to detailed or high-data communications.

The unique properties of ELF radio waves make them indispensable for secure and reliable submarine communication, but the trade-off for their penetrating ability is a severely limited capacity for data transmission. Hence, these frequencies are reserved for specific scenarios where other more data-rich communication methods cannot effectively function.